Decomposed multidimensional control grid interpolation for common consumer electronic image processing applications

NASA Astrophysics Data System (ADS)

Zwart, Christine M.; Venkatesan, Ragav; Frakes, David H.

2012-10-01

Interpolation is an essential and broadly employed function of signal processing. Accordingly, considerable development has focused on advancing interpolation algorithms toward optimal accuracy. Such development has motivated a clear shift in the state-of-the art from classical interpolation to more intelligent and resourceful approaches, registration-based interpolation for example. As a natural result, many of the most accurate current algorithms are highly complex, specific, and computationally demanding. However, the diverse hardware destinations for interpolation algorithms present unique constraints that often preclude use of the most accurate available options. For example, while computationally demanding interpolators may be suitable for highly equipped image processing platforms (e.g., computer workstations and clusters), only more efficient interpolators may be practical for less well equipped platforms (e.g., smartphones and tablet computers). The latter examples of consumer electronics present a design tradeoff in this regard: high accuracy interpolation benefits the consumer experience but computing capabilities are limited. It follows that interpolators with favorable combinations of accuracy and efficiency are of great practical value to the consumer electronics industry. We address multidimensional interpolation-based image processing problems that are common to consumer electronic devices through a decomposition approach. The multidimensional problems are first broken down into multiple, independent, one-dimensional (1-D) interpolation steps that are then executed with a newly modified registration-based one-dimensional control grid interpolator. The proposed approach, decomposed multidimensional control grid interpolation (DMCGI), combines the accuracy of registration-based interpolation with the simplicity, flexibility, and computational efficiency of a 1-D interpolation framework. Results demonstrate that DMCGI provides improved interpolation accuracy (and other benefits) in image resizing, color sample demosaicing, and video deinterlacing applications, at a computational cost that is manageable or reduced in comparison to popular alternatives.

Elliptic Cylinder Airborne Sampling and Geostatistical Mass Balance Approach for Quantifying Local Greenhouse Gas Emissions.

PubMed

Tadić, Jovan M; Michalak, Anna M; Iraci, Laura; Ilić, Velibor; Biraud, Sébastien C; Feldman, Daniel R; Bui, Thaopaul; Johnson, Matthew S; Loewenstein, Max; Jeong, Seongeun; Fischer, Marc L; Yates, Emma L; Ryoo, Ju-Mee

2017-09-05

In this study, we explore observational, experimental, methodological, and practical aspects of the flux quantification of greenhouse gases from local point sources by using in situ airborne observations, and suggest a series of conceptual changes to improve flux estimates. We address the major sources of uncertainty reported in previous studies by modifying (1) the shape of the typical flight path, (2) the modeling of covariance and anisotropy, and (3) the type of interpolation tools used. We show that a cylindrical flight profile offers considerable advantages compared to traditional profiles collected as curtains, although this new approach brings with it the need for a more comprehensive subsequent analysis. The proposed flight pattern design does not require prior knowledge of wind direction and allows for the derivation of an ad hoc empirical correction factor to partially alleviate errors resulting from interpolation and measurement inaccuracies. The modified approach is applied to a use-case for quantifying CH 4 emission from an oil field south of San Ardo, CA, and compared to a bottom-up CH 4 emission estimate.

SutraPlot, a graphical post-processor for SUTRA, a model for ground-water flow with solute or energy transport

USGS Publications Warehouse

Souza, W.R.

1999-01-01

This report documents a graphical display post-processor (SutraPlot) for the U.S. Geological Survey Saturated-Unsaturated flow and solute or energy TRAnsport simulation model SUTRA, Version 2D3D.1. This version of SutraPlot is an upgrade to SutraPlot for the 2D-only SUTRA model (Souza, 1987). It has been modified to add 3D functionality, a graphical user interface (GUI), and enhanced graphic output options. Graphical options for 2D SUTRA (2-dimension) simulations include: drawing the 2D finite-element mesh, mesh boundary, and velocity vectors; plots of contours for pressure, saturation, concentration, and temperature within the model region; 2D finite-element based gridding and interpolation; and 2D gridded data export files. Graphical options for 3D SUTRA (3-dimension) simulations include: drawing the 3D finite-element mesh; plots of contours for pressure, saturation, concentration, and temperature in 2D sections of the 3D model region; 3D finite-element based gridding and interpolation; drawing selected regions of velocity vectors (projected on principal coordinate planes); and 3D gridded data export files. Installation instructions and a description of all graphic options are presented. A sample SUTRA problem is described and three step-by-step SutraPlot applications are provided. In addition, the methodology and numerical algorithms for the 2D and 3D finite-element based gridding and interpolation, developed for SutraPlot, are described. 1

DOE Office of Scientific and Technical Information (OSTI.GOV)

D’Arcy, Jordan H.; Kolmann, Stephen J.; Jordan, Meredith J. T.

Quantum and anharmonic effects are investigated in (H{sub 2}){sub 2}–Li{sup +}–benzene, a model for hydrogen adsorption in metal-organic frameworks and carbon-based materials, using rigid-body diffusion Monte Carlo (RBDMC) simulations. The potential-energy surface (PES) is calculated as a modified Shepard interpolation of M05-2X/6-311+G(2df,p) electronic structure data. The RBDMC simulations yield zero-point energies (ZPE) and probability density histograms that describe the ground-state nuclear wavefunction. Binding a second H{sub 2} molecule to the H{sub 2}–Li{sup +}–benzene complex increases the ZPE of the system by 5.6 kJ mol{sup −1} to 17.6 kJ mol{sup −1}. This ZPE is 42% of the total electronic binding energymore » of (H{sub 2}){sub 2}–Li{sup +}–benzene and cannot be neglected. Our best estimate of the 0 K binding enthalpy of the second H{sub 2} to H{sub 2}–Li{sup +}–benzene is 7.7 kJ mol{sup −1}, compared to 12.4 kJ mol{sup −1} for the first H{sub 2} molecule. Anharmonicity is found to be even more important when a second (and subsequent) H{sub 2} molecule is adsorbed; use of harmonic ZPEs results in significant error in the 0 K binding enthalpy. Probability density histograms reveal that the two H{sub 2} molecules are found at larger distance from the Li{sup +} ion and are more confined in the θ coordinate than in H{sub 2}–Li{sup +}–benzene. They also show that both H{sub 2} molecules are delocalized in the azimuthal coordinate, ϕ. That is, adding a second H{sub 2} molecule is insufficient to localize the wavefunction in ϕ. Two fragment-based (H{sub 2}){sub 2}–Li{sup +}–benzene PESs are developed. These use a modified Shepard interpolation for the Li{sup +}–benzene and H{sub 2}–Li{sup +}–benzene fragments, and either modified Shepard interpolation or a cubic spline to model the H{sub 2}–H{sub 2} interaction. Because of the neglect of three-body H{sub 2}, H{sub 2}, Li{sup +} terms, both fragment PESs lead to overbinding of the second H{sub 2} molecule by 1.5 kJ mol{sup −1}. Probability density histograms, however, indicate that the wavefunctions for the two H{sub 2} molecules are effectively identical on the “full” and fragment PESs. This suggests that the 1.5 kJ mol{sup −1} error is systematic over the regions of configuration space explored by our simulations. Notwithstanding this, modified Shepard interpolation of the weak H{sub 2}–H{sub 2} interaction is problematic and we obtain more accurate results, at considerably lower computational cost, using a cubic spline interpolation. Indeed, the ZPE of the fragment-with-spline PES is identical, within error, to the ZPE of the full PES. This fragmentation scheme therefore provides an accurate and inexpensive method to study higher hydrogen loading in this and similar systems.« less

The US Navy Coupled Ocean-Wave Prediction System

DTIC Science & Technology

2014-09-01

Stokes drift to be the dominant wave effect and that it increased surface drift speeds by 35% and veered the current in the direction of the wind...ocean model has been modified to incorporate the effect of the Stokes drift current, wave radiation stresses due to horizontal gradients of the momentum...for fourth-order differences for horizontal baroclinic pressure gradients and for interpolation of Coriolis terms. There is an option to use the

Model Based Predictive Control of Multivariable Hammerstein Processes with Fuzzy Logic Hypercube Interpolated Models

PubMed Central

Coelho, Antonio Augusto Rodrigues

2016-01-01

This paper introduces the Fuzzy Logic Hypercube Interpolator (FLHI) and demonstrates applications in control of multiple-input single-output (MISO) and multiple-input multiple-output (MIMO) processes with Hammerstein nonlinearities. FLHI consists of a Takagi-Sugeno fuzzy inference system where membership functions act as kernel functions of an interpolator. Conjunction of membership functions in an unitary hypercube space enables multivariable interpolation of N-dimensions. Membership functions act as interpolation kernels, such that choice of membership functions determines interpolation characteristics, allowing FLHI to behave as a nearest-neighbor, linear, cubic, spline or Lanczos interpolator, to name a few. The proposed interpolator is presented as a solution to the modeling problem of static nonlinearities since it is capable of modeling both a function and its inverse function. Three study cases from literature are presented, a single-input single-output (SISO) system, a MISO and a MIMO system. Good results are obtained regarding performance metrics such as set-point tracking, control variation and robustness. Results demonstrate applicability of the proposed method in modeling Hammerstein nonlinearities and their inverse functions for implementation of an output compensator with Model Based Predictive Control (MBPC), in particular Dynamic Matrix Control (DMC). PMID:27657723

On the paradoxical evolution of the number of photons in a new model of interpolating Hamiltonians

NASA Astrophysics Data System (ADS)

Valverde, Clodoaldo; Baseia, Basílio

2018-01-01

We introduce a new Hamiltonian model which interpolates between the Jaynes-Cummings model (JCM) and other types of such Hamiltonians. It works with two interpolating parameters, rather than one as traditional. Taking advantage of this greater degree of freedom, we can perform continuous interpolation between the various types of these Hamiltonians. As applications, we discuss a paradox raised in literature and compare the time evolution of the photon statistics obtained in the various interpolating models. The role played by the average excitation in these comparisons is also highlighted.

Modified Hyperspheres Algorithm to Trace Homotopy Curves of Nonlinear Circuits Composed by Piecewise Linear Modelled Devices

PubMed Central

Vazquez-Leal, H.; Jimenez-Fernandez, V. M.; Benhammouda, B.; Filobello-Nino, U.; Sarmiento-Reyes, A.; Ramirez-Pinero, A.; Marin-Hernandez, A.; Huerta-Chua, J.

2014-01-01

We present a homotopy continuation method (HCM) for finding multiple operating points of nonlinear circuits composed of devices modelled by using piecewise linear (PWL) representations. We propose an adaptation of the modified spheres path tracking algorithm to trace the homotopy trajectories of PWL circuits. In order to assess the benefits of this proposal, four nonlinear circuits composed of piecewise linear modelled devices are analysed to determine their multiple operating points. The results show that HCM can find multiple solutions within a single homotopy trajectory. Furthermore, we take advantage of the fact that homotopy trajectories are PWL curves meant to replace the multidimensional interpolation and fine tuning stages of the path tracking algorithm with a simple and highly accurate procedure based on the parametric straight line equation. PMID:25184157

Full-field stress determination in photoelasticity with phase shifting technique

NASA Astrophysics Data System (ADS)

Guo, Enhai; Liu, Yonggang; Han, Yongsheng; Arola, Dwayne; Zhang, Dongsheng

2018-04-01

Photoelasticity is an effective method for evaluating the stress and its spatial variations within a stressed body. In the present study, a method to determine the stress distribution by means of phase shifting and a modified shear-difference is proposed. First, the orientation of the first principal stress and the retardation between the principal stresses are determined in the full-field through phase shifting. Then, through bicubic interpolation and derivation of a modified shear-difference method, the internal stress is calculated from the point with a free boundary along its normal direction. A method to reduce integration error in the shear difference scheme is proposed and compared to the existing methods; the integration error is reduced when using theoretical photoelastic parameters to calculate the stress component with the same points. Results show that when the value of Δx/Δy approaches one, the error is minimum, and although the interpolation error is inevitable, it has limited influence on the accuracy of the result. Finally, examples are presented for determining the stresses in a circular plate and ring subjected to diametric loading. Results show that the proposed approach provides a complete solution for determining the full-field stresses in photoelastic models.

Performance evaluations of demons and free form deformation algorithms for the liver region.

PubMed

Wang, Hui; Gong, Guanzhong; Wang, Hongjun; Li, Dengwang; Yin, Yong; Lu, Jie

2014-04-01

We investigated the influence of breathing motion on radiation therapy according to four- dimensional computed tomography (4D-CT) technology and indicated the registration of 4D-CT images was significant. The demons algorithm in two interpolation modes was compared to the FFD model algorithm to register the different phase images of 4D-CT in tumor tracking, using iodipin as verification. Linear interpolation was used in both mode 1 and mode 2. Mode 1 set outside pixels to nearest pixel, while mode 2 set outside pixels to zero. We used normalized mutual information (NMI), sum of squared differences, modified Hausdorff-distance, and registration speed to evaluate the performance of each algorithm. The average NMI after demons registration method in mode 1 improved 1.76% and 4.75% when compared to mode 2 and FFD model algorithm, respectively. Further, the modified Hausdorff-distance was no different between demons modes 1 and 2, but mode 1 was 15.2% lower than FFD. Finally, demons algorithm has the absolute advantage in registration speed. The demons algorithm in mode 1 was therefore found to be much more suitable for the registration of 4D-CT images. The subtractions of floating images and reference image before and after registration by demons further verified that influence of breathing motion cannot be ignored and the demons registration method is feasible.

Exploring the Role of Genetic Algorithms and Artificial Neural Networks for Interpolation of Elevation in Geoinformation Models

NASA Astrophysics Data System (ADS)

Bagheri, H.; Sadjadi, S. Y.; Sadeghian, S.

2013-09-01

One of the most significant tools to study many engineering projects is three-dimensional modelling of the Earth that has many applications in the Geospatial Information System (GIS), e.g. creating Digital Train Modelling (DTM). DTM has numerous applications in the fields of sciences, engineering, design and various project administrations. One of the most significant events in DTM technique is the interpolation of elevation to create a continuous surface. There are several methods for interpolation, which have shown many results due to the environmental conditions and input data. The usual methods of interpolation used in this study along with Genetic Algorithms (GA) have been optimised and consisting of polynomials and the Inverse Distance Weighting (IDW) method. In this paper, the Artificial Intelligent (AI) techniques such as GA and Neural Networks (NN) are used on the samples to optimise the interpolation methods and production of Digital Elevation Model (DEM). The aim of entire interpolation methods is to evaluate the accuracy of interpolation methods. Universal interpolation occurs in the entire neighbouring regions can be suggested for larger regions, which can be divided into smaller regions. The results obtained from applying GA and ANN individually, will be compared with the typical method of interpolation for creation of elevations. The resulting had performed that AI methods have a high potential in the interpolation of elevations. Using artificial networks algorithms for the interpolation and optimisation based on the IDW method with GA could be estimated the high precise elevations.

Interpolation between spatial frameworks: an application of process convolution to estimating neighbourhood disease prevalence.

PubMed

Congdon, Peter

2014-04-01

Health data may be collected across one spatial framework (e.g. health provider agencies), but contrasts in health over another spatial framework (neighbourhoods) may be of policy interest. In the UK, population prevalence totals for chronic diseases are provided for populations served by general practitioner practices, but not for neighbourhoods (small areas of circa 1500 people), raising the question whether data for one framework can be used to provide spatially interpolated estimates of disease prevalence for the other. A discrete process convolution is applied to this end and has advantages when there are a relatively large number of area units in one or other framework. Additionally, the interpolation is modified to take account of the observed neighbourhood indicators (e.g. hospitalisation rates) of neighbourhood disease prevalence. These are reflective indicators of neighbourhood prevalence viewed as a latent construct. An illustrative application is to prevalence of psychosis in northeast London, containing 190 general practitioner practices and 562 neighbourhoods, including an assessment of sensitivity to kernel choice (e.g. normal vs exponential). This application illustrates how a zero-inflated Poisson can be used as the likelihood model for a reflective indicator.

Image interpolation by adaptive 2-D autoregressive modeling and soft-decision estimation.

PubMed

Zhang, Xiangjun; Wu, Xiaolin

2008-06-01

The challenge of image interpolation is to preserve spatial details. We propose a soft-decision interpolation technique that estimates missing pixels in groups rather than one at a time. The new technique learns and adapts to varying scene structures using a 2-D piecewise autoregressive model. The model parameters are estimated in a moving window in the input low-resolution image. The pixel structure dictated by the learnt model is enforced by the soft-decision estimation process onto a block of pixels, including both observed and estimated. The result is equivalent to that of a high-order adaptive nonseparable 2-D interpolation filter. This new image interpolation approach preserves spatial coherence of interpolated images better than the existing methods, and it produces the best results so far over a wide range of scenes in both PSNR measure and subjective visual quality. Edges and textures are well preserved, and common interpolation artifacts (blurring, ringing, jaggies, zippering, etc.) are greatly reduced.

A fast and accurate dihedral interpolation loop subdivision scheme

NASA Astrophysics Data System (ADS)

Shi, Zhuo; An, Yalei; Wang, Zhongshuai; Yu, Ke; Zhong, Si; Lan, Rushi; Luo, Xiaonan

2018-04-01

In this paper, we propose a fast and accurate dihedral interpolation Loop subdivision scheme for subdivision surfaces based on triangular meshes. In order to solve the problem of surface shrinkage, we keep the limit condition unchanged, which is important. Extraordinary vertices are handled using modified Butterfly rules. Subdivision schemes are computationally costly as the number of faces grows exponentially at higher levels of subdivision. To address this problem, our approach is to use local surface information to adaptively refine the model. This is achieved simply by changing the threshold value of the dihedral angle parameter, i.e., the angle between the normals of a triangular face and its adjacent faces. We then demonstrate the effectiveness of the proposed method for various 3D graphic triangular meshes, and extensive experimental results show that it can match or exceed the expected results at lower computational cost.

Local-metrics error-based Shepard interpolation as surrogate for highly non-linear material models in high dimensions

NASA Astrophysics Data System (ADS)

Lorenzi, Juan M.; Stecher, Thomas; Reuter, Karsten; Matera, Sebastian

2017-10-01

Many problems in computational materials science and chemistry require the evaluation of expensive functions with locally rapid changes, such as the turn-over frequency of first principles kinetic Monte Carlo models for heterogeneous catalysis. Because of the high computational cost, it is often desirable to replace the original with a surrogate model, e.g., for use in coupled multiscale simulations. The construction of surrogates becomes particularly challenging in high-dimensions. Here, we present a novel version of the modified Shepard interpolation method which can overcome the curse of dimensionality for such functions to give faithful reconstructions even from very modest numbers of function evaluations. The introduction of local metrics allows us to take advantage of the fact that, on a local scale, rapid variation often occurs only across a small number of directions. Furthermore, we use local error estimates to weigh different local approximations, which helps avoid artificial oscillations. Finally, we test our approach on a number of challenging analytic functions as well as a realistic kinetic Monte Carlo model. Our method not only outperforms existing isotropic metric Shepard methods but also state-of-the-art Gaussian process regression.

Local-metrics error-based Shepard interpolation as surrogate for highly non-linear material models in high dimensions.

PubMed

Lorenzi, Juan M; Stecher, Thomas; Reuter, Karsten; Matera, Sebastian

2017-10-28

Many problems in computational materials science and chemistry require the evaluation of expensive functions with locally rapid changes, such as the turn-over frequency of first principles kinetic Monte Carlo models for heterogeneous catalysis. Because of the high computational cost, it is often desirable to replace the original with a surrogate model, e.g., for use in coupled multiscale simulations. The construction of surrogates becomes particularly challenging in high-dimensions. Here, we present a novel version of the modified Shepard interpolation method which can overcome the curse of dimensionality for such functions to give faithful reconstructions even from very modest numbers of function evaluations. The introduction of local metrics allows us to take advantage of the fact that, on a local scale, rapid variation often occurs only across a small number of directions. Furthermore, we use local error estimates to weigh different local approximations, which helps avoid artificial oscillations. Finally, we test our approach on a number of challenging analytic functions as well as a realistic kinetic Monte Carlo model. Our method not only outperforms existing isotropic metric Shepard methods but also state-of-the-art Gaussian process regression.

Visual information processing; Proceedings of the Meeting, Orlando, FL, Apr. 20-22, 1992

NASA Technical Reports Server (NTRS)

Huck, Friedrich O. (Editor); Juday, Richard D. (Editor)

1992-01-01

Topics discussed in these proceedings include nonlinear processing and communications; feature extraction and recognition; image gathering, interpolation, and restoration; image coding; and wavelet transform. Papers are presented on noise reduction for signals from nonlinear systems; driving nonlinear systems with chaotic signals; edge detection and image segmentation of space scenes using fractal analyses; a vision system for telerobotic operation; a fidelity analysis of image gathering, interpolation, and restoration; restoration of images degraded by motion; and information, entropy, and fidelity in visual communication. Attention is also given to image coding methods and their assessment, hybrid JPEG/recursive block coding of images, modified wavelets that accommodate causality, modified wavelet transform for unbiased frequency representation, and continuous wavelet transform of one-dimensional signals by Fourier filtering.

A modified Monte Carlo model for the ionospheric heating rates

NASA Technical Reports Server (NTRS)

Mayr, H. G.; Fontheim, E. G.; Robertson, S. C.

1972-01-01

A Monte Carlo method is adopted as a basis for the derivation of the photoelectron heat input into the ionospheric plasma. This approach is modified in an attempt to minimize the computation time. The heat input distributions are computed for arbitrarily small source elements that are spaced at distances apart corresponding to the photoelectron dissipation range. By means of a nonlinear interpolation procedure their individual heating rate distributions are utilized to produce synthetic ones that fill the gaps between the Monte Carlo generated distributions. By varying these gaps and the corresponding number of Monte Carlo runs the accuracy of the results is tested to verify the validity of this procedure. It is concluded that this model can reduce the computation time by more than a factor of three, thus improving the feasibility of including Monte Carlo calculations in self-consistent ionosphere models.

Spatial uncertainty analysis: Propagation of interpolation errors in spatially distributed models

USGS Publications Warehouse

Phillips, D.L.; Marks, D.G.

1996-01-01

In simulation modelling, it is desirable to quantify model uncertainties and provide not only point estimates for output variables but confidence intervals as well. Spatially distributed physical and ecological process models are becoming widely used, with runs being made over a grid of points that represent the landscape. This requires input values at each grid point, which often have to be interpolated from irregularly scattered measurement sites, e.g., weather stations. Interpolation introduces spatially varying errors which propagate through the model We extended established uncertainty analysis methods to a spatial domain for quantifying spatial patterns of input variable interpolation errors and how they propagate through a model to affect the uncertainty of the model output. We applied this to a model of potential evapotranspiration (PET) as a demonstration. We modelled PET for three time periods in 1990 as a function of temperature, humidity, and wind on a 10-km grid across the U.S. portion of the Columbia River Basin. Temperature, humidity, and wind speed were interpolated using kriging from 700- 1000 supporting data points. Kriging standard deviations (SD) were used to quantify the spatially varying interpolation uncertainties. For each of 5693 grid points, 100 Monte Carlo simulations were done, using the kriged values of temperature, humidity, and wind, plus random error terms determined by the kriging SDs and the correlations of interpolation errors among the three variables. For the spring season example, kriging SDs averaged 2.6??C for temperature, 8.7% for relative humidity, and 0.38 m s-1 for wind. The resultant PET estimates had coefficients of variation (CVs) ranging from 14% to 27% for the 10-km grid cells. Maps of PET means and CVs showed the spatial patterns of PET with a measure of its uncertainty due to interpolation of the input variables. This methodology should be applicable to a variety of spatially distributed models using interpolated inputs.

A MAP-based image interpolation method via Viterbi decoding of Markov chains of interpolation functions.

PubMed

Vedadi, Farhang; Shirani, Shahram

2014-01-01

A new method of image resolution up-conversion (image interpolation) based on maximum a posteriori sequence estimation is proposed. Instead of making a hard decision about the value of each missing pixel, we estimate the missing pixels in groups. At each missing pixel of the high resolution (HR) image, we consider an ensemble of candidate interpolation methods (interpolation functions). The interpolation functions are interpreted as states of a Markov model. In other words, the proposed method undergoes state transitions from one missing pixel position to the next. Accordingly, the interpolation problem is translated to the problem of estimating the optimal sequence of interpolation functions corresponding to the sequence of missing HR pixel positions. We derive a parameter-free probabilistic model for this to-be-estimated sequence of interpolation functions. Then, we solve the estimation problem using a trellis representation and the Viterbi algorithm. Using directional interpolation functions and sequence estimation techniques, we classify the new algorithm as an adaptive directional interpolation using soft-decision estimation techniques. Experimental results show that the proposed algorithm yields images with higher or comparable peak signal-to-noise ratios compared with some benchmark interpolation methods in the literature while being efficient in terms of implementation and complexity considerations.

Simulation of interaction between ground water in an alluvial aquifer and surface water in a large braided river

USGS Publications Warehouse

Leake, S.A.; Lilly, M.R.

1995-01-01

The Fairbanks, Alaska, area has many contaminated sites in a shallow alluvial aquifer. A ground-water flow model is being developed using the MODFLOW finite-difference ground-water flow model program with the River Package. The modeled area is discretized in the horizontal dimensions into 118 rows and 158 columns of approximately 150-meter square cells. The fine grid spacing has the advantage of providing needed detail at the contaminated sites and surface-water features that bound the aquifer. However, the fine spacing of cells adds difficulty to simulating interaction between the aquifer and the large, braided Tanana River. In particular, the assignment of a river head is difficult if cells are much smaller than the river width. This was solved by developing a procedure for interpolating and extrapolating river head using a river distance function. Another problem is that future transient simulations would require excessive numbers of input records using the current version of the River Package. The proposed solution to this problem is to modify the River Package to linearly interpolate river head for time steps within each stress period, thereby reducing the number of stress periods required.

Fast dose kernel interpolation using Fourier transform with application to permanent prostate brachytherapy dosimetry.

PubMed

Liu, Derek; Sloboda, Ron S

2014-05-01

Boyer and Mok proposed a fast calculation method employing the Fourier transform (FT), for which calculation time is independent of the number of seeds but seed placement is restricted to calculation grid points. Here an interpolation method is described enabling unrestricted seed placement while preserving the computational efficiency of the original method. The Iodine-125 seed dose kernel was sampled and selected values were modified to optimize interpolation accuracy for clinically relevant doses. For each seed, the kernel was shifted to the nearest grid point via convolution with a unit impulse, implemented in the Fourier domain. The remaining fractional shift was performed using a piecewise third-order Lagrange filter. Implementation of the interpolation method greatly improved FT-based dose calculation accuracy. The dose distribution was accurate to within 2% beyond 3 mm from each seed. Isodose contours were indistinguishable from explicit TG-43 calculation. Dose-volume metric errors were negligible. Computation time for the FT interpolation method was essentially the same as Boyer's method. A FT interpolation method for permanent prostate brachytherapy TG-43 dose calculation was developed which expands upon Boyer's original method and enables unrestricted seed placement. The proposed method substantially improves the clinically relevant dose accuracy with negligible additional computation cost, preserving the efficiency of the original method.

Comparison of global sst analyses for atmospheric data assimilation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Phoebus, P.A.; Cummings, J.A.

1995-03-17

Traditionally, atmospheric models were executed using a climatological estimate of the sea surface temperature (SST) to define the marine boundary layer. More recently, particularly since the deployment of remote sensing instruments and the advent of multichannel SST observations atmospheric models have been improved by using more timely estimates of the actual state of the ocean. Typically, some type of objective analysis is performed using the data from satellites along with ship, buoy, and bathythermograph observations, and perhaps even climatology, to produce a weekly or daily analysis of global SST. Some of the earlier efforts to produce real-time global temperature analysesmore » have been described by Clancy and Pollak (1983) and Reynolds (1988). However, just as new techniques have been developed for atmospheric data assimilation, improvements have been made to ocean data assimilation systems as well. In 1988, the U.S. Navy`s Fleet Numerical Meteorology and Oceanography Center (FNMOC) implemented a global three-dimensional ocean temperature analysis that was based on the optimum interpolation methodology (Clancy et al., 1990). This system, the Optimum Thermal Interpolation System (OTIS 1.0), was initially distributed on a 2.50 resolution grid, and was later modified to generate fields on a 1.250 grid (OTIS 1.1; Clancy et al., 1992). Other optimum interpolation-based analyses (OTIS 3.0) were developed by FNMOC to perform high-resolution three-dimensional ocean thermal analyses in areas with strong frontal gradients and clearly defined water mass characteristics.« less

Interpolation bias for the inverse compositional Gauss-Newton algorithm in digital image correlation

NASA Astrophysics Data System (ADS)

Su, Yong; Zhang, Qingchuan; Xu, Xiaohai; Gao, Zeren; Wu, Shangquan

2018-01-01

It is believed that the classic forward additive Newton-Raphson (FA-NR) algorithm and the recently introduced inverse compositional Gauss-Newton (IC-GN) algorithm give rise to roughly equal interpolation bias. Questioning the correctness of this statement, this paper presents a thorough analysis of interpolation bias for the IC-GN algorithm. A theoretical model is built to analytically characterize the dependence of interpolation bias upon speckle image, target image interpolation, and reference image gradient estimation. The interpolation biases of the FA-NR algorithm and the IC-GN algorithm can be significantly different, whose relative difference can exceed 80%. For the IC-GN algorithm, the gradient estimator can strongly affect the interpolation bias; the relative difference can reach 178%. Since the mean bias errors are insensitive to image noise, the theoretical model proposed remains valid in the presence of noise. To provide more implementation details, source codes are uploaded as a supplement.

Markov random field model-based edge-directed image interpolation.

PubMed

Li, Min; Nguyen, Truong Q

2008-07-01

This paper presents an edge-directed image interpolation algorithm. In the proposed algorithm, the edge directions are implicitly estimated with a statistical-based approach. In opposite to explicit edge directions, the local edge directions are indicated by length-16 weighting vectors. Implicitly, the weighting vectors are used to formulate geometric regularity (GR) constraint (smoothness along edges and sharpness across edges) and the GR constraint is imposed on the interpolated image through the Markov random field (MRF) model. Furthermore, under the maximum a posteriori-MRF framework, the desired interpolated image corresponds to the minimal energy state of a 2-D random field given the low-resolution image. Simulated annealing methods are used to search for the minimal energy state from the state space. To lower the computational complexity of MRF, a single-pass implementation is designed, which performs nearly as well as the iterative optimization. Simulation results show that the proposed MRF model-based edge-directed interpolation method produces edges with strong geometric regularity. Compared to traditional methods and other edge-directed interpolation methods, the proposed method improves the subjective quality of the interpolated edges while maintaining a high PSNR level.

Mechanical analysis of non-uniform bi-directional functionally graded intelligent micro-beams using modified couple stress theory

NASA Astrophysics Data System (ADS)

Bakhshi Khaniki, Hossein; Rajasekaran, Sundaramoorthy

2018-05-01

This study develops a comprehensive investigation on mechanical behavior of non-uniform bi-directional functionally graded beam sensors in the framework of modified couple stress theory. Material variation is modelled through both length and thickness directions using power-law, sigmoid and exponential functions. Moreover, beam is assumed with linear, exponential and parabolic cross-section variation through the length using power-law and sigmoid varying functions. Using these assumptions, a general model for microbeams is presented and formulated by employing Hamilton’s principle. Governing equations are solved using a mixed finite element method with Lagrangian interpolation technique, Gaussian quadrature method and Wilson’s Lagrangian multiplier method. It is shown that by using bi-directional functionally graded materials in nonuniform microbeams, mechanical behavior of such structures could be affected noticeably and scale parameter has a significant effect in changing the rigidity of nonuniform bi-directional functionally graded beams.

Effects of empty bins on image upscaling in capsule endoscopy

NASA Astrophysics Data System (ADS)

Rukundo, Olivier

2017-07-01

This paper presents a preliminary study of the effect of empty bins on image upscaling in capsule endoscopy. The presented study was conducted based on results of existing contrast enhancement and interpolation methods. A low contrast enhancement method based on pixels consecutiveness and modified bilinear weighting scheme has been developed to distinguish between necessary empty bins and unnecessary empty bins in the effort to minimize the number of empty bins in the input image, before further processing. Linear interpolation methods have been used for upscaling input images with stretched histograms. Upscaling error differences and similarity indices between pairs of interpolation methods have been quantified using the mean squared error and feature similarity index techniques. Simulation results demonstrated more promising effects using the developed method than other contrast enhancement methods mentioned.

Interpolative modeling of GaAs FET S-parameter data bases for use in Monte Carlo simulations

NASA Technical Reports Server (NTRS)

Campbell, L.; Purviance, J.

1992-01-01

A statistical interpolation technique is presented for modeling GaAs FET S-parameter measurements for use in the statistical analysis and design of circuits. This is accomplished by interpolating among the measurements in a GaAs FET S-parameter data base in a statistically valid manner.

Accurate Energy Transaction Allocation using Path Integration and Interpolation

NASA Astrophysics Data System (ADS)

Bhide, Mandar Mohan

This thesis investigates many of the popular cost allocation methods which are based on actual usage of the transmission network. The Energy Transaction Allocation (ETA) method originally proposed by A.Fradi, S.Brigonne and B.Wollenberg which gives unique advantage of accurately allocating the transmission network usage is discussed subsequently. Modified calculation of ETA based on simple interpolation technique is then proposed. The proposed methodology not only increase the accuracy of calculation but also decreases number of calculations to less than half of the number of calculations required in original ETAs.

A general method for generating bathymetric data for hydrodynamic computer models

USGS Publications Warehouse

Burau, J.R.; Cheng, R.T.

1989-01-01

To generate water depth data from randomly distributed bathymetric data for numerical hydrodymamic models, raw input data from field surveys, water depth data digitized from nautical charts, or a combination of the two are sorted to given an ordered data set on which a search algorithm is used to isolate data for interpolation. Water depths at locations required by hydrodynamic models are interpolated from the bathymetric data base using linear or cubic shape functions used in the finite-element method. The bathymetric database organization and preprocessing, the search algorithm used in finding the bounding points for interpolation, the mathematics of the interpolation formulae, and the features of the automatic generation of water depths at hydrodynamic model grid points are included in the analysis. This report includes documentation of two computer programs which are used to: (1) organize the input bathymetric data; and (2) to interpolate depths for hydrodynamic models. An example of computer program operation is drawn from a realistic application to the San Francisco Bay estuarine system. (Author 's abstract)

Effective Interpolation of Incomplete Satellite-Derived Leaf-Area Index Time Series for the Continental United States

NASA Technical Reports Server (NTRS)

Jasinski, Michael F.; Borak, Jordan S.

2008-01-01

Many earth science modeling applications employ continuous input data fields derived from satellite data. Environmental factors, sensor limitations and algorithmic constraints lead to data products of inherently variable quality. This necessitates interpolation of one form or another in order to produce high quality input fields free of missing data. The present research tests several interpolation techniques as applied to satellite-derived leaf area index, an important quantity in many global climate and ecological models. The study evaluates and applies a variety of interpolation techniques for the Moderate Resolution Imaging Spectroradiometer (MODIS) Leaf-Area Index Product over the time period 2001-2006 for a region containing the conterminous United States. Results indicate that the accuracy of an individual interpolation technique depends upon the underlying land cover. Spatial interpolation provides better results in forested areas, while temporal interpolation performs more effectively over non-forest cover types. Combination of spatial and temporal approaches offers superior interpolative capabilities to any single method, and in fact, generation of continuous data fields requires a hybrid approach such as this.

Spatial interpolation of river channel topography using the shortest temporal distance

NASA Astrophysics Data System (ADS)

Zhang, Yanjun; Xian, Cuiling; Chen, Huajin; Grieneisen, Michael L.; Liu, Jiaming; Zhang, Minghua

2016-11-01

It is difficult to interpolate river channel topography due to complex anisotropy. As the anisotropy is often caused by river flow, especially the hydrodynamic and transport mechanisms, it is reasonable to incorporate flow velocity into topography interpolator for decreasing the effect of anisotropy. In this study, two new distance metrics defined as the time taken by water flow to travel between two locations are developed, and replace the spatial distance metric or Euclidean distance that is currently used to interpolate topography. One is a shortest temporal distance (STD) metric. The temporal distance (TD) of a path between two nodes is calculated by spatial distance divided by the tangent component of flow velocity along the path, and the STD is searched using the Dijkstra algorithm in all possible paths between two nodes. The other is a modified shortest temporal distance (MSTD) metric in which both the tangent and normal components of flow velocity were combined. They are used to construct the methods for the interpolation of river channel topography. The proposed methods are used to generate the topography of Wuhan Section of Changjiang River and compared with Universal Kriging (UK) and Inverse Distance Weighting (IDW). The results clearly showed that the STD and MSTD based on flow velocity were reliable spatial interpolators. The MSTD, followed by the STD, presents improvement in prediction accuracy relative to both UK and IDW.

Interpolation of property-values between electron numbers is inconsistent with ensemble averaging

DOE Office of Scientific and Technical Information (OSTI.GOV)

Miranda-Quintana, Ramón Alain; Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario L8S 4M1; Ayers, Paul W.

2016-06-28

In this work we explore the physical foundations of models that study the variation of the ground state energy with respect to the number of electrons (E vs. N models), in terms of general grand-canonical (GC) ensemble formulations. In particular, we focus on E vs. N models that interpolate the energy between states with integer number of electrons. We show that if the interpolation of the energy corresponds to a GC ensemble, it is not differentiable. Conversely, if the interpolation is smooth, then it cannot be formulated as any GC ensemble. This proves that interpolation of electronic properties between integermore » electron numbers is inconsistent with any form of ensemble averaging. This emphasizes the role of derivative discontinuities and the critical role of a subsystem’s surroundings in determining its properties.« less

Modelling the Velocity Field in a Regular Grid in the Area of Poland on the Basis of the Velocities of European Permanent Stations

NASA Astrophysics Data System (ADS)

Bogusz, Janusz; Kłos, Anna; Grzempowski, Piotr; Kontny, Bernard

2014-06-01

The paper presents the results of testing the various methods of permanent stations' velocity residua interpolation in a regular grid, which constitutes a continuous model of the velocity field in the territory of Poland. Three packages of software were used in the research from the point of view of interpolation: GMT ( The Generic Mapping Tools), Surfer and ArcGIS. The following methods were tested in the softwares: the Nearest Neighbor, Triangulation (TIN), Spline Interpolation, Surface, Inverse Distance to a Power, Minimum Curvature and Kriging. The presented research used the absolute velocities' values expressed in the ITRF2005 reference frame and the intraplate velocities related to the NUVEL model of over 300 permanent reference stations of the EPN and ASG-EUPOS networks covering the area of Europe. Interpolation for the area of Poland was done using data from the whole area of Europe to make the results at the borders of the interpolation area reliable. As a result of this research, an optimum method of such data interpolation was developed. All the mentioned methods were tested for being local or global, for the possibility to compute errors of the interpolated values, for explicitness and fidelity of the interpolation functions or the smoothing mode. In the authors' opinion, the best data interpolation method is Kriging with the linear semivariogram model run in the Surfer programme because it allows for the computation of errors in the interpolated values and it is a global method (it distorts the results in the least way). Alternately, it is acceptable to use the Minimum Curvature method. Empirical analysis of the interpolation results obtained by means of the two methods showed that the results are identical. The tests were conducted using the intraplate velocities of the European sites. Statistics in the form of computing the minimum, maximum and mean values of the interpolated North and East components of the velocity residuum were prepared for all the tested methods, and each of the resulting continuous velocity fields was visualized by means of the GMT programme. The interpolated components of the velocities and their residua are presented in the form of tables and bar diagrams.

Missing RRI interpolation for HRV analysis using locally-weighted partial least squares regression.

PubMed

Kamata, Keisuke; Fujiwara, Koichi; Yamakawa, Toshiki; Kano, Manabu

2016-08-01

The R-R interval (RRI) fluctuation in electrocardiogram (ECG) is called heart rate variability (HRV). Since HRV reflects autonomic nervous function, HRV-based health monitoring services, such as stress estimation, drowsy driving detection, and epileptic seizure prediction, have been proposed. In these HRV-based health monitoring services, precise R wave detection from ECG is required; however, R waves cannot always be detected due to ECG artifacts. Missing RRI data should be interpolated appropriately for HRV analysis. The present work proposes a missing RRI interpolation method by utilizing using just-in-time (JIT) modeling. The proposed method adopts locally weighted partial least squares (LW-PLS) for RRI interpolation, which is a well-known JIT modeling method used in the filed of process control. The usefulness of the proposed method was demonstrated through a case study of real RRI data collected from healthy persons. The proposed JIT-based interpolation method could improve the interpolation accuracy in comparison with a static interpolation method.

Investigation of dynamic characteristics of a rotor system with surface coatings

NASA Astrophysics Data System (ADS)

Yang, Yang; Cao, Dengqing; Wang, Deyou

2017-02-01

A Jeffcott rotor system with surface coatings capable of describing the mechanical vibration resulting from unbalance and rub-impact is formulated in this article. A contact force model proposed recently to describe the impact force between the disc and casing with coatings is employed to do the dynamic analysis for the rotor system with rubbing fault. Due to the variation of penetration, the contact force model is correspondingly modified. Meanwhile, the Coulomb friction model is applied to simulate the friction characteristics. Then, the case study of rub-impact with surface coatings is simulated by the Runge-Kutta method, in which a linear interpolation method is adopted to predict the rubbing instant. Moreover, the dynamic characteristics of the rotor system with surface coatings are analyzed in terms of bifurcation plot, waveform, whirl orbit, Poincaré map and spectrum plot. And the effects of the hardness of surface coatings on the response are investigated as well. Finally, compared with the classical models, the modified contact force model is shown to be more suitable to solve the rub-impact of aero-engine with surface coatings.

LIP: The Livermore Interpolation Package, Version 1.4

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fritsch, F N

2011-07-06

This report describes LIP, the Livermore Interpolation Package. Because LIP is a stand-alone version of the interpolation package in the Livermore Equation of State (LEOS) access library, the initials LIP alternatively stand for the 'LEOS Interpolation Package'. LIP was totally rewritten from the package described in [1]. In particular, the independent variables are now referred to as x and y, since the package need not be restricted to equation of state data, which uses variables {rho} (density) and T (temperature). LIP is primarily concerned with the interpolation of two-dimensional data on a rectangular mesh. The interpolation methods provided include piecewisemore » bilinear, reduced (12-term) bicubic, and bicubic Hermite (biherm). There is a monotonicity-preserving variant of the latter, known as bimond. For historical reasons, there is also a biquadratic interpolator, but this option is not recommended for general use. A birational method was added at version 1.3. In addition to direct interpolation of two-dimensional data, LIP includes a facility for inverse interpolation (at present, only in the second independent variable). For completeness, however, the package also supports a compatible one-dimensional interpolation capability. Parametric interpolation of points on a two-dimensional curve can be accomplished by treating the components as a pair of one-dimensional functions with a common independent variable. LIP has an object-oriented design, but it is implemented in ANSI Standard C for efficiency and compatibility with existing applications. First, a 'LIP interpolation object' is created and initialized with the data to be interpolated. Then the interpolation coefficients for the selected method are computed and added to the object. Since version 1.1, LIP has options to instead estimate derivative values or merely store data in the object. (These are referred to as 'partial setup' options.) It is then possible to pass the object to functions that interpolate or invert the interpolant at an arbitrary number of points. The first section of this report describes the overall design of the package, including both forward and inverse interpolation. Sections 2-6 describe each interpolation method in detail. The software that implements this design is summarized function-by-function in Section 7. For a complete example of package usage, refer to Section 8. The report concludes with a few brief notes on possible software enhancements. For guidance on adding other functional forms to LIP, refer to Appendix B. The reader who is primarily interested in using LIP to solve a problem should skim Section 1, then skip to Sections 7.1-4. Finally, jump ahead to Section 8 and study the example. The remaining sections can be referred to in case more details are desired. Changes since version 1.1 of this document include the new Section 3.2.1 that discusses derivative estimation and new Section 6 that discusses the birational interpolation method. Section numbers following the latter have been modified accordingly.« less

LIP: The Livermore Interpolation Package, Version 1.3

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fritsch, F N

2011-01-04

This report describes LIP, the Livermore Interpolation Package. Because LIP is a stand-alone version of the interpolation package in the Livermore Equation of State (LEOS) access library, the initials LIP alternatively stand for the ''LEOS Interpolation Package''. LIP was totally rewritten from the package described in [1]. In particular, the independent variables are now referred to as x and y, since the package need not be restricted to equation of state data, which uses variables {rho} (density) and T (temperature). LIP is primarily concerned with the interpolation of two-dimensional data on a rectangular mesh. The interpolation methods provided include piecewisemore » bilinear, reduced (12-term) bicubic, and bicubic Hermite (biherm). There is a monotonicity-preserving variant of the latter, known as bimond. For historical reasons, there is also a biquadratic interpolator, but this option is not recommended for general use. A birational method was added at version 1.3. In addition to direct interpolation of two-dimensional data, LIP includes a facility for inverse interpolation (at present, only in the second independent variable). For completeness, however, the package also supports a compatible one-dimensional interpolation capability. Parametric interpolation of points on a two-dimensional curve can be accomplished by treating the components as a pair of one-dimensional functions with a common independent variable. LIP has an object-oriented design, but it is implemented in ANSI Standard C for efficiency and compatibility with existing applications. First, a ''LIP interpolation object'' is created and initialized with the data to be interpolated. Then the interpolation coefficients for the selected method are computed and added to the object. Since version 1.1, LIP has options to instead estimate derivative values or merely store data in the object. (These are referred to as ''partial setup'' options.) It is then possible to pass the object to functions that interpolate or invert the interpolant at an arbitrary number of points. The first section of this report describes the overall design of the package, including both forward and inverse interpolation. Sections 2-6 describe each interpolation method in detail. The software that implements this design is summarized function-by-function in Section 7. For a complete example of package usage, refer to Section 8. The report concludes with a few brief notes on possible software enhancements. For guidance on adding other functional forms to LIP, refer to Appendix B. The reader who is primarily interested in using LIP to solve a problem should skim Section 1, then skip to Sections 7.1-4. Finally, jump ahead to Section 8 and study the example. The remaining sections can be referred to in case more details are desired. Changes since version 1.1 of this document include the new Section 3.2.1 that discusses derivative estimation and new Section 6 that discusses the birational interpolation method. Section numbers following the latter have been modified accordingly.« less

Analysis and Validation of a Predictive Model for Growth and Death of Aeromonas hydrophila under Modified Atmospheres at Refrigeration Temperatures

PubMed Central

Pin, Carmen; Velasco de Diego, Raquel; George, Susan; García de Fernando, Gonzalo D.; Baranyi, József

2004-01-01

Specific growth and death rates of Aeromonas hydrophila were measured in laboratory media under various combinations of temperature, pH, and percent CO2 and O2 in the atmosphere. Predictive models were developed from the data and validated by means of observations obtained from (i) seafood experiments set up for this purpose and (ii) the ComBase database (http://www.combase.cc; http://wyndmoor.arserrc.gov/combase/).Two main reasons were identified for the differences between the predicted and observed growth in food: they were the variability of the growth rates in food and the bias of the model predictions when applied to food environments. A statistical method is presented to quantitatively analyze these differences. The method was also used to extend the interpolation region of the model. In this extension, the concept of generalized Z values (C. Pin, G. García de Fernando, J. A. Ordóñez, and J. Baranyi, Food Microbiol. 18:539-545, 2001) played an important role. The extension depended partly on the density of the model-generating observations and partly on the accuracy of extrapolated predictions close to the boundary of the interpolation region. The boundary of the growth region of the organism was also estimated by means of experimental results for growth and death rates. PMID:15240265

The Natural Neighbour Radial Point Interpolation Meshless Method Applied to the Non-Linear Analysis

NASA Astrophysics Data System (ADS)

Dinis, L. M. J. S.; Jorge, R. M. Natal; Belinha, J.

2011-05-01

In this work the Natural Neighbour Radial Point Interpolation Method (NNRPIM), is extended to large deformation analysis of elastic and elasto-plastic structures. The NNPRIM uses the Natural Neighbour concept in order to enforce the nodal connectivity and to create a node-depending background mesh, used in the numerical integration of the NNRPIM interpolation functions. Unlike the FEM, where geometrical restrictions on elements are imposed for the convergence of the method, in the NNRPIM there are no such restrictions, which permits a random node distribution for the discretized problem. The NNRPIM interpolation functions, used in the Galerkin weak form, are constructed using the Radial Point Interpolators, with some differences that modify the method performance. In the construction of the NNRPIM interpolation functions no polynomial base is required and the used Radial Basis Function (RBF) is the Multiquadric RBF. The NNRPIM interpolation functions posses the delta Kronecker property, which simplify the imposition of the natural and essential boundary conditions. One of the scopes of this work is to present the validation the NNRPIM in the large-deformation elasto-plastic analysis, thus the used non-linear solution algorithm is the Newton-Rapson initial stiffness method and the efficient "forward-Euler" procedure is used in order to return the stress state to the yield surface. Several non-linear examples, exhibiting elastic and elasto-plastic material properties, are studied to demonstrate the effectiveness of the method. The numerical results indicated that NNRPIM handles large material distortion effectively and provides an accurate solution under large deformation.

Single-Image Super-Resolution Based on Rational Fractal Interpolation.

PubMed

Zhang, Yunfeng; Fan, Qinglan; Bao, Fangxun; Liu, Yifang; Zhang, Caiming

2018-08-01

This paper presents a novel single-image super-resolution (SR) procedure, which upscales a given low-resolution (LR) input image to a high-resolution image while preserving the textural and structural information. First, we construct a new type of bivariate rational fractal interpolation model and investigate its analytical properties. This model has different forms of expression with various values of the scaling factors and shape parameters; thus, it can be employed to better describe image features than current interpolation schemes. Furthermore, this model combines the advantages of rational interpolation and fractal interpolation, and its effectiveness is validated through theoretical analysis. Second, we develop a single-image SR algorithm based on the proposed model. The LR input image is divided into texture and non-texture regions, and then, the image is interpolated according to the characteristics of the local structure. Specifically, in the texture region, the scaling factor calculation is the critical step. We present a method to accurately calculate scaling factors based on local fractal analysis. Extensive experiments and comparisons with the other state-of-the-art methods show that our algorithm achieves competitive performance, with finer details and sharper edges.

Implementation of higher-order vertical finite elements in ISSM v4.13 for improved ice sheet flow modeling over paleoclimate timescales

NASA Astrophysics Data System (ADS)

Cuzzone, Joshua K.; Morlighem, Mathieu; Larour, Eric; Schlegel, Nicole; Seroussi, Helene

2018-05-01

Paleoclimate proxies are being used in conjunction with ice sheet modeling experiments to determine how the Greenland ice sheet responded to past changes, particularly during the last deglaciation. Although these comparisons have been a critical component in our understanding of the Greenland ice sheet sensitivity to past warming, they often rely on modeling experiments that favor minimizing computational expense over increased model physics. Over Paleoclimate timescales, simulating the thermal structure of the ice sheet has large implications on the modeled ice viscosity, which can feedback onto the basal sliding and ice flow. To accurately capture the thermal field, models often require a high number of vertical layers. This is not the case for the stress balance computation, however, where a high vertical resolution is not necessary. Consequently, since stress balance and thermal equations are generally performed on the same mesh, more time is spent on the stress balance computation than is otherwise necessary. For these reasons, running a higher-order ice sheet model (e.g., Blatter-Pattyn) over timescales equivalent to the paleoclimate record has not been possible without incurring a large computational expense. To mitigate this issue, we propose a method that can be implemented within ice sheet models, whereby the vertical interpolation along the z axis relies on higher-order polynomials, rather than the traditional linear interpolation. This method is tested within the Ice Sheet System Model (ISSM) using quadratic and cubic finite elements for the vertical interpolation on an idealized case and a realistic Greenland configuration. A transient experiment for the ice thickness evolution of a single-dome ice sheet demonstrates improved accuracy using the higher-order vertical interpolation compared to models using the linear vertical interpolation, despite having fewer degrees of freedom. This method is also shown to improve a model's ability to capture sharp thermal gradients in an ice sheet particularly close to the bed, when compared to models using a linear vertical interpolation. This is corroborated in a thermal steady-state simulation of the Greenland ice sheet using a higher-order model. In general, we find that using a higher-order vertical interpolation decreases the need for a high number of vertical layers, while dramatically reducing model runtime for transient simulations. Results indicate that when using a higher-order vertical interpolation, runtimes for a transient ice sheet relaxation are upwards of 5 to 7 times faster than using a model which has a linear vertical interpolation, and this thus requires a higher number of vertical layers to achieve a similar result in simulated ice volume, basal temperature, and ice divide thickness. The findings suggest that this method will allow higher-order models to be used in studies investigating ice sheet behavior over paleoclimate timescales at a fraction of the computational cost than would otherwise be needed for a model using a linear vertical interpolation.

An optical systems analysis approach to image resampling

NASA Technical Reports Server (NTRS)

Lyon, Richard G.

1997-01-01

All types of image registration require some type of resampling, either during the registration or as a final step in the registration process. Thus the image(s) must be regridded into a spatially uniform, or angularly uniform, coordinate system with some pre-defined resolution. Frequently the ending resolution is not the resolution at which the data was observed with. The registration algorithm designer and end product user are presented with a multitude of possible resampling methods each of which modify the spatial frequency content of the data in some way. The purpose of this paper is threefold: (1) to show how an imaging system modifies the scene from an end to end optical systems analysis approach, (2) to develop a generalized resampling model, and (3) empirically apply the model to simulated radiometric scene data and tabulate the results. A Hanning windowed sinc interpolator method will be developed based upon the optical characterization of the system. It will be discussed in terms of the effects and limitations of sampling, aliasing, spectral leakage, and computational complexity. Simulated radiometric scene data will be used to demonstrate each of the algorithms. A high resolution scene will be "grown" using a fractal growth algorithm based on mid-point recursion techniques. The result scene data will be convolved with a point spread function representing the optical response. The resultant scene will be convolved with the detection systems response and subsampled to the desired resolution. The resultant data product will be subsequently resampled to the correct grid using the Hanning windowed sinc interpolator and the results and errors tabulated and discussed.

The Choice of Spatial Interpolation Method Affects Research Conclusions

NASA Astrophysics Data System (ADS)

Eludoyin, A. O.; Ijisesan, O. S.; Eludoyin, O. M.

2017-12-01

Studies from developing countries using spatial interpolations in geographical information systems (GIS) are few and recent. Many of the studies have adopted interpolation procedures including kriging, moving average or Inverse Weighted Average (IDW) and nearest point without the necessary recourse to their uncertainties. This study compared the results of modelled representations of popular interpolation procedures from two commonly used GIS software (ILWIS and ArcGIS) at the Obafemi Awolowo University, Ile-Ife, Nigeria. Data used were concentrations of selected biochemical variables (BOD5, COD, SO4, NO3, pH, suspended and dissolved solids) in Ere stream at Ayepe-Olode, in the southwest Nigeria. Water samples were collected using a depth-integrated grab sampling approach at three locations (upstream, downstream and along a palm oil effluent discharge point in the stream); four stations were sited along each location (Figure 1). Data were first subjected to examination of their spatial distributions and associated variogram variables (nugget, sill and range), using the PAleontological STatistics (PAST3), before the mean values were interpolated in selected GIS software for the variables using each of kriging (simple), moving average and nearest point approaches. Further, the determined variogram variables were substituted with the default values in the selected software, and their results were compared. The study showed that the different point interpolation methods did not produce similar results. For example, whereas the values of conductivity was interpolated to vary as 120.1 - 219.5 µScm-1 with kriging interpolation, it varied as 105.6 - 220.0 µScm-1 and 135.0 - 173.9µScm-1 with nearest point and moving average interpolations, respectively (Figure 2). It also showed that whereas the computed variogram model produced the best fit lines (with least associated error value, Sserror) with Gaussian model, the Spherical model was assumed default for all the distributions in the software, such that the value of nugget was assumed as 0.00, when it was rarely so (Figure 3). The study concluded that interpolation procedures may affect decisions and conclusions on modelling inferences.

Spatiotemporal Interpolation for Environmental Modelling

PubMed Central

Susanto, Ferry; de Souza, Paulo; He, Jing

2016-01-01

A variation of the reduction-based approach to spatiotemporal interpolation (STI), in which time is treated independently from the spatial dimensions, is proposed in this paper. We reviewed and compared three widely-used spatial interpolation techniques: ordinary kriging, inverse distance weighting and the triangular irregular network. We also proposed a new distribution-based distance weighting (DDW) spatial interpolation method. In this study, we utilised one year of Tasmania’s South Esk Hydrology model developed by CSIRO. Root mean squared error statistical methods were performed for performance evaluations. Our results show that the proposed reduction approach is superior to the extension approach to STI. However, the proposed DDW provides little benefit compared to the conventional inverse distance weighting (IDW) method. We suggest that the improved IDW technique, with the reduction approach used for the temporal dimension, is the optimal combination for large-scale spatiotemporal interpolation within environmental modelling applications. PMID:27509497

Comparison of air-kerma strength determinations for HDR (192)Ir sources.

PubMed

Rasmussen, Brian E; Davis, Stephen D; Schmidt, Cal R; Micka, John A; Dewerd, Larry A

2011-12-01

To perform a comparison of the interim air-kerma strength standard for high dose rate (HDR) (192)Ir brachytherapy sources maintained by the University of Wisconsin Accredited Dosimetry Calibration Laboratory (UWADCL) with measurements of the various source models using modified techniques from the literature. The current interim standard was established by Goetsch et al. in 1991 and has remained unchanged to date. The improved, laser-aligned seven-distance apparatus of the University of Wisconsin Medical Radiation Research Center (UWMRRC) was used to perform air-kerma strength measurements of five different HDR (192)Ir source models. The results of these measurements were compared with those from well chambers traceable to the original standard. Alternative methodologies for interpolating the (192)Ir air-kerma calibration coefficient from the NIST air-kerma standards at (137)Cs and 250 kVp x rays (M250) were investigated and intercompared. As part of the interpolation method comparison, the Monte Carlo code EGSnrc was used to calculate updated values of A(wall) for the Exradin A3 chamber used for air-kerma strength measurements. The effects of air attenuation and scatter, room scatter, as well as the solution method were investigated in detail. The average measurements when using the inverse N(K) interpolation method for the Classic Nucletron, Nucletron microSelectron, VariSource VS2000, GammaMed Plus, and Flexisource were found to be 0.47%, -0.10%, -1.13%, -0.20%, and 0.89% different than the existing standard, respectively. A further investigation of the differences observed between the sources was performed using MCNP5 Monte Carlo simulations of each source model inside a full model of an HDR 1000 Plus well chamber. Although the differences between the source models were found to be statistically significant, the equally weighted average difference between the seven-distance measurements and the well chambers was 0.01%, confirming that it is not necessary to update the current standard maintained at the UWADCL.

A novel interpolation approach for the generation of 3D-geometric digital bone models from image stacks

PubMed Central

Mittag, U.; Kriechbaumer, A.; Rittweger, J.

2017-01-01

The authors propose a new 3D interpolation algorithm for the generation of digital geometric 3D-models of bones from existing image stacks obtained by peripheral Quantitative Computed Tomography (pQCT) or Magnetic Resonance Imaging (MRI). The technique is based on the interpolation of radial gray value profiles of the pQCT cross sections. The method has been validated by using an ex-vivo human tibia and by comparing interpolated pQCT images with images from scans taken at the same position. A diversity index of <0.4 (1 meaning maximal diversity) even for the structurally complex region of the epiphysis, along with the good agreement of mineral-density-weighted cross-sectional moment of inertia (CSMI), demonstrate the high quality of our interpolation approach. Thus the authors demonstrate that this interpolation scheme can substantially improve the generation of 3D models from sparse scan sets, not only with respect to the outer shape but also with respect to the internal gray-value derived material property distribution. PMID:28574415

Geographic patterns and dynamics of Alaskan climate interpolated from a sparse station record

USGS Publications Warehouse

Fleming, Michael D.; Chapin, F. Stuart; Cramer, W.; Hufford, Gary L.; Serreze, Mark C.

2000-01-01

Data from a sparse network of climate stations in Alaska were interpolated to provide 1-km resolution maps of mean monthly temperature and precipitation-variables that are required at high spatial resolution for input into regional models of ecological processes and resource management. The interpolation model is based on thin-plate smoothing splines, which uses the spatial data along with a digital elevation model to incorporate local topography. The model provides maps that are consistent with regional climatology and with patterns recognized by experienced weather forecasters. The broad patterns of Alaskan climate are well represented and include latitudinal and altitudinal trends in temperature and precipitation and gradients in continentality. Variations within these broad patterns reflect both the weakening and reduction in frequency of low-pressure centres in their eastward movement across southern Alaska during the summer, and the shift of the storm tracks into central and northern Alaska in late summer. Not surprisingly, apparent artifacts of the interpolated climate occur primarily in regions with few or no stations. The interpolation model did not accurately represent low-level winter temperature inversions that occur within large valleys and basins. Along with well-recognized climate patterns, the model captures local topographic effects that would not be depicted using standard interpolation techniques. This suggests that similar procedures could be used to generate high-resolution maps for other high-latitude regions with a sparse density of data.

Influence of survey strategy and interpolation model on DEM quality

NASA Astrophysics Data System (ADS)

Heritage, George L.; Milan, David J.; Large, Andrew R. G.; Fuller, Ian C.

2009-11-01

Accurate characterisation of morphology is critical to many studies in the field of geomorphology, particularly those dealing with changes over time. Digital elevation models (DEMs) are commonly used to represent morphology in three dimensions. The quality of the DEM is largely a function of the accuracy of individual survey points, field survey strategy, and the method of interpolation. Recommendations concerning field survey strategy and appropriate methods of interpolation are currently lacking. Furthermore, the majority of studies to date consider error to be uniform across a surface. This study quantifies survey strategy and interpolation error for a gravel bar on the River Nent, Blagill, Cumbria, UK. Five sampling strategies were compared: (i) cross section; (ii) bar outline only; (iii) bar and chute outline; (iv) bar and chute outline with spot heights; and (v) aerial LiDAR equivalent, derived from degraded terrestrial laser scan (TLS) data. Digital Elevation Models were then produced using five different common interpolation algorithms. Each resultant DEM was differentiated from a terrestrial laser scan of the gravel bar surface in order to define the spatial distribution of vertical and volumetric error. Overall triangulation with linear interpolation (TIN) or point kriging appeared to provide the best interpolators for the bar surface. Lowest error on average was found for the simulated aerial LiDAR survey strategy, regardless of interpolation technique. However, comparably low errors were also found for the bar-chute-spot sampling strategy when TINs or point kriging was used as the interpolator. The magnitude of the errors between survey strategy exceeded those found between interpolation technique for a specific survey strategy. Strong relationships between local surface topographic variation (as defined by the standard deviation of vertical elevations in a 0.2-m diameter moving window), and DEM errors were also found, with much greater errors found at slope breaks such as bank edges. A series of curves are presented that demonstrate these relationships for each interpolation and survey strategy. The simulated aerial LiDAR data set displayed the lowest errors across the flatter surfaces; however, sharp slope breaks are better modelled by the morphologically based survey strategy. The curves presented have general application to spatially distributed data of river beds and may be applied to standard deviation grids to predict spatial error within a surface, depending upon sampling strategy and interpolation algorithm.

Single-stage interpolation flaps in facial reconstruction.

PubMed

Hollmig, S Tyler; Leach, Brian C; Cook, Joel

2014-09-01

Relatively deep and complex surgical defects, particularly when adjacent to or involving free margins, present significant reconstructive challenges. When the use of local flaps is precluded by native anatomic restrictions, interpolation flaps may be modified to address these difficult wounds in a single operative session. To provide a framework to approach difficult soft tissue defects arising near or involving free margins and to demonstrate appropriate design and execution of single-stage interpolation flaps for reconstruction of these wounds. Examination of our utilization of these flaps based on an anatomic region and surgical approach. A region-based demonstration of flap conceptualization, design, and execution is provided. Tunneled, transposed, and deepithelialized variations of single-stage interpolation flaps provide versatile options for reconstruction of a variety of defects encroaching on or involving free margins. The inherently robust vascularity of these flaps supports importation of necessary tissue bulk while allowing aggressive contouring to restore an intricate native topography. Critical flap design allows access to distant tissue reservoirs and placement of favorable incision lines while preserving the inherent advantages of a single operative procedure.

Tropospheric Correction for InSAR Using Interpolated ECMWF Data and GPS Zenith Total Delay

NASA Technical Reports Server (NTRS)

Webb, Frank H.; Fishbein, Evan F.; Moore, Angelyn W.; Owen, Susan E.; Fielding, Eric J.; Granger, Stephanie L.; Bjorndahl, Fredrik; Lofgren Johan

2011-01-01

To mitigate atmospheric errors caused by the troposphere, which is a limiting error source for spaceborne interferometric synthetic aperture radar (InSAR) imaging, a tropospheric correction method has been developed using data from the European Centre for Medium- Range Weather Forecasts (ECMWF) and the Global Positioning System (GPS). The ECMWF data was interpolated using a Stretched Boundary Layer Model (SBLM), and ground-based GPS estimates of the tropospheric delay from the Southern California Integrated GPS Network were interpolated using modified Gaussian and inverse distance weighted interpolations. The resulting Zenith Total Delay (ZTD) correction maps have been evaluated, both separately and using a combination of the two data sets, for three short-interval InSAR pairs from Envisat during 2006 on an area stretching from northeast from the Los Angeles basin towards Death Valley. Results show that the root mean square (rms) in the InSAR images was greatly reduced, meaning a significant reduction in the atmospheric noise of up to 32 percent. However, for some of the images, the rms increased and large errors remained after applying the tropospheric correction. The residuals showed a constant gradient over the area, suggesting that a remaining orbit error from Envisat was present. The orbit reprocessing in ROI_pac and the plane fitting both require that the only remaining error in the InSAR image be the orbit error. If this is not fulfilled, the correction can be made anyway, but it will be done using all remaining errors assuming them to be orbit errors. By correcting for tropospheric noise, the biggest error source is removed, and the orbit error becomes apparent and can be corrected for

The cancellous bone multiscale morphology-elasticity relationship.

PubMed

Agić, Ante; Nikolić, Vasilije; Mijović, Budimir

2006-06-01

The cancellous bone effective properties relations are analysed on multiscale across two aspects; properties of representative volume element on micro scale and statistical measure of trabecular trajectory orientation on mesoscale. Anisotropy of the microstructure is described across fabric tensor measure with trajectory orientation tensor as bridging scale connection. The scatter measured data (elastic modulus, trajectory orientation, apparent density) from compression test are fitted by stochastic interpolation procedure. The engineering constants of the elasticity tensor are estimated by last square fitt procedure in multidimensional space by Nelder-Mead simplex. The multiaxial failure surface in strain space is constructed and interpolated by modified super-ellipsoid.

Efficient Craig Interpolation for Linear Diophantine (Dis)Equations and Linear Modular Equations

DTIC Science & Technology

2008-02-01

Craig interpolants has enabled the development of powerful hardware and software model checking techniques. Efficient algorithms are known for computing...interpolants in rational and real linear arithmetic. We focus on subsets of integer linear arithmetic. Our main results are polynomial time algorithms ...congruences), and linear diophantine disequations. We show the utility of the proposed interpolation algorithms for discovering modular/divisibility predicates

Sparse representation based image interpolation with nonlocal autoregressive modeling.

PubMed

Dong, Weisheng; Zhang, Lei; Lukac, Rastislav; Shi, Guangming

2013-04-01

Sparse representation is proven to be a promising approach to image super-resolution, where the low-resolution (LR) image is usually modeled as the down-sampled version of its high-resolution (HR) counterpart after blurring. When the blurring kernel is the Dirac delta function, i.e., the LR image is directly down-sampled from its HR counterpart without blurring, the super-resolution problem becomes an image interpolation problem. In such cases, however, the conventional sparse representation models (SRM) become less effective, because the data fidelity term fails to constrain the image local structures. In natural images, fortunately, many nonlocal similar patches to a given patch could provide nonlocal constraint to the local structure. In this paper, we incorporate the image nonlocal self-similarity into SRM for image interpolation. More specifically, a nonlocal autoregressive model (NARM) is proposed and taken as the data fidelity term in SRM. We show that the NARM-induced sampling matrix is less coherent with the representation dictionary, and consequently makes SRM more effective for image interpolation. Our extensive experimental results demonstrate that the proposed NARM-based image interpolation method can effectively reconstruct the edge structures and suppress the jaggy/ringing artifacts, achieving the best image interpolation results so far in terms of PSNR as well as perceptual quality metrics such as SSIM and FSIM.

Rapidity distribution of photons from an anisotropic quark-gluon plasma

NASA Astrophysics Data System (ADS)

Bhattacharya, Lusaka; Roy, Pradip

2010-05-01

We calculate rapidity distribution of photons due to Compton and annihilation processes from quark gluon plasma with pre-equilibrium momentum-space anisotropy. We also include contributions from hadronic matter with late-stage transverse expansion. A phenomenological model has been used for the time evolution of hard momentum scale, phard(τ), and anisotropy parameter, ξ(τ). As a result of pre-equilibrium momentum-space anisotropy, we find significant modification of photons rapidity distribution. For example, with the fixed initial condition (FIC) free-streaming (δ=2) interpolating model we observe significant enhancement of photon rapidity distribution at fixed pT, where as for FIC collisionally broadened (δ=2/3) interpolating model the yield increases till y~1. Beyond that suppression is observed. With fixed final multiplicity (FFM) free-streaming interpolating model we predict enhancement of photon yield which is less than the case of FIC. Suppression is always observed for FFM collisionally broadened interpolating model.

A new interpolation method for gridded extensive variables with application in Lagrangian transport and dispersion models

NASA Astrophysics Data System (ADS)

Hittmeir, Sabine; Philipp, Anne; Seibert, Petra

2017-04-01

In discretised form, an extensive variable usually represents an integral over a 3-dimensional (x,y,z) grid cell. In the case of vertical fluxes, gridded values represent integrals over a horizontal (x,y) grid face. In meteorological models, fluxes (precipitation, turbulent fluxes, etc.) are usually written out as temporally integrated values, thus effectively forming 3D (x,y,t) integrals. Lagrangian transport models require interpolation of all relevant variables towards the location in 4D space of each of the computational particles. Trivial interpolation algorithms usually implicitly assume the integral value to be a point value valid at the grid centre. If the integral value would be reconstructed from the interpolated point values, it would in general not be correct. If nonlinear interpolation methods are used, non-negativity cannot easily be ensured. This problem became obvious with respect to the interpolation of precipitation for the calculation of wet deposition FLEXPART (http://flexpart.eu) which uses ECMWF model output or other gridded input data. The presently implemented method consists of a special preprocessing in the input preparation software and subsequent linear interpolation in the model. The interpolated values are positive but the criterion of cell-wise conservation of the integral property is violated; it is also not very accurate as it smoothes the field. A new interpolation algorithm was developed which introduces additional supporting grid points in each time interval with linear interpolation to be applied in FLEXPART later between them. It preserves the integral precipitation in each time interval, guarantees the continuity of the time series, and maintains non-negativity. The function values of the remapping algorithm at these subgrid points constitute the degrees of freedom which can be prescribed in various ways. Combining the advantages of different approaches leads to a final algorithm respecting all the required conditions. To improve the monotonicity behaviour we additionally derived a filter to restrict over- or undershooting. At the current stage, the algorithm is meant primarily for the temporal dimension. It can also be applied with operator-splitting to include the two horizontal dimensions. An extension to 2D appears feasible, while a fully 3D version would most likely not justify the effort compared to the operator-splitting approach.

Non-hydrostatic semi-elastic hybrid-coordinate SISL extension of HIRLAM. Part I: numerical scheme

NASA Astrophysics Data System (ADS)

Rõõm, Rein; Männik, Aarne; Luhamaa, Andres

2007-10-01

Two-time-level, semi-implicit, semi-Lagrangian (SISL) scheme is applied to the non-hydrostatic pressure coordinate equations, constituting a modified Miller-Pearce-White model, in hybrid-coordinate framework. Neutral background is subtracted in the initial continuous dynamics, yielding modified equations for geopotential, temperature and logarithmic surface pressure fluctuation. Implicit Lagrangian marching formulae for single time-step are derived. A disclosure scheme is presented, which results in an uncoupled diagnostic system, consisting of 3-D Poisson equation for omega velocity and 2-D Helmholtz equation for logarithmic pressure fluctuation. The model is discretized to create a non-hydrostatic extension to numerical weather prediction model HIRLAM. The discretization schemes, trajectory computation algorithms and interpolation routines, as well as the physical parametrization package are maintained from parent hydrostatic HIRLAM. For stability investigation, the derived SISL model is linearized with respect to the initial, thermally non-equilibrium resting state. Explicit residuals of the linear model prove to be sensitive to the relative departures of temperature and static stability from the reference state. Relayed on the stability study, the semi-implicit term in the vertical momentum equation is replaced to the implicit term, which results in stability increase of the model.

A parametrisation of modified gravity on nonlinear cosmological scales

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lombriser, Lucas, E-mail: llo@roe.ac.uk

2016-11-01

Viable modifications of gravity on cosmological scales predominantly rely on screening mechanisms to recover Einstein's Theory of General Relativity in the Solar System, where it has been well tested. A parametrisation of the effects of such modifications in the spherical collapse model is presented here for the use of modelling the modified nonlinear cosmological structure. The formalism allows an embedding of the different screening mechanisms operating in scalar-tensor theories through large values of the gravitational potential or its first or second derivatives as well as of linear suppression effects or more general transitions between modified and Einstein gravity limits. Eachmore » screening or suppression mechanism is parametrised by a time, mass, and environment dependent screening scale, an effective modified gravitational coupling in the fully unscreened limit that can be matched to linear theory, the exponent of a power-law radial profile of the screened coupling, determined by derivatives, symmetries, and potentials in the scalar field equation, and an interpolation rate between the screened and unscreened limits. Along with generalised perturbative methods, the parametrisation may be used to formulate a nonlinear extension to the linear parametrised post-Friedmannian framework to enable generalised tests of gravity with the wealth of observations from the nonlinear cosmological regime.« less

Dental implant customization using numerical optimization design and 3-dimensional printing fabrication of zirconia ceramic.

PubMed

Cheng, Yung-Chang; Lin, Deng-Huei; Jiang, Cho-Pei; Lin, Yuan-Min

2017-05-01

This study proposes a new methodology for dental implant customization consisting of numerical geometric optimization and 3-dimensional printing fabrication of zirconia ceramic. In the numerical modeling, exogenous factors for implant shape include the thread pitch, thread depth, maximal diameter of implant neck, and body size. Endogenous factors are bone density, cortical bone thickness, and non-osseointegration. An integration procedure, including uniform design method, Kriging interpolation and genetic algorithm, is applied to optimize the geometry of dental implants. The threshold of minimal micromotion for optimization evaluation was 100 μm. The optimized model is imported to the 3-dimensional slurry printer to fabricate the zirconia green body (powder is bonded by polymer weakly) of the implant. The sintered implant is obtained using a 2-stage sintering process. Twelve models are constructed according to uniform design method and simulated the micromotion behavior using finite element modeling. The result of uniform design models yields a set of exogenous factors that can provide the minimal micromotion (30.61 μm), as a suitable model. Kriging interpolation and genetic algorithm modified the exogenous factor of the suitable model, resulting in 27.11 μm as an optimization model. Experimental results show that the 3-dimensional slurry printer successfully fabricated the green body of the optimization model, but the accuracy of sintered part still needs to be improved. In addition, the scanning electron microscopy morphology is a stabilized t-phase microstructure, and the average compressive strength of the sintered part is 632.1 MPa. Copyright © 2016 John Wiley & Sons, Ltd.

Generation of real-time mode high-resolution water vapor fields from GPS observations

NASA Astrophysics Data System (ADS)

Yu, Chen; Penna, Nigel T.; Li, Zhenhong

2017-02-01

Pointwise GPS measurements of tropospheric zenith total delay can be interpolated to provide high-resolution water vapor maps which may be used for correcting synthetic aperture radar images, for numeral weather prediction, and for correcting Network Real-time Kinematic GPS observations. Several previous studies have addressed the importance of the elevation dependency of water vapor, but it is often a challenge to separate elevation-dependent tropospheric delays from turbulent components. In this paper, we present an iterative tropospheric decomposition interpolation model that decouples the elevation and turbulent tropospheric delay components. For a 150 km × 150 km California study region, we estimate real-time mode zenith total delays at 41 GPS stations over 1 year by using the precise point positioning technique and demonstrate that the decoupled interpolation model generates improved high-resolution tropospheric delay maps compared with previous tropospheric turbulence- and elevation-dependent models. Cross validation of the GPS zenith total delays yields an RMS error of 4.6 mm with the decoupled interpolation model, compared with 8.4 mm with the previous model. On converting the GPS zenith wet delays to precipitable water vapor and interpolating to 1 km grid cells across the region, validations with the Moderate Resolution Imaging Spectroradiometer near-IR water vapor product show 1.7 mm RMS differences by using the decoupled model, compared with 2.0 mm for the previous interpolation model. Such results are obtained without differencing the tropospheric delays or water vapor estimates in time or space, while the errors are similar over flat and mountainous terrains, as well as for both inland and coastal areas.

Shape Control in Multivariate Barycentric Rational Interpolation

NASA Astrophysics Data System (ADS)

Nguyen, Hoa Thang; Cuyt, Annie; Celis, Oliver Salazar

2010-09-01

The most stable formula for a rational interpolant for use on a finite interval is the barycentric form [1, 2]. A simple choice of the barycentric weights ensures the absence of (unwanted) poles on the real line [3]. In [4] we indicate that a more refined choice of the weights in barycentric rational interpolation can guarantee comonotonicity and coconvexity of the rational interpolant in addition to a polefree region of interest. In this presentation we generalize the above to the multivariate case. We use a product-like form of univariate barycentric rational interpolants and indicate how the location of the poles and the shape of the function can be controlled. This functionality is of importance in the construction of mathematical models that need to express a certain trend, such as in probability distributions, economics, population dynamics, tumor growth models etc.

Modifications made to ModelMuse to add support for the Saturated-Unsaturated Transport model (SUTRA)

USGS Publications Warehouse

Winston, Richard B.

2014-01-01

This report (1) describes modifications to ModelMuse,as described in U.S. Geological Survey (USGS) Techniques and Methods (TM) 6–A29 (Winston, 2009), to add support for the Saturated-Unsaturated Transport model (SUTRA) (Voss and Provost, 2002; version of September 22, 2010) and (2) supplements USGS TM 6–A29. Modifications include changes to the main ModelMuse window where the model is designed, addition of methods for generating a finite-element mesh suitable for SUTRA, defining how some functions shouldapply when using a finite-element mesh rather than a finite-difference grid (as originally programmed in ModelMuse), and applying spatial interpolation to angles. In addition, the report describes ways of handling objects on the front view of the model and displaying data. A tabulation contains a summary of the new or modified dialog boxes.

A new stellar spectrum interpolation algorithm and its application to Yunnan-III evolutionary population synthesis models

NASA Astrophysics Data System (ADS)

Cheng, Liantao; Zhang, Fenghui; Kang, Xiaoyu; Wang, Lang

2018-05-01

In evolutionary population synthesis (EPS) models, we need to convert stellar evolutionary parameters into spectra via interpolation in a stellar spectral library. For theoretical stellar spectral libraries, the spectrum grid is homogeneous on the effective-temperature and gravity plane for a given metallicity. It is relatively easy to derive stellar spectra. For empirical stellar spectral libraries, stellar parameters are irregularly distributed and the interpolation algorithm is relatively complicated. In those EPS models that use empirical stellar spectral libraries, different algorithms are used and the codes are often not released. Moreover, these algorithms are often complicated. In this work, based on a radial basis function (RBF) network, we present a new spectrum interpolation algorithm and its code. Compared with the other interpolation algorithms that are used in EPS models, it can be easily understood and is highly efficient in terms of computation. The code is written in MATLAB scripts and can be used on any computer system. Using it, we can obtain the interpolated spectra from a library or a combination of libraries. We apply this algorithm to several stellar spectral libraries (such as MILES, ELODIE-3.1 and STELIB-3.2) and give the integrated spectral energy distributions (ISEDs) of stellar populations (with ages from 1 Myr to 14 Gyr) by combining them with Yunnan-III isochrones. Our results show that the differences caused by the adoption of different EPS model components are less than 0.2 dex. All data about the stellar population ISEDs in this work and the RBF spectrum interpolation code can be obtained by request from the first author or downloaded from http://www1.ynao.ac.cn/˜zhangfh.

Spacecraft Orbit Anomaly Representation Using Thrust-Fourier-Coefficients with Orbit Determination Toolbox

NASA Astrophysics Data System (ADS)

Ko, H.; Scheeres, D.

2014-09-01

Representing spacecraft orbit anomalies between two separate states is a challenging but an important problem in achieving space situational awareness for an active spacecraft. Incorporation of such a capability could play an essential role in analyzing satellite behaviors as well as trajectory estimation of the space object. A general way to deal with the anomaly problem is to add an estimated perturbing acceleration such as dynamic model compensation (DMC) into an orbit determination process based on pre- and post-anomaly tracking data. It is a time-consuming numerical process to find valid coefficients to compensate for unknown dynamics for the anomaly. Even if the orbit determination filter with DMC can crudely estimate an unknown acceleration, this approach does not consider any fundamental element of the unknown dynamics for a given anomaly. In this paper, a new way of representing a spacecraft anomaly using an interpolation technique with the Thrust-Fourier-Coefficients (TFCs) is introduced and several anomaly cases are studied using this interpolation method. It provides a very efficient way of reconstructing the fundamental elements of the dynamics for a given spacecraft anomaly. Any maneuver performed by a satellite transitioning between two arbitrary orbital states can be represented as an equivalent maneuver using an interpolation technique with the TFCs. Given unconnected orbit states between two epochs due to a spacecraft anomaly, it is possible to obtain a unique control law using the TFCs that is able to generate the desired secular behavior for the given orbital changes. This interpolation technique can capture the fundamental elements of combined unmodeled anomaly events. The interpolated orbit trajectory, using the TFCs compensating for a given anomaly, can be used to improve the quality of orbit fits through the anomaly period and therefore help to obtain a good orbit determination solution after the anomaly. Orbit Determination Toolbox (ODTBX) is modified to adapt this technique in order to verify the performance of this interpolation approach. Spacecraft anomaly cases are based on either single or multiple low or high thrust maneuvers and the unknown thrust accelerations are recovered and compared with the true thrust acceleration. The advantage of this approach is to easily append TFCs and its dynamics to the pre-built ODTBX, which enables us to blend post-anomaly tracking data to improve the performance of the interpolation representation in the absence of detailed information about a maneuver. It allows us to improve space situational awareness in the areas of uncertainty propagation, anomaly characterization and track correlation.

Strong lensing probability in TeVeS (tensor-vector-scalar) theory

NASA Astrophysics Data System (ADS)

Chen, Da-Ming

2008-01-01

We recalculate the strong lensing probability as a function of the image separation in TeVeS (tensor-vector-scalar) cosmology, which is a relativistic version of MOND (MOdified Newtonian Dynamics). The lens is modeled by the Hernquist profile. We assume an open cosmology with Ωb = 0.04 and ΩΛ = 0.5 and three different kinds of interpolating functions. Two different galaxy stellar mass functions (GSMF) are adopted: PHJ (Panter, Heavens and Jimenez 2004 Mon. Not. R. Astron. Soc. 355 764) determined from SDSS data release 1 and Fontana (Fontana et al 2006 Astron. Astrophys. 459 745) from GOODS-MUSIC catalog. We compare our results with both the predicted probabilities for lenses from singular isothermal sphere galaxy halos in LCDM (Lambda cold dark matter) with a Schechter-fit velocity function, and the observational results for the well defined combined sample of the Cosmic Lens All-Sky Survey (CLASS) and Jodrell Bank/Very Large Array Astrometric Survey (JVAS). It turns out that the interpolating function μ(x) = x/(1+x) combined with Fontana GSMF matches the results from CLASS/JVAS quite well.

Object Interpolation in Three Dimensions

ERIC Educational Resources Information Center

Kellman, Philip J.; Garrigan, Patrick; Shipley, Thomas F.

2005-01-01

Perception of objects in ordinary scenes requires interpolation processes connecting visible areas across spatial gaps. Most research has focused on 2-D displays, and models have been based on 2-D, orientation-sensitive units. The authors present a view of interpolation processes as intrinsically 3-D and producing representations of contours and…

New gridded database of clear-sky solar radiation derived from ground-based observations over Europe

NASA Astrophysics Data System (ADS)

Bartok, Blanka; Wild, Martin; Sanchez-Lorenzo, Arturo; Hakuba, Maria Z.

2017-04-01

Since aerosols modify the entire energy balance of the climate system through different processes, assessments regarding aerosol multiannual variability are highly required by the climate modelling community. Because of the scarcity of long-term direct aerosol measurements, the retrieval of aerosol data/information from other type of observations or satellite measurements are very relevant. One approach frequently used in the literature is analyze of the clear-sky solar radiation which offer a better overview of changes in aerosol content. In the study first two empirical methods are elaborated in order to separate clear-sky situations from observed values of surface solar radiation available at the World Radiation Data Center (WRDC), St. Petersburg. The daily data has been checked for temporal homogeneity by applying the MASH method (Szentimrey, 2003). In the first approach, clear sky situations are detected based on clearness index, namely the ratio of the surface solar radiation to the extraterrestrial solar irradiation. In the second approach the observed values of surface solar radiation are compared to the climatology of clear-sky surface solar radiation calculated by the MAGIC radiation code (Muller et al. 2009). In both approaches the clear-sky radiation values highly depend on the applied thresholds. In order to eliminate this methodological error a verification of clear-sky detection is envisaged through a comparison with the values obtained by a high time resolution clear-sky detection and interpolation algorithm (Long and Ackermann, 2000) making use of the high quality data from the Baseline Surface Radiation Network (BSRN). As the consequences clear-sky data series are obtained for 118 European meteorological stations. Next a first attempt has been done in order to interpolate the point-wise clear-sky radiation data by applying the MISH (Meteorological Interpolation based on Surface Homogenized Data Basis) method for the spatial interpolation of surface meteorological elements developed at the Hungarian Meteorological Service (Szentimrey 2007). In this way new gridded database of clear-sky solar radiation is created suitable for further investigations regarding the role of aerosols in the energy budget, and also for validations of climate model outputs. References 1. Long CN, Ackerman TP. 2000. Identification of clear skies from broadband pyranometer measurements and calculation of downwelling shortwave cloud effects, J. Geophys. Res., 105(D12), 15609-15626, doi:10.1029/2000JD900077. 2. Mueller R, Matsoukas C, Gratzki A, Behr H, Hollmann R. 2009. The CM-SAF operational scheme for the satellite based retrieval of solar surface irradiance - a LUT based eigenvector hybrid approach, Remote Sensing of Environment, 113 (5), 1012-1024, doi:10.1016/j.rse.2009. 01.012 3. Szentimrey T. 2014. Multiple Analysis of Series for Homogenization (MASHv3.03), Hungarian Meteorological Service, https://www.met.hu/en/omsz/rendezvenyek/homogenization_and_interpolation/software/ 4. Szentimrey T. Bihari Z. 2014: Meteorological Interpolation based on Surface Homogenized Data Basis (MISHv1.03) https://www.met.hu/en/omsz/rendezvenyek/homogenization_and_interpolation/software/

Studies of the structure of massive hybrid stars within a modified NJL model

NASA Astrophysics Data System (ADS)

Li, Cheng-Ming; Zhang, Jin-Li; Yan, Yan; Huang, Yong-Feng; Zong, Hong-Shi

2018-05-01

In this paper, we use the equation of state based on a modification of the 2 +1 flavors Nambu-Jona-Lasinio (NJL) model to study the quark matter of hybrid stars. For comparison, we utilize five EOSs of the relativistic mean-field (RMF) model to describe the hadronic phase. With the three-window crossover interpolation approach, we try to construct relatively soft hybrid EOSs but find the maximum masses of hybrid stars do not differ much. The results are quite close to the 2 solar mass, which is consistent with the mass constraint of PSR J 0348 +0432 . Furthermore, it is noteworthy that the heaviest stable stars have central densities higher than that of the deconfinement transition, suggesting a pure quark core in the hybrid star.

Detection and correction of laser induced breakdown spectroscopy spectral background based on spline interpolation method

NASA Astrophysics Data System (ADS)

Tan, Bing; Huang, Min; Zhu, Qibing; Guo, Ya; Qin, Jianwei

2017-12-01

Laser-induced breakdown spectroscopy (LIBS) is an analytical technique that has gained increasing attention because of many applications. The production of continuous background in LIBS is inevitable because of factors associated with laser energy, gate width, time delay, and experimental environment. The continuous background significantly influences the analysis of the spectrum. Researchers have proposed several background correction methods, such as polynomial fitting, Lorenz fitting and model-free methods. However, less of them apply these methods in the field of LIBS Technology, particularly in qualitative and quantitative analyses. This study proposes a method based on spline interpolation for detecting and estimating the continuous background spectrum according to its smooth property characteristic. Experiment on the background correction simulation indicated that, the spline interpolation method acquired the largest signal-to-background ratio (SBR) over polynomial fitting, Lorenz fitting and model-free method after background correction. These background correction methods all acquire larger SBR values than that acquired before background correction (The SBR value before background correction is 10.0992, whereas the SBR values after background correction by spline interpolation, polynomial fitting, Lorentz fitting, and model-free methods are 26.9576, 24.6828, 18.9770, and 25.6273 respectively). After adding random noise with different kinds of signal-to-noise ratio to the spectrum, spline interpolation method acquires large SBR value, whereas polynomial fitting and model-free method obtain low SBR values. All of the background correction methods exhibit improved quantitative results of Cu than those acquired before background correction (The linear correlation coefficient value before background correction is 0.9776. Moreover, the linear correlation coefficient values after background correction using spline interpolation, polynomial fitting, Lorentz fitting, and model-free methods are 0.9998, 0.9915, 0.9895, and 0.9940 respectively). The proposed spline interpolation method exhibits better linear correlation and smaller error in the results of the quantitative analysis of Cu compared with polynomial fitting, Lorentz fitting and model-free methods, The simulation and quantitative experimental results show that the spline interpolation method can effectively detect and correct the continuous background.

Well-conditioned fractional collocation methods using fractional Birkhoff interpolation basis

NASA Astrophysics Data System (ADS)

Jiao, Yujian; Wang, Li-Lian; Huang, Can

2016-01-01

The purpose of this paper is twofold. Firstly, we provide explicit and compact formulas for computing both Caputo and (modified) Riemann-Liouville (RL) fractional pseudospectral differentiation matrices (F-PSDMs) of any order at general Jacobi-Gauss-Lobatto (JGL) points. We show that in the Caputo case, it suffices to compute F-PSDM of order μ ∈ (0 , 1) to compute that of any order k + μ with integer k ≥ 0, while in the modified RL case, it is only necessary to evaluate a fractional integral matrix of order μ ∈ (0 , 1). Secondly, we introduce suitable fractional JGL Birkhoff interpolation problems leading to new interpolation polynomial basis functions with remarkable properties: (i) the matrix generated from the new basis yields the exact inverse of F-PSDM at "interior" JGL points; (ii) the matrix of the highest fractional derivative in a collocation scheme under the new basis is diagonal; and (iii) the resulted linear system is well-conditioned in the Caputo case, while in the modified RL case, the eigenvalues of the coefficient matrix are highly concentrated. In both cases, the linear systems of the collocation schemes using the new basis can be solved by an iterative solver within a few iterations. Notably, the inverse can be computed in a very stable manner, so this offers optimal preconditioners for usual fractional collocation methods for fractional differential equations (FDEs). It is also noteworthy that the choice of certain special JGL points with parameters related to the order of the equations can ease the implementation. We highlight that the use of the Bateman's fractional integral formulas and fast transforms between Jacobi polynomials with different parameters, is essential for our algorithm development.

DEM interpolation weight calculation modulus based on maximum entropy

NASA Astrophysics Data System (ADS)

Chen, Tian-wei; Yang, Xia

2015-12-01

There is negative-weight in traditional interpolation of gridding DEM, in the article, the principle of Maximum Entropy is utilized to analyze the model system which depends on modulus of space weight. Negative-weight problem of the DEM interpolation is researched via building Maximum Entropy model, and adding nonnegative, first and second order's Moment constraints, the negative-weight problem is solved. The correctness and accuracy of the method was validated with genetic algorithm in matlab program. The method is compared with the method of Yang Chizhong interpolation and quadratic program. Comparison shows that the volume and scaling of Maximum Entropy's weight is fit to relations of space and the accuracy is superior to the latter two.

CFA-aware features for steganalysis of color images

NASA Astrophysics Data System (ADS)

Goljan, Miroslav; Fridrich, Jessica

2015-03-01

Color interpolation is a form of upsampling, which introduces constraints on the relationship between neighboring pixels in a color image. These constraints can be utilized to substantially boost the accuracy of steganography detectors. In this paper, we introduce a rich model formed by 3D co-occurrences of color noise residuals split according to the structure of the Bayer color filter array to further improve detection. Some color interpolation algorithms, AHD and PPG, impose pixel constraints so tight that extremely accurate detection becomes possible with merely eight features eliminating the need for model richification. We carry out experiments on non-adaptive LSB matching and the content-adaptive algorithm WOW on five different color interpolation algorithms. In contrast to grayscale images, in color images that exhibit traces of color interpolation the security of WOW is significantly lower and, depending on the interpolation algorithm, may even be lower than non-adaptive LSB matching.

Prediction of LDEF exposure to the ionizing radiation environment

NASA Technical Reports Server (NTRS)

Watts, J. W.; Armstrong, T. W.; Colborn, B. L.

1996-01-01

Predictions of the LDEF mission's trapped proton and electron and galactic cosmic ray proton exposures have been made using the currently accepted models with improved resolution near mission end and better modeling of solar cycle effects. An extension of previous calculations, to provide a more definitive description of the LDEF exposure to ionizing radiation, is represented by trapped proton and electron flux as a function of mission time, presented considering altitude and solar activity variation during the mission and the change in galactic cosmic ray proton flux over the mission. Modifications of the AP8MAX and AP8MIN fluence led to a reduction of fluence by 20%. A modified interpolation model developed by Daly and Evans resulted in 30% higher dose and activation levels, which better agreed with measured values than results predicted using the Vette model.

Modeling of earthquake ground motion in the frequency domain

NASA Astrophysics Data System (ADS)

Thrainsson, Hjortur

In recent years, the utilization of time histories of earthquake ground motion has grown considerably in the design and analysis of civil structures. It is very unlikely, however, that recordings of earthquake ground motion will be available for all sites and conditions of interest. Hence, there is a need for efficient methods for the simulation and spatial interpolation of earthquake ground motion. In addition to providing estimates of the ground motion at a site using data from adjacent recording stations, spatially interpolated ground motions can also be used in design and analysis of long-span structures, such as bridges and pipelines, where differential movement is important. The objective of this research is to develop a methodology for rapid generation of horizontal earthquake ground motion at any site for a given region, based on readily available source, path and site characteristics, or (sparse) recordings. The research includes two main topics: (i) the simulation of earthquake ground motion at a given site, and (ii) the spatial interpolation of earthquake ground motion. In topic (i), models are developed to simulate acceleration time histories using the inverse discrete Fourier transform. The Fourier phase differences, defined as the difference in phase angle between adjacent frequency components, are simulated conditional on the Fourier amplitude. Uniformly processed recordings from recent California earthquakes are used to validate the simulation models, as well as to develop prediction formulas for the model parameters. The models developed in this research provide rapid simulation of earthquake ground motion over a wide range of magnitudes and distances, but they are not intended to replace more robust geophysical models. In topic (ii), a model is developed in which Fourier amplitudes and Fourier phase angles are interpolated separately. A simple dispersion relationship is included in the phase angle interpolation. The accuracy of the interpolation model is assessed using data from the SMART-1 array in Taiwan. The interpolation model provides an effective method to estimate ground motion at a site using recordings from stations located up to several kilometers away. Reliable estimates of differential ground motion are restricted to relatively limited ranges of frequencies and inter-station spacings.

[Research on fast implementation method of image Gaussian RBF interpolation based on CUDA].

PubMed

Chen, Hao; Yu, Haizhong

2014-04-01

Image interpolation is often required during medical image processing and analysis. Although interpolation method based on Gaussian radial basis function (GRBF) has high precision, the long calculation time still limits its application in field of image interpolation. To overcome this problem, a method of two-dimensional and three-dimensional medical image GRBF interpolation based on computing unified device architecture (CUDA) is proposed in this paper. According to single instruction multiple threads (SIMT) executive model of CUDA, various optimizing measures such as coalesced access and shared memory are adopted in this study. To eliminate the edge distortion of image interpolation, natural suture algorithm is utilized in overlapping regions while adopting data space strategy of separating 2D images into blocks or dividing 3D images into sub-volumes. Keeping a high interpolation precision, the 2D and 3D medical image GRBF interpolation achieved great acceleration in each basic computing step. The experiments showed that the operative efficiency of image GRBF interpolation based on CUDA platform was obviously improved compared with CPU calculation. The present method is of a considerable reference value in the application field of image interpolation.

On the error propagation of semi-Lagrange and Fourier methods for advection problems☆

PubMed Central

Einkemmer, Lukas; Ostermann, Alexander

2015-01-01

In this paper we study the error propagation of numerical schemes for the advection equation in the case where high precision is desired. The numerical methods considered are based on the fast Fourier transform, polynomial interpolation (semi-Lagrangian methods using a Lagrange or spline interpolation), and a discontinuous Galerkin semi-Lagrangian approach (which is conservative and has to store more than a single value per cell). We demonstrate, by carrying out numerical experiments, that the worst case error estimates given in the literature provide a good explanation for the error propagation of the interpolation-based semi-Lagrangian methods. For the discontinuous Galerkin semi-Lagrangian method, however, we find that the characteristic property of semi-Lagrangian error estimates (namely the fact that the error increases proportionally to the number of time steps) is not observed. We provide an explanation for this behavior and conduct numerical simulations that corroborate the different qualitative features of the error in the two respective types of semi-Lagrangian methods. The method based on the fast Fourier transform is exact but, due to round-off errors, susceptible to a linear increase of the error in the number of time steps. We show how to modify the Cooley–Tukey algorithm in order to obtain an error growth that is proportional to the square root of the number of time steps. Finally, we show, for a simple model, that our conclusions hold true if the advection solver is used as part of a splitting scheme. PMID:25844018

Methodology for Image-Based Reconstruction of Ventricular Geometry for Patient-Specific Modeling of Cardiac Electrophysiology

PubMed Central

Prakosa, A.; Malamas, P.; Zhang, S.; Pashakhanloo, F.; Arevalo, H.; Herzka, D. A.; Lardo, A.; Halperin, H.; McVeigh, E.; Trayanova, N.; Vadakkumpadan, F.

2014-01-01

Patient-specific modeling of ventricular electrophysiology requires an interpolated reconstruction of the 3-dimensional (3D) geometry of the patient ventricles from the low-resolution (Lo-res) clinical images. The goal of this study was to implement a processing pipeline for obtaining the interpolated reconstruction, and thoroughly evaluate the efficacy of this pipeline in comparison with alternative methods. The pipeline implemented here involves contouring the epi- and endocardial boundaries in Lo-res images, interpolating the contours using the variational implicit functions method, and merging the interpolation results to obtain the ventricular reconstruction. Five alternative interpolation methods, namely linear, cubic spline, spherical harmonics, cylindrical harmonics, and shape-based interpolation were implemented for comparison. In the thorough evaluation of the processing pipeline, Hi-res magnetic resonance (MR), computed tomography (CT), and diffusion tensor (DT) MR images from numerous hearts were used. Reconstructions obtained from the Hi-res images were compared with the reconstructions computed by each of the interpolation methods from a sparse sample of the Hi-res contours, which mimicked Lo-res clinical images. Qualitative and quantitative comparison of these ventricular geometry reconstructions showed that the variational implicit functions approach performed better than others. Additionally, the outcomes of electrophysiological simulations (sinus rhythm activation maps and pseudo-ECGs) conducted using models based on the various reconstructions were compared. These electrophysiological simulations demonstrated that our implementation of the variational implicit functions-based method had the best accuracy. PMID:25148771

3-d interpolation in object perception: evidence from an objective performance paradigm.

PubMed

Kellman, Philip J; Garrigan, Patrick; Shipley, Thomas F; Yin, Carol; Machado, Liana

2005-06-01

Object perception requires interpolation processes that connect visible regions despite spatial gaps. Some research has suggested that interpolation may be a 3-D process, but objective performance data and evidence about the conditions leading to interpolation are needed. The authors developed an objective performance paradigm for testing 3-D interpolation and tested a new theory of 3-D contour interpolation, termed 3-D relatability. The theory indicates for a given edge which orientations and positions of other edges in space may be connected to it by interpolation. Results of 5 experiments showed that processing of orientation relations in 3-D relatable displays was superior to processing in 3-D nonrelatable displays and that these effects depended on object formation. 3-D interpolation and 3-D relatabilty are discussed in terms of their implications for computational and neural models of object perception, which have typically been based on 2-D-orientation-sensitive units. ((c) 2005 APA, all rights reserved).

Directional kriging implementation for gridded data interpolation and comparative study with common methods

NASA Astrophysics Data System (ADS)

Mahmoudabadi, H.; Briggs, G.

2016-12-01

Gridded data sets, such as geoid models or datum shift grids, are commonly used in coordinate transformation algorithms. Grid files typically contain known or measured values at regular fixed intervals. The process of computing a value at an unknown location from the values in the grid data set is called "interpolation". Generally, interpolation methods predict a value at a given point by computing a weighted average of the known values in the neighborhood of the point. Geostatistical Kriging is a widely used interpolation method for irregular networks. Kriging interpolation first analyzes the spatial structure of the input data, then generates a general model to describe spatial dependencies. This model is used to calculate values at unsampled locations by finding direction, shape, size, and weight of neighborhood points. Because it is based on a linear formulation for the best estimation, Kriging it the optimal interpolation method in statistical terms. The Kriging interpolation algorithm produces an unbiased prediction, as well as the ability to calculate the spatial distribution of uncertainty, allowing you to estimate the errors in an interpolation for any particular point. Kriging is not widely used in geospatial applications today, especially applications that run on low power devices or deal with large data files. This is due to the computational power and memory requirements of standard Kriging techniques. In this paper, improvements are introduced in directional kriging implementation by taking advantage of the structure of the grid files. The regular spacing of points simplifies finding the neighborhood points and computing their pairwise distances, reducing the the complexity and improving the execution time of the Kriging algorithm. Also, the proposed method iteratively loads small portion of interest areas in different directions to reduce the amount of required memory. This makes the technique feasible on almost any computer processor. Comparison between kriging and other standard interpolation methods demonstrated more accurate estimations in less denser data files.

Using "snapshot" measurements of CH4 fluxes from peatlands to estimate annual budgets: interpolation vs. modelling.

NASA Astrophysics Data System (ADS)

Green, Sophie M.; Baird, Andy J.

2016-04-01

There is growing interest in estimating annual budgets of peatland-atmosphere carbon dioxide (CO2) and methane (CH4) exchanges. Such budgeting is required for calculating peatland carbon balance and the radiative forcing impact of peatlands on climate. There have been multiple approaches used to estimate CO2 budgets; however, there is a limited literature regarding the modelling of annual CH4 budgets. Using data collected from flux chamber tests in an area of blanket peatland in North Wales, we compared annual estimates of peatland-atmosphere CH4 emissions using an interpolation approach and an additive and multiplicative modelling approach. Flux-chamber measurements represent a snapshot of the conditions on a particular site. In contrast to CO2, most studies that have estimated the time-integrated flux of CH4 have not used models. Typically, linear interpolation is used to estimate CH4 fluxes during the time periods between flux-chamber measurements. It is unclear how much error is involved with such a simple integration method. CH4 fluxes generally show a rise followed by a fall through the growing season that may be captured reasonably well by interpolation, provided there are sufficiently frequent measurements. However, day-to-day and week-to-week variability is also often evident in CH4 flux data, and will not necessarily be properly represented by interpolation. Our fits of the CH4 flux models yielded r2 > 0.5 in 38 of the 48 models constructed, with 55% of these having a weighted rw2 > 0.4. Comparison of annualised CH4 fluxes estimated by interpolation and modelling reveals no correlation between the two data sets; indeed, in some cases even the sign of the flux differs. The difference between the methods seems also to be related to the size of the flux - for modest annual fluxes there is a fairly even scatter of points around the 1:1 line, whereas when the modelled fluxes are high, the corresponding interpolated fluxes tend to be low. We consider the implications of these results for the calculation of the radiative forcing effect of peatlands.

A robust interpolation procedure for producing tidal current ellipse inputs for regional and coastal ocean numerical models

NASA Astrophysics Data System (ADS)

Byun, Do-Seong; Hart, Deirdre E.

2017-04-01

Regional and/or coastal ocean models can use tidal current harmonic forcing, together with tidal harmonic forcing along open boundaries in order to successfully simulate tides and tidal currents. These inputs can be freely generated using online open-access data, but the data produced are not always at the resolution required for regional or coastal models. Subsequent interpolation procedures can produce tidal current forcing data errors for parts of the world's coastal ocean where tidal ellipse inclinations and phases move across the invisible mathematical "boundaries" between 359° and 0° degrees (or 179° and 0°). In nature, such "boundaries" are in fact smooth transitions, but if these mathematical "boundaries" are not treated correctly during interpolation, they can produce inaccurate input data and hamper the accurate simulation of tidal currents in regional and coastal ocean models. These avoidable errors arise due to procedural shortcomings involving vector embodiment problems (i.e., how a vector is represented mathematically, for example as velocities or as coordinates). Automated solutions for producing correct tidal ellipse parameter input data are possible if a series of steps are followed correctly, including the use of Cartesian coordinates during interpolation. This note comprises the first published description of scenarios where tidal ellipse parameter interpolation errors can arise, and of a procedure to successfully avoid these errors when generating tidal inputs for regional and/or coastal ocean numerical models. We explain how a straightforward sequence of data production, format conversion, interpolation, and format reconversion steps may be used to check for the potential occurrence and avoidance of tidal ellipse interpolation and phase errors. This sequence is demonstrated via a case study of the M2 tidal constituent in the seas around Korea but is designed to be universally applicable. We also recommend employing tidal ellipse parameter calculation methods that avoid the use of Foreman's (1978) "northern semi-major axis convention" since, as revealed in our analysis, this commonly used conversion can result in inclination interpolation errors even when Cartesian coordinate-based "vector embodiment" solutions are employed.

Statistical comparison of various interpolation algorithms for reconstructing regional grid ionospheric maps over China

NASA Astrophysics Data System (ADS)

Li, Min; Yuan, Yunbin; Wang, Ningbo; Li, Zishen; Liu, Xifeng; Zhang, Xiao

2018-07-01

This paper presents a quantitative comparison of several widely used interpolation algorithms, i.e., Ordinary Kriging (OrK), Universal Kriging (UnK), planar fit and Inverse Distance Weighting (IDW), based on a grid-based single-shell ionosphere model over China. The experimental data were collected from the Crustal Movement Observation Network of China (CMONOC) and the International GNSS Service (IGS), covering the days of year 60-90 in 2015. The quality of these interpolation algorithms was assessed by cross-validation in terms of both the ionospheric correction performance and Single-Frequency (SF) Precise Point Positioning (PPP) accuracy on an epoch-by-epoch basis. The results indicate that the interpolation models perform better at mid-latitudes than low latitudes. For the China region, the performance of OrK and UnK is relatively better than the planar fit and IDW model for estimating ionospheric delay and positioning. In addition, the computational efficiencies of the IDW and planar fit models are better than those of OrK and UnK.

Interpolating Non-Parametric Distributions of Hourly Rainfall Intensities Using Random Mixing

NASA Astrophysics Data System (ADS)

Mosthaf, Tobias; Bárdossy, András; Hörning, Sebastian

2015-04-01

The correct spatial interpolation of hourly rainfall intensity distributions is of great importance for stochastical rainfall models. Poorly interpolated distributions may lead to over- or underestimation of rainfall and consequently to wrong estimates of following applications, like hydrological or hydraulic models. By analyzing the spatial relation of empirical rainfall distribution functions, a persistent order of the quantile values over a wide range of non-exceedance probabilities is observed. As the order remains similar, the interpolation weights of quantile values for one certain non-exceedance probability can be applied to the other probabilities. This assumption enables the use of kernel smoothed distribution functions for interpolation purposes. Comparing the order of hourly quantile values over different gauges with the order of their daily quantile values for equal probabilities, results in high correlations. The hourly quantile values also show high correlations with elevation. The incorporation of these two covariates into the interpolation is therefore tested. As only positive interpolation weights for the quantile values assure a monotonically increasing distribution function, the use of geostatistical methods like kriging is problematic. Employing kriging with external drift to incorporate secondary information is not applicable. Nonetheless, it would be fruitful to make use of covariates. To overcome this shortcoming, a new random mixing approach of spatial random fields is applied. Within the mixing process hourly quantile values are considered as equality constraints and correlations with elevation values are included as relationship constraints. To profit from the dependence of daily quantile values, distribution functions of daily gauges are used to set up lower equal and greater equal constraints at their locations. In this way the denser daily gauge network can be included in the interpolation of the hourly distribution functions. The applicability of this new interpolation procedure will be shown for around 250 hourly rainfall gauges in the German federal state of Baden-Württemberg. The performance of the random mixing technique within the interpolation is compared to applicable kriging methods. Additionally, the interpolation of kernel smoothed distribution functions is compared with the interpolation of fitted parametric distributions.

Image interpolation via regularized local linear regression.

PubMed

Liu, Xianming; Zhao, Debin; Xiong, Ruiqin; Ma, Siwei; Gao, Wen; Sun, Huifang

2011-12-01

The linear regression model is a very attractive tool to design effective image interpolation schemes. Some regression-based image interpolation algorithms have been proposed in the literature, in which the objective functions are optimized by ordinary least squares (OLS). However, it is shown that interpolation with OLS may have some undesirable properties from a robustness point of view: even small amounts of outliers can dramatically affect the estimates. To address these issues, in this paper we propose a novel image interpolation algorithm based on regularized local linear regression (RLLR). Starting with the linear regression model where we replace the OLS error norm with the moving least squares (MLS) error norm leads to a robust estimator of local image structure. To keep the solution stable and avoid overfitting, we incorporate the l(2)-norm as the estimator complexity penalty. Moreover, motivated by recent progress on manifold-based semi-supervised learning, we explicitly consider the intrinsic manifold structure by making use of both measured and unmeasured data points. Specifically, our framework incorporates the geometric structure of the marginal probability distribution induced by unmeasured samples as an additional local smoothness preserving constraint. The optimal model parameters can be obtained with a closed-form solution by solving a convex optimization problem. Experimental results on benchmark test images demonstrate that the proposed method achieves very competitive performance with the state-of-the-art interpolation algorithms, especially in image edge structure preservation. © 2011 IEEE

Cognitive-graphic method for constructing of hierarchical forms of basic functions of biquadratic finite element

NASA Astrophysics Data System (ADS)

Astionenko, I. O.; Litvinenko, O. I.; Osipova, N. V.; Tuluchenko, G. Ya.; Khomchenko, A. N.

2016-10-01

Recently the interpolation bases of the hierarchical type have been used for the problem solving of the approximation of multiple arguments functions (such as in the finite-element method). In this work the cognitive graphical method of constructing of the hierarchical form bases on the serendipity finite elements is suggested, which allowed to get the alternative bases on a biquadratic finite element from the serendipity family without internal knots' inclusion. The cognitive-graphic method allowed to improve the known interpolation procedure of Taylor and to get the modified elements with irregular arrangement of knots. The proposed procedures are universal and are spread in the area of finite-elements.

Use of shape-preserving interpolation methods in surface modeling

NASA Technical Reports Server (NTRS)

Ftitsch, F. N.

1984-01-01

In many large-scale scientific computations, it is necessary to use surface models based on information provided at only a finite number of points (rather than determined everywhere via an analytic formula). As an example, an equation of state (EOS) table may provide values of pressure as a function of temperature and density for a particular material. These values, while known quite accurately, are typically known only on a rectangular (but generally quite nonuniform) mesh in (T,d)-space. Thus interpolation methods are necessary to completely determine the EOS surface. The most primitive EOS interpolation scheme is bilinear interpolation. This has the advantages of depending only on local information, so that changes in data remote from a mesh element have no effect on the surface over the element, and of preserving shape information, such as monotonicity. Most scientific calculations, however, require greater smoothness. Standard higher-order interpolation schemes, such as Coons patches or bicubic splines, while providing the requisite smoothness, tend to produce surfaces that are not physically reasonable. This means that the interpolant may have bumps or wiggles that are not supported by the data. The mathematical quantification of ideas such as physically reasonable and visually pleasing is examined.

High-resolution daily gridded datasets of air temperature and wind speed for Europe

NASA Astrophysics Data System (ADS)

Brinckmann, S.; Krähenmann, S.; Bissolli, P.

2015-08-01

New high-resolution datasets for near surface daily air temperature (minimum, maximum and mean) and daily mean wind speed for Europe (the CORDEX domain) are provided for the period 2001-2010 for the purpose of regional model validation in the framework of DecReg, a sub-project of the German MiKlip project, which aims to develop decadal climate predictions. The main input data sources are hourly SYNOP observations, partly supplemented by station data from the ECA&D dataset (http://www.ecad.eu). These data are quality tested to eliminate erroneous data and various kinds of inhomogeneities. Grids in a resolution of 0.044° (5 km) are derived by spatial interpolation of these station data into the CORDEX area. For temperature interpolation a modified version of a regression kriging method developed by Krähenmann et al. (2011) is used. At first, predictor fields of altitude, continentality and zonal mean temperature are chosen for a regression applied to monthly station data. The residuals of the monthly regression and the deviations of the daily data from the monthly averages are interpolated using simple kriging in a second and third step. For wind speed a new method based on the concept used for temperature was developed, involving predictor fields of exposure, roughness length, coastal distance and ERA Interim reanalysis wind speed at 850 hPa. Interpolation uncertainty is estimated by means of the kriging variance and regression uncertainties. Furthermore, to assess the quality of the final daily grid data, cross validation is performed. Explained variance ranges from 70 to 90 % for monthly temperature and from 50 to 60 % for monthly wind speed. The resulting RMSE for the final daily grid data amounts to 1-2 °C and 1-1.5 m s-1 (depending on season and parameter) for daily temperature parameters and daily mean wind speed, respectively. The datasets presented in this article are published at http://dx.doi.org/10.5676/DWD_CDC/DECREG0110v1.

A novel iterative modified bicubic interpolation method enables high-contrast and high-resolution image generation for F-18 FDG-PET.

PubMed

Okizaki, Atsutaka; Nakayama, Michihiro; Nakajima, Kaori; Takahashi, Koji

2017-12-01

Positron emission tomography (PET) has become a useful and important technique in oncology. However, spatial resolution of PET is not high; therefore, small abnormalities can sometimes be overlooked with PET. To address this problem, we devised a novel algorithm, iterative modified bicubic interpolation method (IMBIM). IMBIM generates high resolution and -contrast image. The purpose of this study was to investigate the utility of IMBIM for clinical FDG positron emission tomography/X-ray computed tomography (PET/CT) imaging.We evaluated PET images from 1435 patients with malignant tumor and compared the contrast (uptake ratio of abnormal lesions to background) in high resolution image with the standard bicubic interpolation method (SBIM) and IMBIM. In addition to the contrast analysis, 340 out of 1435 patients were selected for visual evaluation by nuclear medicine physicians to investigate lesion detectability. Abnormal uptakes on the images were categorized as either absolutely abnormal or equivocal finding.The average of contrast with IMBIM was significantly higher than that with SBIM (P < .001). The improvements were prominent with large matrix sizes and small lesions. SBIM images showed abnormalities in 198 of 340 lesions (58.2%), while IMBIM indicated abnormalities in 312 (91.8%). There was statistically significant improvement in lesion detectability with IMBIM (P < .001).In conclusion, IMBIM generates high-resolution images with improved contrast and, therefore, may facilitate more accurate diagnoses in clinical practice. Copyright © 2017 The Authors. Published by Wolters Kluwer Health, Inc. All rights reserved.

Spatial interpolation schemes of daily precipitation for hydrologic modeling

USGS Publications Warehouse

Hwang, Y.; Clark, M.R.; Rajagopalan, B.; Leavesley, G.

2012-01-01

Distributed hydrologic models typically require spatial estimates of precipitation interpolated from sparsely located observational points to the specific grid points. We compare and contrast the performance of regression-based statistical methods for the spatial estimation of precipitation in two hydrologically different basins and confirmed that widely used regression-based estimation schemes fail to describe the realistic spatial variability of daily precipitation field. The methods assessed are: (1) inverse distance weighted average; (2) multiple linear regression (MLR); (3) climatological MLR; and (4) locally weighted polynomial regression (LWP). In order to improve the performance of the interpolations, the authors propose a two-step regression technique for effective daily precipitation estimation. In this simple two-step estimation process, precipitation occurrence is first generated via a logistic regression model before estimate the amount of precipitation separately on wet days. This process generated the precipitation occurrence, amount, and spatial correlation effectively. A distributed hydrologic model (PRMS) was used for the impact analysis in daily time step simulation. Multiple simulations suggested noticeable differences between the input alternatives generated by three different interpolation schemes. Differences are shown in overall simulation error against the observations, degree of explained variability, and seasonal volumes. Simulated streamflows also showed different characteristics in mean, maximum, minimum, and peak flows. Given the same parameter optimization technique, LWP input showed least streamflow error in Alapaha basin and CMLR input showed least error (still very close to LWP) in Animas basin. All of the two-step interpolation inputs resulted in lower streamflow error compared to the directly interpolated inputs. ?? 2011 Springer-Verlag.

Selection of Optimal Auxiliary Soil Nutrient Variables for Cokriging Interpolation

PubMed Central

Song, Genxin; Zhang, Jing; Wang, Ke

2014-01-01

In order to explore the selection of the best auxiliary variables (BAVs) when using the Cokriging method for soil attribute interpolation, this paper investigated the selection of BAVs from terrain parameters, soil trace elements, and soil nutrient attributes when applying Cokriging interpolation to soil nutrients (organic matter, total N, available P, and available K). In total, 670 soil samples were collected in Fuyang, and the nutrient and trace element attributes of the soil samples were determined. Based on the spatial autocorrelation of soil attributes, the Digital Elevation Model (DEM) data for Fuyang was combined to explore the coordinate relationship among terrain parameters, trace elements, and soil nutrient attributes. Variables with a high correlation to soil nutrient attributes were selected as BAVs for Cokriging interpolation of soil nutrients, and variables with poor correlation were selected as poor auxiliary variables (PAVs). The results of Cokriging interpolations using BAVs and PAVs were then compared. The results indicated that Cokriging interpolation with BAVs yielded more accurate results than Cokriging interpolation with PAVs (the mean absolute error of BAV interpolation results for organic matter, total N, available P, and available K were 0.020, 0.002, 7.616, and 12.4702, respectively, and the mean absolute error of PAV interpolation results were 0.052, 0.037, 15.619, and 0.037, respectively). The results indicated that Cokriging interpolation with BAVs can significantly improve the accuracy of Cokriging interpolation for soil nutrient attributes. This study provides meaningful guidance and reference for the selection of auxiliary parameters for the application of Cokriging interpolation to soil nutrient attributes. PMID:24927129

Constructing polyatomic potential energy surfaces by interpolating diabatic Hamiltonian matrices with demonstration on green fluorescent protein chromophore

DOE Office of Scientific and Technical Information (OSTI.GOV)

Park, Jae Woo; Rhee, Young Min, E-mail: ymrhee@postech.ac.kr; Department of Chemistry, Pohang University of Science and Technology

2014-04-28

Simulating molecular dynamics directly on quantum chemically obtained potential energy surfaces is generally time consuming. The cost becomes overwhelming especially when excited state dynamics is aimed with multiple electronic states. The interpolated potential has been suggested as a remedy for the cost issue in various simulation settings ranging from fast gas phase reactions of small molecules to relatively slow condensed phase dynamics with complex surrounding. Here, we present a scheme for interpolating multiple electronic surfaces of a relatively large molecule, with an intention of applying it to studying nonadiabatic behaviors. The scheme starts with adiabatic potential information and its diabaticmore » transformation, both of which can be readily obtained, in principle, with quantum chemical calculations. The adiabatic energies and their derivatives on each interpolation center are combined with the derivative coupling vectors to generate the corresponding diabatic Hamiltonian and its derivatives, and they are subsequently adopted in producing a globally defined diabatic Hamiltonian function. As a demonstration, we employ the scheme to build an interpolated Hamiltonian of a relatively large chromophore, para-hydroxybenzylidene imidazolinone, in reference to its all-atom analytical surface model. We show that the interpolation is indeed reliable enough to reproduce important features of the reference surface model, such as its adiabatic energies and derivative couplings. In addition, nonadiabatic surface hopping simulations with interpolation yield population transfer dynamics that is well in accord with the result generated with the reference analytic surface. With these, we conclude by suggesting that the interpolation of diabatic Hamiltonians will be applicable for studying nonadiabatic behaviors of sizeable molecules.« less

RCHILD - an R-package for flexible use of the landscape evolution model CHILD

NASA Astrophysics Data System (ADS)

Dietze, Michael

2014-05-01

Landscape evolution models provide powerful approaches to numerically assess earth surface processes, to quantify rates of landscape change, infer sediment transfer rates, estimate sediment budgets, investigate the consequences of changes in external drivers on a geomorphic system, to provide spatio-temporal interpolations between known landscape states or to test conceptual hypotheses. CHILD (Channel-Hillslope Integrated Landscape Development Model) is one of the most-used models of landscape change in the context of at least tectonic and geomorphologic process interactions. Running CHILD from command line and working with the model output can be a rather awkward task (static model control via text input file, only numeric output in text files). The package RCHILD is a collection of functions for the free statistical software R that help using CHILD in a flexible, dynamic and user-friendly way. The comprised functions allow creating maps, real-time scenes, animations and further thematic plots from model output. The model input files can be modified dynamically and, hence, (feedback-related) changes in external factors can be implemented iteratively. Output files can be written to common formats that can be readily imported to standard GIS software. This contribution presents the basic functionality of the model CHILD as visualised and modified by the package. A rough overview of the available functions is given. Application examples help to illustrate the great potential of numeric modelling of geomorphologic processes.

An empirical model of diagnostic x-ray attenuation under narrow-beam geometry.

PubMed

Mathieu, Kelsey B; Kappadath, S Cheenu; White, R Allen; Atkinson, E Neely; Cody, Dianna D

2011-08-01

The purpose of this study was to develop and validate a mathematical model to describe narrow-beam attenuation of kilovoltage x-ray beams for the intended applications of half-value layer (HVL) and quarter-value layer (QVL) estimations, patient organ shielding, and computer modeling. An empirical model, which uses the Lambert W function and represents a generalized Lambert-Beer law, was developed. To validate this model, transmission of diagnostic energy x-ray beams was measured over a wide range of attenuator thicknesses [0.49-33.03 mm Al on a computed tomography (CT) scanner, 0.09-1.93 mm Al on two mammography systems, and 0.1-0.45 mm Cu and 0.49-14.87 mm Al using general radiography]. Exposure measurements were acquired under narrow-beam geometry using standard methods, including the appropriate ionization chamber, for each radiographic system. Nonlinear regression was used to find the best-fit curve of the proposed Lambert W model to each measured transmission versus attenuator thickness data set. In addition to validating the Lambert W model, we also assessed the performance of two-point Lambert W interpolation compared to traditional methods for estimating the HVL and QVL [i.e., semi-logarithmic (exponential) and linear interpolation]. The Lambert W model was validated for modeling attenuation versus attenuator thickness with respect to the data collected in this study (R2 > 0.99). Furthermore, Lambert W interpolation was more accurate and less sensitive to the choice of interpolation points used to estimate the HVL and/or QVL than the traditional methods of semilogarithmic and linear interpolation. The proposed Lambert W model accurately describes attenuation of both monoenergetic radiation and (kilovoltage) polyenergetic beams (under narrow-beam geometry).

An empirical model of diagnostic x-ray attenuation under narrow-beam geometry

PubMed Central

Mathieu, Kelsey B.; Kappadath, S. Cheenu; White, R. Allen; Atkinson, E. Neely; Cody, Dianna D.

2011-01-01

Purpose: The purpose of this study was to develop and validate a mathematical model to describe narrow-beam attenuation of kilovoltage x-ray beams for the intended applications of half-value layer (HVL) and quarter-value layer (QVL) estimations, patient organ shielding, and computer modeling. Methods: An empirical model, which uses the Lambert W function and represents a generalized Lambert-Beer law, was developed. To validate this model, transmission of diagnostic energy x-ray beams was measured over a wide range of attenuator thicknesses [0.49–33.03 mm Al on a computed tomography (CT) scanner, 0.09–1.93 mm Al on two mammography systems, and 0.1–0.45 mm Cu and 0.49–14.87 mm Al using general radiography]. Exposure measurements were acquired under narrow-beam geometry using standard methods, including the appropriate ionization chamber, for each radiographic system. Nonlinear regression was used to find the best-fit curve of the proposed Lambert W model to each measured transmission versus attenuator thickness data set. In addition to validating the Lambert W model, we also assessed the performance of two-point Lambert W interpolation compared to traditional methods for estimating the HVL and QVL [i.e., semilogarithmic (exponential) and linear interpolation]. Results: The Lambert W model was validated for modeling attenuation versus attenuator thickness with respect to the data collected in this study (R2 > 0.99). Furthermore, Lambert W interpolation was more accurate and less sensitive to the choice of interpolation points used to estimate the HVL and∕or QVL than the traditional methods of semilogarithmic and linear interpolation. Conclusions: The proposed Lambert W model accurately describes attenuation of both monoenergetic radiation and (kilovoltage) polyenergetic beams (under narrow-beam geometry). PMID:21928626

An empirical model of diagnostic x-ray attenuation under narrow-beam geometry

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mathieu, Kelsey B.; Kappadath, S. Cheenu; White, R. Allen

2011-08-15

Purpose: The purpose of this study was to develop and validate a mathematical model to describe narrow-beam attenuation of kilovoltage x-ray beams for the intended applications of half-value layer (HVL) and quarter-value layer (QVL) estimations, patient organ shielding, and computer modeling. Methods: An empirical model, which uses the Lambert W function and represents a generalized Lambert-Beer law, was developed. To validate this model, transmission of diagnostic energy x-ray beams was measured over a wide range of attenuator thicknesses [0.49-33.03 mm Al on a computed tomography (CT) scanner, 0.09-1.93 mm Al on two mammography systems, and 0.1-0.45 mm Cu and 0.49-14.87more » mm Al using general radiography]. Exposure measurements were acquired under narrow-beam geometry using standard methods, including the appropriate ionization chamber, for each radiographic system. Nonlinear regression was used to find the best-fit curve of the proposed Lambert W model to each measured transmission versus attenuator thickness data set. In addition to validating the Lambert W model, we also assessed the performance of two-point Lambert W interpolation compared to traditional methods for estimating the HVL and QVL [i.e., semilogarithmic (exponential) and linear interpolation]. Results: The Lambert W model was validated for modeling attenuation versus attenuator thickness with respect to the data collected in this study (R{sup 2} > 0.99). Furthermore, Lambert W interpolation was more accurate and less sensitive to the choice of interpolation points used to estimate the HVL and/or QVL than the traditional methods of semilogarithmic and linear interpolation. Conclusions: The proposed Lambert W model accurately describes attenuation of both monoenergetic radiation and (kilovoltage) polyenergetic beams (under narrow-beam geometry).« less

Impact of Lidar Wind Sounding on Mesoscale Forecast

NASA Technical Reports Server (NTRS)

Miller, Timothy L.; Chou, Shih-Hung; Goodman, H. Michael (Technical Monitor)

2001-01-01

An Observing System Simulation Experiment (OSSE) was conducted to study the impact of airborne lidar wind sounding on mesoscale weather forecast. A wind retrieval scheme, which interpolates wind data from a grid data system, simulates the retrieval of wind profile from a satellite lidar system. A mesoscale forecast system based on the PSU/NCAR MM5 model is developed and incorporated the assimilation of the retrieved line-of-sight wind. To avoid the "identical twin" problem, the NCEP reanalysis data is used as our reference "nature" atmosphere. The simulated space-based lidar wind observations were retrieved by interpolating the NCEP values to the observation locations. A modified dataset obtained by smoothing the NCEP dataset was used as the initial state whose forecast was sought to be improved by assimilating the retrieved lidar observations. Forecasts using wind profiles with various lidar instrument parameters has been conducted. The results show that to significantly improve the mesoscale forecast the satellite should fly near the storm center with large scanning radius. Increasing lidar firing rate also improves the forecast. Cloud cover and lack of aerosol degrade the quality of the lidar wind data and, subsequently, the forecast.

Strong lensing probability in TeVeS (tensor-vector-scalar) theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen Daming, E-mail: cdm@bao.ac.cn

2008-01-15

We recalculate the strong lensing probability as a function of the image separation in TeVeS (tensor-vector-scalar) cosmology, which is a relativistic version of MOND (MOdified Newtonian Dynamics). The lens is modeled by the Hernquist profile. We assume an open cosmology with {Omega}{sub b} = 0.04 and {Omega}{sub {Lambda}} = 0.5 and three different kinds of interpolating functions. Two different galaxy stellar mass functions (GSMF) are adopted: PHJ (Panter, Heavens and Jimenez 2004 Mon. Not. R. Astron. Soc. 355 764) determined from SDSS data release 1 and Fontana (Fontana et al 2006 Astron. Astrophys. 459 745) from GOODS-MUSIC catalog. We comparemore » our results with both the predicted probabilities for lenses from singular isothermal sphere galaxy halos in LCDM (Lambda cold dark matter) with a Schechter-fit velocity function, and the observational results for the well defined combined sample of the Cosmic Lens All-Sky Survey (CLASS) and Jodrell Bank/Very Large Array Astrometric Survey (JVAS). It turns out that the interpolating function {mu}(x) = x/(1+x) combined with Fontana GSMF matches the results from CLASS/JVAS quite well.« less

Dynamics of open quantum systems by interpolation of von Neumann and classical master equations, and its application to quantum annealing

NASA Astrophysics Data System (ADS)

Kadowaki, Tadashi

2018-02-01

We propose a method to interpolate dynamics of von Neumann and classical master equations with an arbitrary mixing parameter to investigate the thermal effects in quantum dynamics. The two dynamics are mixed by intervening to continuously modify their solutions, thus coupling them indirectly instead of directly introducing a coupling term. This maintains the quantum system in a pure state even after the introduction of thermal effects and obtains not only a density matrix but also a state vector representation. Further, we demonstrate that the dynamics of a two-level system can be rewritten as a set of standard differential equations, resulting in quantum dynamics that includes thermal relaxation. These equations are equivalent to the optical Bloch equations at the weak coupling and asymptotic limits, implying that the dynamics cause thermal effects naturally. Numerical simulations of ferromagnetic and frustrated systems support this idea. Finally, we use this method to study thermal effects in quantum annealing, revealing nontrivial performance improvements for a spin glass model over a certain range of annealing time. This result may enable us to optimize the annealing time of real annealing machines.

Programming an Artificial Neural Network Tool for Spatial Interpolation in GIS - A Case Study for Indoor Radio Wave Propagation of WLAN.

PubMed

Sen, Alper; Gümüsay, M Umit; Kavas, Aktül; Bulucu, Umut

2008-09-25

Wireless communication networks offer subscribers the possibilities of free mobility and access to information anywhere at any time. Therefore, electromagnetic coverage calculations are important for wireless mobile communication systems, especially in Wireless Local Area Networks (WLANs). Before any propagation computation is performed, modeling of indoor radio wave propagation needs accurate geographical information in order to avoid the interruption of data transmissions. Geographic Information Systems (GIS) and spatial interpolation techniques are very efficient for performing indoor radio wave propagation modeling. This paper describes the spatial interpolation of electromagnetic field measurements using a feed-forward back-propagation neural network programmed as a tool in GIS. The accuracy of Artificial Neural Networks (ANN) and geostatistical Kriging were compared by adjusting procedures. The feedforward back-propagation ANN provides adequate accuracy for spatial interpolation, but the predictions of Kriging interpolation are more accurate than the selected ANN. The proposed GIS ensures indoor radio wave propagation model and electromagnetic coverage, the number, position and transmitter power of access points and electromagnetic radiation level. Pollution analysis in a given propagation environment was done and it was demonstrated that WLAN (2.4 GHz) electromagnetic coverage does not lead to any electromagnetic pollution due to the low power levels used. Example interpolated electromagnetic field values for WLAN system in a building of Yildiz Technical University, Turkey, were generated using the selected network architectures to illustrate the results with an ANN.

Programming an Artificial Neural Network Tool for Spatial Interpolation in GIS - A Case Study for Indoor Radio Wave Propagation of WLAN

PubMed Central

Şen, Alper; Gümüşay, M. Ümit; Kavas, Aktül; Bulucu, Umut

2008-01-01

Wireless communication networks offer subscribers the possibilities of free mobility and access to information anywhere at any time. Therefore, electromagnetic coverage calculations are important for wireless mobile communication systems, especially in Wireless Local Area Networks (WLANs). Before any propagation computation is performed, modeling of indoor radio wave propagation needs accurate geographical information in order to avoid the interruption of data transmissions. Geographic Information Systems (GIS) and spatial interpolation techniques are very efficient for performing indoor radio wave propagation modeling. This paper describes the spatial interpolation of electromagnetic field measurements using a feed-forward back-propagation neural network programmed as a tool in GIS. The accuracy of Artificial Neural Networks (ANN) and geostatistical Kriging were compared by adjusting procedures. The feedforward back-propagation ANN provides adequate accuracy for spatial interpolation, but the predictions of Kriging interpolation are more accurate than the selected ANN. The proposed GIS ensures indoor radio wave propagation model and electromagnetic coverage, the number, position and transmitter power of access points and electromagnetic radiation level. Pollution analysis in a given propagation environment was done and it was demonstrated that WLAN (2.4 GHz) electromagnetic coverage does not lead to any electromagnetic pollution due to the low power levels used. Example interpolated electromagnetic field values for WLAN system in a building of Yildiz Technical University, Turkey, were generated using the selected network architectures to illustrate the results with an ANN. PMID:27873854

Improving the numerical integration solution of satellite orbits in the presence of solar radiation pressure using modified back differences

NASA Technical Reports Server (NTRS)

Lundberg, J. B.; Feulner, M. R.; Abusali, P. A. M.; Ho, C. S.

1991-01-01

The method of modified back differences, a technique that significantly reduces the numerical integration errors associated with crossing shadow boundaries using a fixed-mesh multistep integrator without a significant increase in computer run time, is presented. While Hubbard's integral approach can produce significant improvements to the trajectory solution, the interpolation method provides the best overall results. It is demonstrated that iterating on the point mass term correction is also important for achieving the best overall results. It is also shown that the method of modified back differences can be implemented with only a small increase in execution time.

Continuous assimilation of simulated Geosat altimetric sea level into an eddy-resolving numerical ocean model. I - Sea level differences. II - Referenced sea level differences

NASA Technical Reports Server (NTRS)

White, Warren B.; Tai, Chang-Kou; Holland, William R.

1990-01-01

The optimal interpolation method of Lorenc (1981) was used to conduct continuous assimilation of altimetric sea level differences from the simulated Geosat exact repeat mission (ERM) into a three-layer quasi-geostrophic eddy-resolving numerical ocean box model that simulates the statistics of mesoscale eddy activity in the western North Pacific. Assimilation was conducted continuously as the Geosat tracks appeared in simulated real time/space, with each track repeating every 17 days, but occurring at different times and locations within the 17-day period, as would have occurred in a realistic nowcast situation. This interpolation method was also used to conduct the assimilation of referenced altimetric sea level differences into the same model, performing the referencing of altimetric sea sevel differences by using the simulated sea level. The results of this dynamical interpolation procedure are compared with those of a statistical (i.e., optimum) interpolation procedure.

Optimization and comparison of three spatial interpolation methods for electromagnetic levels in the AM band within an urban area.

PubMed

Rufo, Montaña; Antolín, Alicia; Paniagua, Jesús M; Jiménez, Antonio

2018-04-01

A comparative study was made of three methods of interpolation - inverse distance weighting (IDW), spline and ordinary kriging - after optimization of their characteristic parameters. These interpolation methods were used to represent the electric field levels for three emission frequencies (774kHz, 900kHz, and 1107kHz) and for the electrical stimulation quotient, Q E , characteristic of complex electromagnetic environments. Measurements were made with a spectrum analyser in a village in the vicinity of medium-wave radio broadcasting antennas. The accuracy of the models was quantified by comparing their predictions with levels measured at the control points not used to generate the models. The results showed that optimizing the characteristic parameters of each interpolation method allows any of them to be used. However, the best results in terms of the regression coefficient between each model's predictions and the actual control point field measurements were for the IDW method. Copyright © 2018 Elsevier Inc. All rights reserved.

Comparison of the common spatial interpolation methods used to analyze potentially toxic elements surrounding mining regions.

PubMed

Ding, Qian; Wang, Yong; Zhuang, Dafang

2018-04-15

The appropriate spatial interpolation methods must be selected to analyze the spatial distributions of Potentially Toxic Elements (PTEs), which is a precondition for evaluating PTE pollution. The accuracy and effect of different spatial interpolation methods, which include inverse distance weighting interpolation (IDW) (power = 1, 2, 3), radial basis function interpolation (RBF) (basis function: thin-plate spline (TPS), spline with tension (ST), completely regularized spline (CRS), multiquadric (MQ) and inverse multiquadric (IMQ)) and ordinary kriging interpolation (OK) (semivariogram model: spherical, exponential, gaussian and linear), were compared using 166 unevenly distributed soil PTE samples (As, Pb, Cu and Zn) in the Suxian District, Chenzhou City, Hunan Province as the study subject. The reasons for the accuracy differences of the interpolation methods and the uncertainties of the interpolation results are discussed, then several suggestions for improving the interpolation accuracy are proposed, and the direction of pollution control is determined. The results of this study are as follows: (i) RBF-ST and OK (exponential) are the optimal interpolation methods for As and Cu, and the optimal interpolation method for Pb and Zn is RBF-IMQ. (ii) The interpolation uncertainty is positively correlated with the PTE concentration, and higher uncertainties are primarily distributed around mines, which is related to the strong spatial variability of PTE concentrations caused by human interference. (iii) The interpolation accuracy can be improved by increasing the sample size around the mines, introducing auxiliary variables in the case of incomplete sampling and adopting the partition prediction method. (iv) It is necessary to strengthen the prevention and control of As and Pb pollution, particularly in the central and northern areas. The results of this study can provide an effective reference for the optimization of interpolation methods and parameters for unevenly distributed soil PTE data in mining areas. Copyright © 2018 Elsevier Ltd. All rights reserved.

A new stochastic model considering satellite clock interpolation errors in precise point positioning

NASA Astrophysics Data System (ADS)

Wang, Shengli; Yang, Fanlin; Gao, Wang; Yan, Lizi; Ge, Yulong

2018-03-01

Precise clock products are typically interpolated based on the sampling interval of the observational data when they are used for in precise point positioning. However, due to the occurrence of white noise in atomic clocks, a residual component of such noise will inevitable reside within the observations when clock errors are interpolated, and such noise will affect the resolution of the positioning results. In this paper, which is based on a twenty-one-week analysis of the atomic clock noise characteristics of numerous satellites, a new stochastic observation model that considers satellite clock interpolation errors is proposed. First, the systematic error of each satellite in the IGR clock product was extracted using a wavelet de-noising method to obtain the empirical characteristics of atomic clock noise within each clock product. Then, based on those empirical characteristics, a stochastic observation model was structured that considered the satellite clock interpolation errors. Subsequently, the IGR and IGS clock products at different time intervals were used for experimental validation. A verification using 179 stations worldwide from the IGS showed that, compared with the conventional model, the convergence times using the stochastic model proposed in this study were respectively shortened by 4.8% and 4.0% when the IGR and IGS 300-s-interval clock products were used and by 19.1% and 19.4% when the 900-s-interval clock products were used. Furthermore, the disturbances during the initial phase of the calculation were also effectively improved.

Color characterization of cine film

NASA Astrophysics Data System (ADS)

Noriega, Leonardo; Morovic, Jan; MacDonald, Lindsay W.; Lempp, Wolfgang

2002-06-01

This paper describes the characterization of cine film, by identifying the relationship between the Status A density values of positive print film and the XYZ values of conventional colorimetry. Several approaches are tried including least-squares modeling, tetrahedral interpolation, and distance weighted interpolation. The distance weighted technique has been improved by the use of the Mahalanobis distance metric in order to perform the interpolation, and this is presented as an innovation.

Fast image interpolation via random forests.

PubMed

Huang, Jun-Jie; Siu, Wan-Chi; Liu, Tian-Rui

2015-10-01

This paper proposes a two-stage framework for fast image interpolation via random forests (FIRF). The proposed FIRF method gives high accuracy, as well as requires low computation. The underlying idea of this proposed work is to apply random forests to classify the natural image patch space into numerous subspaces and learn a linear regression model for each subspace to map the low-resolution image patch to high-resolution image patch. The FIRF framework consists of two stages. Stage 1 of the framework removes most of the ringing and aliasing artifacts in the initial bicubic interpolated image, while Stage 2 further refines the Stage 1 interpolated image. By varying the number of decision trees in the random forests and the number of stages applied, the proposed FIRF method can realize computationally scalable image interpolation. Extensive experimental results show that the proposed FIRF(3, 2) method achieves more than 0.3 dB improvement in peak signal-to-noise ratio over the state-of-the-art nonlocal autoregressive modeling (NARM) method. Moreover, the proposed FIRF(1, 1) obtains similar or better results as NARM while only takes its 0.3% computational time.

Accuracy improvement of the H-drive air-levitating wafer inspection stage based on error analysis and compensation

NASA Astrophysics Data System (ADS)

Zhang, Fan; Liu, Pinkuan

2018-04-01

In order to improve the inspection precision of the H-drive air-bearing stage for wafer inspection, in this paper the geometric error of the stage is analyzed and compensated. The relationship between the positioning errors and error sources are initially modeled, and seven error components are identified that are closely related to the inspection accuracy. The most effective factor that affects the geometric error is identified by error sensitivity analysis. Then, the Spearman rank correlation method is applied to find the correlation between different error components, aiming at guiding the accuracy design and error compensation of the stage. Finally, different compensation methods, including the three-error curve interpolation method, the polynomial interpolation method, the Chebyshev polynomial interpolation method, and the B-spline interpolation method, are employed within the full range of the stage, and their results are compared. Simulation and experiment show that the B-spline interpolation method based on the error model has better compensation results. In addition, the research result is valuable for promoting wafer inspection accuracy and will greatly benefit the semiconductor industry.

A novel power harmonic analysis method based on Nuttall-Kaiser combination window double spectrum interpolated FFT algorithm

NASA Astrophysics Data System (ADS)

Jin, Tao; Chen, Yiyang; Flesch, Rodolfo C. C.

2017-11-01

Harmonics pose a great threat to safe and economical operation of power grids. Therefore, it is critical to detect harmonic parameters accurately to design harmonic compensation equipment. The fast Fourier transform (FFT) is widely used for electrical popular power harmonics analysis. However, the barrier effect produced by the algorithm itself and spectrum leakage caused by asynchronous sampling often affects the harmonic analysis accuracy. This paper examines a new approach for harmonic analysis based on deducing the modifier formulas of frequency, phase angle, and amplitude, utilizing the Nuttall-Kaiser window double spectrum line interpolation method, which overcomes the shortcomings in traditional FFT harmonic calculations. The proposed approach is verified numerically and experimentally to be accurate and reliable.

Evaluation of rainfall structure on hydrograph simulation: Comparison of radar and interpolated methods, a study case in a tropical catchment

NASA Astrophysics Data System (ADS)

Velasquez, N.; Ochoa, A.; Castillo, S.; Hoyos Ortiz, C. D.

2017-12-01

The skill of river discharge simulation using hydrological models strongly depends on the quality and spatio-temporal representativeness of precipitation during storm events. All precipitation measurement strategies have their own strengths and weaknesses that translate into discharge simulation uncertainties. Distributed hydrological models are based on evolving rainfall fields in the same time scale as the hydrological simulation. In general, rainfall measurements from a dense and well maintained rain gauge network provide a very good estimation of the total volume for each rainfall event, however, the spatial structure relies on interpolation strategies introducing considerable uncertainty in the simulation process. On the other hand, rainfall retrievals from radar reflectivity achieve a better spatial structure representation but with higher uncertainty in the surface precipitation intensity and volume depending on the vertical rainfall characteristics and radar scan strategy. To assess the impact of both rainfall measurement methodologies on hydrological simulations, and in particular the effects of the rainfall spatio-temporal variability, a numerical modeling experiment is proposed including the use of a novel QPE (Quantitative Precipitation Estimation) method based on disdrometer data in order to estimate surface rainfall from radar reflectivity. The experiment is based on the simulation of 84 storms, the hydrological simulations are carried out using radar QPE and two different interpolation methods (IDW and TIN), and the assessment of simulated peak flow. Results show significant rainfall differences between radar QPE and the interpolated fields, evidencing a poor representation of storms in the interpolated fields, which tend to miss the precise location of the intense precipitation cores, and to artificially generate rainfall in some areas of the catchment. Regarding streamflow modelling, the potential improvement achieved by using radar QPE depends on the density of the rain gauge network and its distribution relative to the precipitation events. The results for the 84 storms show a better model skill using radar QPE than the interpolated fields. Results using interpolated fields are highly affected by the dominant rainfall type and the basin scale.

On the Quality of Velocity Interpolation Schemes for Marker-in-Cell Method and Staggered Grids

NASA Astrophysics Data System (ADS)

Pusok, Adina E.; Kaus, Boris J. P.; Popov, Anton A.

2017-03-01

The marker-in-cell method is generally considered a flexible and robust method to model the advection of heterogenous non-diffusive properties (i.e., rock type or composition) in geodynamic problems. In this method, Lagrangian points carrying compositional information are advected with the ambient velocity field on an Eulerian grid. However, velocity interpolation from grid points to marker locations is often performed without considering the divergence of the velocity field at the interpolated locations (i.e., non-conservative). Such interpolation schemes can induce non-physical clustering of markers when strong velocity gradients are present (Journal of Computational Physics 166:218-252, 2001) and this may, eventually, result in empty grid cells, a serious numerical violation of the marker-in-cell method. To remedy this at low computational costs, Jenny et al. (Journal of Computational Physics 166:218-252, 2001) and Meyer and Jenny (Proceedings in Applied Mathematics and Mechanics 4:466-467, 2004) proposed a simple, conservative velocity interpolation scheme for 2-D staggered grid, while Wang et al. (Geochemistry, Geophysics, Geosystems 16(6):2015-2023, 2015) extended the formulation to 3-D finite element methods. Here, we adapt this formulation for 3-D staggered grids (correction interpolation) and we report on the quality of various velocity interpolation methods for 2-D and 3-D staggered grids. We test the interpolation schemes in combination with different advection schemes on incompressible Stokes problems with strong velocity gradients, which are discretized using a finite difference method. Our results suggest that a conservative formulation reduces the dispersion and clustering of markers, minimizing the need of unphysical marker control in geodynamic models.

Geostatistical interpolation model selection based on ArcGIS and spatio-temporal variability analysis of groundwater level in piedmont plains, northwest China.

PubMed

Xiao, Yong; Gu, Xiaomin; Yin, Shiyang; Shao, Jingli; Cui, Yali; Zhang, Qiulan; Niu, Yong

2016-01-01

Based on the geo-statistical theory and ArcGIS geo-statistical module, datas of 30 groundwater level observation wells were used to estimate the decline of groundwater level in Beijing piedmont. Seven different interpolation methods (inverse distance weighted interpolation, global polynomial interpolation, local polynomial interpolation, tension spline interpolation, ordinary Kriging interpolation, simple Kriging interpolation and universal Kriging interpolation) were used for interpolating groundwater level between 2001 and 2013. Cross-validation, absolute error and coefficient of determination (R(2)) was applied to evaluate the accuracy of different methods. The result shows that simple Kriging method gave the best fit. The analysis of spatial and temporal variability suggest that the nugget effects from 2001 to 2013 were increasing, which means the spatial correlation weakened gradually under the influence of human activities. The spatial variability in the middle areas of the alluvial-proluvial fan is relatively higher than area in top and bottom. Since the changes of the land use, groundwater level also has a temporal variation, the average decline rate of groundwater level between 2007 and 2013 increases compared with 2001-2006. Urban development and population growth cause over-exploitation of residential and industrial areas. The decline rate of the groundwater level in residential, industrial and river areas is relatively high, while the decreasing of farmland area and development of water-saving irrigation reduce the quantity of water using by agriculture and decline rate of groundwater level in agricultural area is not significant.

LADAR Range Image Interpolation Exploiting Pulse Width Expansion

DTIC Science & Technology

2012-03-22

normal to each other. The LADAR model needs to include the complete BRDF model covered in Section 2.1.3, which includes speckle reflection as well as...the gradient of a surface. This study estimates the gradi- ent of the surface of an object from a modeled LADAR return pulse that includes accurate...probabilistic noise models . The range and surface gradient estimations are incorporated into a novel interpolator that facilitates an effective three

Improved PPP Ambiguity Resolution Considering the Stochastic Characteristics of Atmospheric Corrections from Regional Networks

PubMed Central

Li, Yihe; Li, Bofeng; Gao, Yang

2015-01-01

With the increased availability of regional reference networks, Precise Point Positioning (PPP) can achieve fast ambiguity resolution (AR) and precise positioning by assimilating the satellite fractional cycle biases (FCBs) and atmospheric corrections derived from these networks. In such processing, the atmospheric corrections are usually treated as deterministic quantities. This is however unrealistic since the estimated atmospheric corrections obtained from the network data are random and furthermore the interpolated corrections diverge from the realistic corrections. This paper is dedicated to the stochastic modelling of atmospheric corrections and analyzing their effects on the PPP AR efficiency. The random errors of the interpolated corrections are processed as two components: one is from the random errors of estimated corrections at reference stations, while the other arises from the atmospheric delay discrepancies between reference stations and users. The interpolated atmospheric corrections are then applied by users as pseudo-observations with the estimated stochastic model. Two data sets are processed to assess the performance of interpolated corrections with the estimated stochastic models. The results show that when the stochastic characteristics of interpolated corrections are properly taken into account, the successful fix rate reaches 93.3% within 5 min for a medium inter-station distance network and 80.6% within 10 min for a long inter-station distance network. PMID:26633400

Improved PPP Ambiguity Resolution Considering the Stochastic Characteristics of Atmospheric Corrections from Regional Networks.

PubMed

Li, Yihe; Li, Bofeng; Gao, Yang

2015-11-30

With the increased availability of regional reference networks, Precise Point Positioning (PPP) can achieve fast ambiguity resolution (AR) and precise positioning by assimilating the satellite fractional cycle biases (FCBs) and atmospheric corrections derived from these networks. In such processing, the atmospheric corrections are usually treated as deterministic quantities. This is however unrealistic since the estimated atmospheric corrections obtained from the network data are random and furthermore the interpolated corrections diverge from the realistic corrections. This paper is dedicated to the stochastic modelling of atmospheric corrections and analyzing their effects on the PPP AR efficiency. The random errors of the interpolated corrections are processed as two components: one is from the random errors of estimated corrections at reference stations, while the other arises from the atmospheric delay discrepancies between reference stations and users. The interpolated atmospheric corrections are then applied by users as pseudo-observations with the estimated stochastic model. Two data sets are processed to assess the performance of interpolated corrections with the estimated stochastic models. The results show that when the stochastic characteristics of interpolated corrections are properly taken into account, the successful fix rate reaches 93.3% within 5 min for a medium inter-station distance network and 80.6% within 10 min for a long inter-station distance network.

Comparison of different wind data interpolation methods for a region with complex terrain in Central Asia

NASA Astrophysics Data System (ADS)

Reinhardt, Katja; Samimi, Cyrus

2018-01-01

While climatological data of high spatial resolution are largely available in most developed countries, the network of climatological stations in many other regions of the world still constitutes large gaps. Especially for those regions, interpolation methods are important tools to fill these gaps and to improve the data base indispensible for climatological research. Over the last years, new hybrid methods of machine learning and geostatistics have been developed which provide innovative prospects in spatial predictive modelling. This study will focus on evaluating the performance of 12 different interpolation methods for the wind components \\overrightarrow{u} and \\overrightarrow{v} in a mountainous region of Central Asia. Thereby, a special focus will be on applying new hybrid methods on spatial interpolation of wind data. This study is the first evaluating and comparing the performance of several of these hybrid methods. The overall aim of this study is to determine whether an optimal interpolation method exists, which can equally be applied for all pressure levels, or whether different interpolation methods have to be used for the different pressure levels. Deterministic (inverse distance weighting) and geostatistical interpolation methods (ordinary kriging) were explored, which take into account only the initial values of \\overrightarrow{u} and \\overrightarrow{v} . In addition, more complex methods (generalized additive model, support vector machine and neural networks as single methods and as hybrid methods as well as regression-kriging) that consider additional variables were applied. The analysis of the error indices revealed that regression-kriging provided the most accurate interpolation results for both wind components and all pressure heights. At 200 and 500 hPa, regression-kriging is followed by the different kinds of neural networks and support vector machines and for 850 hPa it is followed by the different types of support vector machine and ordinary kriging. Overall, explanatory variables improve the interpolation results.

Comparison of elevation and remote sensing derived products as auxiliary data for climate surface interpolation

USGS Publications Warehouse

Alvarez, Otto; Guo, Qinghua; Klinger, Robert C.; Li, Wenkai; Doherty, Paul

2013-01-01

Climate models may be limited in their inferential use if they cannot be locally validated or do not account for spatial uncertainty. Much of the focus has gone into determining which interpolation method is best suited for creating gridded climate surfaces, which often a covariate such as elevation (Digital Elevation Model, DEM) is used to improve the interpolation accuracy. One key area where little research has addressed is in determining which covariate best improves the accuracy in the interpolation. In this study, a comprehensive evaluation was carried out in determining which covariates were most suitable for interpolating climatic variables (e.g. precipitation, mean temperature, minimum temperature, and maximum temperature). We compiled data for each climate variable from 1950 to 1999 from approximately 500 weather stations across the Western United States (32° to 49° latitude and −124.7° to −112.9° longitude). In addition, we examined the uncertainty of the interpolated climate surface. Specifically, Thin Plate Spline (TPS) was used as the interpolation method since it is one of the most popular interpolation techniques to generate climate surfaces. We considered several covariates, including DEM, slope, distance to coast (Euclidean distance), aspect, solar potential, radar, and two Normalized Difference Vegetation Index (NDVI) products derived from Advanced Very High Resolution Radiometer (AVHRR) and Moderate Resolution Imaging Spectroradiometer (MODIS). A tenfold cross-validation was applied to determine the uncertainty of the interpolation based on each covariate. In general, the leading covariate for precipitation was radar, while DEM was the leading covariate for maximum, mean, and minimum temperatures. A comparison to other products such as PRISM and WorldClim showed strong agreement across large geographic areas but climate surfaces generated in this study (ClimSurf) had greater variability at high elevation regions, such as in the Sierra Nevada Mountains.

Validation of China-wide interpolated daily climate variables from 1960 to 2011

NASA Astrophysics Data System (ADS)

Yuan, Wenping; Xu, Bing; Chen, Zhuoqi; Xia, Jiangzhou; Xu, Wenfang; Chen, Yang; Wu, Xiaoxu; Fu, Yang

2015-02-01

Temporally and spatially continuous meteorological variables are increasingly in demand to support many different types of applications related to climate studies. Using measurements from 600 climate stations, a thin-plate spline method was applied to generate daily gridded climate datasets for mean air temperature, maximum temperature, minimum temperature, relative humidity, sunshine duration, wind speed, atmospheric pressure, and precipitation over China for the period 1961-2011. A comprehensive evaluation of interpolated climate was conducted at 150 independent validation sites. The results showed superior performance for most of the estimated variables. Except for wind speed, determination coefficients ( R 2) varied from 0.65 to 0.90, and interpolations showed high consistency with observations. Most of the estimated climate variables showed relatively consistent accuracy among all seasons according to the root mean square error, R 2, and relative predictive error. The interpolated data correctly predicted the occurrence of daily precipitation at validation sites with an accuracy of 83 %. Moreover, the interpolation data successfully explained the interannual variability trend for the eight meteorological variables at most validation sites. Consistent interannual variability trends were observed at 66-95 % of the sites for the eight meteorological variables. Accuracy in distinguishing extreme weather events differed substantially among the meteorological variables. The interpolated data identified extreme events for the three temperature variables, relative humidity, and sunshine duration with an accuracy ranging from 63 to 77 %. However, for wind speed, air pressure, and precipitation, the interpolation model correctly identified only 41, 48, and 58 % of extreme events, respectively. The validation indicates that the interpolations can be applied with high confidence for the three temperatures variables, as well as relative humidity and sunshine duration based on the performance of these variables in estimating daily variations, interannual variability, and extreme events. Although longitude, latitude, and elevation data are included in the model, additional information, such as topography and cloud cover, should be integrated into the interpolation algorithm to improve performance in estimating wind speed, atmospheric pressure, and precipitation.

Interpolation of the Extended Boolean Retrieval Model.

ERIC Educational Resources Information Center

Zanger, Daniel Z.

2002-01-01

Presents an interpolation theorem for an extended Boolean information retrieval model. Results show that whenever two or more documents are similarly ranked at any two points for a query containing exactly two terms, then they are similarly ranked at all points in between; and that results can fail for queries with more than two terms. (Author/LRW)

Potentials Unbounded Below

NASA Astrophysics Data System (ADS)

Curtright, Thomas

2011-04-01

Continuous interpolates are described for classical dynamical systems defined by discrete time-steps. Functional conjugation methods play a central role in obtaining the interpolations. The interpolates correspond to particle motion in an underlying potential, V. Typically, V has no lower bound and can exhibit switchbacks wherein V changes form when turning points are encountered by the particle. The Beverton-Holt and Skellam models of population dynamics, and particular cases of the logistic map are used to illustrate these features.

Color filter array pattern identification using variance of color difference image

NASA Astrophysics Data System (ADS)

Shin, Hyun Jun; Jeon, Jong Ju; Eom, Il Kyu

2017-07-01

A color filter array is placed on the image sensor of a digital camera to acquire color images. Each pixel uses only one color, since the image sensor can measure only one color per pixel. Therefore, empty pixels are filled using an interpolation process called demosaicing. The original and the interpolated pixels have different statistical characteristics. If the image is modified by manipulation or forgery, the color filter array pattern is altered. This pattern change can be a clue for image forgery detection. However, most forgery detection algorithms have the disadvantage of assuming the color filter array pattern. We present an identification method of the color filter array pattern. Initially, the local mean is eliminated to remove the background effect. Subsequently, the color difference block is constructed to emphasize the difference between the original pixel and the interpolated pixel. The variance measure of the color difference image is proposed as a means of estimating the color filter array configuration. The experimental results show that the proposed method is effective in identifying the color filter array pattern. Compared with conventional methods, our method provides superior performance.

Scientific data interpolation with low dimensional manifold model

NASA Astrophysics Data System (ADS)

Zhu, Wei; Wang, Bao; Barnard, Richard; Hauck, Cory D.; Jenko, Frank; Osher, Stanley

2018-01-01

We propose to apply a low dimensional manifold model to scientific data interpolation from regular and irregular samplings with a significant amount of missing information. The low dimensionality of the patch manifold for general scientific data sets has been used as a regularizer in a variational formulation. The problem is solved via alternating minimization with respect to the manifold and the data set, and the Laplace-Beltrami operator in the Euler-Lagrange equation is discretized using the weighted graph Laplacian. Various scientific data sets from different fields of study are used to illustrate the performance of the proposed algorithm on data compression and interpolation from both regular and irregular samplings.

Estimating monthly temperature using point based interpolation techniques

NASA Astrophysics Data System (ADS)

Saaban, Azizan; Mah Hashim, Noridayu; Murat, Rusdi Indra Zuhdi

2013-04-01

This paper discusses the use of point based interpolation to estimate the value of temperature at an unallocated meteorology stations in Peninsular Malaysia using data of year 2010 collected from the Malaysian Meteorology Department. Two point based interpolation methods which are Inverse Distance Weighted (IDW) and Radial Basis Function (RBF) are considered. The accuracy of the methods is evaluated using Root Mean Square Error (RMSE). The results show that RBF with thin plate spline model is suitable to be used as temperature estimator for the months of January and December, while RBF with multiquadric model is suitable to estimate the temperature for the rest of the months.

An efficient interpolation technique for jump proposals in reversible-jump Markov chain Monte Carlo calculations

PubMed Central

Farr, W. M.; Mandel, I.; Stevens, D.

2015-01-01

Selection among alternative theoretical models given an observed dataset is an important challenge in many areas of physics and astronomy. Reversible-jump Markov chain Monte Carlo (RJMCMC) is an extremely powerful technique for performing Bayesian model selection, but it suffers from a fundamental difficulty and it requires jumps between model parameter spaces, but cannot efficiently explore both parameter spaces at once. Thus, a naive jump between parameter spaces is unlikely to be accepted in the Markov chain Monte Carlo (MCMC) algorithm and convergence is correspondingly slow. Here, we demonstrate an interpolation technique that uses samples from single-model MCMCs to propose intermodel jumps from an approximation to the single-model posterior of the target parameter space. The interpolation technique, based on a kD-tree data structure, is adaptive and efficient in modest dimensionality. We show that our technique leads to improved convergence over naive jumps in an RJMCMC, and compare it to other proposals in the literature to improve the convergence of RJMCMCs. We also demonstrate the use of the same interpolation technique as a way to construct efficient ‘global’ proposal distributions for single-model MCMCs without prior knowledge of the structure of the posterior distribution, and discuss improvements that permit the method to be used in higher dimensional spaces efficiently. PMID:26543580

Nonlinear effects in the time measurement device based on surface acoustic wave filter excitation.

PubMed

Prochazka, Ivan; Panek, Petr

2009-07-01

A transversal surface acoustic wave filter has been used as a time interpolator in a time interval measurement device. We are presenting the experiments and results of an analysis of the nonlinear effects in such a time interpolator. The analysis shows that the nonlinear distortion in the time interpolator circuits causes a deterministic measurement error which can be understood as the time interpolation nonlinearity. The dependence of this error on time of the measured events can be expressed as a sparse Fourier series thus it usually oscillates very quickly in comparison to the clock period. The theoretical model is in good agreement with experiments carried out on an experimental two-channel timing system. Using highly linear amplifiers in the time interpolator and adjusting the filter excitation level to the optimum, we have achieved the interpolation nonlinearity below 0.2 ps. The overall single-shot precision of the experimental timing device is 0.9 ps rms in each channel.

Comparison of the accuracy of kriging and IDW interpolations in estimating groundwater arsenic concentrations in Texas.

PubMed

Gong, Gordon; Mattevada, Sravan; O'Bryant, Sid E

2014-04-01

Exposure to arsenic causes many diseases. Most Americans in rural areas use groundwater for drinking, which may contain arsenic above the currently allowable level, 10µg/L. It is cost-effective to estimate groundwater arsenic levels based on data from wells with known arsenic concentrations. We compared the accuracy of several commonly used interpolation methods in estimating arsenic concentrations in >8000 wells in Texas by the leave-one-out-cross-validation technique. Correlation coefficient between measured and estimated arsenic levels was greater with inverse distance weighted (IDW) than kriging Gaussian, kriging spherical or cokriging interpolations when analyzing data from wells in the entire Texas (p<0.0001). Correlation coefficient was significantly lower with cokriging than any other methods (p<0.006) for wells in Texas, east Texas or the Edwards aquifer. Correlation coefficient was significantly greater for wells in southwestern Texas Panhandle than in east Texas, and was higher for wells in Ogallala aquifer than in Edwards aquifer (p<0.0001) regardless of interpolation methods. In regression analysis, the best models are when well depth and/or elevation were entered into the model as covariates regardless of area/aquifer or interpolation methods, and models with IDW are better than kriging in any area/aquifer. In conclusion, the accuracy in estimating groundwater arsenic level depends on both interpolation methods and wells' geographic distributions and characteristics in Texas. Taking well depth and elevation into regression analysis as covariates significantly increases the accuracy in estimating groundwater arsenic level in Texas with IDW in particular. Published by Elsevier Inc.

Impact of rain gauge quality control and interpolation on streamflow simulation: an application to the Warwick catchment, Australia

NASA Astrophysics Data System (ADS)

Liu, Shulun; Li, Yuan; Pauwels, Valentijn R. N.; Walker, Jeffrey P.

2017-12-01

Rain gauges are widely used to obtain temporally continuous point rainfall records, which are then interpolated into spatially continuous data to force hydrological models. However, rainfall measurements and interpolation procedure are subject to various uncertainties, which can be reduced by applying quality control and selecting appropriate spatial interpolation approaches. Consequently, the integrated impact of rainfall quality control and interpolation on streamflow simulation has attracted increased attention but not been fully addressed. This study applies a quality control procedure to the hourly rainfall measurements obtained in the Warwick catchment in eastern Australia. The grid-based daily precipitation from the Australian Water Availability Project was used as a reference. The Pearson correlation coefficient between the daily accumulation of gauged rainfall and the reference data was used to eliminate gauges with significant quality issues. The unrealistic outliers were censored based on a comparison between gauged rainfall and the reference. Four interpolation methods, including the inverse distance weighting (IDW), nearest neighbors (NN), linear spline (LN), and ordinary Kriging (OK), were implemented. The four methods were firstly assessed through a cross-validation using the quality-controlled rainfall data. The impacts of the quality control and interpolation on streamflow simulation were then evaluated through a semi-distributed hydrological model. The results showed that the Nash–Sutcliffe model efficiency coefficient (NSE) and Bias of the streamflow simulations were significantly improved after quality control. In the cross-validation, the IDW and OK methods resulted in good interpolation rainfall, while the NN led to the worst result. In term of the impact on hydrological prediction, the IDW led to the most consistent streamflow predictions with the observations, according to the validation at five streamflow-gauged locations. The OK method performed second best according to streamflow predictions at the five gauges in the calibration period (01/01/2007–31/12/2011) and four gauges during the validation period (01/01/2012–30/06/2014). However, NN produced the worst prediction at the outlet of the catchment in the validation period, indicating a low robustness. While the IDW exhibited the best performance in the study catchment in terms of accuracy, robustness and efficiency, more general recommendations on the selection of rainfall interpolation methods need to be further explored.

Impact of rain gauge quality control and interpolation on streamflow simulation: an application to the Warwick catchment, Australia

NASA Astrophysics Data System (ADS)

Liu, Shulun; Li, Yuan; Pauwels, Valentijn R. N.; Walker, Jeffrey P.

2018-01-01

Rain gauges are widely used to obtain temporally continuous point rainfall records, which are then interpolated into spatially continuous data to force hydrological models. However, rainfall measurements and interpolation procedure are subject to various uncertainties, which can be reduced by applying quality control and selecting appropriate spatial interpolation approaches. Consequently, the integrated impact of rainfall quality control and interpolation on streamflow simulation has attracted increased attention but not been fully addressed. This study applies a quality control procedure to the hourly rainfall measurements obtained in the Warwick catchment in eastern Australia. The grid-based daily precipitation from the Australian Water Availability Project was used as a reference. The Pearson correlation coefficient between the daily accumulation of gauged rainfall and the reference data was used to eliminate gauges with significant quality issues. The unrealistic outliers were censored based on a comparison between gauged rainfall and the reference. Four interpolation methods, including the inverse distance weighting (IDW), nearest neighbors (NN), linear spline (LN), and ordinary Kriging (OK), were implemented. The four methods were firstly assessed through a cross-validation using the quality-controlled rainfall data. The impacts of the quality control and interpolation on streamflow simulation were then evaluated through a semi-distributed hydrological model. The results showed that the Nash–Sutcliffe model efficiency coefficient (NSE) and Bias of the streamflow simulations were significantly improved after quality control. In the cross-validation, the IDW and OK methods resulted in good interpolation rainfall, while the NN led to the worst result. In term of the impact on hydrological prediction, the IDW led to the most consistent streamflow predictions with the observations, according to the validation at five streamflow-gauged locations. The OK method performed second best according to streamflow predictions at the five gauges in the calibration period (01/01/2007–31/12/2011) and four gauges during the validation period (01/01/2012–30/06/2014). However, NN produced the worst prediction at the outlet of the catchment in the validation period, indicating a low robustness. While the IDW exhibited the best performance in the study catchment in terms of accuracy, robustness and efficiency, more general recommendations on the selection of rainfall interpolation methods need to be further explored.

Effect of the precipitation interpolation method on the performance of a snowmelt runoff model

NASA Astrophysics Data System (ADS)

Jacquin, Alexandra

2014-05-01

Uncertainties on the spatial distribution of precipitation seriously affect the reliability of the discharge estimates produced by watershed models. Although there is abundant research evaluating the goodness of fit of precipitation estimates obtained with different gauge interpolation methods, few studies have focused on the influence of the interpolation strategy on the response of watershed models. The relevance of this choice may be even greater in the case of mountain catchments, because of the influence of orography on precipitation. This study evaluates the effect of the precipitation interpolation method on the performance of conceptual type snowmelt runoff models. The HBV Light model version 4.0.0.2, operating at daily time steps, is used as a case study. The model is applied in Aconcagua at Chacabuquito catchment, located in the Andes Mountains of Central Chile. The catchment's area is 2110[Km2] and elevation ranges from 950[m.a.s.l.] to 5930[m.a.s.l.] The local meteorological network is sparse, with all precipitation gauges located below 3000[m.a.s.l.] Precipitation amounts corresponding to different elevation zones are estimated through areal averaging of precipitation fields interpolated from gauge data. Interpolation methods applied include kriging with external drift (KED), optimal interpolation method (OIM), Thiessen polygons (TP), multiquadratic functions fitting (MFF) and inverse distance weighting (IDW). Both KED and OIM are able to account for the existence of a spatial trend in the expectation of precipitation. By contrast, TP, MFF and IDW, traditional methods widely used in engineering hydrology, cannot explicitly incorporate this information. Preliminary analysis confirmed that these methods notably underestimate precipitation in the study catchment, while KED and OIM are able to reduce the bias; this analysis also revealed that OIM provides more reliable estimations than KED in this region. Using input precipitation obtained by each method, HBV parameters are calibrated with respect to Nash-Sutcliffe efficiency. The performance of HBV in the study catchment is not satisfactory. Although volumetric errors are modest, efficiency values are lower than 70%. Discharge estimates resulting from the application of TP, MFF and IDW obtain similar model efficiencies and volumetric errors. These error statistics moderately improve if KED or OIM are used instead. Even though the quality of precipitation estimates of distinct interpolation methods is dissimilar, the results of this study show that these differences do not necessarily produce noticeable changes in HBV's model performance statistics. This situation arises because the calibration of the model parameters allows some degree of compensation of deficient areal precipitation estimates, mainly through the adjustment of model simulated evaporation and glacier melt, as revealed by the analysis of water balances. In general, even if there is a good agreement between model estimated and observed discharge, this information is not sufficient to assert that the internal hydrological processes of the catchment are properly simulated by a watershed model. Other calibration criteria should be incorporated if a more reliable representation of these processes is desired. Acknowledgements: This research was funded by FONDECYT, Research Project 1110279. The HBV Light software used in this study was kindly provided by J. Seibert, Department of Geography, University of Zürich.

Estimation of chirp rates of music-adapted prolate spheroidal atoms using reassignment

NASA Astrophysics Data System (ADS)

Mesz, Bruno; Serrano, Eduardo

2007-09-01

We introduce a modified Matching Pursuit algorithm for estimating frequency and frequency slope of FM-modulated music signals. The use of Matching Pursuit with constant frequency atoms provides coarse estimates which could be improved with chirped atoms, more suited in principle to this kind of signals. Application of the reassignment method is suggested by its good localization properties for chirps. We start considering a family of atoms generated by modulation and scaling of a prolate spheroidal wave function. These functions are concentrated in frequency on intervals of a semitone centered at the frequencies of the well-tempered scale. At each stage of the pursuit, we search the atom most correlated with the signal. We then consider the spectral peaks at each frame of the spectrogram and calculate a modified frequency and frequency slope using the derivatives of the reassignment operators; this is then used to estimate the parameters of a cubic interpolation polynomial that models local pitch fluctuations. We apply the method both to synthetic and music signals.

A Modified Kriging Method to Interpolate the Soil Moisture Measured by Wireless Sensor Network with the Aid of Remote Sensing Images

NASA Astrophysics Data System (ADS)

Zhang, J.; Liu, Q.; Li, X.; Niu, H.; Cai, E.

2015-12-01

In recent years, wireless sensor network (WSN) emerges to collect Earth observation data at relatively low cost and light labor load, while its observations are still point-data. To learn the spatial distribution of a land surface parameter, interpolating the point data is necessary. Taking soil moisture (SM) for example, its spatial distribution is critical information for agriculture management, hydrological and ecological researches. This study developed a method to interpolate the WSN-measured SM to acquire the spatial distribution in a 5km*5km study area, located in the middle reaches of HEIHE River, western China. As SM is related to many factors such as topology, soil type, vegetation and etc., even the WSN observation grid is not dense enough to reflect the SM distribution pattern. Our idea is to revise the traditional Kriging algorithm, introducing spectral variables, i.e., vegetation index (VI) and abledo, from satellite imagery as supplementary information to aid the interpolation. Thus, the new Extended-Kriging algorithm operates on the spatial & spectral combined space. To run the algorithm, first we need to estimate the SM variance function, which is also extended to the combined space. As the number of WSN samples in the study area is not enough to gather robust statistics, we have to assume that the SM variance function is invariant over time. So, the variance function is estimated from a SM map, derived from the airborne CASI/TASI images acquired in July 10, 2012, and then applied to interpolate WSN data in that season. Data analysis indicates that the new algorithm can provide more details to the variation of land SM. Then, the Leave-one-out cross-validation is adopted to estimate the interpolation accuracy. Although a reasonable accuracy can be achieved, the result is not yet satisfactory. Besides improving the algorithm, the uncertainties in WSN measurements may also need to be controlled in our further work.

Image interpolation and denoising for division of focal plane sensors using Gaussian processes.

PubMed

Gilboa, Elad; Cunningham, John P; Nehorai, Arye; Gruev, Viktor

2014-06-16

Image interpolation and denoising are important techniques in image processing. These methods are inherent to digital image acquisition as most digital cameras are composed of a 2D grid of heterogeneous imaging sensors. Current polarization imaging employ four different pixelated polarization filters, commonly referred to as division of focal plane polarization sensors. The sensors capture only partial information of the true scene, leading to a loss of spatial resolution as well as inaccuracy of the captured polarization information. Interpolation is a standard technique to recover the missing information and increase the accuracy of the captured polarization information. Here we focus specifically on Gaussian process regression as a way to perform a statistical image interpolation, where estimates of sensor noise are used to improve the accuracy of the estimated pixel information. We further exploit the inherent grid structure of this data to create a fast exact algorithm that operates in ����(N(3/2)) (vs. the naive ���� (N³)), thus making the Gaussian process method computationally tractable for image data. This modeling advance and the enabling computational advance combine to produce significant improvements over previously published interpolation methods for polarimeters, which is most pronounced in cases of low signal-to-noise ratio (SNR). We provide the comprehensive mathematical model as well as experimental results of the GP interpolation performance for division of focal plane polarimeter.

A Comparison of Approximation Modeling Techniques: Polynomial Versus Interpolating Models

NASA Technical Reports Server (NTRS)

Giunta, Anthony A.; Watson, Layne T.

1998-01-01

Two methods of creating approximation models are compared through the calculation of the modeling accuracy on test problems involving one, five, and ten independent variables. Here, the test problems are representative of the modeling challenges typically encountered in realistic engineering optimization problems. The first approximation model is a quadratic polynomial created using the method of least squares. This type of polynomial model has seen considerable use in recent engineering optimization studies due to its computational simplicity and ease of use. However, quadratic polynomial models may be of limited accuracy when the response data to be modeled have multiple local extrema. The second approximation model employs an interpolation scheme known as kriging developed in the fields of spatial statistics and geostatistics. This class of interpolating model has the flexibility to model response data with multiple local extrema. However, this flexibility is obtained at an increase in computational expense and a decrease in ease of use. The intent of this study is to provide an initial exploration of the accuracy and modeling capabilities of these two approximation methods.

Enhancing GIS Capabilities for High Resolution Earth Science Grids

NASA Astrophysics Data System (ADS)

Koziol, B. W.; Oehmke, R.; Li, P.; O'Kuinghttons, R.; Theurich, G.; DeLuca, C.

2017-12-01

Applications for high performance GIS will continue to increase as Earth system models pursue more realistic representations of Earth system processes. Finer spatial resolution model input and output, unstructured or irregular modeling grids, data assimilation, and regional coordinate systems present novel challenges for GIS frameworks operating in the Earth system modeling domain. This presentation provides an overview of two GIS-driven applications that combine high performance software with big geospatial datasets to produce value-added tools for the modeling and geoscientific community. First, a large-scale interpolation experiment using National Hydrography Dataset (NHD) catchments, a high resolution rectilinear CONUS grid, and the Earth System Modeling Framework's (ESMF) conservative interpolation capability will be described. ESMF is a parallel, high-performance software toolkit that provides capabilities (e.g. interpolation) for building and coupling Earth science applications. ESMF is developed primarily by the NOAA Environmental Software Infrastructure and Interoperability (NESII) group. The purpose of this experiment was to test and demonstrate the utility of high performance scientific software in traditional GIS domains. Special attention will be paid to the nuanced requirements for dealing with high resolution, unstructured grids in scientific data formats. Second, a chunked interpolation application using ESMF and OpenClimateGIS (OCGIS) will demonstrate how spatial subsetting can virtually remove computing resource ceilings for very high spatial resolution interpolation operations. OCGIS is a NESII-developed Python software package designed for the geospatial manipulation of high-dimensional scientific datasets. An overview of the data processing workflow, why a chunked approach is required, and how the application could be adapted to meet operational requirements will be discussed here. In addition, we'll provide a general overview of OCGIS's parallel subsetting capabilities including challenges in the design and implementation of a scientific data subsetter.

Space-Time Modelling of Groundwater Level Using Spartan Covariance Function

NASA Astrophysics Data System (ADS)

Varouchakis, Emmanouil; Hristopulos, Dionissios

2014-05-01

Geostatistical models often need to handle variables that change in space and in time, such as the groundwater level of aquifers. A major advantage of space-time observations is that a higher number of data supports parameter estimation and prediction. In a statistical context, space-time data can be considered as realizations of random fields that are spatially extended and evolve in time. The combination of spatial and temporal measurements in sparsely monitored watersheds can provide very useful information by incorporating spatiotemporal correlations. Spatiotemporal interpolation is usually performed by applying the standard Kriging algorithms extended in a space-time framework. Spatiotemoral covariance functions for groundwater level modelling, however, have not been widely developed. We present a new non-separable theoretical spatiotemporal variogram function which is based on the Spartan covariance family and evaluate its performance in spatiotemporal Kriging (STRK) interpolation. The original spatial expression (Hristopulos and Elogne 2007) that has been successfully used for the spatial interpolation of groundwater level (Varouchakis and Hristopulos 2013) is modified by defining the following space-time normalized distance h = °h2r-+-α h2τ, hr=r- ξr, hτ=τ- ξτ; where r is the spatial lag vector, τ the temporal lag vector, ξr is the correlation length in position space (r) and ξτ in time (τ), h the normalized space-time lag vector, h = |h| is its Euclidean norm of the normalized space-time lag and α the coefficient that determines the relative weight of the time lag. The space-time experimental semivariogram is determined from the biannual (wet and dry period) time series of groundwater level residuals (obtained from the original series after trend removal) between the years 1981 and 2003 at ten sampling stations located in the Mires hydrological basin in the island of Crete (Greece). After the hydrological year 2002-2003 there is a significant groundwater level increase during the wet period of 2003-2004 and a considerable drop during the dry period of 2005-2006. Both periods are associated with significant annual changes in the precipitation compared to the basin average, i.e., a 40% increase and 65% decrease, respectively. We use STRK to 'predict' the groundwater level for the two selected hydrological periods (wet period of 2003-2004 and dry period of 2005-2006) at each sampling station. The predictions are validated using the respective measured values. The novel Spartan spatiotemporal covariance function gives a mean absolute relative prediction error of 12%. This is 45% lower than the respective value obtained with the commonly used product-sum covariance function, and 31% lower than the respective value obtained with a non-separable function based on the diffusion equation (Kolovos et al. 2010). The advantage of the Spartan space-time covariance model is confirmed with statistical measures such as the root mean square standardized error (RMSSE), the modified coefficient of model efficiency, E' (Legates and McCabe, 1999) and the modified Index of Agreement, IoA'(Janssen and Heuberger, 1995). Hristopulos, D. T. and Elogne, S. N. 2007. Analytic properties and covariance functions for a new class of generalized Gibbs random fields. IEEE Transactions on Information Theory, 53, 4667-4467. Janssen, P.H.M. and Heuberger P.S.C. 1995. Calibration of process-oriented models. Ecological Modelling, 83, 55-66. Kolovos, A., Christakos, G., Hristopulos, D. T. and Serre, M. L. 2004. Methods for generating non-separable spatiotemporal covariance models with potential environmental applications. Advances in Water Resources, 27 (8), 815-830. Legates, D.R. and McCabe Jr., G.J. 1999. Evaluating the use of 'goodness-of-fit' measures in hydrologic and hydro climatic model validation. Water Resources Research, 35, 233-241. Varouchakis, E. A. and Hristopulos, D. T. 2013. Improvement of groundwater level prediction in sparsely gauged basins using physical laws and local geographic features as auxiliary variables. Advances in Water Resources, 52, 34-49.

Meshless Modeling of Deformable Shapes and their Motion

PubMed Central

Adams, Bart; Ovsjanikov, Maks; Wand, Michael; Seidel, Hans-Peter; Guibas, Leonidas J.

2010-01-01

We present a new framework for interactive shape deformation modeling and key frame interpolation based on a meshless finite element formulation. Starting from a coarse nodal sampling of an object’s volume, we formulate rigidity and volume preservation constraints that are enforced to yield realistic shape deformations at interactive frame rates. Additionally, by specifying key frame poses of the deforming shape and optimizing the nodal displacements while targeting smooth interpolated motion, our algorithm extends to a motion planning framework for deformable objects. This allows reconstructing smooth and plausible deformable shape trajectories in the presence of possibly moving obstacles. The presented results illustrate that our framework can handle complex shapes at interactive rates and hence is a valuable tool for animators to realistically and efficiently model and interpolate deforming 3D shapes. PMID:24839614

Evaluation of interpolation methods for TG-43 dosimetric parameters based on comparison with Monte Carlo data for high-energy brachytherapy sources.

PubMed

Pujades-Claumarchirant, Ma Carmen; Granero, Domingo; Perez-Calatayud, Jose; Ballester, Facundo; Melhus, Christopher; Rivard, Mark

2010-03-01

The aim of this work was to determine dose distributions for high-energy brachytherapy sources at spatial locations not included in the radial dose function g L ( r ) and 2D anisotropy function F ( r , θ ) table entries for radial distance r and polar angle θ . The objectives of this study are as follows: 1) to evaluate interpolation methods in order to accurately derive g L ( r ) and F ( r , θ ) from the reported data; 2) to determine the minimum number of entries in g L ( r ) and F ( r , θ ) that allow reproduction of dose distributions with sufficient accuracy. Four high-energy photon-emitting brachytherapy sources were studied: 60 Co model Co0.A86, 137 Cs model CSM-3, 192 Ir model Ir2.A85-2, and 169 Yb hypothetical model. The mesh used for r was: 0.25, 0.5, 0.75, 1, 1.5, 2-8 (integer steps) and 10 cm. Four different angular steps were evaluated for F ( r , θ ): 1°, 2°, 5° and 10°. Linear-linear and logarithmic-linear interpolation was evaluated for g L ( r ). Linear-linear interpolation was used to obtain F ( r , θ ) with resolution of 0.05 cm and 1°. Results were compared with values obtained from the Monte Carlo (MC) calculations for the four sources with the same grid. Linear interpolation of g L ( r ) provided differences ≤ 0.5% compared to MC for all four sources. Bilinear interpolation of F ( r , θ ) using 1° and 2° angular steps resulted in agreement ≤ 0.5% with MC for 60 Co, 192 Ir, and 169 Yb, while 137 Cs agreement was ≤ 1.5% for θ < 15°. The radial mesh studied was adequate for interpolating g L ( r ) for high-energy brachytherapy sources, and was similar to commonly found examples in the published literature. For F ( r , θ ) close to the source longitudinal-axis, polar angle step sizes of 1°-2° were sufficient to provide 2% accuracy for all sources.

Remote sensing, geographical information systems, and spatial modeling for analyzing public transit services

NASA Astrophysics Data System (ADS)

Wu, Changshan

Public transit service is a promising transportation mode because of its potential to address urban sustainability. Current ridership of public transit, however, is very low in most urban regions, particularly those in the United States. This woeful transit ridership can be attributed to many factors, among which poor service quality is key. Given this, there is a need for transit planning and analysis to improve service quality. Traditionally, spatially aggregate data are utilized in transit analysis and planning. Examples include data associated with the census, zip codes, states, etc. Few studies, however, address the influences of spatially aggregate data on transit planning results. In this research, previous studies in transit planning that use spatially aggregate data are reviewed. Next, problems associated with the utilization of aggregate data, the so-called modifiable areal unit problem (MAUP), are detailed and the need for fine resolution data to support public transit planning is argued. Fine resolution data is generated using intelligent interpolation techniques with the help of remote sensing imagery. In particular, impervious surface fraction, an important socio-economic indicator, is estimated through a fully constrained linear spectral mixture model using Landsat Enhanced Thematic Mapper Plus (ETM+) data within the metropolitan area of Columbus, Ohio in the United States. Four endmembers, low albedo, high albedo, vegetation, and soil are selected to model heterogeneous urban land cover. Impervious surface fraction is estimated by analyzing low and high albedo endmembers. With the derived impervious surface fraction, three spatial interpolation methods, spatial regression, dasymetric mapping, and cokriging, are developed to interpolate detailed population density. Results suggest that cokriging applied to impervious surface is a better alternative for estimating fine resolution population density. With the derived fine resolution data, a multiple route maximal covering/shortest path (MRMCSP) model is proposed to address the tradeoff between public transit service quality and access coverage in an established bus-based transit system. Results show that it is possible to improve current transit service quality by eliminating redundant or underutilized service stops. This research illustrates that fine resolution data can be efficiently generated to support urban planning, management and analysis. Further, this detailed data may necessitate the development of new spatial optimization models for use in analysis.

Performance comparison of LUR and OK in PM2.5 concentration mapping: a multidimensional perspective

PubMed Central

Zou, Bin; Luo, Yanqing; Wan, Neng; Zheng, Zhong; Sternberg, Troy; Liao, Yilan

2015-01-01

Methods of Land Use Regression (LUR) modeling and Ordinary Kriging (OK) interpolation have been widely used to offset the shortcomings of PM2.5 data observed at sparse monitoring sites. However, traditional point-based performance evaluation strategy for these methods remains stagnant, which could cause unreasonable mapping results. To address this challenge, this study employs ‘information entropy’, an area-based statistic, along with traditional point-based statistics (e.g. error rate, RMSE) to evaluate the performance of LUR model and OK interpolation in mapping PM2.5 concentrations in Houston from a multidimensional perspective. The point-based validation reveals significant differences between LUR and OK at different test sites despite the similar end-result accuracy (e.g. error rate 6.13% vs. 7.01%). Meanwhile, the area-based validation demonstrates that the PM2.5 concentrations simulated by the LUR model exhibits more detailed variations than those interpolated by the OK method (i.e. information entropy, 7.79 vs. 3.63). Results suggest that LUR modeling could better refine the spatial distribution scenario of PM2.5 concentrations compared to OK interpolation. The significance of this study primarily lies in promoting the integration of point- and area-based statistics for model performance evaluation in air pollution mapping. PMID:25731103

Fast inverse distance weighting-based spatiotemporal interpolation: a web-based application of interpolating daily fine particulate matter PM2:5 in the contiguous U.S. using parallel programming and k-d tree.

PubMed

Li, Lixin; Losser, Travis; Yorke, Charles; Piltner, Reinhard

2014-09-03

Epidemiological studies have identified associations between mortality and changes in concentration of particulate matter. These studies have highlighted the public concerns about health effects of particulate air pollution. Modeling fine particulate matter PM2.5 exposure risk and monitoring day-to-day changes in PM2.5 concentration is a critical step for understanding the pollution problem and embarking on the necessary remedy. This research designs, implements and compares two inverse distance weighting (IDW)-based spatiotemporal interpolation methods, in order to assess the trend of daily PM2.5 concentration for the contiguous United States over the year of 2009, at both the census block group level and county level. Traditionally, when handling spatiotemporal interpolation, researchers tend to treat space and time separately and reduce the spatiotemporal interpolation problems to a sequence of snapshots of spatial interpolations. In this paper, PM2.5 data interpolation is conducted in the continuous space-time domain by integrating space and time simultaneously, using the so-called extension approach. Time values are calculated with the help of a factor under the assumption that spatial and temporal dimensions are equally important when interpolating a continuous changing phenomenon in the space-time domain. Various IDW-based spatiotemporal interpolation methods with different parameter configurations are evaluated by cross-validation. In addition, this study explores computational issues (computer processing speed) faced during implementation of spatiotemporal interpolation for huge data sets. Parallel programming techniques and an advanced data structure, named k-d tree, are adapted in this paper to address the computational challenges. Significant computational improvement has been achieved. Finally, a web-based spatiotemporal IDW-based interpolation application is designed and implemented where users can visualize and animate spatiotemporal interpolation results.

Fast Inverse Distance Weighting-Based Spatiotemporal Interpolation: A Web-Based Application of Interpolating Daily Fine Particulate Matter PM2.5 in the Contiguous U.S. Using Parallel Programming and k-d Tree

PubMed Central

Li, Lixin; Losser, Travis; Yorke, Charles; Piltner, Reinhard

2014-01-01

Epidemiological studies have identified associations between mortality and changes in concentration of particulate matter. These studies have highlighted the public concerns about health effects of particulate air pollution. Modeling fine particulate matter PM2.5 exposure risk and monitoring day-to-day changes in PM2.5 concentration is a critical step for understanding the pollution problem and embarking on the necessary remedy. This research designs, implements and compares two inverse distance weighting (IDW)-based spatiotemporal interpolation methods, in order to assess the trend of daily PM2.5 concentration for the contiguous United States over the year of 2009, at both the census block group level and county level. Traditionally, when handling spatiotemporal interpolation, researchers tend to treat space and time separately and reduce the spatiotemporal interpolation problems to a sequence of snapshots of spatial interpolations. In this paper, PM2.5 data interpolation is conducted in the continuous space-time domain by integrating space and time simultaneously, using the so-called extension approach. Time values are calculated with the help of a factor under the assumption that spatial and temporal dimensions are equally important when interpolating a continuous changing phenomenon in the space-time domain. Various IDW-based spatiotemporal interpolation methods with different parameter configurations are evaluated by cross-validation. In addition, this study explores computational issues (computer processing speed) faced during implementation of spatiotemporal interpolation for huge data sets. Parallel programming techniques and an advanced data structure, named k-d tree, are adapted in this paper to address the computational challenges. Significant computational improvement has been achieved. Finally, a web-based spatiotemporal IDW-based interpolation application is designed and implemented where users can visualize and animate spatiotemporal interpolation results. PMID:25192146

Interdimensional effects in systems with quasirelativistic fermions

NASA Astrophysics Data System (ADS)

Zulkoskey, A. C.; Dick, R.; Tanaka, K.

2017-07-01

We examine the Green function and the density of states for fermions moving in three-dimensional Dirac materials with interfaces which affect the propagation properties of particles. Motivation for our research comes from interest in materials that exhibit quasirelativistic dispersion relations. By modifying Dirac-type contributions to the Hamiltonian in an interface we are able to calculate the Green function and the density of states. The density of states inside the interface exhibits interpolating behavior between two and three dimensions, with two-dimensional behavior at high energies and three-dimensional behavior at low energies, provided that the shift in the mass parameter in the interface is small. We also discuss the impact of the interpolating density of states on optical absorption in Dirac materials with a two-dimensional substructure.

Development of a 3D Stream Network and Topography for Improved Large-Scale Hydraulic Modeling

NASA Astrophysics Data System (ADS)

Saksena, S.; Dey, S.; Merwade, V.

2016-12-01

Most digital elevation models (DEMs) used for hydraulic modeling do not include channel bed elevations. As a result, the DEMs are complimented with additional bathymetric data for accurate hydraulic simulations. Existing methods to acquire bathymetric information through field surveys or through conceptual models are limited to reach-scale applications. With an increasing focus on large scale hydraulic modeling of rivers, a framework to estimate and incorporate bathymetry for an entire stream network is needed. This study proposes an interpolation-based algorithm to estimate bathymetry for a stream network by modifying the reach-based empirical River Channel Morphology Model (RCMM). The effect of a 3D stream network that includes river bathymetry is then investigated by creating a 1D hydraulic model (HEC-RAS) and 2D hydrodynamic model (Integrated Channel and Pond Routing) for the Upper Wabash River Basin in Indiana, USA. Results show improved simulation of flood depths and storage in the floodplain. Similarly, the impact of river bathymetry incorporation is more significant in the 2D model as compared to the 1D model.

The use of propagation path corrections to improve regional seismic event location in western China

DOE Office of Scientific and Technical Information (OSTI.GOV)

Steck, L.K.; Cogbill, A.H.; Velasco, A.A.

1999-03-01

In an effort to improve the ability to locate seismic events in western China using only regional data, the authors have developed empirical propagation path corrections (PPCs) and applied such corrections using both traditional location routines as well as a nonlinear grid search method. Thus far, the authors have concentrated on corrections to observed P arrival times for shallow events using travel-time observations available from the USGS EDRs, the ISC catalogs, their own travel-tim picks from regional data, and data from other catalogs. They relocate events with the algorithm of Bratt and Bache (1988) from a region encompassing China. Formore » individual stations having sufficient data, they produce a map of the regional travel-time residuals from all well-located teleseismic events. From these maps, interpolated PPC surfaces have been constructed using both surface fitting under tension and modified Bayesian kriging. The latter method offers the advantage of providing well-behaved interpolants, but requires that the authors have adequate error estimates associated with the travel-time residuals. To improve error estimates for kriging and event location, they separate measurement error from modeling error. The modeling error is defined as the travel-time variance of a particular model as a function of distance, while the measurement error is defined as the picking error associated with each phase. They estimate measurement errors for arrivals from the EDRs based on roundoff or truncation, and use signal-to-noise for the travel-time picks from the waveform data set.« less

Scientific data interpolation with low dimensional manifold model

DOE PAGES

Zhu, Wei; Wang, Bao; Barnard, Richard C.; ...

2017-09-28

Here, we propose to apply a low dimensional manifold model to scientific data interpolation from regular and irregular samplings with a significant amount of missing information. The low dimensionality of the patch manifold for general scientific data sets has been used as a regularizer in a variational formulation. The problem is solved via alternating minimization with respect to the manifold and the data set, and the Laplace–Beltrami operator in the Euler–Lagrange equation is discretized using the weighted graph Laplacian. Various scientific data sets from different fields of study are used to illustrate the performance of the proposed algorithm on datamore » compression and interpolation from both regular and irregular samplings.« less

Scientific data interpolation with low dimensional manifold model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhu, Wei; Wang, Bao; Barnard, Richard C.

Here, we propose to apply a low dimensional manifold model to scientific data interpolation from regular and irregular samplings with a significant amount of missing information. The low dimensionality of the patch manifold for general scientific data sets has been used as a regularizer in a variational formulation. The problem is solved via alternating minimization with respect to the manifold and the data set, and the Laplace–Beltrami operator in the Euler–Lagrange equation is discretized using the weighted graph Laplacian. Various scientific data sets from different fields of study are used to illustrate the performance of the proposed algorithm on datamore » compression and interpolation from both regular and irregular samplings.« less

Spatio-temporal interpolation of precipitation during monsoon periods in Pakistan

NASA Astrophysics Data System (ADS)

Hussain, Ijaz; Spöck, Gunter; Pilz, Jürgen; Yu, Hwa-Lung

2010-08-01

Spatio-temporal estimation of precipitation over a region is essential to the modeling of hydrologic processes for water resources management. The changes of magnitude and space-time heterogeneity of rainfall observations make space-time estimation of precipitation a challenging task. In this paper we propose a Box-Cox transformed hierarchical Bayesian multivariate spatio-temporal interpolation method for the skewed response variable. The proposed method is applied to estimate space-time monthly precipitation in the monsoon periods during 1974-2000, and 27-year monthly average precipitation data are obtained from 51 stations in Pakistan. The results of transformed hierarchical Bayesian multivariate spatio-temporal interpolation are compared to those of non-transformed hierarchical Bayesian interpolation by using cross-validation. The software developed by [11] is used for Bayesian non-stationary multivariate space-time interpolation. It is observed that the transformed hierarchical Bayesian method provides more accuracy than the non-transformed hierarchical Bayesian method.

Single image interpolation via adaptive nonlocal sparsity-based modeling.

PubMed

Romano, Yaniv; Protter, Matan; Elad, Michael

2014-07-01

Single image interpolation is a central and extensively studied problem in image processing. A common approach toward the treatment of this problem in recent years is to divide the given image into overlapping patches and process each of them based on a model for natural image patches. Adaptive sparse representation modeling is one such promising image prior, which has been shown to be powerful in filling-in missing pixels in an image. Another force that such algorithms may use is the self-similarity that exists within natural images. Processing groups of related patches together exploits their correspondence, leading often times to improved results. In this paper, we propose a novel image interpolation method, which combines these two forces-nonlocal self-similarities and sparse representation modeling. The proposed method is contrasted with competitive and related algorithms, and demonstrated to achieve state-of-the-art results.

Spherical Demons: Fast Surface Registration

PubMed Central

Yeo, B.T. Thomas; Sabuncu, Mert; Vercauteren, Tom; Ayache, Nicholas; Fischl, Bruce; Golland, Polina

2009-01-01

We present the fast Spherical Demons algorithm for registering two spherical images. By exploiting spherical vector spline interpolation theory, we show that a large class of regularizers for the modified demons objective function can be efficiently implemented on the sphere using convolution. Based on the one parameter subgroups of diffeomorphisms, the resulting registration is diffeomorphic and fast – registration of two cortical mesh models with more than 100k nodes takes less than 5 minutes, comparable to the fastest surface registration algorithms. Moreover, the accuracy of our method compares favorably to the popular FreeSurfer registration algorithm. We validate the technique in two different settings: (1) parcellation in a set of in-vivo cortical surfaces and (2) Brodmann area localization in ex-vivo cortical surfaces. PMID:18979813

Spherical demons: fast surface registration.

PubMed

Yeo, B T Thomas; Sabuncu, Mert; Vercauteren, Tom; Ayache, Nicholas; Fischl, Bruce; Golland, Polina

2008-01-01

We present the fast Spherical Demons algorithm for registering two spherical images. By exploiting spherical vector spline interpolation theory, we show that a large class of regularizers for the modified demons objective function can be efficiently implemented on the sphere using convolution. Based on the one parameter subgroups of diffeomorphisms, the resulting registration is diffeomorphic and fast - registration of two cortical mesh models with more than 100k nodes takes less than 5 minutes, comparable to the fastest surface registration algorithms. Moreover, the accuracy of our method compares favorably to the popular FreeSurfer registration algorithm. We validate the technique in two different settings: (1) parcellation in a set of in-vivo cortical surfaces and (2) Brodmann area localization in ex-vivo cortical surfaces.

On the need of mode interpolation for data-driven Galerkin models of a transient flow around a sphere

NASA Astrophysics Data System (ADS)

Stankiewicz, Witold; Morzyński, Marek; Kotecki, Krzysztof; Noack, Bernd R.

2017-04-01

We present a low-dimensional Galerkin model with state-dependent modes capturing linear and nonlinear dynamics. Departure point is a direct numerical simulation of the three-dimensional incompressible flow around a sphere at Reynolds numbers 400. This solution starts near the unstable steady Navier-Stokes solution and converges to a periodic limit cycle. The investigated Galerkin models are based on the dynamic mode decomposition (DMD) and derive the dynamical system from first principles, the Navier-Stokes equations. A DMD model with training data from the initial linear transient fails to predict the limit cycle. Conversely, a model from limit-cycle data underpredicts the initial growth rate roughly by a factor 5. Key enablers for uniform accuracy throughout the transient are a continuous mode interpolation between both oscillatory fluctuations and the addition of a shift mode. This interpolated model is shown to capture both the transient growth of the oscillation and the limit cycle.

Fiber orientation interpolation for the multiscale analysis of short fiber reinforced composite parts

NASA Astrophysics Data System (ADS)

Köbler, Jonathan; Schneider, Matti; Ospald, Felix; Andrä, Heiko; Müller, Ralf

2018-06-01

For short fiber reinforced plastic parts the local fiber orientation has a strong influence on the mechanical properties. To enable multiscale computations using surrogate models we advocate a two-step identification strategy. Firstly, for a number of sample orientations an effective model is derived by numerical methods available in the literature. Secondly, to cover a general orientation state, these effective models are interpolated. In this article we develop a novel and effective strategy to carry out this interpolation. Firstly, taking into account symmetry arguments, we reduce the fiber orientation phase space to a triangle in R^2 . For an associated triangulation of this triangle we furnish each node with an surrogate model. Then, we use linear interpolation on the fiber orientation triangle to equip each fiber orientation state with an effective stress. The proposed approach is quite general, and works for any physically nonlinear constitutive law on the micro-scale, as long as surrogate models for single fiber orientation states can be extracted. To demonstrate the capabilities of our scheme we study the viscoelastic creep behavior of short glass fiber reinforced PA66, and use Schapery's collocation method together with FFT-based computational homogenization to derive single orientation state effective models. We discuss the efficient implementation of our method, and present results of a component scale computation on a benchmark component by using ABAQUS ®.

Fiber orientation interpolation for the multiscale analysis of short fiber reinforced composite parts

NASA Astrophysics Data System (ADS)

Köbler, Jonathan; Schneider, Matti; Ospald, Felix; Andrä, Heiko; Müller, Ralf

2018-04-01

For short fiber reinforced plastic parts the local fiber orientation has a strong influence on the mechanical properties. To enable multiscale computations using surrogate models we advocate a two-step identification strategy. Firstly, for a number of sample orientations an effective model is derived by numerical methods available in the literature. Secondly, to cover a general orientation state, these effective models are interpolated. In this article we develop a novel and effective strategy to carry out this interpolation. Firstly, taking into account symmetry arguments, we reduce the fiber orientation phase space to a triangle in R^2 . For an associated triangulation of this triangle we furnish each node with an surrogate model. Then, we use linear interpolation on the fiber orientation triangle to equip each fiber orientation state with an effective stress. The proposed approach is quite general, and works for any physically nonlinear constitutive law on the micro-scale, as long as surrogate models for single fiber orientation states can be extracted. To demonstrate the capabilities of our scheme we study the viscoelastic creep behavior of short glass fiber reinforced PA66, and use Schapery's collocation method together with FFT-based computational homogenization to derive single orientation state effective models. We discuss the efficient implementation of our method, and present results of a component scale computation on a benchmark component by using ABAQUS ®.

Specialty functions singularity mechanics problems

NASA Technical Reports Server (NTRS)

Sarigul, Nesrin

1989-01-01

The focus is in the development of more accurate and efficient advanced methods for solution of singular problems encountered in mechanics. At present, finite element methods in conjunction with special functions, boolean sum and blending interpolations are being considered. In dealing with systems which contain a singularity, special finite elements are being formulated to be used in singular regions. Further, special transition elements are being formulated to couple the special element to the mesh that models the rest of the system, and to be used in conjunction with 1-D, 2-D and 3-D elements within the same mesh. Computational simulation with a least squares fit is being utilized to construct special elements, if there is an unknown singularity in the system. A novel approach is taken in formulation of the elements in that: (1) the material properties are modified to include time, temperature, coordinate and stress dependant behavior within the element; (2) material properties vary at nodal points of the elements; (3) a hidden-symbolic computation scheme is developed and utilized in formulating the elements; and (4) special functions and boolean sum are utilized in order to interpolate the field variables and their derivatives along the boundary of the elements. It may be noted that the proposed methods are also applicable to fluids and coupled problems.

Modeling the Hydrogen Solubility in Liquid Aluminum Alloys

NASA Astrophysics Data System (ADS)

Harvey, Jean-Philippe; Chartrand, Patrice

2010-08-01

The modeling of hydrogen solubility in multicomponent Al-(Li, Mg, Cu, and Si) liquid phase has been performed with a thermodynamic approach using the modified quasichemical model with the pair approximation (MQMPA). All hydrogen solubility data available in literature was assessed critically to obtain the binary parameters of the MQMPA model for the Al-H, Li-H, Mg-H, Cu-H, Zn-H, and Si-H melts. For the Li-H system, a new thermodynamic description of the stable solid lithium hydride was determined based on the c p found in literature. The thermodynamic model for the Al-Li system also was reassessed in this work to take into account the short-range ordering observed for this system. Built-in interpolation techniques allow the model to estimate the thermodynamic properties of the multicomponent liquid solution from the liquid model parameters of the lower order subsystems. A comparison of the calculated hydrogen solubility performed at various equilibrium conditions of temperature, pressure, and composition with the available experimental data found in the literature is presented in this work, as well as a comparison with some results from previous modeling.

Ensemble learning for spatial interpolation of soil potassium content based on environmental information.

PubMed

Liu, Wei; Du, Peijun; Wang, Dongchen

2015-01-01

One important method to obtain the continuous surfaces of soil properties from point samples is spatial interpolation. In this paper, we propose a method that combines ensemble learning with ancillary environmental information for improved interpolation of soil properties (hereafter, EL-SP). First, we calculated the trend value for soil potassium contents at the Qinghai Lake region in China based on measured values. Then, based on soil types, geology types, land use types, and slope data, the remaining residual was simulated with the ensemble learning model. Next, the EL-SP method was applied to interpolate soil potassium contents at the study site. To evaluate the utility of the EL-SP method, we compared its performance with other interpolation methods including universal kriging, inverse distance weighting, ordinary kriging, and ordinary kriging combined geographic information. Results show that EL-SP had a lower mean absolute error and root mean square error than the data produced by the other models tested in this paper. Notably, the EL-SP maps can describe more locally detailed information and more accurate spatial patterns for soil potassium content than the other methods because of the combined use of different types of environmental information; these maps are capable of showing abrupt boundary information for soil potassium content. Furthermore, the EL-SP method not only reduces prediction errors, but it also compliments other environmental information, which makes the spatial interpolation of soil potassium content more reasonable and useful.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schreiner, S.; Paschal, C.B.; Galloway, R.L.

Four methods of producing maximum intensity projection (MIP) images were studied and compared. Three of the projection methods differ in the interpolation kernel used for ray tracing. The interpolation kernels include nearest neighbor interpolation, linear interpolation, and cubic convolution interpolation. The fourth projection method is a voxel projection method that is not explicitly a ray-tracing technique. The four algorithms` performance was evaluated using a computer-generated model of a vessel and using real MR angiography data. The evaluation centered around how well an algorithm transferred an object`s width to the projection plane. The voxel projection algorithm does not suffer from artifactsmore » associated with the nearest neighbor algorithm. Also, a speed-up in the calculation of the projection is seen with the voxel projection method. Linear interpolation dramatically improves the transfer of width information from the 3D MRA data set over both nearest neighbor and voxel projection methods. Even though the cubic convolution interpolation kernel is theoretically superior to the linear kernel, it did not project widths more accurately than linear interpolation. A possible advantage to the nearest neighbor interpolation is that the size of small vessels tends to be exaggerated in the projection plane, thereby increasing their visibility. The results confirm that the way in which an MIP image is constructed has a dramatic effect on information contained in the projection. The construction method must be chosen with the knowledge that the clinical information in the 2D projections in general will be different from that contained in the original 3D data volume. 27 refs., 16 figs., 2 tabs.« less

Gaussian Process Interpolation for Uncertainty Estimation in Image Registration

PubMed Central

Wachinger, Christian; Golland, Polina; Reuter, Martin; Wells, William

2014-01-01

Intensity-based image registration requires resampling images on a common grid to evaluate the similarity function. The uncertainty of interpolation varies across the image, depending on the location of resampled points relative to the base grid. We propose to perform Bayesian inference with Gaussian processes, where the covariance matrix of the Gaussian process posterior distribution estimates the uncertainty in interpolation. The Gaussian process replaces a single image with a distribution over images that we integrate into a generative model for registration. Marginalization over resampled images leads to a new similarity measure that includes the uncertainty of the interpolation. We demonstrate that our approach increases the registration accuracy and propose an efficient approximation scheme that enables seamless integration with existing registration methods. PMID:25333127

Variational data assimilation with a semi-Lagrangian semi-implicit global shallow-water equation model and its adjoint

NASA Technical Reports Server (NTRS)

Li, Y.; Navon, I. M.; Courtier, P.; Gauthier, P.

1993-01-01

An adjoint model is developed for variational data assimilation using the 2D semi-Lagrangian semi-implicit (SLSI) shallow-water equation global model of Bates et al. with special attention being paid to the linearization of the interpolation routines. It is demonstrated that with larger time steps the limit of the validity of the tangent linear model will be curtailed due to the interpolations, especially in regions where sharp gradients in the interpolated variables coupled with strong advective wind occur, a synoptic situation common in the high latitudes. This effect is particularly evident near the pole in the Northern Hemisphere during the winter season. Variational data assimilation experiments of 'identical twin' type with observations available only at the end of the assimilation period perform well with this adjoint model. It is confirmed that the computational efficiency of the semi-Lagrangian scheme is preserved during the minimization process, related to the variational data assimilation procedure.

Scaling a Human Body Finite Element Model with Radial Basis Function Interpolation

DTIC Science & Technology

Human body models are currently used to evaluate the body’s response to a variety of threats to the Soldier. The ability to adjust the size of human...body models is currently limited because of the complex shape changes that are required. Here, a radial basis function interpolation method is used to...morph the shape on an existing finite element mesh. Tools are developed and integrated into the Blender computer graphics software to assist with

Hypersonic research engine project. Phase 2: Aerothermodynamic Integration Model (AIM) data reduction computer program, data item no. 54.16

NASA Technical Reports Server (NTRS)

Gaede, A. E.; Platte, W. (Editor)

1975-01-01

The data reduction program used to analyze the performance of the Aerothermodynamic Integration Model is described. Routines to acquire, calibrate, and interpolate the test data, to calculate the axial components of the pressure area integrals and the skin function coefficients, and to report the raw data in engineering units are included along with routines to calculate flow conditions in the wind tunnel, inlet, combustor, and nozzle, and the overall engine performance. Various subroutines were modified and used to obtain species concentrations and transport properties in chemical equilibrium at each of the internal and external engine stations. It is recommended that future test plans include the configuration, calibration, and channel assignment data on a magnetic tape generated at the test site immediately before or after a test, and that the data reduction program be designed to operate in a batch environment.

Heat Flow Contours and Well Data Around the Milford FORGE Site

DOE Data Explorer

Joe Moore

2016-03-09

This submission contains a shapefile of heat flow contour lines around the FORGE site located in Milford, Utah. The model was interpolated from data points in the Milford_wells shapefile. This heat flow model was interpolated from 66 data points using the kriging method in Geostatistical Analyst tool of ArcGIS. The resulting model was smoothed 100%. The well dataset contains 59 wells from various sources, with lat/long coordinates, temperature, quality, basement depth, and heat flow. This data was used to make models of the specific characteristics.

Fundamental techniques for resolution enhancement of average subsampled images

NASA Astrophysics Data System (ADS)

Shen, Day-Fann; Chiu, Chui-Wen

2012-07-01

Although single image resolution enhancement, otherwise known as super-resolution, is widely regarded as an ill-posed inverse problem, we re-examine the fundamental relationship between a high-resolution (HR) image acquisition module and its low-resolution (LR) counterpart. Analysis shows that partial HR information is attenuated but still exists, in its LR version, through the fundamental averaging-and-subsampling process. As a result, we propose a modified Laplacian filter (MLF) and an intensity correction process (ICP) as the pre and post process, respectively, with an interpolation algorithm to partially restore the attenuated information in a super-resolution (SR) enhanced image image. Experiments show that the proposed MLF and ICP provide significant and consistent quality improvements on all 10 test images with three well known interpolation methods including bilinear, bi-cubic, and the SR graphical user interface program provided by Ecole Polytechnique Federale de Lausanne. The proposed MLF and ICP are simple in implementation and generally applicable to all average-subsampled LR images. MLF and ICP, separately or together, can be integrated into most interpolation methods that attempt to restore the original HR contents. Finally, the idea of MLF and ICP can also be applied for average, subsampled one-dimensional signal.

Estimation bias from using nonlinear Fourier plane correlators for sub-pixel image shift measurement and implications for the binary joint transform correlator

NASA Astrophysics Data System (ADS)

Grycewicz, Thomas J.; Florio, Christopher J.; Franz, Geoffrey A.; Robinson, Ross E.

2007-09-01

When using Fourier plane digital algorithms or an optical correlator to measure the correlation between digital images, interpolation by center-of-mass or quadratic estimation techniques can be used to estimate image displacement to the sub-pixel level. However, this can lead to a bias in the correlation measurement. This bias shifts the sub-pixel output measurement to be closer to the nearest pixel center than the actual location. The paper investigates the bias in the outputs of both digital and optical correlators, and proposes methods to minimize this effect. We use digital studies and optical implementations of the joint transform correlator to demonstrate optical registration with accuracies better than 0.1 pixels. We use both simulations of image shift and movies of a moving target as inputs. We demonstrate bias error for both center-of-mass and quadratic interpolation, and discuss the reasons that this bias is present. Finally, we suggest measures to reduce or eliminate the bias effects. We show that when sub-pixel bias is present, it can be eliminated by modifying the interpolation method. By removing the bias error, we improve registration accuracy by thirty percent.

Joint seismic data denoising and interpolation with double-sparsity dictionary learning

NASA Astrophysics Data System (ADS)

Zhu, Lingchen; Liu, Entao; McClellan, James H.

2017-08-01

Seismic data quality is vital to geophysical applications, so that methods of data recovery, including denoising and interpolation, are common initial steps in the seismic data processing flow. We present a method to perform simultaneous interpolation and denoising, which is based on double-sparsity dictionary learning. This extends previous work that was for denoising only. The original double-sparsity dictionary learning algorithm is modified to track the traces with missing data by defining a masking operator that is integrated into the sparse representation of the dictionary. A weighted low-rank approximation algorithm is adopted to handle the dictionary updating as a sparse recovery optimization problem constrained by the masking operator. Compared to traditional sparse transforms with fixed dictionaries that lack the ability to adapt to complex data structures, the double-sparsity dictionary learning method learns the signal adaptively from selected patches of the corrupted seismic data, while preserving compact forward and inverse transform operators. Numerical experiments on synthetic seismic data indicate that this new method preserves more subtle features in the data set without introducing pseudo-Gibbs artifacts when compared to other directional multi-scale transform methods such as curvelets.

Postscript: Identity and Constraints in Models of Object Formation

ERIC Educational Resources Information Center

Kellman, Philip J.; Garrigan, Patrick; Shipley, Thomas F.; Keane, Brian P.

2007-01-01

Presents some additional comments from the current authors regarding their original article Interpolation processes in object perception: Reply to Anderson (2007). As this exchange concludes, we believe that the account of interpolation and object formation proposed by Kellman and Shipley (1991), further developed in recent years (Kellman, 2003;…

Spatial interpolation of monthly mean air temperature data for Latvia

NASA Astrophysics Data System (ADS)

Aniskevich, Svetlana

2016-04-01

Temperature data with high spatial resolution are essential for appropriate and qualitative local characteristics analysis. Nowadays the surface observation station network in Latvia consists of 22 stations recording daily air temperature, thus in order to analyze very specific and local features in the spatial distribution of temperature values in the whole Latvia, a high quality spatial interpolation method is required. Until now inverse distance weighted interpolation was used for the interpolation of air temperature data at the meteorological and climatological service of the Latvian Environment, Geology and Meteorology Centre, and no additional topographical information was taken into account. This method made it almost impossible to reasonably assess the actual temperature gradient and distribution between the observation points. During this project a new interpolation method was applied and tested, considering auxiliary explanatory parameters. In order to spatially interpolate monthly mean temperature values, kriging with external drift was used over a grid of 1 km resolution, which contains parameters such as 5 km mean elevation, continentality, distance from the Gulf of Riga and the Baltic Sea, biggest lakes and rivers, population density. As the most appropriate of these parameters, based on a complex situation analysis, mean elevation and continentality was chosen. In order to validate interpolation results, several statistical indicators of the differences between predicted values and the values actually observed were used. Overall, the introduced model visually and statistically outperforms the previous interpolation method and provides a meteorologically reasonable result, taking into account factors that influence the spatial distribution of the monthly mean temperature.

Modified Gompertz equation for electrotherapy murine tumor growth kinetics: predictions and new hypotheses.

PubMed

Cabrales, Luis E Bergues; Nava, Juan J Godina; Aguilera, Andrés Ramírez; Joa, Javier A González; Ciria, Héctor M Camué; González, Maraelys Morales; Salas, Miriam Fariñas; Jarque, Manuel Verdecia; González, Tamara Rubio; Mateus, Miguel A O'Farril; Brooks, Soraida C Acosta; Palencia, Fabiola Suárez; Zamora, Lisset Ortiz; Quevedo, María C Céspedes; Seringe, Sarah Edward; Cuitié, Vladimir Crombet; Cabrales, Idelisa Bergues; González, Gustavo Sierra

2010-10-28

Electrotherapy effectiveness at different doses has been demonstrated in preclinical and clinical studies; however, several aspects that occur in the tumor growth kinetics before and after treatment have not yet been revealed. Mathematical modeling is a useful instrument that can reveal some of these aspects. The aim of this paper is to describe the complete growth kinetics of unperturbed and perturbed tumors through use of the modified Gompertz equation in order to generate useful insight into the mechanisms that underpin this devastating disease. The complete tumor growth kinetics for control and treated groups are obtained by interpolation and extrapolation methods with different time steps, using experimental data of fibrosarcoma Sa-37. In the modified Gompertz equation, a delay time is introduced to describe the tumor's natural history before treatment. Different graphical strategies are used in order to reveal new information in the complete kinetics of this tumor type. The first stage of complete tumor growth kinetics is highly non linear. The model, at this stage, shows different aspects that agree with those reported theoretically and experimentally. Tumor reversibility and the proportionality between regions before and after electrotherapy are demonstrated. In tumors that reach partial remission, two antagonistic post-treatment processes are induced, whereas in complete remission, two unknown antitumor mechanisms are induced. The modified Gompertz equation is likely to lead to insights within cancer research. Such insights hold promise for increasing our understanding of tumors as self-organizing systems and, the possible existence of phase transitions in tumor growth kinetics, which, in turn, may have significant impacts both on cancer research and on clinical practice.

Adaptive image coding based on cubic-spline interpolation

NASA Astrophysics Data System (ADS)

Jiang, Jian-Xing; Hong, Shao-Hua; Lin, Tsung-Ching; Wang, Lin; Truong, Trieu-Kien

2014-09-01

It has been investigated that at low bit rates, downsampling prior to coding and upsampling after decoding can achieve better compression performance than standard coding algorithms, e.g., JPEG and H. 264/AVC. However, at high bit rates, the sampling-based schemes generate more distortion. Additionally, the maximum bit rate for the sampling-based scheme to outperform the standard algorithm is image-dependent. In this paper, a practical adaptive image coding algorithm based on the cubic-spline interpolation (CSI) is proposed. This proposed algorithm adaptively selects the image coding method from CSI-based modified JPEG and standard JPEG under a given target bit rate utilizing the so called ρ-domain analysis. The experimental results indicate that compared with the standard JPEG, the proposed algorithm can show better performance at low bit rates and maintain the same performance at high bit rates.

High-temperature behavior of a deformed Fermi gas obeying interpolating statistics.

PubMed

Algin, Abdullah; Senay, Mustafa

2012-04-01

An outstanding idea originally introduced by Greenberg is to investigate whether there is equivalence between intermediate statistics, which may be different from anyonic statistics, and q-deformed particle algebra. Also, a model to be studied for addressing such an idea could possibly provide us some new consequences about the interactions of particles as well as their internal structures. Motivated mainly by this idea, in this work, we consider a q-deformed Fermi gas model whose statistical properties enable us to effectively study interpolating statistics. Starting with a generalized Fermi-Dirac distribution function, we derive several thermostatistical functions of a gas of these deformed fermions in the thermodynamical limit. We study the high-temperature behavior of the system by analyzing the effects of q deformation on the most important thermostatistical characteristics of the system such as the entropy, specific heat, and equation of state. It is shown that such a deformed fermion model in two and three spatial dimensions exhibits the interpolating statistics in a specific interval of the model deformation parameter 0 < q < 1. In particular, for two and three spatial dimensions, it is found from the behavior of the third virial coefficient of the model that the deformation parameter q interpolates completely between attractive and repulsive systems, including the free boson and fermion cases. From the results obtained in this work, we conclude that such a model could provide much physical insight into some interacting theories of fermions, and could be useful to further study the particle systems with intermediate statistics.

Using Neural Networks to Improve the Performance of Radiative Transfer Modeling Used for Geometry Dependent LER Calculations

NASA Astrophysics Data System (ADS)

Fasnacht, Z.; Qin, W.; Haffner, D. P.; Loyola, D. G.; Joiner, J.; Krotkov, N. A.; Vasilkov, A. P.; Spurr, R. J. D.

2017-12-01

In order to estimate surface reflectance used in trace gas retrieval algorithms, radiative transfer models (RTM) such as the Vector Linearized Discrete Ordinate Radiative Transfer Model (VLIDORT) can be used to simulate the top of the atmosphere (TOA) radiances with advanced models of surface properties. With large volumes of satellite data, these model simulations can become computationally expensive. Look up table interpolation can improve the computational cost of the calculations, but the non-linear nature of the radiances requires a dense node structure if interpolation errors are to be minimized. In order to reduce our computational effort and improve the performance of look-up tables, neural networks can be trained to predict these radiances. We investigate the impact of using look-up table interpolation versus a neural network trained using the smart sampling technique, and show that neural networks can speed up calculations and reduce errors while using significantly less memory and RTM calls. In future work we will implement a neural network in operational processing to meet growing demands for reflectance modeling in support of high spatial resolution satellite missions.

Accuracy of stream habitat interpolations across spatial scales

USGS Publications Warehouse

Sheehan, Kenneth R.; Welsh, Stuart A.

2013-01-01

Stream habitat data are often collected across spatial scales because relationships among habitat, species occurrence, and management plans are linked at multiple spatial scales. Unfortunately, scale is often a factor limiting insight gained from spatial analysis of stream habitat data. Considerable cost is often expended to collect data at several spatial scales to provide accurate evaluation of spatial relationships in streams. To address utility of single scale set of stream habitat data used at varying scales, we examined the influence that data scaling had on accuracy of natural neighbor predictions of depth, flow, and benthic substrate. To achieve this goal, we measured two streams at gridded resolution of 0.33 × 0.33 meter cell size over a combined area of 934 m2 to create a baseline for natural neighbor interpolated maps at 12 incremental scales ranging from a raster cell size of 0.11 m2 to 16 m2 . Analysis of predictive maps showed a logarithmic linear decay pattern in RMSE values in interpolation accuracy for variables as resolution of data used to interpolate study areas became coarser. Proportional accuracy of interpolated models (r2 ) decreased, but it was maintained up to 78% as interpolation scale moved from 0.11 m2 to 16 m2 . Results indicated that accuracy retention was suitable for assessment and management purposes at various scales different from the data collection scale. Our study is relevant to spatial modeling, fish habitat assessment, and stream habitat management because it highlights the potential of using a single dataset to fulfill analysis needs rather than investing considerable cost to develop several scaled datasets.

Subcellular localization for Gram positive and Gram negative bacterial proteins using linear interpolation smoothing model.

PubMed

Saini, Harsh; Raicar, Gaurav; Dehzangi, Abdollah; Lal, Sunil; Sharma, Alok

2015-12-07

Protein subcellular localization is an important topic in proteomics since it is related to a protein׳s overall function, helps in the understanding of metabolic pathways, and in drug design and discovery. In this paper, a basic approximation technique from natural language processing called the linear interpolation smoothing model is applied for predicting protein subcellular localizations. The proposed approach extracts features from syntactical information in protein sequences to build probabilistic profiles using dependency models, which are used in linear interpolation to determine how likely is a sequence to belong to a particular subcellular location. This technique builds a statistical model based on maximum likelihood. It is able to deal effectively with high dimensionality that hinders other traditional classifiers such as Support Vector Machines or k-Nearest Neighbours without sacrificing performance. This approach has been evaluated by predicting subcellular localizations of Gram positive and Gram negative bacterial proteins. Copyright © 2015 Elsevier Ltd. All rights reserved.

Surface models of the male urogenital organs built from the Visible Korean using popular software

PubMed Central

Shin, Dong Sun; Park, Jin Seo; Shin, Byeong-Seok

2011-01-01

Unlike volume models, surface models, which are empty three-dimensional images, have a small file size, so they can be displayed, rotated, and modified in real time. Thus, surface models of male urogenital organs can be effectively applied to an interactive computer simulation and contribute to the clinical practice of urologists. To create high-quality surface models, the urogenital organs and other neighboring structures were outlined in 464 sectioned images of the Visible Korean male using Adobe Photoshop; the outlines were interpolated on Discreet Combustion; then an almost automatic volume reconstruction followed by surface reconstruction was performed on 3D-DOCTOR. The surface models were refined and assembled in their proper positions on Maya, and a surface model was coated with actual surface texture acquired from the volume model of the structure on specially programmed software. In total, 95 surface models were prepared, particularly complete models of the urinary and genital tracts. These surface models will be distributed to encourage other investigators to develop various kinds of medical training simulations. Increasingly automated surface reconstruction technology using commercial software will enable other researchers to produce their own surface models more effectively. PMID:21829759

Spatial interpolation of solar global radiation

NASA Astrophysics Data System (ADS)

Lussana, C.; Uboldi, F.; Antoniazzi, C.

2010-09-01

Solar global radiation is defined as the radiant flux incident onto an area element of the terrestrial surface. Its direct knowledge plays a crucial role in many applications, from agrometeorology to environmental meteorology. The ARPA Lombardia's meteorological network includes about one hundred of pyranometers, mostly distributed in the southern part of the Alps and in the centre of the Po Plain. A statistical interpolation method based on an implementation of the Optimal Interpolation is applied to the hourly average of the solar global radiation observations measured by the ARPA Lombardia's network. The background field is obtained using SMARTS (The Simple Model of the Atmospheric Radiative Transfer of Sunshine, Gueymard, 2001). The model is initialised by assuming clear sky conditions and it takes into account the solar position and orography related effects (shade and reflection). The interpolation of pyranometric observations introduces in the analysis fields information about cloud presence and influence. A particular effort is devoted to prevent observations affected by large errors of different kinds (representativity errors, systematic errors, gross errors) from entering the analysis procedure. The inclusion of direct cloud information from satellite observations is also planned.

CBEO:N, Chesapeake Bay Environmental Observatory as a Cyberinfrastructure Node

NASA Astrophysics Data System (ADS)

Zaslavsky, I.; Piasecki, M.; Whitenack, T.; Ball, W. P.; Murphy, R.

2008-12-01

Chesapeake Bay Environmental Observatory (CBEO) is an NSF-supported project focused on studying hypoxia in Chesapeake Bay using advanced cyberinfrastructure (CI) technologies. The project is organized around four concurrent and interacting activities: 1) CBEO:S provides science and management context for the use of CI technologies, focusing on hypoxia and its non-linear dynamics as affected by management and climate; 2) CBEO:T constructs a locally-accessible CBEO test bed prototype centered on spatio-temporal interpolation and advanced querying of model runs; 3) CBEO:N incorporates the test bed CI into national environmental observation networks, and 4) CBEO:E develops education and outreach components of the project that translate observational science for public consumption. CBEO:N activities, which are the focus of this paper, are four-fold: - constructing an online project portal to enable researchers to publish, discover, query, visualize and integrate project-related datasets of different types. The portal is based on the technologies developed within the GEON (the Geosciences Network) project, and has established the CBEO project data server as part of the GEON network of servers; * developing a CBEO node within the WATERS network, taking advantage of the CUAHSI Hydrologic Information System (HIS) Server technology that supports online publication of observation data as web services, and ontology-assisted data discovery; *developing new data structures and metadata in order to describe water quality observational data, and model run output, obtained for the Chesapeake Bay area, using data structures adopted and modified from the Observations Data Model of CUAHSI HIS; * prototyping CBEO tools that can be re-used through the portal, in particular implementing a portal version of R-based spatial interpolation tools. The paper describes recent accomplishments in these four development areas, and demonstrates how CI approaches transform research and data sharing in environmental observing systems.

[Research on Kalman interpolation prediction model based on micro-region PM2.5 concentration].

PubMed

Wang, Wei; Zheng, Bin; Chen, Binlin; An, Yaoming; Jiang, Xiaoming; Li, Zhangyong

2018-02-01

In recent years, the pollution problem of particulate matter, especially PM2.5, is becoming more and more serious, which has attracted many people's attention from all over the world. In this paper, a Kalman prediction model combined with cubic spline interpolation is proposed, which is applied to predict the concentration of PM2.5 in the micro-regional environment of campus, and to realize interpolation simulation diagram of concentration of PM2.5 and simulate the spatial distribution of PM2.5. The experiment data are based on the environmental information monitoring system which has been set up by our laboratory. And the predicted and actual values of PM2.5 concentration data have been checked by the way of Wilcoxon signed-rank test. We find that the value of bilateral progressive significance probability was 0.527, which is much greater than the significant level α = 0.05. The mean absolute error (MEA) of Kalman prediction model was 1.8 μg/m 3 , the average relative error (MER) was 6%, and the correlation coefficient R was 0.87. Thus, the Kalman prediction model has a better effect on the prediction of concentration of PM2.5 than those of the back propagation (BP) prediction and support vector machine (SVM) prediction. In addition, with the combination of Kalman prediction model and the spline interpolation method, the spatial distribution and local pollution characteristics of PM2.5 can be simulated.

Interpolation Approaches for Characterizing Spatial Variability of Soil Properties in Tuz Lake Basin of Turkey

NASA Astrophysics Data System (ADS)

Gorji, Taha; Sertel, Elif; Tanik, Aysegul

2017-12-01

Soil management is an essential concern in protecting soil properties, in enhancing appropriate soil quality for plant growth and agricultural productivity, and in preventing soil erosion. Soil scientists and decision makers require accurate and well-distributed spatially continuous soil data across a region for risk assessment and for effectively monitoring and managing soils. Recently, spatial interpolation approaches have been utilized in various disciplines including soil sciences for analysing, predicting and mapping distribution and surface modelling of environmental factors such as soil properties. The study area selected in this research is Tuz Lake Basin in Turkey bearing ecological and economic importance. Fertile soil plays a significant role in agricultural activities, which is one of the main industries having great impact on economy of the region. Loss of trees and bushes due to intense agricultural activities in some parts of the basin lead to soil erosion. Besides, soil salinization due to both human-induced activities and natural factors has exacerbated its condition regarding agricultural land development. This study aims to compare capability of Local Polynomial Interpolation (LPI) and Radial Basis Functions (RBF) as two interpolation methods for mapping spatial pattern of soil properties including organic matter, phosphorus, lime and boron. Both LPI and RBF methods demonstrated promising results for predicting lime, organic matter, phosphorous and boron. Soil samples collected in the field were used for interpolation analysis in which approximately 80% of data was used for interpolation modelling whereas the remaining for validation of the predicted results. Relationship between validation points and their corresponding estimated values in the same location is examined by conducting linear regression analysis. Eight prediction maps generated from two different interpolation methods for soil organic matter, phosphorus, lime and boron parameters were examined based on R2 and RMSE values. The outcomes indicate that RBF performance in predicting lime, organic matter and boron put forth better results than LPI. However, LPI shows better results for predicting phosphorus.

Context dependent anti-aliasing image reconstruction

NASA Technical Reports Server (NTRS)

Beaudet, Paul R.; Hunt, A.; Arlia, N.

1989-01-01

Image Reconstruction has been mostly confined to context free linear processes; the traditional continuum interpretation of digital array data uses a linear interpolator with or without an enhancement filter. Here, anti-aliasing context dependent interpretation techniques are investigated for image reconstruction. Pattern classification is applied to each neighborhood to assign it a context class; a different interpolation/filter is applied to neighborhoods of differing context. It is shown how the context dependent interpolation is computed through ensemble average statistics using high resolution training imagery from which the lower resolution image array data is obtained (simulation). A quadratic least squares (LS) context-free image quality model is described from which the context dependent interpolation coefficients are derived. It is shown how ensembles of high-resolution images can be used to capture the a priori special character of different context classes. As a consequence, a priori information such as the translational invariance of edges along the edge direction, edge discontinuity, and the character of corners is captured and can be used to interpret image array data with greater spatial resolution than would be expected by the Nyquist limit. A Gibb-like artifact associated with this super-resolution is discussed. More realistic context dependent image quality models are needed and a suggestion is made for using a quality model which now is finding application in data compression.

Quantum effects and anharmonicity in the H2-Li+-benzene complex: A model for hydrogen storage materials

NASA Astrophysics Data System (ADS)

Kolmann, Stephen J.; D'Arcy, Jordan H.; Jordan, Meredith J. T.

2013-12-01

Quantum and anharmonic effects are investigated in H2-Li+-benzene, a model for hydrogen adsorption in metal-organic frameworks and carbon-based materials. Three- and 8-dimensional quantum diffusion Monte Carlo (QDMC) and rigid-body diffusion Monte Carlo (RBDMC) simulations are performed on potential energy surfaces interpolated from electronic structure calculations at the M05-2X/6-31+G(d,p) and M05-2X/6-311+G(2df,p) levels of theory using a three-dimensional spline or a modified Shepard interpolation. These calculations investigate the intermolecular interactions in this system, with three- and 8-dimensional 0 K H2 binding enthalpy estimates, ΔHbind (0 K), being 16.5 kJ mol-1 and 12.4 kJ mol-1, respectively: 0.1 and 0.6 kJ mol-1 higher than harmonic values. Zero-point energy effects are 35% of the value of ΔHbind (0 K) at M05-2X/6-311+G(2df,p) and cannot be neglected; uncorrected electronic binding energies overestimate ΔHbind (0 K) by at least 6 kJ mol-1. Harmonic intermolecular binding enthalpies can be corrected by treating the H2 "helicopter" and "ferris wheel" rotations as free and hindered rotations, respectively. These simple corrections yield results within 2% of the 8-dimensional anharmonic calculations. Nuclear ground state probability density histograms obtained from the QDMC and RBDMC simulations indicate the H2 molecule is delocalized above the Li+-benzene system at 0 K.

On the Problem of Deformed Spherical Systems in Modified Newtonian Dynamics

NASA Astrophysics Data System (ADS)

Ko, Chung-Ming

2016-04-01

Based on Newtonian dynamics, observations show that the luminous masses of astrophysical objects that are the size of a galaxy or larger are not enough to generate the measured motions which they supposedly determine. This is typically attributed to the existence of dark matter, which possesses mass but does not radiate (or absorb radiation). Alternatively, the mismatch can be explained if the underlying dynamics is not Newtonian. Within this conceptual scheme, Modified Newtonian Dynamics (MOND) is a successful theoretical paradigm. MOND is usually expressed in terms of a nonlinear Poisson equation, which is difficult to analyze for arbitrary matter distributions. We study the MONDian gravitational field generated by slightly non-spherically symmetric mass distributions based on the fact that both Newtonian and MONDian fields are conservative (which we refer to as the compatibility condition). As the non-relativistic version of MOND has two different formulations (AQUAL and QuMOND) and the compatibility condition can be expressed in two ways, there are four approaches to the problem in total. The method involves solving a suitably defined linear deformation potential, which generally depends on the choice of MOND interpolation function. However, for some specific form of the deformation potential, the solution is independent of the interpolation function.

Hydraulic head interpolation using ANFIS—model selection and sensitivity analysis

NASA Astrophysics Data System (ADS)

Kurtulus, Bedri; Flipo, Nicolas

2012-01-01

The aim of this study is to investigate the efficiency of ANFIS (adaptive neuro fuzzy inference system) for interpolating hydraulic head in a 40-km 2 agricultural watershed of the Seine basin (France). Inputs of ANFIS are Cartesian coordinates and the elevation of the ground. Hydraulic head was measured at 73 locations during a snapshot campaign on September 2009, which characterizes low-water-flow regime in the aquifer unit. The dataset was then split into three subsets using a square-based selection method: a calibration one (55%), a training one (27%), and a test one (18%). First, a method is proposed to select the best ANFIS model, which corresponds to a sensitivity analysis of ANFIS to the type and number of membership functions (MF). Triangular, Gaussian, general bell, and spline-based MF are used with 2, 3, 4, and 5 MF per input node. Performance criteria on the test subset are used to select the 5 best ANFIS models among 16. Then each is used to interpolate the hydraulic head distribution on a (50×50)-m grid, which is compared to the soil elevation. The cells where the hydraulic head is higher than the soil elevation are counted as "error cells." The ANFIS model that exhibits the less "error cells" is selected as the best ANFIS model. The best model selection reveals that ANFIS models are very sensitive to the type and number of MF. Finally, a sensibility analysis of the best ANFIS model with four triangular MF is performed on the interpolation grid, which shows that ANFIS remains stable to error propagation with a higher sensitivity to soil elevation.

The modal surface interpolation method for damage localization

NASA Astrophysics Data System (ADS)

Pina Limongelli, Maria

2017-05-01

The Interpolation Method (IM) has been previously proposed and successfully applied for damage localization in plate like structures. The method is based on the detection of localized reductions of smoothness in the Operational Deformed Shapes (ODSs) of the structure. The IM can be applied to any type of structure provided the ODSs are estimated accurately in the original and in the damaged configurations. If the latter circumstance fails to occur, for example when the structure is subjected to an unknown input(s) or if the structural responses are strongly corrupted by noise, both false and missing alarms occur when the IM is applied to localize a concentrated damage. In order to overcome these drawbacks a modification of the method is herein investigated. An ODS is the deformed shape of a structure subjected to a harmonic excitation: at resonances the ODS are dominated by the relevant mode shapes. The effect of noise at resonance is usually lower with respect to other frequency values hence the relevant ODS are estimated with higher reliability. Several methods have been proposed to reliably estimate modal shapes in case of unknown input. These two circumstances can be exploited to improve the reliability of the IM. In order to reduce or eliminate the drawbacks related to the estimation of the ODSs in case of noisy signals, in this paper is investigated a modified version of the method based on a damage feature calculated considering the interpolation error relevant only to the modal shapes and not to all the operational shapes in the significant frequency range. Herein will be reported the comparison between the results of the IM in its actual version (with the interpolation error calculated summing up the contributions of all the operational shapes) and in the new proposed version (with the estimation of the interpolation error limited to the modal shapes).

Research on interpolation methods in medical image processing.

PubMed

Pan, Mei-Sen; Yang, Xiao-Li; Tang, Jing-Tian

2012-04-01

Image interpolation is widely used for the field of medical image processing. In this paper, interpolation methods are divided into three groups: filter interpolation, ordinary interpolation and general partial volume interpolation. Some commonly-used filter methods for image interpolation are pioneered, but the interpolation effects need to be further improved. When analyzing and discussing ordinary interpolation, many asymmetrical kernel interpolation methods are proposed. Compared with symmetrical kernel ones, the former are have some advantages. After analyzing the partial volume and generalized partial volume estimation interpolations, the new concept and constraint conditions of the general partial volume interpolation are defined, and several new partial volume interpolation functions are derived. By performing the experiments of image scaling, rotation and self-registration, the interpolation methods mentioned in this paper are compared in the entropy, peak signal-to-noise ratio, cross entropy, normalized cross-correlation coefficient and running time. Among the filter interpolation methods, the median and B-spline filter interpolations have a relatively better interpolating performance. Among the ordinary interpolation methods, on the whole, the symmetrical cubic kernel interpolations demonstrate a strong advantage, especially the symmetrical cubic B-spline interpolation. However, we have to mention that they are very time-consuming and have lower time efficiency. As for the general partial volume interpolation methods, from the total error of image self-registration, the symmetrical interpolations provide certain superiority; but considering the processing efficiency, the asymmetrical interpolations are better.

Jimena: efficient computing and system state identification for genetic regulatory networks.

PubMed

Karl, Stefan; Dandekar, Thomas

2013-10-11

Boolean networks capture switching behavior of many naturally occurring regulatory networks. For semi-quantitative modeling, interpolation between ON and OFF states is necessary. The high degree polynomial interpolation of Boolean genetic regulatory networks (GRNs) in cellular processes such as apoptosis or proliferation allows for the modeling of a wider range of node interactions than continuous activator-inhibitor models, but suffers from scaling problems for networks which contain nodes with more than ~10 inputs. Many GRNs from literature or new gene expression experiments exceed those limitations and a new approach was developed. (i) As a part of our new GRN simulation framework Jimena we introduce and setup Boolean-tree-based data structures; (ii) corresponding algorithms greatly expedite the calculation of the polynomial interpolation in almost all cases, thereby expanding the range of networks which can be simulated by this model in reasonable time. (iii) Stable states for discrete models are efficiently counted and identified using binary decision diagrams. As application example, we show how system states can now be sampled efficiently in small up to large scale hormone disease networks (Arabidopsis thaliana development and immunity, pathogen Pseudomonas syringae and modulation by cytokinins and plant hormones). Jimena simulates currently available GRNs about 10-100 times faster than the previous implementation of the polynomial interpolation model and even greater gains are achieved for large scale-free networks. This speed-up also facilitates a much more thorough sampling of continuous state spaces which may lead to the identification of new stable states. Mutants of large networks can be constructed and analyzed very quickly enabling new insights into network robustness and behavior.

Filling-In Models of Completion: Rejoinder to Kellman, Garrigan, Shipley, and Keane (2007) and Albert (2007)

ERIC Educational Resources Information Center

Anderson, Barton L.

2007-01-01

There has been a growing interest in understanding the computations involved in the processes underlying visual segmentation and interpolation in conditions of occlusion. P. J. Kellman, P. Garrigan, T. F. Shipley, and B. P. Keane and M. K. Albert defended the view that identical contour interpolation mechanisms underlie modal and amodal…

An adaptive proper orthogonal decomposition method for model order reduction of multi-disc rotor system

NASA Astrophysics Data System (ADS)

Jin, Yulin; Lu, Kuan; Hou, Lei; Chen, Yushu

2017-12-01

The proper orthogonal decomposition (POD) method is a main and efficient tool for order reduction of high-dimensional complex systems in many research fields. However, the robustness problem of this method is always unsolved, although there are some modified POD methods which were proposed to solve this problem. In this paper, a new adaptive POD method called the interpolation Grassmann manifold (IGM) method is proposed to address the weakness of local property of the interpolation tangent-space of Grassmann manifold (ITGM) method in a wider parametric region. This method is demonstrated here by a nonlinear rotor system of 33-degrees of freedom (DOFs) with a pair of liquid-film bearings and a pedestal looseness fault. The motion region of the rotor system is divided into two parts: simple motion region and complex motion region. The adaptive POD method is compared with the ITGM method for the large and small spans of parameter in the two parametric regions to present the advantage of this method and disadvantage of the ITGM method. The comparisons of the responses are applied to verify the accuracy and robustness of the adaptive POD method, as well as the computational efficiency is also analyzed. As a result, the new adaptive POD method has a strong robustness and high computational efficiency and accuracy in a wide scope of parameter.

Topological analysis of group fragmentation in multiagent systems

NASA Astrophysics Data System (ADS)

DeLellis, Pietro; Porfiri, Maurizio; Bollt, Erik M.

2013-02-01

In social animals, the presence of conflicts of interest or multiple leaders can promote the emergence of two or more subgroups. Such subgroups are easily recognizable by human observers, yet a quantitative and objective measure of group fragmentation is currently lacking. In this paper, we explore the feasibility of detecting group fragmentation by embedding the raw data from the individuals' motions on a low-dimensional manifold and analyzing the topological features of this manifold. To perform the embedding, we employ the isomap algorithm, which is a data-driven machine learning tool extensively used in computer vision. We implement this procedure on a data set generated by a modified à la Vicsek model, where agents are partitioned into two or more subsets and an independent leader is assigned to each subset. The dimensionality of the embedding manifold is shown to be a measure of the number of emerging subgroups in the selected observation window and a cluster analysis is proposed to aid the interpretation of these findings. To explore the feasibility of using this approach to characterize group fragmentation in real time and thus reduce the computational cost in data processing and storage, we propose an interpolation method based on an inverse mapping from the embedding space to the original space. The effectiveness of the interpolation technique is illustrated on a test-bed example with potential impact on the regulation of collective behavior of animal groups using robotic stimuli.

Assimilation of the AVISO Altimetry Data into the Ocean Dynamics Model with a High Spatial Resolution Using Ensemble Optimal Interpolation (EnOI)

NASA Astrophysics Data System (ADS)

Kaurkin, M. N.; Ibrayev, R. A.; Belyaev, K. P.

2018-01-01

A parallel realization of the Ensemble Optimal Interpolation (EnOI) data assimilation (DA) method in conjunction with the eddy-resolving global circulation model is implemented. The results of DA experiments in the North Atlantic with the assimilation of the Archiving, Validation and Interpretation of Satellite Oceanographic (AVISO) data from the Jason-1 satellite are analyzed. The results of simulation are compared with the independent temperature and salinity data from the ARGO drifters.

A comparison of interpolation methods on the basis of data obtained from a bathymetric survey of Lake Vrana, Croatia

NASA Astrophysics Data System (ADS)

Šiljeg, A.; Lozić, S.; Šiljeg, S.

2014-12-01

The bathymetric survey of Lake Vrana included a wide range of activities that were performed in several different stages, in accordance with the standards set by the International Hydrographic Organization. The survey was conducted using an integrated measuring system which consisted of three main parts: a single-beam sonar Hydrostar 4300, GPS devices Ashtech Promark 500 - base, and a Thales Z-Max - rover. A total of 12 851 points were gathered. In order to find continuous surfaces necessary for analysing the morphology of the bed of Lake Vrana, it was necessary to approximate values in certain areas that were not directly measured, by using an appropriate interpolation method. The main aims of this research were as follows: to compare the efficiency of 16 different interpolation methods, to discover the most appropriate interpolators for the development of a raster model, to calculate the surface area and volume of Lake Vrana, and to compare the differences in calculations between separate raster models. The best deterministic method of interpolation was ROF multi-quadratic, and the best geostatistical, ordinary cokriging. The mean quadratic error in both methods measured less than 0.3 m. The quality of the interpolation methods was analysed in 2 phases. The first phase used only points gathered by bathymetric measurement, while the second phase also included points gathered by photogrammetric restitution. The first bathymetric map of Lake Vrana in Croatia was produced, as well as scenarios of minimum and maximum water levels. The calculation also included the percentage of flooded areas and cadastre plots in the case of a 2 m increase in the water level. The research presented new scientific and methodological data related to the bathymetric features, surface area and volume of Lake Vrana.

Design of interpolation functions for subpixel-accuracy stereo-vision systems.

PubMed

Haller, Istvan; Nedevschi, Sergiu

2012-02-01

Traditionally, subpixel interpolation in stereo-vision systems was designed for the block-matching algorithm. During the evaluation of different interpolation strategies, a strong correlation was observed between the type of the stereo algorithm and the subpixel accuracy of the different solutions. Subpixel interpolation should be adapted to each stereo algorithm to achieve maximum accuracy. In consequence, it is more important to propose methodologies for interpolation function generation than specific function shapes. We propose two such methodologies based on data generated by the stereo algorithms. The first proposal uses a histogram to model the environment and applies histogram equalization to an existing solution adapting it to the data. The second proposal employs synthetic images of a known environment and applies function fitting to the resulted data. The resulting function matches the algorithm and the data as best as possible. An extensive evaluation set is used to validate the findings. Both real and synthetic test cases were employed in different scenarios. The test results are consistent and show significant improvements compared with traditional solutions. © 2011 IEEE

Applications of Space-Filling-Curves to Cartesian Methods for CFD

NASA Technical Reports Server (NTRS)

Aftosmis, Michael J.; Berger, Marsha J.; Murman, Scott M.

2003-01-01

The proposed paper presents a variety novel uses of Space-Filling-Curves (SFCs) for Cartesian mesh methods in 0. While these techniques will be demonstrated using non-body-fitted Cartesian meshes, most are applicable on general body-fitted meshes -both structured and unstructured. We demonstrate the use of single O(N log N) SFC-based reordering to produce single-pass (O(N)) algorithms for mesh partitioning, multigrid coarsening, and inter-mesh interpolation. The intermesh interpolation operator has many practical applications including warm starts on modified geometry, or as an inter-grid transfer operator on remeshed regions in moving-body simulations. Exploiting the compact construction of these operators, we further show that these algorithms are highly amenable to parallelization. Examples using the SFC-based mesh partitioner show nearly linear speedup to 512 CPUs even when using multigrid as a smoother. Partition statistics are presented showing that the SFC partitions are, on-average, within 10% of ideal even with only around 50,000 cells in each subdomain. The inter-mesh interpolation operator also has linear asymptotic complexity and can be used to map a solution with N unknowns to another mesh with M unknowns with O(max(M,N)) operations. This capability is demonstrated both on moving-body simulations and in mapping solutions to perturbed meshes for finite-difference-based gradient design methods.

Noise and drift analysis of non-equally spaced timing data

NASA Technical Reports Server (NTRS)

Vernotte, F.; Zalamansky, G.; Lantz, E.

1994-01-01

Generally, it is possible to obtain equally spaced timing data from oscillators. The measurement of the drifts and noises affecting oscillators is then performed by using a variance (Allan variance, modified Allan variance, or time variance) or a system of several variances (multivariance method). However, in some cases, several samples, or even several sets of samples, are missing. In the case of millisecond pulsar timing data, for instance, observations are quite irregularly spaced in time. Nevertheless, since some observations are very close together (one minute) and since the timing data sequence is very long (more than ten years), information on both short-term and long-term stability is available. Unfortunately, a direct variance analysis is not possible without interpolating missing data. Different interpolation algorithms (linear interpolation, cubic spline) are used to calculate variances in order to verify that they neither lose information nor add erroneous information. A comparison of the results of the different algorithms is given. Finally, the multivariance method was adapted to the measurement sequence of the millisecond pulsar timing data: the responses of each variance of the system are calculated for each type of noise and drift, with the same missing samples as in the pulsar timing sequence. An estimation of precision, dynamics, and separability of this method is given.

Evaluation of interpolation methods for surface-based motion compensated tomographic reconstruction for cardiac angiographic C-arm data

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mueller, Kerstin; Schwemmer, Chris; Hornegger, Joachim

2013-03-15

Purpose: For interventional cardiac procedures, anatomical and functional information about the cardiac chambers is of major interest. With the technology of angiographic C-arm systems it is possible to reconstruct intraprocedural three-dimensional (3D) images from 2D rotational angiographic projection data (C-arm CT). However, 3D reconstruction of a dynamic object is a fundamental problem in C-arm CT reconstruction. The 2D projections are acquired over a scan time of several seconds, thus the projection data show different states of the heart. A standard FDK reconstruction algorithm would use all acquired data for a filtered backprojection and result in a motion-blurred image. In thismore » approach, a motion compensated reconstruction algorithm requiring knowledge of the 3D heart motion is used. The motion is estimated from a previously presented 3D dynamic surface model. This dynamic surface model results in a sparse motion vector field (MVF) defined at control points. In order to perform a motion compensated reconstruction, a dense motion vector field is required. The dense MVF is generated by interpolation of the sparse MVF. Therefore, the influence of different motion interpolation methods on the reconstructed image quality is evaluated. Methods: Four different interpolation methods, thin-plate splines (TPS), Shepard's method, a smoothed weighting function, and a simple averaging, were evaluated. The reconstruction quality was measured on phantom data, a porcine model as well as on in vivo clinical data sets. As a quality index, the 2D overlap of the forward projected motion compensated reconstructed ventricle and the segmented 2D ventricle blood pool was quantitatively measured with the Dice similarity coefficient and the mean deviation between extracted ventricle contours. For the phantom data set, the normalized root mean square error (nRMSE) and the universal quality index (UQI) were also evaluated in 3D image space. Results: The quantitative evaluation of all experiments showed that TPS interpolation provided the best results. The quantitative results in the phantom experiments showed comparable nRMSE of Almost-Equal-To 0.047 {+-} 0.004 for the TPS and Shepard's method. Only slightly inferior results for the smoothed weighting function and the linear approach were achieved. The UQI resulted in a value of Almost-Equal-To 99% for all four interpolation methods. On clinical human data sets, the best results were clearly obtained with the TPS interpolation. The mean contour deviation between the TPS reconstruction and the standard FDK reconstruction improved in the three human cases by 1.52, 1.34, and 1.55 mm. The Dice coefficient showed less sensitivity with respect to variations in the ventricle boundary. Conclusions: In this work, the influence of different motion interpolation methods on left ventricle motion compensated tomographic reconstructions was investigated. The best quantitative reconstruction results of a phantom, a porcine, and human clinical data sets were achieved with the TPS approach. In general, the framework of motion estimation using a surface model and motion interpolation to a dense MVF provides the ability for tomographic reconstruction using a motion compensation technique.« less

Modified Gompertz equation for electrotherapy murine tumor growth kinetics: predictions and new hypotheses

PubMed Central

2010-01-01

Background Electrotherapy effectiveness at different doses has been demonstrated in preclinical and clinical studies; however, several aspects that occur in the tumor growth kinetics before and after treatment have not yet been revealed. Mathematical modeling is a useful instrument that can reveal some of these aspects. The aim of this paper is to describe the complete growth kinetics of unperturbed and perturbed tumors through use of the modified Gompertz equation in order to generate useful insight into the mechanisms that underpin this devastating disease. Methods The complete tumor growth kinetics for control and treated groups are obtained by interpolation and extrapolation methods with different time steps, using experimental data of fibrosarcoma Sa-37. In the modified Gompertz equation, a delay time is introduced to describe the tumor's natural history before treatment. Different graphical strategies are used in order to reveal new information in the complete kinetics of this tumor type. Results The first stage of complete tumor growth kinetics is highly non linear. The model, at this stage, shows different aspects that agree with those reported theoretically and experimentally. Tumor reversibility and the proportionality between regions before and after electrotherapy are demonstrated. In tumors that reach partial remission, two antagonistic post-treatment processes are induced, whereas in complete remission, two unknown antitumor mechanisms are induced. Conclusion The modified Gompertz equation is likely to lead to insights within cancer research. Such insights hold promise for increasing our understanding of tumors as self-organizing systems and, the possible existence of phase transitions in tumor growth kinetics, which, in turn, may have significant impacts both on cancer research and on clinical practice. PMID:21029411

Selection of a Geostatistical Method to Interpolate Soil Properties of the State Crop Testing Fields using Attributes of a Digital Terrain Model

NASA Astrophysics Data System (ADS)

Sahabiev, I. A.; Ryazanov, S. S.; Kolcova, T. G.; Grigoryan, B. R.

2018-03-01

The three most common techniques to interpolate soil properties at a field scale—ordinary kriging (OK), regression kriging with multiple linear regression drift model (RK + MLR), and regression kriging with principal component regression drift model (RK + PCR)—were examined. The results of the performed study were compiled into an algorithm of choosing the most appropriate soil mapping technique. Relief attributes were used as the auxiliary variables. When spatial dependence of a target variable was strong, the OK method showed more accurate interpolation results, and the inclusion of the auxiliary data resulted in an insignificant improvement in prediction accuracy. According to the algorithm, the RK + PCR method effectively eliminates multicollinearity of explanatory variables. However, if the number of predictors is less than ten, the probability of multicollinearity is reduced, and application of the PCR becomes irrational. In that case, the multiple linear regression should be used instead.

Accuracy of parameterized proton range models; A comparison

NASA Astrophysics Data System (ADS)

Pettersen, H. E. S.; Chaar, M.; Meric, I.; Odland, O. H.; Sølie, J. R.; Röhrich, D.

2018-03-01

An accurate calculation of proton ranges in phantoms or detector geometries is crucial for decision making in proton therapy and proton imaging. To this end, several parameterizations of the range-energy relationship exist, with different levels of complexity and accuracy. In this study we compare the accuracy of four different parameterizations models for proton range in water: Two analytical models derived from the Bethe equation, and two different interpolation schemes applied to range-energy tables. In conclusion, a spline interpolation scheme yields the highest reproduction accuracy, while the shape of the energy loss-curve is best reproduced with the differentiated Bragg-Kleeman equation.

An operator calculus for surface and volume modeling

NASA Technical Reports Server (NTRS)

Gordon, W. J.

1984-01-01

The mathematical techniques which form the foundation for most of the surface and volume modeling techniques used in practice are briefly described. An outline of what may be termed an operator calculus for the approximation and interpolation of functions of more than one independent variable is presented. By considering the linear operators associated with bivariate and multivariate interpolation/approximation schemes, it is shown how they can be compounded by operator multiplication and Boolean addition to obtain a distributive lattice of approximation operators. It is then demonstrated via specific examples how this operator calculus leads to practical techniques for sculptured surface and volume modeling.

An adaptive interpolation scheme for molecular potential energy surfaces

NASA Astrophysics Data System (ADS)

Kowalewski, Markus; Larsson, Elisabeth; Heryudono, Alfa

2016-08-01

The calculation of potential energy surfaces for quantum dynamics can be a time consuming task—especially when a high level of theory for the electronic structure calculation is required. We propose an adaptive interpolation algorithm based on polyharmonic splines combined with a partition of unity approach. The adaptive node refinement allows to greatly reduce the number of sample points by employing a local error estimate. The algorithm and its scaling behavior are evaluated for a model function in 2, 3, and 4 dimensions. The developed algorithm allows for a more rapid and reliable interpolation of a potential energy surface within a given accuracy compared to the non-adaptive version.

Turning Avatar into Realistic Human Expression Using Linear and Bilinear Interpolations

NASA Astrophysics Data System (ADS)

Hazim Alkawaz, Mohammed; Mohamad, Dzulkifli; Rehman, Amjad; Basori, Ahmad Hoirul

2014-06-01

The facial animation in term of 3D facial data has accurate research support of the laser scan and advance 3D tools for complex facial model production. However, the approach still lacks facial expression based on emotional condition. Though, facial skin colour is required to offers an effect of facial expression improvement, closely related to the human emotion. This paper presents innovative techniques for facial animation transformation using the facial skin colour based on linear interpolation and bilinear interpolation. The generated expressions are almost same to the genuine human expression and also enhance the facial expression of the virtual human.

Interpolation Environment of Tensor Mathematics at the Corpuscular Stage of Computational Experiments in Hydromechanics

NASA Astrophysics Data System (ADS)

Bogdanov, Alexander; Degtyarev, Alexander; Khramushin, Vasily; Shichkina, Yulia

2018-02-01

Stages of direct computational experiments in hydromechanics based on tensor mathematics tools are represented by conditionally independent mathematical models for calculations separation in accordance with physical processes. Continual stage of numerical modeling is constructed on a small time interval in a stationary grid space. Here coordination of continuity conditions and energy conservation is carried out. Then, at the subsequent corpuscular stage of the computational experiment, kinematic parameters of mass centers and surface stresses at the boundaries of the grid cells are used in modeling of free unsteady motions of volume cells that are considered as independent particles. These particles can be subject to vortex and discontinuous interactions, when restructuring of free boundaries and internal rheological states has place. Transition from one stage to another is provided by interpolation operations of tensor mathematics. Such interpolation environment formalizes the use of physical laws for mechanics of continuous media modeling, provides control of rheological state and conditions for existence of discontinuous solutions: rigid and free boundaries, vortex layers, their turbulent or empirical generalizations.

Elastic-wave-mode separation in TTI media with inverse-distance weighted interpolation involving position shading

NASA Astrophysics Data System (ADS)

Wang, Jian; Meng, Xiaohong; Zheng, Wanqiu

2017-10-01

The elastic-wave reverse-time migration of inhomogeneous anisotropic media is becoming the hotspot of research today. In order to ensure the accuracy of the migration, it is necessary to separate the wave mode into P-wave and S-wave before migration. For inhomogeneous media, the Kelvin-Christoffel equation can be solved in the wave-number domain by using the anisotropic parameters of the mesh nodes, and the polarization vector of the P-wave and S-wave at each node can be calculated and transformed into the space domain to obtain the quasi-differential operators. However, this method is computationally expensive, especially for the process of quasi-differential operators. In order to reduce the computational complexity, the wave-mode separation of mixed domain can be realized on the basis of a reference model in the wave-number domain. But conventional interpolation methods and reference model selection methods reduce the separation accuracy. In order to further improve the separation effect, this paper introduces an inverse-distance interpolation method involving position shading and uses the reference model selection method of random points scheme. This method adds the spatial weight coefficient K, which reflects the orientation of the reference point on the conventional IDW algorithm, and the interpolation process takes into account the combined effects of the distance and azimuth of the reference points. Numerical simulation shows that the proposed method can separate the wave mode more accurately using fewer reference models and has better practical value.

Analysis and simulation of wireless signal propagation applying geostatistical interpolation techniques

NASA Astrophysics Data System (ADS)

Kolyaie, S.; Yaghooti, M.; Majidi, G.

2011-12-01

This paper is a part of an ongoing research to examine the capability of geostatistical analysis for mobile networks coverage prediction, simulation and tuning. Mobile network coverage predictions are used to find network coverage gaps and areas with poor serviceability. They are essential data for engineering and management in order to make better decision regarding rollout, planning and optimisation of mobile networks.The objective of this research is to evaluate different interpolation techniques in coverage prediction. In method presented here, raw data collected from drive testing a sample of roads in study area is analysed and various continuous surfaces are created using different interpolation methods. Two general interpolation methods are used in this paper with different variables; first, Inverse Distance Weighting (IDW) with various powers and number of neighbours and second, ordinary kriging with Gaussian, spherical, circular and exponential semivariogram models with different number of neighbours. For the result comparison, we have used check points coming from the same drive test data. Prediction values for check points are extracted from each surface and the differences with actual value are computed. The output of this research helps finding an optimised and accurate model for coverage prediction.

A Modified Kirchhoff plate theory for Free Vibration analysis of functionally graded material plates using meshfree method

NASA Astrophysics Data System (ADS)

Nguyen Van Do, Vuong

2018-04-01

In this paper, a modified Kirchhoff theory is presented for free vibration analyses of functionally graded material (FGM) plate based on modified radial point interpolation method (RPIM). The shear deformation effects are taken account into modified theory to ignore the locking phenomenon of thin plates. Due to the proposed refined plate theory, the number of independent unknowns reduces one variable and exists with four degrees of freedom per node. The simulated free vibration results employed by the modified RPIM are compared with the other analytical solutions to verify the effectiveness and the accuracy of the developed mesh-free method. Detail parametric studies of the proposed method are then conducted including the effectiveness of thickness ratio, boundary condition and material inhomogeneity on the sample problems of square plates. Results illustrated that the modified mesh-free RPIM can effectively predict the numerical calculation as compared to the exact solutions. The obtained numerical results are indicated that the proposed method are stable and well accurate prediction to evaluate with other published analyses.

Topsoil pollution forecasting using artificial neural networks on the example of the abnormally distributed heavy metal at Russian subarctic

NASA Astrophysics Data System (ADS)

Tarasov, D. A.; Buevich, A. G.; Sergeev, A. P.; Shichkin, A. V.; Baglaeva, E. M.

2017-06-01

Forecasting the soil pollution is a considerable field of study in the light of the general concern of environmental protection issues. Due to the variation of content and spatial heterogeneity of pollutants distribution at urban areas, the conventional spatial interpolation models implemented in many GIS packages mostly cannot provide appreciate interpolation accuracy. Moreover, the problem of prediction the distribution of the element with high variability in the concentration at the study site is particularly difficult. The work presents two neural networks models forecasting a spatial content of the abnormally distributed soil pollutant (Cr) at a particular location of the subarctic Novy Urengoy, Russia. A method of generalized regression neural network (GRNN) was compared to a common multilayer perceptron (MLP) model. The proposed techniques have been built, implemented and tested using ArcGIS and MATLAB. To verify the models performances, 150 scattered input data points (pollutant concentrations) have been selected from 8.5 km2 area and then split into independent training data set (105 points) and validation data set (45 points). The training data set was generated for the interpolation using ordinary kriging while the validation data set was used to test their accuracies. The networks structures have been chosen during a computer simulation based on the minimization of the RMSE. The predictive accuracy of both models was confirmed to be significantly higher than those achieved by the geostatistical approach (kriging). It is shown that MLP could achieve better accuracy than both kriging and even GRNN for interpolating surfaces.

High-resolution daily gridded data sets of air temperature and wind speed for Europe

NASA Astrophysics Data System (ADS)

Brinckmann, Sven; Krähenmann, Stefan; Bissolli, Peter

2016-10-01

New high-resolution data sets for near-surface daily air temperature (minimum, maximum and mean) and daily mean wind speed for Europe (the CORDEX domain) are provided for the period 2001-2010 for the purpose of regional model validation in the framework of DecReg, a sub-project of the German MiKlip project, which aims to develop decadal climate predictions. The main input data sources are SYNOP observations, partly supplemented by station data from the ECA&D data set (http://www.ecad.eu). These data are quality tested to eliminate erroneous data. By spatial interpolation of these station observations, grid data in a resolution of 0.044° (≈ 5km) on a rotated grid with virtual North Pole at 39.25° N, 162° W are derived. For temperature interpolation a modified version of a regression kriging method developed by Krähenmann et al.(2011) is used. At first, predictor fields of altitude, continentality and zonal mean temperature are used for a regression applied to monthly station data. The residuals of the monthly regression and the deviations of the daily data from the monthly averages are interpolated using simple kriging in a second and third step. For wind speed a new method based on the concept used for temperature was developed, involving predictor fields of exposure, roughness length, coastal distance and ERA-Interim reanalysis wind speed at 850 hPa. Interpolation uncertainty is estimated by means of the kriging variance and regression uncertainties. Furthermore, to assess the quality of the final daily grid data, cross validation is performed. Variance explained by the regression ranges from 70 to 90 % for monthly temperature and from 50 to 60 % for monthly wind speed. The resulting RMSE for the final daily grid data amounts to 1-2 K and 1-1.5 ms-1 (depending on season and parameter) for daily temperature parameters and daily mean wind speed, respectively. The data sets presented in this article are published at doi:10.5676/DWD_CDC/DECREG0110v2.

Population at risk: using areal interpolation and Twitter messages to create population models for burglaries and robberies

PubMed Central

2018-01-01

ABSTRACT Population at risk of crime varies due to the characteristics of a population as well as the crime generator and attractor places where crime is located. This establishes different crime opportunities for different crimes. However, there are very few efforts of modeling structures that derive spatiotemporal population models to allow accurate assessment of population exposure to crime. This study develops population models to depict the spatial distribution of people who have a heightened crime risk for burglaries and robberies. The data used in the study include: Census data as source data for the existing population, Twitter geo-located data, and locations of schools as ancillary data to redistribute the source data more accurately in the space, and finally gridded population and crime data to evaluate the derived population models. To create the models, a density-weighted areal interpolation technique was used that disaggregates the source data in smaller spatial units considering the spatial distribution of the ancillary data. The models were evaluated with validation data that assess the interpolation error and spatial statistics that examine their relationship with the crime types. Our approach derived population models of a finer resolution that can assist in more precise spatial crime analyses and also provide accurate information about crime rates to the public. PMID:29887766

SU-F-T-143: Implementation of a Correction-Based Output Model for a Compact Passively Scattered Proton Therapy System

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ferguson, S; Ahmad, S; Chen, Y

2016-06-15

Purpose: To commission and investigate the accuracy of an output (cGy/MU) prediction model for a compact passively scattered proton therapy system. Methods: A previously published output prediction model (Sahoo et al, Med Phys, 35, 5088–5097, 2008) was commissioned for our Mevion S250 proton therapy system. This model is a correction-based model that multiplies correction factors (d/MUwnc=ROFxSOBPF xRSFxSOBPOCFxOCRxFSFxISF). These factors accounted for changes in output due to options (12 large, 5 deep, and 7 small), modulation width M, range R, off-center, off-axis, field-size, and off-isocenter. In this study, the model was modified to ROFxSOBPFxRSFxOCRxFSFxISF-OCFxGACF by merging SOBPOCF and ISF for simplicitymore » and introducing a gantry angle correction factor (GACF). To commission the model, outputs over 1,000 data points were taken at the time of the system commissioning. The output was predicted by interpolation (1D for SOBPF, FSF, and GACF; 2D for RSF and OCR) with inverse-square calculation (ISF-OCR). The outputs of 273 combinations of R and M covering total 24 options were measured to test the model. To minimize fluence perturbation, scattered dose from range compensator and patient was not considered. The percent differences between the predicted (P) and measured (M) outputs were calculated to test the prediction accuracy ([P-M]/Mx100%). Results: GACF was required because of up to 3.5% output variation dependence on the gantry angle. A 2D interpolation was required for OCR because the dose distribution was not radially symmetric especially for the deep options. The average percent differences were −0.03±0.98% (mean±SD) and the differences of all the measurements fell within ±3%. Conclusion: It is concluded that the model can be clinically used for the compact passively scattered proton therapy system. However, great care should be taken when the field-size is less than 5×5 cm{sup 2} where a direct output measurement is required due to substantial output change by irregular block shape.« less

Performance of Statistical Temporal Downscaling Techniques of Wind Speed Data Over Aegean Sea

NASA Astrophysics Data System (ADS)

Gokhan Guler, Hasan; Baykal, Cuneyt; Ozyurt, Gulizar; Kisacik, Dogan

2016-04-01

Wind speed data is a key input for many meteorological and engineering applications. Many institutions provide wind speed data with temporal resolutions ranging from one hour to twenty four hours. Higher temporal resolution is generally required for some applications such as reliable wave hindcasting studies. One solution to generate wind data at high sampling frequencies is to use statistical downscaling techniques to interpolate values of the finer sampling intervals from the available data. In this study, the major aim is to assess temporal downscaling performance of nine statistical interpolation techniques by quantifying the inherent uncertainty due to selection of different techniques. For this purpose, hourly 10-m wind speed data taken from 227 data points over Aegean Sea between 1979 and 2010 having a spatial resolution of approximately 0.3 degrees are analyzed from the National Centers for Environmental Prediction (NCEP) The Climate Forecast System Reanalysis database. Additionally, hourly 10-m wind speed data of two in-situ measurement stations between June, 2014 and June, 2015 are considered to understand effect of dataset properties on the uncertainty generated by interpolation technique. In this study, nine statistical interpolation techniques are selected as w0 (left constant) interpolation, w6 (right constant) interpolation, averaging step function interpolation, linear interpolation, 1D Fast Fourier Transform interpolation, 2nd and 3rd degree Lagrange polynomial interpolation, cubic spline interpolation, piecewise cubic Hermite interpolating polynomials. Original data is down sampled to 6 hours (i.e. wind speeds at 0th, 6th, 12th and 18th hours of each day are selected), then 6 hourly data is temporally downscaled to hourly data (i.e. the wind speeds at each hour between the intervals are computed) using nine interpolation technique, and finally original data is compared with the temporally downscaled data. A penalty point system based on coefficient of variation root mean square error, normalized mean absolute error, and prediction skill is selected to rank nine interpolation techniques according to their performance. Thus, error originated from the temporal downscaling technique is quantified which is an important output to determine wind and wave modelling uncertainties, and the performance of these techniques are demonstrated over Aegean Sea indicating spatial trends and discussing relevance to data type (i.e. reanalysis data or in-situ measurements). Furthermore, bias introduced by the best temporal downscaling technique is discussed. Preliminary results show that overall piecewise cubic Hermite interpolating polynomials have the highest performance to temporally downscale wind speed data for both reanalysis data and in-situ measurements over Aegean Sea. However, it is observed that cubic spline interpolation performs much better along Aegean coastline where the data points are close to the land. Acknowledgement: This research was partly supported by TUBITAK Grant number 213M534 according to Turkish Russian Joint research grant with RFBR and the CoCoNET (Towards Coast to Coast Network of Marine Protected Areas Coupled by Wİnd Energy Potential) project funded by European Union FP7/2007-2013 program.

Improved interpolation of meteorological forcings for hydrologic applications in a Swiss Alpine region

NASA Astrophysics Data System (ADS)

Tobin, Cara; Nicotina, Ludovico; Parlange, Marc B.; Berne, Alexis; Rinaldo, Andrea

2011-04-01

SummaryThis paper presents a comparative study on the mapping of temperature and precipitation fields in complex Alpine terrain. Its relevance hinges on the major impact that inadequate interpolations of meteorological forcings bear on the accuracy of hydrologic predictions regardless of the specifics of the models, particularly during flood events. Three flood events measured in the Swiss Alps are analyzed in detail to determine the interpolation methods which best capture the distribution of intense, orographically-induced precipitation. The interpolation techniques comparatively examined include: Inverse Distance Weighting (IDW), Ordinary Kriging (OK), and Kriging with External Drift (KED). Geostatistical methods rely on a robust anisotropic variogram for the definition of the spatial rainfall structure. Results indicate that IDW tends to significantly underestimate rainfall volumes whereas OK and KED methods capture spatial patterns and rainfall volumes induced by storm advection. Using numerical weather forecasts and elevation data as covariates for precipitation, we provide evidence for KED to outperform the other methods. Most significantly, the use of elevation as auxiliary information in KED of temperatures demonstrates minimal errors in estimated instantaneous rainfall volumes and provides instantaneous lapse rates which better capture snow/rainfall partitioning. Incorporation of the temperature and precipitation input fields into a hydrological model used for operational management was found to provide vastly improved outputs with respect to measured discharge volumes and flood peaks, with notable implications for flood modeling.

Validation of the Soil Moisture Active Passive (SMAP) satellite soil moisture retrieval in an Arctic tundra environment

NASA Astrophysics Data System (ADS)

Wrona, Elizabeth; Rowlandson, Tracy L.; Nambiar, Manoj; Berg, Aaron A.; Colliander, Andreas; Marsh, Philip

2017-05-01

This study examines the Soil Moisture Active Passive soil moisture product on the Equal Area Scalable Earth-2 (EASE-2) 36 km Global cylindrical and North Polar azimuthal grids relative to two in situ soil moisture monitoring networks that were installed in 2015 and 2016. Results indicate that there is no relationship between the Soil Moisture Active Passive (SMAP) Level-2 passive soil moisture product and the upscaled in situ measurements. Additionally, there is very low correlation between modeled brightness temperature using the Community Microwave Emission Model and the Level-1 C SMAP brightness temperature interpolated to the EASE-2 Global grid; however, there is a much stronger relationship to the brightness temperature measurements interpolated to the North Polar grid, suggesting that the soil moisture product could be improved with interpolation on the North Polar grid.

CONORBIT: constrained optimization by radial basis function interpolation in trust regions

DOE PAGES

Regis, Rommel G.; Wild, Stefan M.

2016-09-26

Here, this paper presents CONORBIT (CONstrained Optimization by Radial Basis function Interpolation in Trust regions), a derivative-free algorithm for constrained black-box optimization where the objective and constraint functions are computationally expensive. CONORBIT employs a trust-region framework that uses interpolating radial basis function (RBF) models for the objective and constraint functions, and is an extension of the ORBIT algorithm. It uses a small margin for the RBF constraint models to facilitate the generation of feasible iterates, and extensive numerical tests confirm that such a margin is helpful in improving performance. CONORBIT is compared with other algorithms on 27 test problems, amore » chemical process optimization problem, and an automotive application. Numerical results show that CONORBIT performs better than COBYLA, a sequential penalty derivative-free method, an augmented Lagrangian method, a direct search method, and another RBF-based algorithm on the test problems and on the automotive application.« less

Sedna and the cloud of comets surrounding the solar system in Milgromian dynamics

NASA Astrophysics Data System (ADS)

Paučo, R.; Klačka, J.

2016-05-01

We reconsider the hypothesis of a vast cometary reservoir surrounding the solar system - the Oort cloud of comets - within the framework of Milgromian dynamics (MD or MOND). For this purpose we built a numerical model of the cloud, assuming the theory of modified gravity, QUMOND. In modified gravity versions of MD, the internal dynamics of a system is influenced by the external gravitational field in which the system is embedded, even when this external field is constant and uniform, a phenomenon dubbed the external field effect (EFE). Adopting the popular pair ν(x) = [1-exp(-x1 / 2)] -1 for the MD interpolating function and a0 = 1.2 × 10-10 m s-2 for the MD acceleration scale, we found that the observationally inferred Milgromian cloud of comets is much more radially compact than its Newtonian counterpart. The comets of the Milgromian cloud stay away from the zone where the Galactic tide can torque their orbits significantly. However, this does not need to be an obstacle for the injection of the comets into the inner solar system as the EFE can induce significant change in perihelion distance during one revolution of a comet around the Sun. Adopting constraints on different interpolating function families and a revised value of a0 (provided recently by the Cassini spacecraft), the aforementioned qualitative results no longer hold, and, in conclusion, the Milgromian cloud is very similar to the Newtonian in its overall size, binding energies of comets and hence the operation of the Jupiter-Saturn barrier. However, EFE torquing of perihelia still play a significant role in the inner parts of the cloud. Consequently Sedna-like orbits and orbits of large semi-major axis Centaurs are easily comprehensible in MD. In MD, they both belong to the same population, just in different modes of their evolution.

Data-Driven Haptic Modeling and Rendering of Viscoelastic and Frictional Responses of Deformable Objects.

PubMed

Yim, Sunghoon; Jeon, Seokhee; Choi, Seungmoon

2016-01-01

In this paper, we present an extended data-driven haptic rendering method capable of reproducing force responses during pushing and sliding interaction on a large surface area. The main part of the approach is a novel input variable set for the training of an interpolation model, which incorporates the position of a proxy - an imaginary contact point on the undeformed surface. This allows us to estimate friction in both sliding and sticking states in a unified framework. Estimating the proxy position is done in real-time based on simulation using a sliding yield surface - a surface defining a border between the sliding and sticking regions in the external force space. During modeling, the sliding yield surface is first identified via an automated palpation procedure. Then, through manual palpation on a target surface, input data and resultant force data are acquired. The data are used to build a radial basis interpolation model. During rendering, this input-output mapping interpolation model is used to estimate force responses in real-time in accordance with the interaction input. Physical performance evaluation demonstrates that our approach achieves reasonably high estimation accuracy. A user study also shows plausible perceptual realism under diverse and extensive exploration.

Interpolation of diffusion weighted imaging datasets.

PubMed

Dyrby, Tim B; Lundell, Henrik; Burke, Mark W; Reislev, Nina L; Paulson, Olaf B; Ptito, Maurice; Siebner, Hartwig R

2014-12-01

Diffusion weighted imaging (DWI) is used to study white-matter fibre organisation, orientation and structural connectivity by means of fibre reconstruction algorithms and tractography. For clinical settings, limited scan time compromises the possibilities to achieve high image resolution for finer anatomical details and signal-to-noise-ratio for reliable fibre reconstruction. We assessed the potential benefits of interpolating DWI datasets to a higher image resolution before fibre reconstruction using a diffusion tensor model. Simulations of straight and curved crossing tracts smaller than or equal to the voxel size showed that conventional higher-order interpolation methods improved the geometrical representation of white-matter tracts with reduced partial-volume-effect (PVE), except at tract boundaries. Simulations and interpolation of ex-vivo monkey brain DWI datasets revealed that conventional interpolation methods fail to disentangle fine anatomical details if PVE is too pronounced in the original data. As for validation we used ex-vivo DWI datasets acquired at various image resolutions as well as Nissl-stained sections. Increasing the image resolution by a factor of eight yielded finer geometrical resolution and more anatomical details in complex regions such as tract boundaries and cortical layers, which are normally only visualized at higher image resolutions. Similar results were found with typical clinical human DWI dataset. However, a possible bias in quantitative values imposed by the interpolation method used should be considered. The results indicate that conventional interpolation methods can be successfully applied to DWI datasets for mining anatomical details that are normally seen only at higher resolutions, which will aid in tractography and microstructural mapping of tissue compartments. Copyright © 2014. Published by Elsevier Inc.

Color management with a hammer: the B-spline fitter

NASA Astrophysics Data System (ADS)

Bell, Ian E.; Liu, Bonny H. P.

2003-01-01

To paraphrase Abraham Maslow: If the only tool you have is a hammer, every problem looks like a nail. We have a B-spline fitter customized for 3D color data, and many problems in color management can be solved with this tool. Whereas color devices were once modeled with extensive measurement, look-up tables and trilinear interpolation, recent improvements in hardware have made B-spline models an affordable alternative. Such device characterizations require fewer color measurements than piecewise linear models, and have uses beyond simple interpolation. A B-spline fitter, for example, can act as a filter to remove noise from measurements, leaving a model with guaranteed smoothness. Inversion of the device model can then be carried out consistently and efficiently, as the spline model is well behaved and its derivatives easily computed. Spline-based algorithms also exist for gamut mapping, the composition of maps, and the extrapolation of a gamut. Trilinear interpolation---a degree-one spline---can still be used after nonlinear spline smoothing for high-speed evaluation with robust convergence. Using data from several color devices, this paper examines the use of B-splines as a generic tool for modeling devices and mapping one gamut to another, and concludes with applications to high-dimensional and spectral data.

Investigation of Back-off Based Interpolation Between Recurrent Neural Network and N-gram Language Models (Author’s Manuscript)

DTIC Science & Technology

2016-02-11

INVESTIGATION OF BACK-OFF BASED INTERPOLATION BETWEEN RECURRENT NEURAL NETWORK AND N- GRAM LANGUAGE MODELS X. Chen, X. Liu, M. J. F. Gales, and P. C...As the gener- alization patterns of RNNLMs and n- gram LMs are inherently dif- ferent, RNNLMs are usually combined with n- gram LMs via a fixed...RNNLMs and n- gram LMs as n- gram level changes. In order to fully exploit the detailed n- gram level comple- mentary attributes between the two LMs, a

Development of the general interpolants method for the CYBER 200 series of supercomputers

NASA Technical Reports Server (NTRS)

Stalnaker, J. F.; Robinson, M. A.; Spradley, L. W.; Kurzius, S. C.; Thoenes, J.

1988-01-01

The General Interpolants Method (GIM) is a 3-D, time-dependent, hybrid procedure for generating numerical analogs of the conservation laws. This study is directed toward the development and application of the GIM computer code for fluid dynamic research applications as implemented for the Cyber 200 series of supercomputers. An elliptic and quasi-parabolic version of the GIM code are discussed. Turbulence models, algebraic and differential equations, were added to the basic viscous code. An equilibrium reacting chemistry model and an implicit finite difference scheme are also included.

A two-dimensional numerical study of the flow inside the combustion chambers of a motored rotary engine

NASA Technical Reports Server (NTRS)

Shih, T. I. P.; Yang, S. L.; Schock, H. J.

1986-01-01

A numerical study was performed to investigate the unsteady, multidimensional flow inside the combustion chambers of an idealized, two-dimensional, rotary engine under motored conditions. The numerical study was based on the time-dependent, two-dimensional, density-weighted, ensemble-averaged conservation equations of mass, species, momentum, and total energy valid for two-component ideal gas mixtures. The ensemble-averaged conservation equations were closed by a K-epsilon model of turbulence. This K-epsilon model of turbulence was modified to account for some of the effects of compressibility, streamline curvature, low-Reynolds number, and preferential stress dissipation. Numerical solutions to the conservation equations were obtained by the highly efficient implicit-factored method of Beam and Warming. The grid system needed to obtain solutions were generated by an algebraic grid generation technique based on transfinite interpolation. Results of the numerical study are presented in graphical form illustrating the flow patterns during intake, compression, gaseous fuel injection, expansion, and exhaust.

A two-dimensional numerical study of the flow inside the combustion chamber of a motored rotary engine

NASA Technical Reports Server (NTRS)

Shih, T. I-P.; Yang, S. L.; Schock, H. J.

1986-01-01

A numerical study was performed to investigate the unsteady, multidimensional flow inside the combustion chambers of an idealized, two-dimensional, rotary engine under motored conditions. The numerical study was based on the time-dependent, two-dimensional, density-weighted, ensemble-averaged conservation equations of mass, species, momentum, and total energy valid for two-component ideal gas mixtures. The ensemble-averaged conservation equations were closed by a K-epsilon model of turbulence. This K-epsilon model of turbulence was modified to account for some of the effects of compressibility, streamline curvature, low-Reynolds number, and preferential stress dissipation. Numerical solutions to the conservation equations were obtained by the highly efficient implicit-factored method of Beam and Warming. The grid system needed to obtain solutions were generated by an algebraic grid generation technique based on transfinite interpolation. Results of the numerical study are presented in graphical form illustrating the flow patterns during intake, compression, gaseous fuel injection, expansion, and exhaust.

The moving-least-squares-particle hydrodynamics method (MLSPH)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dilts, G.

1997-12-31

An enhancement of the smooth-particle hydrodynamics (SPH) method has been developed using the moving-least-squares (MLS) interpolants of Lancaster and Salkauskas which simultaneously relieves the method of several well-known undesirable behaviors, including spurious boundary effects, inaccurate strain and rotation rates, pressure spikes at impact boundaries, and the infamous tension instability. The classical SPH method is derived in a novel manner by means of a Galerkin approximation applied to the Lagrangian equations of motion for continua using as basis functions the SPH kernel function multiplied by the particle volume. This derivation is then modified by simply substituting the MLS interpolants for themore » SPH Galerkin basis, taking care to redefine the particle volume and mass appropriately. The familiar SPH kernel approximation is now equivalent to a colocation-Galerkin method. Both classical conservative and recent non-conservative formulations of SPH can be derived and emulated. The non-conservative forms can be made conservative by adding terms that are zero within the approximation at the expense of boundary-value considerations. The familiar Monaghan viscosity is used. Test calculations of uniformly expanding fluids, the Swegle example, spinning solid disks, impacting bars, and spherically symmetric flow illustrate the superiority of the technique over SPH. In all cases it is seen that the marvelous ability of the MLS interpolants to add up correctly everywhere civilizes the noisy, unpredictable nature of SPH. Being a relatively minor perturbation of the SPH method, it is easily retrofitted into existing SPH codes. On the down side, computational expense at this point is significant, the Monaghan viscosity undoes the contribution of the MLS interpolants, and one-point quadrature (colocation) is not accurate enough. Solutions to these difficulties are being pursued vigorously.« less

Ab initio potential-energy surfaces for complex, multichannel systems using modified novelty sampling and feedforward neural networks

NASA Astrophysics Data System (ADS)

Raff, L. M.; Malshe, M.; Hagan, M.; Doughan, D. I.; Rockley, M. G.; Komanduri, R.

2005-02-01

A neural network/trajectory approach is presented for the development of accurate potential-energy hypersurfaces that can be utilized to conduct ab initio molecular dynamics (AIMD) and Monte Carlo studies of gas-phase chemical reactions, nanometric cutting, and nanotribology, and of a variety of mechanical properties of importance in potential microelectromechanical systems applications. The method is sufficiently robust that it can be applied to a wide range of polyatomic systems. The overall method integrates ab initio electronic structure calculations with importance sampling techniques that permit the critical regions of configuration space to be determined. The computed ab initio energies and gradients are then accurately interpolated using neural networks (NN) rather than arbitrary parametrized analytical functional forms, moving interpolation or least-squares methods. The sampling method involves a tight integration of molecular dynamics calculations with neural networks that employ early stopping and regularization procedures to improve network performance and test for convergence. The procedure can be initiated using an empirical potential surface or direct dynamics. The accuracy and interpolation power of the method has been tested for two cases, the global potential surface for vinyl bromide undergoing unimolecular decomposition via four different reaction channels and nanometric cutting of silicon. The results show that the sampling methods permit the important regions of configuration space to be easily and rapidly identified, that convergence of the NN fit to the ab initio electronic structure database can be easily monitored, and that the interpolation accuracy of the NN fits is excellent, even for systems involving five atoms or more. The method permits a substantial computational speed and accuracy advantage over existing methods, is robust, and relatively easy to implement.

Modelling vertical error in LiDAR-derived digital elevation models

NASA Astrophysics Data System (ADS)

Aguilar, Fernando J.; Mills, Jon P.; Delgado, Jorge; Aguilar, Manuel A.; Negreiros, J. G.; Pérez, José L.

2010-01-01

A hybrid theoretical-empirical model has been developed for modelling the error in LiDAR-derived digital elevation models (DEMs) of non-open terrain. The theoretical component seeks to model the propagation of the sample data error (SDE), i.e. the error from light detection and ranging (LiDAR) data capture of ground sampled points in open terrain, towards interpolated points. The interpolation methods used for infilling gaps may produce a non-negligible error that is referred to as gridding error. In this case, interpolation is performed using an inverse distance weighting (IDW) method with the local support of the five closest neighbours, although it would be possible to utilize other interpolation methods. The empirical component refers to what is known as "information loss". This is the error purely due to modelling the continuous terrain surface from only a discrete number of points plus the error arising from the interpolation process. The SDE must be previously calculated from a suitable number of check points located in open terrain and assumes that the LiDAR point density was sufficiently high to neglect the gridding error. For model calibration, data for 29 study sites, 200×200 m in size, belonging to different areas around Almeria province, south-east Spain, were acquired by means of stereo photogrammetric methods. The developed methodology was validated against two different LiDAR datasets. The first dataset used was an Ordnance Survey (OS) LiDAR survey carried out over a region of Bristol in the UK. The second dataset was an area located at Gador mountain range, south of Almería province, Spain. Both terrain slope and sampling density were incorporated in the empirical component through the calibration phase, resulting in a very good agreement between predicted and observed data (R2 = 0.9856 ; p < 0.001). In validation, Bristol observed vertical errors, corresponding to different LiDAR point densities, offered a reasonably good fit to the predicted errors. Even better results were achieved in the more rugged morphology of the Gador mountain range dataset. The findings presented in this article could be used as a guide for the selection of appropriate operational parameters (essentially point density in order to optimize survey cost), in projects related to LiDAR survey in non-open terrain, for instance those projects dealing with forestry applications.

Hydro-meteorological evaluation of downscaled global ensemble rainfall forecasts

NASA Astrophysics Data System (ADS)

Gaborit, Étienne; Anctil, François; Fortin, Vincent; Pelletier, Geneviève

2013-04-01

Ensemble rainfall forecasts are of high interest for decision making, as they provide an explicit and dynamic assessment of the uncertainty in the forecast (Ruiz et al. 2009). However, for hydrological forecasting, their low resolution currently limits their use to large watersheds (Maraun et al. 2010). In order to bridge this gap, various implementations of the statistic-stochastic multi-fractal downscaling technique presented by Perica and Foufoula-Georgiou (1996) were compared, bringing Environment Canada's global ensemble rainfall forecasts from a 100 by 70-km resolution down to 6 by 4-km, while increasing each pixel's rainfall variance and preserving its original mean. For comparison purposes, simpler methods were also implemented such as the bi-linear interpolation, which disaggregates global forecasts without modifying their variance. The downscaled meteorological products were evaluated using different scores and diagrams, from both a meteorological and a hydrological view points. The meteorological evaluation was conducted comparing the forecasted rainfall depths against nine days of observed values taken from Québec City rain gauge database. These 9 days present strong precipitation events occurring during the summer of 2009. For the hydrologic evaluation, the hydrological models SWMM5 and (a modified version of) GR4J were implemented on a small 6 km2 urban catchment located in the Québec City region. Ensemble hydrologic forecasts with a time step of 3 hours were then performed over a 3-months period of the summer of 2010 using the original and downscaled ensemble rainfall forecasts. The most important conclusions of this work are that the overall quality of the forecasts was preserved during the disaggregation procedure and that the disaggregated products using this variance-enhancing method were of similar quality than bi-linear interpolation products. However, variance and dispersion of the different members were, of course, much improved for the variance-enhanced products, compared to the bi-linear interpolation, which is a decisive advantage. The disaggregation technique of Perica and Foufoula-Georgiou (1996) hence represents an interesting way of bridging the gap between the meteorological models' resolution and the high degree of spatial precision sometimes required by hydrological models in their precipitation representation. References Maraun, D., Wetterhall, F., Ireson, A. M., Chandler, R. E., Kendon, E. J., Widmann, M., Brienen, S., Rust, H. W., Sauter, T., Themeßl, M., Venema, V. K. C., Chun, K. P., Goodess, C. M., Jones, R. G., Onof, C., Vrac, M., and Thiele-Eich, I. 2010. Precipitation downscaling under climate change: recent developments to bridge the gap between dynamical models and the end user. Reviews of Geophysics, 48 (3): RG3003, [np]. Doi: 10.1029/2009RG000314. Perica, S., and Foufoula-Georgiou, E. 1996. Model for multiscale disaggregation of spatial rainfall based on coupling meteorological and scaling descriptions. Journal Of Geophysical Research, 101(D21): 26347-26361. Ruiz, J., Saulo, C. and Kalnay, E. 2009. Comparison of Methods Used to Generate Probabilistic Quantitative Precipitation Forecasts over South America. Weather and forecasting, 24: 319-336. DOI: 10.1175/2008WAF2007098.1 This work is distributed under the Creative Commons Attribution 3.0 Unported License together with an author copyright. This license does not conflict with the regulations of the Crown Copyright.

Charmonium excited state spectrum in lattice QCD

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jozef Dudek; Robert Edwards; Nilmani Mathur

2008-02-01

Working with a large basis of covariant derivative-based meson interpolating fields we demonstrate the feasibility of reliably extracting multiple excited states using a variational method. The study is performed on quenched anisotropic lattices with clover quarks at the charm mass. We demonstrate how a knowledge of the continuum limit of a lattice interpolating field can give additional spin-assignment information, even at a single lattice spacing, via the overlap factors of interpolating field and state. Excited state masses are systematically high with respect to quark potential model predictions and, where they exist, experimental states. We conclude that this is most likelymore » a result of the quenched approximation.« less

Persons Camp Using Interpolation Method

NASA Astrophysics Data System (ADS)

Tawfiq, Luma Naji Mohammed; Najm Abood, Israa

2018-05-01

The aim of this paper is to estimate the rate of contaminated soils by using suitable interpolation method as an alternative accurate tool to evaluate the concentration of heavy metals in soil then compared with standard universal value to determine the rate of contamination in the soil. In particular, interpolation methods are extensively applied in the models of the different phenomena where experimental data must be used in computer studies where expressions of those data are required. In this paper the extended divided difference method in two dimensions is used to solve suggested problem. Then, the modification method is applied to estimate the rate of contaminated soils of displaced persons camp in Diyala Governorate, in Iraq.

An adaptive interpolation scheme for molecular potential energy surfaces

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kowalewski, Markus, E-mail: mkowalew@uci.edu; Larsson, Elisabeth; Heryudono, Alfa

The calculation of potential energy surfaces for quantum dynamics can be a time consuming task—especially when a high level of theory for the electronic structure calculation is required. We propose an adaptive interpolation algorithm based on polyharmonic splines combined with a partition of unity approach. The adaptive node refinement allows to greatly reduce the number of sample points by employing a local error estimate. The algorithm and its scaling behavior are evaluated for a model function in 2, 3, and 4 dimensions. The developed algorithm allows for a more rapid and reliable interpolation of a potential energy surface within amore » given accuracy compared to the non-adaptive version.« less

Information geometry and its application to theoretical statistics and diffusion tensor magnetic resonance imaging

NASA Astrophysics Data System (ADS)

Wisniewski, Nicholas Andrew

This dissertation is divided into two parts. First we present an exact solution to a generalization of the Behrens-Fisher problem by embedding the problem in the Riemannian manifold of Normal distributions. From this we construct a geometric hypothesis testing scheme. Secondly we investigate the most commonly used geometric methods employed in tensor field interpolation for DT-MRI analysis and cardiac computer modeling. We computationally investigate a class of physiologically motivated orthogonal tensor invariants, both at the full tensor field scale and at the scale of a single interpolation by doing a decimation/interpolation experiment. We show that Riemannian-based methods give the best results in preserving desirable physiological features.

Novel Integration of Frame Rate Up Conversion and HEVC Coding Based on Rate-Distortion Optimization.

PubMed

Guo Lu; Xiaoyun Zhang; Li Chen; Zhiyong Gao

2018-02-01

Frame rate up conversion (FRUC) can improve the visual quality by interpolating new intermediate frames. However, high frame rate videos by FRUC are confronted with more bitrate consumption or annoying artifacts of interpolated frames. In this paper, a novel integration framework of FRUC and high efficiency video coding (HEVC) is proposed based on rate-distortion optimization, and the interpolated frames can be reconstructed at encoder side with low bitrate cost and high visual quality. First, joint motion estimation (JME) algorithm is proposed to obtain robust motion vectors, which are shared between FRUC and video coding. What's more, JME is embedded into the coding loop and employs the original motion search strategy in HEVC coding. Then, the frame interpolation is formulated as a rate-distortion optimization problem, where both the coding bitrate consumption and visual quality are taken into account. Due to the absence of original frames, the distortion model for interpolated frames is established according to the motion vector reliability and coding quantization error. Experimental results demonstrate that the proposed framework can achieve 21% ~ 42% reduction in BDBR, when compared with the traditional methods of FRUC cascaded with coding.

Comparing Vibrationally Averaged Nuclear Shielding Constants by Quantum Diffusion Monte Carlo and Second-Order Perturbation Theory.

PubMed

Ng, Yee-Hong; Bettens, Ryan P A

2016-03-03

Using the method of modified Shepard's interpolation to construct potential energy surfaces of the H2O, O3, and HCOOH molecules, we compute vibrationally averaged isotropic nuclear shielding constants ⟨σ⟩ of the three molecules via quantum diffusion Monte Carlo (QDMC). The QDMC results are compared to that of second-order perturbation theory (PT), to see if second-order PT is adequate for obtaining accurate values of nuclear shielding constants of molecules with large amplitude motions. ⟨σ⟩ computed by the two approaches differ for the hydrogens and carbonyl oxygen of HCOOH, suggesting that for certain molecules such as HCOOH where big displacements away from equilibrium happen (internal OH rotation), ⟨σ⟩ of experimental quality may only be obtainable with the use of more sophisticated and accurate methods, such as quantum diffusion Monte Carlo. The approach of modified Shepard's interpolation is also extended to construct shielding constants σ surfaces of the three molecules. By using a σ surface with the equilibrium geometry as a single data point to compute isotropic nuclear shielding constants for each descendant in the QDMC ensemble representing the ground state wave function, we reproduce the results obtained through ab initio computed σ to within statistical noise. Development of such an approach could thereby alleviate the need for any future costly ab initio σ calculations.

Modeling of the WSTF frictional heating apparatus in high pressure systems

NASA Technical Reports Server (NTRS)

Skowlund, Christopher T.

1992-01-01

In order to develop a computer program able to model the frictional heating of metals in high pressure oxygen or nitrogen a number of additions have been made to the frictional heating model originally developed for tests in low pressure helium. These additions include: (1) a physical property package for the gases to account for departures from the ideal gas state; (2) two methods for spatial discretization (finite differences with quadratic interpolation or orthogonal collocation on finite elements) which substantially reduce the computer time required to solve the transient heat balance; (3) more efficient programs for the integration of the ordinary differential equations resulting from the discretization of the partial differential equations; and (4) two methods for determining the best-fit parameters via minimization of the mean square error (either a direct search multivariable simplex method or a modified Levenburg-Marquardt algorithm). The resulting computer program has been shown to be accurate, efficient and robust for determining the heat flux or friction coefficient vs. time at the interface of the stationary and rotating samples.

Comparison of Benchtop Fourier-Transform (FT) and Portable Grating Scanning Spectrometers for Determination of Total Soluble Solid Contents in Single Grape Berry (Vitis vinifera L.) and Calibration Transfer.

PubMed

Xiao, Hui; Sun, Ke; Sun, Ye; Wei, Kangli; Tu, Kang; Pan, Leiqing

2017-11-22

Near-infrared (NIR) spectroscopy was applied for the determination of total soluble solid contents (SSC) of single Ruby Seedless grape berries using both benchtop Fourier transform (VECTOR 22/N) and portable grating scanning (SupNIR-1500) spectrometers in this study. The results showed that the best SSC prediction was obtained by VECTOR 22/N in the range of 12,000 to 4000 cm -1 (833-2500 nm) for Ruby Seedless with determination coefficient of prediction (R p ²) of 0.918, root mean squares error of prediction (RMSEP) of 0.758% based on least squares support vector machine (LS-SVM). Calibration transfer was conducted on the same spectral range of two instruments (1000-1800 nm) based on the LS-SVM model. By conducting Kennard-Stone (KS) to divide sample sets, selecting the optimal number of standardization samples and applying Passing-Bablok regression to choose the optimal instrument as the master instrument, a modified calibration transfer method between two spectrometers was developed. When 45 samples were selected for the standardization set, the linear interpolation-piecewise direct standardization (linear interpolation-PDS) performed well for calibration transfer with R p ² of 0.857 and RMSEP of 1.099% in the spectral region of 1000-1800 nm. And it was proved that re-calculating the standardization samples into master model could improve the performance of calibration transfer in this study. This work indicated that NIR could be used as a rapid and non-destructive method for SSC prediction, and provided a feasibility to solve the transfer difficulty between totally different NIR spectrometers.

Adaptive kernel regression for freehand 3D ultrasound reconstruction

NASA Astrophysics Data System (ADS)

Alshalalfah, Abdel-Latif; Daoud, Mohammad I.; Al-Najar, Mahasen

2017-03-01

Freehand three-dimensional (3D) ultrasound imaging enables low-cost and flexible 3D scanning of arbitrary-shaped organs, where the operator can freely move a two-dimensional (2D) ultrasound probe to acquire a sequence of tracked cross-sectional images of the anatomy. Often, the acquired 2D ultrasound images are irregularly and sparsely distributed in the 3D space. Several 3D reconstruction algorithms have been proposed to synthesize 3D ultrasound volumes based on the acquired 2D images. A challenging task during the reconstruction process is to preserve the texture patterns in the synthesized volume and ensure that all gaps in the volume are correctly filled. This paper presents an adaptive kernel regression algorithm that can effectively reconstruct high-quality freehand 3D ultrasound volumes. The algorithm employs a kernel regression model that enables nonparametric interpolation of the voxel gray-level values. The kernel size of the regression model is adaptively adjusted based on the characteristics of the voxel that is being interpolated. In particular, when the algorithm is employed to interpolate a voxel located in a region with dense ultrasound data samples, the size of the kernel is reduced to preserve the texture patterns. On the other hand, the size of the kernel is increased in areas that include large gaps to enable effective gap filling. The performance of the proposed algorithm was compared with seven previous interpolation approaches by synthesizing freehand 3D ultrasound volumes of a benign breast tumor. The experimental results show that the proposed algorithm outperforms the other interpolation approaches.

Prediction of soil attributes through interpolators in a deglaciated environment with complex landforms

NASA Astrophysics Data System (ADS)

Schünemann, Adriano Luis; Inácio Fernandes Filho, Elpídio; Rocha Francelino, Marcio; Rodrigues Santos, Gérson; Thomazini, Andre; Batista Pereira, Antônio; Gonçalves Reynaud Schaefer, Carlos Ernesto

2017-04-01

The knowledge of environmental variables values, in non-sampled sites from a minimum data set can be accessed through interpolation technique. Kriging and the classifier Random Forest algorithm are examples of predictors with this aim. The objective of this work was to compare methods of soil attributes spatialization in a recent deglaciated environment with complex landforms. Prediction of the selected soil attributes (potassium, calcium and magnesium) from ice-free areas were tested by using morphometric covariables, and geostatistical models without these covariables. For this, 106 soil samples were collected at 0-10 cm depth in Keller Peninsula, King George Island, Maritime Antarctica. Soil chemical analysis was performed by the gravimetric method, determining values of potassium, calcium and magnesium for each sampled point. Digital terrain models (DTMs) were obtained by using Terrestrial Laser Scanner. DTMs were generated from a cloud of points with spatial resolutions of 1, 5, 10, 20 and 30 m. Hence, 40 morphometric covariates were generated. Simple Kriging was performed using the R package software. The same data set coupled with morphometric covariates, was used to predict values of the studied attributes in non-sampled sites through Random Forest interpolator. Little differences were observed on the DTMs generated by Simple kriging and Random Forest interpolators. Also, DTMs with better spatial resolution did not improved the quality of soil attributes prediction. Results revealed that Simple Kriging can be used as interpolator when morphometric covariates are not available, with little impact regarding quality. It is necessary to go further in soil chemical attributes prediction techniques, especially in periglacial areas with complex landforms.

Distributed snow modeling suitable for use with operational data for the American River watershed.

NASA Astrophysics Data System (ADS)

Shamir, E.; Georgakakos, K. P.

2004-12-01

The mountainous terrain of the American River watershed (~4300 km2) at the Western slope of the Northern Sierra Nevada is subject to significant variability in the atmospheric forcing that controls the snow accumulation and ablations processes (i.e., precipitation, surface temperature, and radiation). For a hydrologic model that attempts to predict both short- and long-term streamflow discharges, a plausible description of the seasonal and intermittent winter snow pack accumulation and ablation is crucial. At present the NWS-CNRFC operational snow model is implemented in a semi distributed manner (modeling unit of about 100-1000 km2) and therefore lump distinct spatial variability of snow processes. In this study we attempt to account for the precipitation, temperature, and radiation spatial variability by constructing a distributed snow accumulation and melting model suitable for use with commonly available sparse data. An adaptation of the NWS-Snow17 energy and mass balance that is used operationally at the NWS River Forecast Centers is implemented at 1 km2 grid cells with distributed input and model parameters. The input to the model (i.e., precipitation and surface temperature) is interpolated from observed point data. The surface temperature was interpolated over the basin based on adiabatic lapse rates using topographic information whereas the precipitation was interpolated based on maps of climatic mean annual rainfall distribution acquired from PRISM. The model parameters that control the melting rate due to radiation were interpolated based on aspect. The study was conducted for the entire American basin for the snow seasons of 1999-2000. Validation of the Snow Water Equivalent (SWE) prediction is done by comparing to observation from 12 snow Sensors. The Snow Cover Area (SCA) prediction was evaluated by comparing to remotely sensed 500m daily snow cover derived from MODIS. The results that the distribution of snow over the area is well captured and the quantity compared to the snow gauges are well estimated in the high elevation.

Modeling moving systems with RELAP5-3D

DOE PAGES

Mesina, G. L.; Aumiller, David L.; Buschman, Francis X.; ...

2015-12-04

RELAP5-3D is typically used to model stationary, land-based reactors. However, it can also model reactors in other inertial and accelerating frames of reference. By changing the magnitude of the gravitational vector through user input, RELAP5-3D can model reactors on a space station or the moon. The field equations have also been modified to model reactors in a non-inertial frame, such as occur in land-based reactors during earthquakes or onboard spacecraft. Transient body forces affect fluid flow in thermal-fluid machinery aboard accelerating crafts during rotational and translational accelerations. It is useful to express the equations of fluid motion in the acceleratingmore » frame of reference attached to the moving craft. However, careful treatment of the rotational and translational kinematics is required to accurately capture the physics of the fluid motion. Correlations for flow at angles between horizontal and vertical are generated via interpolation where no experimental studies or data exist. The equations for three-dimensional fluid motion in a non-inertial frame of reference are developed. As a result, two different systems for describing rotational motion are presented, user input is discussed, and an example is given.« less

A study on characteristics of retrospective optimal interpolation with WRF testbed

NASA Astrophysics Data System (ADS)

Kim, S.; Noh, N.; Lim, G.

2012-12-01

This study presents the application of retrospective optimal interpolation (ROI) with Weather Research and Forecasting model (WRF). Song et al. (2009) suggest ROI method which is an optimal interpolation (OI) that gradually assimilates observations over the analysis window for variance-minimum estimate of an atmospheric state at the initial time of the analysis window. Song and Lim (2011) improve the method by incorporating eigen-decomposition and covariance inflation. ROI method assimilates the data at post analysis time using perturbation method (Errico and Raeder, 1999) without adjoint model. In this study, ROI method is applied to WRF model to validate the algorithm and to investigate the capability. The computational costs for ROI can be reduced due to the eigen-decomposition of background error covariance. Using the background error covariance in eigen-space, 1-profile assimilation experiment is performed. The difference between forecast errors with assimilation and without assimilation is obviously increased as time passed, which means the improvement of forecast error by assimilation. The characteristics and strength/weakness of ROI method are investigated by conducting the experiments with other data assimilation method.

Multi-Objective Optimization of Mixed Variable, Stochastic Systems Using Single-Objective Formulations

DTIC Science & Technology

2008-03-01

investigated, as well as the methodology used . Chapter IV presents the data collection and analysis procedures, and the resulting analysis and...interpolate the data, although a non-interpolating model is possible. For this research Design and Analysis of Computer Experiments (DACE) is used ...followed by the analysis . 4.1. Testing Approach The initial SMOMADS algorithm used for this research was acquired directly from Walston [70]. The

A comparison of interpolation methods on the basis of data obtained from a bathymetric survey of Lake Vrana, Croatia

NASA Astrophysics Data System (ADS)

Šiljeg, A.; Lozić, S.; Šiljeg, S.

2015-08-01

The bathymetric survey of Lake Vrana included a wide range of activities that were performed in several different stages, in accordance with the standards set by the International Hydrographic Organization. The survey was conducted using an integrated measuring system which consisted of three main parts: a single-beam sonar HydroStar 4300 and GPS devices; a Ashtech ProMark 500 base, and a Thales Z-Max® rover. A total of 12 851 points were gathered. In order to find continuous surfaces necessary for analysing the morphology of the bed of Lake Vrana, it was necessary to approximate values in certain areas that were not directly measured, by using an appropriate interpolation method. The main aims of this research were as follows: (a) to compare the efficiency of 14 different interpolation methods and discover the most appropriate interpolators for the development of a raster model; (b) to calculate the surface area and volume of Lake Vrana, and (c) to compare the differences in calculations between separate raster models. The best deterministic method of interpolation was multiquadric RBF (radio basis function), and the best geostatistical method was ordinary cokriging. The root mean square error in both methods measured less than 0.3 m. The quality of the interpolation methods was analysed in two phases. The first phase used only points gathered by bathymetric measurement, while the second phase also included points gathered by photogrammetric restitution. The first bathymetric map of Lake Vrana in Croatia was produced, as well as scenarios of minimum and maximum water levels. The calculation also included the percentage of flooded areas and cadastre plots in the case of a 2 m increase in the water level. The research presented new scientific and methodological data related to the bathymetric features, surface area and volume of Lake Vrana.

A comparison of different interpolation methods for wind data in Central Asia

NASA Astrophysics Data System (ADS)

Reinhardt, Katja; Samimi, Cyrus

2017-04-01

For the assessment of the global climate change and its consequences, the results of computer based climate models are of central importance. The quality of these results and the validity of the derived forecasts are strongly determined by the quality of the underlying climate data. However, in many parts of the world high resolution data are not available. This is particularly true for many regions in Central Asia, where the density of climatological stations has often to be described as thinned out. Due to this insufficient data base the use of statistical methods to improve the resolution of existing climate data is of crucial importance. Only this can provide a substantial data base for a well-founded analysis of past climate changes as well as for a reliable forecast of future climate developments for the particular region. The study presented here shows a comparison of different interpolation methods for the wind components u and v for a region in Central Asia with a pronounced topography. The aim of the study is to find out whether there is an optimal interpolation method which can equally be applied for all pressure levels or if different interpolation methods have to be applied for each pressure level. The European reanalysis data Era-Interim for the years 1989 - 2015 are used as input data for the pressure levels of 850 hPa, 500 hPa and 200 hPa. In order to improve the input data, two different interpolation procedures were applied: On the one hand pure interpolation methods were used, such as inverse distance weighting and ordinary kriging. On the other hand machine learning algorithms, generalized additive models and regression kriging were applied, considering additional influencing factors, e.g. geopotential and topography. As a result it can be concluded that regression kriging provides the best results for all pressure levels, followed by support vector machine, neural networks and ordinary kriging. Inverse distance weighting showed the worst results.

Planning additional drilling campaign using two-space genetic algorithm: A game theoretical approach

NASA Astrophysics Data System (ADS)

Kumral, Mustafa; Ozer, Umit

2013-03-01

Grade and tonnage are the most important technical uncertainties in mining ventures because of the use of estimations/simulations, which are mostly generated from drill data. Open pit mines are planned and designed on the basis of the blocks representing the entire orebody. Each block has different estimation/simulation variance reflecting uncertainty to some extent. The estimation/simulation realizations are submitted to mine production scheduling process. However, the use of a block model with varying estimation/simulation variances will lead to serious risk in the scheduling. In the medium of multiple simulations, the dispersion variances of blocks can be thought to regard technical uncertainties. However, the dispersion variance cannot handle uncertainty associated with varying estimation/simulation variances of blocks. This paper proposes an approach that generates the configuration of the best additional drilling campaign to generate more homogenous estimation/simulation variances of blocks. In other words, the objective is to find the best drilling configuration in such a way as to minimize grade uncertainty under budget constraint. Uncertainty measure of the optimization process in this paper is interpolation variance, which considers data locations and grades. The problem is expressed as a minmax problem, which focuses on finding the best worst-case performance i.e., minimizing interpolation variance of the block generating maximum interpolation variance. Since the optimization model requires computing the interpolation variances of blocks being simulated/estimated in each iteration, the problem cannot be solved by standard optimization tools. This motivates to use two-space genetic algorithm (GA) approach to solve the problem. The technique has two spaces: feasible drill hole configuration with minimization of interpolation variance and drill hole simulations with maximization of interpolation variance. Two-space interacts to find a minmax solution iteratively. A case study was conducted to demonstrate the performance of approach. The findings showed that the approach could be used to plan a new drilling campaign.

Regionalizing nonparametric models of precipitation amounts on different temporal scales

NASA Astrophysics Data System (ADS)

Mosthaf, Tobias; Bárdossy, András

2017-05-01

Parametric distribution functions are commonly used to model precipitation amounts corresponding to different durations. The precipitation amounts themselves are crucial for stochastic rainfall generators and weather generators. Nonparametric kernel density estimates (KDEs) offer a more flexible way to model precipitation amounts. As already stated in their name, these models do not exhibit parameters that can be easily regionalized to run rainfall generators at ungauged locations as well as at gauged locations. To overcome this deficiency, we present a new interpolation scheme for nonparametric models and evaluate it for different temporal resolutions ranging from hourly to monthly. During the evaluation, the nonparametric methods are compared to commonly used parametric models like the two-parameter gamma and the mixed-exponential distribution. As water volume is considered to be an essential parameter for applications like flood modeling, a Lorenz-curve-based criterion is also introduced. To add value to the estimation of data at sub-daily resolutions, we incorporated the plentiful daily measurements in the interpolation scheme, and this idea was evaluated. The study region is the federal state of Baden-Württemberg in the southwest of Germany with more than 500 rain gauges. The validation results show that the newly proposed nonparametric interpolation scheme provides reasonable results and that the incorporation of daily values in the regionalization of sub-daily models is very beneficial.

Applications of Space-Filling-Curves to Cartesian Methods for CFD

NASA Technical Reports Server (NTRS)

Aftosmis, M. J.; Murman, S. M.; Berger, M. J.

2003-01-01

This paper presents a variety of novel uses of space-filling-curves (SFCs) for Cartesian mesh methods in CFD. While these techniques will be demonstrated using non-body-fitted Cartesian meshes, many are applicable on general body-fitted meshes-both structured and unstructured. We demonstrate the use of single theta(N log N) SFC-based reordering to produce single-pass (theta(N)) algorithms for mesh partitioning, multigrid coarsening, and inter-mesh interpolation. The intermesh interpolation operator has many practical applications including warm starts on modified geometry, or as an inter-grid transfer operator on remeshed regions in moving-body simulations Exploiting the compact construction of these operators, we further show that these algorithms are highly amenable to parallelization. Examples using the SFC-based mesh partitioner show nearly linear speedup to 640 CPUs even when using multigrid as a smoother. Partition statistics are presented showing that the SFC partitions are, on-average, within 15% of ideal even with only around 50,000 cells in each sub-domain. The inter-mesh interpolation operator also has linear asymptotic complexity and can be used to map a solution with N unknowns to another mesh with M unknowns with theta(M + N) operations. This capability is demonstrated both on moving-body simulations and in mapping solutions to perturbed meshes for control surface deflection or finite-difference-based gradient design methods.

Mapping snow depth return levels: smooth spatial modeling versus station interpolation

NASA Astrophysics Data System (ADS)

Blanchet, J.; Lehning, M.

2010-12-01

For adequate risk management in mountainous countries, hazard maps for extreme snow events are needed. This requires the computation of spatial estimates of return levels. In this article we use recent developments in extreme value theory and compare two main approaches for mapping snow depth return levels from in situ measurements. The first one is based on the spatial interpolation of pointwise extremal distributions (the so-called Generalized Extreme Value distribution, GEV henceforth) computed at station locations. The second one is new and based on the direct estimation of a spatially smooth GEV distribution with the joint use of all stations. We compare and validate the different approaches for modeling annual maximum snow depth measured at 100 sites in Switzerland during winters 1965-1966 to 2007-2008. The results show a better performance of the smooth GEV distribution fitting, in particular where the station network is sparser. Smooth return level maps can be computed from the fitted model without any further interpolation. Their regional variability can be revealed by removing the altitudinal dependent covariates in the model. We show how return levels and their regional variability are linked to the main climatological patterns of Switzerland.

Importance of interpolation and coincidence errors in data fusion

NASA Astrophysics Data System (ADS)

Ceccherini, Simone; Carli, Bruno; Tirelli, Cecilia; Zoppetti, Nicola; Del Bianco, Samuele; Cortesi, Ugo; Kujanpää, Jukka; Dragani, Rossana

2018-02-01

The complete data fusion (CDF) method is applied to ozone profiles obtained from simulated measurements in the ultraviolet and in the thermal infrared in the framework of the Sentinel 4 mission of the Copernicus programme. We observe that the quality of the fused products is degraded when the fusing profiles are either retrieved on different vertical grids or referred to different true profiles. To address this shortcoming, a generalization of the complete data fusion method, which takes into account interpolation and coincidence errors, is presented. This upgrade overcomes the encountered problems and provides products of good quality when the fusing profiles are both retrieved on different vertical grids and referred to different true profiles. The impact of the interpolation and coincidence errors on number of degrees of freedom and errors of the fused profile is also analysed. The approach developed here to account for the interpolation and coincidence errors can also be followed to include other error components, such as forward model errors.

Dose calculation for photon-emitting brachytherapy sources with average energy higher than 50 keV: report of the AAPM and ESTRO.

PubMed

Perez-Calatayud, Jose; Ballester, Facundo; Das, Rupak K; Dewerd, Larry A; Ibbott, Geoffrey S; Meigooni, Ali S; Ouhib, Zoubir; Rivard, Mark J; Sloboda, Ron S; Williamson, Jeffrey F

2012-05-01

Recommendations of the American Association of Physicists in Medicine (AAPM) and the European Society for Radiotherapy and Oncology (ESTRO) on dose calculations for high-energy (average energy higher than 50 keV) photon-emitting brachytherapy sources are presented, including the physical characteristics of specific (192)Ir, (137)Cs, and (60)Co source models. This report has been prepared by the High Energy Brachytherapy Source Dosimetry (HEBD) Working Group. This report includes considerations in the application of the TG-43U1 formalism to high-energy photon-emitting sources with particular attention to phantom size effects, interpolation accuracy dependence on dose calculation grid size, and dosimetry parameter dependence on source active length. Consensus datasets for commercially available high-energy photon sources are provided, along with recommended methods for evaluating these datasets. Recommendations on dosimetry characterization methods, mainly using experimental procedures and Monte Carlo, are established and discussed. Also included are methodological recommendations on detector choice, detector energy response characterization and phantom materials, and measurement specification methodology. Uncertainty analyses are discussed and recommendations for high-energy sources without consensus datasets are given. Recommended consensus datasets for high-energy sources have been derived for sources that were commercially available as of January 2010. Data are presented according to the AAPM TG-43U1 formalism, with modified interpolation and extrapolation techniques of the AAPM TG-43U1S1 report for the 2D anisotropy function and radial dose function.

Spatiotemporal Interpolation Methods for Solar Event Trajectories

NASA Astrophysics Data System (ADS)

Filali Boubrahimi, Soukaina; Aydin, Berkay; Schuh, Michael A.; Kempton, Dustin; Angryk, Rafal A.; Ma, Ruizhe

2018-05-01

This paper introduces four spatiotemporal interpolation methods that enrich complex, evolving region trajectories that are reported from a variety of ground-based and space-based solar observatories every day. Our interpolation module takes an existing solar event trajectory as its input and generates an enriched trajectory with any number of additional time–geometry pairs created by the most appropriate method. To this end, we designed four different interpolation techniques: MBR-Interpolation (Minimum Bounding Rectangle Interpolation), CP-Interpolation (Complex Polygon Interpolation), FI-Interpolation (Filament Polygon Interpolation), and Areal-Interpolation, which are presented here in detail. These techniques leverage k-means clustering, centroid shape signature representation, dynamic time warping, linear interpolation, and shape buffering to generate the additional polygons of an enriched trajectory. Using ground-truth objects, interpolation effectiveness is evaluated through a variety of measures based on several important characteristics that include spatial distance, area overlap, and shape (boundary) similarity. To our knowledge, this is the first research effort of this kind that attempts to address the broad problem of spatiotemporal interpolation of solar event trajectories. We conclude with a brief outline of future research directions and opportunities for related work in this area.

A bivariate rational interpolation with a bi-quadratic denominator

NASA Astrophysics Data System (ADS)

Duan, Qi; Zhang, Huanling; Liu, Aikui; Li, Huaigu

2006-10-01

In this paper a new rational interpolation with a bi-quadratic denominator is developed to create a space surface using only values of the function being interpolated. The interpolation function has a simple and explicit rational mathematical representation. When the knots are equally spaced, the interpolating function can be expressed in matrix form, and this form has a symmetric property. The concept of integral weights coefficients of the interpolation is given, which describes the "weight" of the interpolation points in the local interpolating region.

Analysis of fast boundary-integral approximations for modeling electrostatic contributions of molecular binding

PubMed Central

Kreienkamp, Amelia B.; Liu, Lucy Y.; Minkara, Mona S.; Knepley, Matthew G.; Bardhan, Jaydeep P.; Radhakrishnan, Mala L.

2013-01-01

We analyze and suggest improvements to a recently developed approximate continuum-electrostatic model for proteins. The model, called BIBEE/I (boundary-integral based electrostatics estimation with interpolation), was able to estimate electrostatic solvation free energies to within a mean unsigned error of 4% on a test set of more than 600 proteins—a significant improvement over previous BIBEE models. In this work, we tested the BIBEE/I model for its capability to predict residue-by-residue interactions in protein–protein binding, using the widely studied model system of trypsin and bovine pancreatic trypsin inhibitor (BPTI). Finding that the BIBEE/I model performs surprisingly less well in this task than simpler BIBEE models, we seek to explain this behavior in terms of the models’ differing spectral approximations of the exact boundary-integral operator. Calculations of analytically solvable systems (spheres and tri-axial ellipsoids) suggest two possibilities for improvement. The first is a modified BIBEE/I approach that captures the asymptotic eigenvalue limit correctly, and the second involves the dipole and quadrupole modes for ellipsoidal approximations of protein geometries. Our analysis suggests that fast, rigorous approximate models derived from reduced-basis approximation of boundary-integral equations might reach unprecedented accuracy, if the dipole and quadrupole modes can be captured quickly for general shapes. PMID:24466561

Spatial Interpolation of Fine Particulate Matter Concentrations Using the Shortest Wind-Field Path Distance

PubMed Central

Li, Longxiang; Gong, Jianhua; Zhou, Jieping

2014-01-01

Effective assessments of air-pollution exposure depend on the ability to accurately predict pollutant concentrations at unmonitored locations, which can be achieved through spatial interpolation. However, most interpolation approaches currently in use are based on the Euclidean distance, which cannot account for the complex nonlinear features displayed by air-pollution distributions in the wind-field. In this study, an interpolation method based on the shortest path distance is developed to characterize the impact of complex urban wind-field on the distribution of the particulate matter concentration. In this method, the wind-field is incorporated by first interpolating the observed wind-field from a meteorological-station network, then using this continuous wind-field to construct a cost surface based on Gaussian dispersion model and calculating the shortest wind-field path distances between locations, and finally replacing the Euclidean distances typically used in Inverse Distance Weighting (IDW) with the shortest wind-field path distances. This proposed methodology is used to generate daily and hourly estimation surfaces for the particulate matter concentration in the urban area of Beijing in May 2013. This study demonstrates that wind-fields can be incorporated into an interpolation framework using the shortest wind-field path distance, which leads to a remarkable improvement in both the prediction accuracy and the visual reproduction of the wind-flow effect, both of which are of great importance for the assessment of the effects of pollutants on human health. PMID:24798197

Spatial interpolation of fine particulate matter concentrations using the shortest wind-field path distance.

PubMed

Li, Longxiang; Gong, Jianhua; Zhou, Jieping

2014-01-01

Effective assessments of air-pollution exposure depend on the ability to accurately predict pollutant concentrations at unmonitored locations, which can be achieved through spatial interpolation. However, most interpolation approaches currently in use are based on the Euclidean distance, which cannot account for the complex nonlinear features displayed by air-pollution distributions in the wind-field. In this study, an interpolation method based on the shortest path distance is developed to characterize the impact of complex urban wind-field on the distribution of the particulate matter concentration. In this method, the wind-field is incorporated by first interpolating the observed wind-field from a meteorological-station network, then using this continuous wind-field to construct a cost surface based on Gaussian dispersion model and calculating the shortest wind-field path distances between locations, and finally replacing the Euclidean distances typically used in Inverse Distance Weighting (IDW) with the shortest wind-field path distances. This proposed methodology is used to generate daily and hourly estimation surfaces for the particulate matter concentration in the urban area of Beijing in May 2013. This study demonstrates that wind-fields can be incorporated into an interpolation framework using the shortest wind-field path distance, which leads to a remarkable improvement in both the prediction accuracy and the visual reproduction of the wind-flow effect, both of which are of great importance for the assessment of the effects of pollutants on human health.

Comparison Study on the Estimation of the Spatial Distribution of Regional Soil Metal(loid)s Pollution Based on Kriging Interpolation and BP Neural Network.

PubMed

Jia, Zhenyi; Zhou, Shenglu; Su, Quanlong; Yi, Haomin; Wang, Junxiao

2017-12-26

Soil pollution by metal(loid)s resulting from rapid economic development is a major concern. Accurately estimating the spatial distribution of soil metal(loid) pollution has great significance in preventing and controlling soil pollution. In this study, 126 topsoil samples were collected in Kunshan City and the geo-accumulation index was selected as a pollution index. We used Kriging interpolation and BP neural network methods to estimate the spatial distribution of arsenic (As) and cadmium (Cd) pollution in the study area. Additionally, we introduced a cross-validation method to measure the errors of the estimation results by the two interpolation methods and discussed the accuracy of the information contained in the estimation results. The conclusions are as follows: data distribution characteristics, spatial variability, and mean square errors (MSE) of the different methods showed large differences. Estimation results from BP neural network models have a higher accuracy, the MSE of As and Cd are 0.0661 and 0.1743, respectively. However, the interpolation results show significant skewed distribution, and spatial autocorrelation is strong. Using Kriging interpolation, the MSE of As and Cd are 0.0804 and 0.2983, respectively. The estimation results have poorer accuracy. Combining the two methods can improve the accuracy of the Kriging interpolation and more comprehensively represent the spatial distribution characteristics of metal(loid)s in regional soil. The study may provide a scientific basis and technical support for the regulation of soil metal(loid) pollution.

A Numerical Method for Calculating Stellar Occultation Light Curves from an Arbitrary Atmospheric Model

NASA Technical Reports Server (NTRS)

Chamberlain, D. M.; Elliot, J. L.

1997-01-01

We present a method for speeding up numerical calculations of a light curve for a stellar occultation by a planetary atmosphere with an arbitrary atmospheric model that has spherical symmetry. This improved speed makes least-squares fitting for model parameters practical. Our method takes as input several sets of values for the first two radial derivatives of the refractivity at different values of model parameters, and interpolates to obtain the light curve at intermediate values of one or more model parameters. It was developed for small occulting bodies such as Pluto and Triton, but is applicable to planets of all sizes. We also present the results of a series of tests showing that our method calculates light curves that are correct to an accuracy of 10(exp -4) of the unocculted stellar flux. The test benchmarks are (i) an atmosphere with a l/r dependence of temperature, which yields an analytic solution for the light curve, (ii) an atmosphere that produces an exponential refraction angle, and (iii) a small-planet isothermal model. With our method, least-squares fits to noiseless data also converge to values of parameters with fractional errors of no more than 10(exp -4), with the largest errors occurring in small planets. These errors are well below the precision of the best stellar occultation data available. Fits to noisy data had formal errors consistent with the level of synthetic noise added to the light curve. We conclude: (i) one should interpolate refractivity derivatives and then form light curves from the interpolated values, rather than interpolating the light curves themselves; (ii) for the most accuracy, one must specify the atmospheric model for radii many scale heights above half light; and (iii) for atmospheres with smoothly varying refractivity with altitude, light curves can be sampled as coarsely as two points per scale height.

Useful properties of spinal circuits for learning and performing planar reaches

NASA Astrophysics Data System (ADS)

Tsianos, George A.; Goodner, Jared; Loeb, Gerald E.

2014-10-01

Objective. We developed a detailed model of the spinal circuitry plus musculoskeletal system (SC + MS) for the primate arm and investigated its role in sensorimotor control, learning and storing of movement repertoires. Approach. Recently developed models of spinal circuit connectivity, neurons and muscle force/energetics were integrated and in some cases refined to construct the most comprehensive model of the SC + MS to date. The SC + MS’s potential contributions to center-out reaching movement were assessed by employing an extremely simple model of the brain that issued only step commands. Main results. The SC + MS was able to generate physiological muscle dynamics underlying reaching across different directions, distances, speeds, and even in the midst of strong dynamic perturbations (i.e. viscous curl field). For each task, there were many different combinations of brain inputs that generated physiological performance. Natural patterns of recruitment and low metabolic cost emerged for about half of the learning trials when a purely kinematic cost function was used and for all of the trials when an estimate of metabolic energy consumption was added to the cost function. Solutions for different tasks could be interpolated to generate intermediate movement and the range over which interpolation was successful was consistent with experimental reports. Significance. This is the first demonstration that a realistic model of the SC + MS is capable of generating the required dynamics of center-out reaching. The interpolability observed is important for the feasibility of storing motor programs in memory rather than computing them from internal models of the musculoskeletal plant. Successful interpolation of command programs required them to have similar muscle recruitment patterns, which are thought by many to arise from hard-wired muscle synergies rather than learned as in our model system. These properties of the SC + MS along with its tendency to generate energetically efficient solutions might usefully be employed by motor cortex to generate voluntary behaviors such as reaching to targets.

Interpolation methods and the accuracy of lattice-Boltzmann mesh refinement

DOE PAGES

Guzik, Stephen M.; Weisgraber, Todd H.; Colella, Phillip; ...

2013-12-10

A lattice-Boltzmann model to solve the equivalent of the Navier-Stokes equations on adap- tively refined grids is presented. A method for transferring information across interfaces between different grid resolutions was developed following established techniques for finite- volume representations. This new approach relies on a space-time interpolation and solving constrained least-squares problems to ensure conservation. The effectiveness of this method at maintaining the second order accuracy of lattice-Boltzmann is demonstrated through a series of benchmark simulations and detailed mesh refinement studies. These results exhibit smaller solution errors and improved convergence when compared with similar approaches relying only on spatial interpolation. Examplesmore » highlighting the mesh adaptivity of this method are also provided.« less

Origin of the fundamental plane of elliptical galaxies in the Coma cluster without fine-tuning

NASA Astrophysics Data System (ADS)

Chiu, Mu-Chen; Ko, Chung-Ming; Shu, Chenggang

2017-03-01

Thirty years after the discovery of the fundamental plane, explanations of the tilt of the fundamental plane with respect to the virial plane are still in need of fine-tuning. In this paper, we try to explore the origin of this tilt from the perspective of modified Newtonian dynamics (MOND) by applying the 16 Coma galaxies available in J. Thomas et al. [Mon. Not. R. Astron. Soc. 415, 545 (2011), 10.1111/j.1365-2966.2011.18725.x]. Based on the mass models that can reproduce de Vaucouleurs' law closely, we find that the tilt of the traditional fundamental plane is naturally explained by the simple form of the MONDian interpolating function, if we assume a well motivated choice of anisotropic velocity distribution, and adopt the Kroupa or Salpeter stellar mass-to-light ratio. Our analysis does not necessarily rule out a varying stellar mass-to-light ratio.

A Novel General Imaging Formation Algorithm for GNSS-Based Bistatic SAR.

PubMed

Zeng, Hong-Cheng; Wang, Peng-Bo; Chen, Jie; Liu, Wei; Ge, LinLin; Yang, Wei

2016-02-26

Global Navigation Satellite System (GNSS)-based bistatic Synthetic Aperture Radar (SAR) recently plays a more and more significant role in remote sensing applications for its low-cost and real-time global coverage capability. In this paper, a general imaging formation algorithm was proposed for accurately and efficiently focusing GNSS-based bistatic SAR data, which avoids the interpolation processing in traditional back projection algorithms (BPAs). A two-dimensional point target spectrum model was firstly presented, and the bulk range cell migration correction (RCMC) was consequently derived for reducing range cell migration (RCM) and coarse focusing. As the bulk RCMC seriously changes the range history of the radar signal, a modified and much more efficient hybrid correlation operation was introduced for compensating residual phase errors. Simulation results were presented based on a general geometric topology with non-parallel trajectories and unequal velocities for both transmitter and receiver platforms, showing a satisfactory performance by the proposed method.

A Novel General Imaging Formation Algorithm for GNSS-Based Bistatic SAR

PubMed Central

Zeng, Hong-Cheng; Wang, Peng-Bo; Chen, Jie; Liu, Wei; Ge, LinLin; Yang, Wei

2016-01-01

Global Navigation Satellite System (GNSS)-based bistatic Synthetic Aperture Radar (SAR) recently plays a more and more significant role in remote sensing applications for its low-cost and real-time global coverage capability. In this paper, a general imaging formation algorithm was proposed for accurately and efficiently focusing GNSS-based bistatic SAR data, which avoids the interpolation processing in traditional back projection algorithms (BPAs). A two-dimensional point target spectrum model was firstly presented, and the bulk range cell migration correction (RCMC) was consequently derived for reducing range cell migration (RCM) and coarse focusing. As the bulk RCMC seriously changes the range history of the radar signal, a modified and much more efficient hybrid correlation operation was introduced for compensating residual phase errors. Simulation results were presented based on a general geometric topology with non-parallel trajectories and unequal velocities for both transmitter and receiver platforms, showing a satisfactory performance by the proposed method. PMID:26927117

Characterization and Modeling of Indium Gallium Antimonide Avalanche Photodiode and of Indium Gallium Arsenide Two-band Detector

NASA Technical Reports Server (NTRS)

2006-01-01

A model of the optical properties of Al(x)Ga(1-x)As(y)Sb(1-y) and In(x)Ga(1-x)As(y)Sb(1-y) is presented, including the refractive, extinction, absorption and reflection coefficients in terms of the optical dielectric function of the materials. Energy levels and model parameters for each binary compound are interpolated to obtain the needed ternaries and quaternaries for various compositions. Bowing parameters are considered in the interpolation scheme to take into account the deviation of the calculated ternary and quaternary values from experimental data due to lattice disorders. The inclusion of temperature effects is currently being considered.

VizieR Online Data Catalog: 3D correction in 5 photometric systems (Bonifacio+, 2018)

NASA Astrophysics Data System (ADS)

Bonifacio, P.; Caffau, E.; Ludwig, H.-G.; Steffen, M.; Castelli, F.; Gallagher, A. J.; Kucinskas, A.; Prakapavicius, D.; Cayrel, R.; Freytag, B.; Plez, B.; Homeier, D.

2018-01-01

We have used the CIFIST grid of CO5BOLD models to investigate the effects of granulation on fluxes and colours of stars of spectral type F, G, and K. We publish tables with 3D corrections that can be applied to colours computed from any 1D model atmosphere. For Teff>=5000K, the corrections are smooth enough, as a function of atmospheric parameters, that it is possible to interpolate the corrections between grid points; thus the coarseness of the CIFIST grid should not be a major limitation. However at the cool end there are still far too few models to allow a reliable interpolation. (20 data files).

[A correction method of baseline drift of discrete spectrum of NIR].

PubMed

Hu, Ai-Qin; Yuan, Hong-Fu; Song, Chun-Feng; Li, Xiao-Yu

2014-10-01

In the present paper, a new correction method of baseline drift of discrete spectrum is proposed by combination of cubic spline interpolation and first order derivative. A fitting spectrum is constructed by cubic spline interpolation, using the datum in discrete spectrum as interpolation nodes. The fitting spectrum is differentiable. First order derivative is applied to the fitting spectrum to calculate derivative spectrum. The spectral wavelengths which are the same as the original discrete spectrum were taken out from the derivative spectrum to constitute the first derivative spectra of the discrete spectra, thereby to correct the baseline drift of the discrete spectra. The effects of the new method were demonstrated by comparison of the performances of multivariate models built using original spectra, direct differential spectra and the spectra pretreated by the new method. The results show that negative effects on the performance of multivariate model caused by baseline drift of discrete spectra can be effectively eliminated by the new method.

Radon-domain interferometric interpolation for reconstruction of the near-offset gap in marine seismic data

NASA Astrophysics Data System (ADS)

Xu, Zhuo; Sopher, Daniel; Juhlin, Christopher; Han, Liguo; Gong, Xiangbo

2018-04-01

In towed marine seismic data acquisition, a gap between the source and the nearest recording channel is typical. Therefore, extrapolation of the missing near-offset traces is often required to avoid unwanted effects in subsequent data processing steps. However, most existing interpolation methods perform poorly when extrapolating traces. Interferometric interpolation methods are one particular method that have been developed for filling in trace gaps in shot gathers. Interferometry-type interpolation methods differ from conventional interpolation methods as they utilize information from several adjacent shot records to fill in the missing traces. In this study, we aim to improve upon the results generated by conventional time-space domain interferometric interpolation by performing interferometric interpolation in the Radon domain, in order to overcome the effects of irregular data sampling and limited source-receiver aperture. We apply both time-space and Radon-domain interferometric interpolation methods to the Sigsbee2B synthetic dataset and a real towed marine dataset from the Baltic Sea with the primary aim to improve the image of the seabed through extrapolation into the near-offset gap. Radon-domain interferometric interpolation performs better at interpolating the missing near-offset traces than conventional interferometric interpolation when applied to data with irregular geometry and limited source-receiver aperture. We also compare the interferometric interpolated results with those obtained using solely Radon transform (RT) based interpolation and show that interferometry-type interpolation performs better than solely RT-based interpolation when extrapolating the missing near-offset traces. After data processing, we show that the image of the seabed is improved by performing interferometry-type interpolation, especially when Radon-domain interferometric interpolation is applied.

Network compensation for missing sensors

NASA Technical Reports Server (NTRS)

Ahumada, Albert J., Jr.; Mulligan, Jeffrey B.

1991-01-01

A network learning translation invariance algorithm to compute interpolation functions is presented. This algorithm with one fixed receptive field can construct a linear transformation compensating for gain changes, sensor position jitter, and sensor loss when there are enough remaining sensors to adequately sample the input images. However, when the images are undersampled and complete compensation is not possible, the algorithm need to be modified. For moderate sensor losses, the algorithm works if the transformation weight adjustment is restricted to the weights to output units affected by the loss.

Applicability of Various Interpolation Approaches for High Resolution Spatial Mapping of Climate Data in Korea

NASA Astrophysics Data System (ADS)

Jo, A.; Ryu, J.; Chung, H.; Choi, Y.; Jeon, S.

2018-04-01

The purpose of this study is to create a new dataset of spatially interpolated monthly climate data for South Korea at high spatial resolution (approximately 30m) by performing various spatio-statistical interpolation and comparing with forecast LDAPS gridded climate data provided from Korea Meterological Administration (KMA). Automatic Weather System (AWS) and Automated Synoptic Observing System (ASOS) data in 2017 obtained from KMA were included for the spatial mapping of temperature and rainfall; instantaneous temperature and 1-hour accumulated precipitation at 09:00 am on 31th March, 21th June, 23th September, and 24th December. Among observation data, 80 percent of the total point (478) and remaining 120 points were used for interpolations and for quantification, respectively. With the training data and digital elevation model (DEM) with 30 m resolution, inverse distance weighting (IDW), co-kriging, and kriging were performed by using ArcGIS10.3.1 software and Python 3.6.4. Bias and root mean square were computed to compare prediction performance quantitatively. When statistical analysis was performed for each cluster using 20 % validation data, co kriging was more suitable for spatialization of instantaneous temperature than other interpolation method. On the other hand, IDW technique was appropriate for spatialization of precipitation.

A thermodynamic description for water, hydrogen fluoride and hydrogen dissolutions in cryolite-base molten salts.

PubMed

Wang, Kun; Chartrand, Patrice

2018-06-15

This paper presents a quantitative thermodynamic description for water, hydrogen fluoride and hydrogen dissolutions in cryolite-base molten salts, which is of technological importance to the Hall-Héroult electrolytic aluminum extraction cell. The Modified Quasichemical Model in the Quadruplet Approximation (MQMQA), as used to treat a large variety of molten salt systems, was adopted to thermodynamically describe the present liquid phase; all solid solutions were modeled using the Compound Energy Formalism (CEF); the gas phase was thermodynamically treated as an ideal mixture of all possible species. The model parameters were mainly obtained by critical evaluations and optimizations of thermodynamic and phase equilibrium data available from relative experimental measurements and theoretical predictions (first-principles calculations and empirical estimations) for the lower-order subsystems. These optimized model parameters were thereafter merged within the Kohler/Toop interpolation scheme, facilitating the prediction of gas solubility (H2O, HF and H2) in multicomponent cryolite-base molten salts using the FactSage thermochemical software. Several interesting diagrams were finally obtained in order to provide useful information for the industrial partners dedicated to the Hall-Héroult electrolytic aluminum production or other molten-salt technologies (the purification process and electroslag refining).

Design and evaluation of a Stochastic Optimal Feed-forward and Feedback Technology (SOFFT) flight control architecture

NASA Technical Reports Server (NTRS)

Ostroff, Aaron J.; Proffitt, Melissa S.

1994-01-01

This paper describes the design and evaluation of a stochastic optimal feed-forward and feedback technology (SOFFT) control architecture with emphasis on the feed-forward controller design. The SOFFT approach allows the designer to independently design the feed-forward and feedback controllers to meet separate objectives and then integrate the two controllers. The feed-forward controller has been integrated with an existing high-angle-of-attack (high-alpha) feedback controller. The feed-forward controller includes a variable command model with parameters selected to satisfy level 1 flying qualities with a high-alpha adjustment to achieve desired agility guidelines, a nonlinear interpolation approach that scales entire matrices for approximation of the plant model, and equations for calculating feed-forward gains developed for perfect plant-model tracking. The SOFFT design was applied to a nonlinear batch simulation model of an F/A-18 aircraft modified for thrust vectoring. Simulation results show that agility guidelines are met and that the SOFFT controller filters undesired pilot-induced frequencies more effectively during a tracking task than a flight controller that has the same feedback control law but does not have the SOFFT feed-forward control.

A Framework for Linear and Non-Linear Registration of Diffusion-Weighted MRIs Using Angular Interpolation

PubMed Central

Duarte-Carvajalino, Julio M.; Sapiro, Guillermo; Harel, Noam; Lenglet, Christophe

2013-01-01

Registration of diffusion-weighted magnetic resonance images (DW-MRIs) is a key step for population studies, or construction of brain atlases, among other important tasks. Given the high dimensionality of the data, registration is usually performed by relying on scalar representative images, such as the fractional anisotropy (FA) and non-diffusion-weighted (b0) images, thereby ignoring much of the directional information conveyed by DW-MR datasets itself. Alternatively, model-based registration algorithms have been proposed to exploit information on the preferred fiber orientation(s) at each voxel. Models such as the diffusion tensor or orientation distribution function (ODF) have been used for this purpose. Tensor-based registration methods rely on a model that does not completely capture the information contained in DW-MRIs, and largely depends on the accurate estimation of tensors. ODF-based approaches are more recent and computationally challenging, but also better describe complex fiber configurations thereby potentially improving the accuracy of DW-MRI registration. A new algorithm based on angular interpolation of the diffusion-weighted volumes was proposed for affine registration, and does not rely on any specific local diffusion model. In this work, we first extensively compare the performance of registration algorithms based on (i) angular interpolation, (ii) non-diffusion-weighted scalar volume (b0), and (iii) diffusion tensor image (DTI). Moreover, we generalize the concept of angular interpolation (AI) to non-linear image registration, and implement it in the FMRIB Software Library (FSL). We demonstrate that AI registration of DW-MRIs is a powerful alternative to volume and tensor-based approaches. In particular, we show that AI improves the registration accuracy in many cases over existing state-of-the-art algorithms, while providing registered raw DW-MRI data, which can be used for any subsequent analysis. PMID:23596381

A Framework for Linear and Non-Linear Registration of Diffusion-Weighted MRIs Using Angular Interpolation.

PubMed

Duarte-Carvajalino, Julio M; Sapiro, Guillermo; Harel, Noam; Lenglet, Christophe

2013-01-01

Registration of diffusion-weighted magnetic resonance images (DW-MRIs) is a key step for population studies, or construction of brain atlases, among other important tasks. Given the high dimensionality of the data, registration is usually performed by relying on scalar representative images, such as the fractional anisotropy (FA) and non-diffusion-weighted (b0) images, thereby ignoring much of the directional information conveyed by DW-MR datasets itself. Alternatively, model-based registration algorithms have been proposed to exploit information on the preferred fiber orientation(s) at each voxel. Models such as the diffusion tensor or orientation distribution function (ODF) have been used for this purpose. Tensor-based registration methods rely on a model that does not completely capture the information contained in DW-MRIs, and largely depends on the accurate estimation of tensors. ODF-based approaches are more recent and computationally challenging, but also better describe complex fiber configurations thereby potentially improving the accuracy of DW-MRI registration. A new algorithm based on angular interpolation of the diffusion-weighted volumes was proposed for affine registration, and does not rely on any specific local diffusion model. In this work, we first extensively compare the performance of registration algorithms based on (i) angular interpolation, (ii) non-diffusion-weighted scalar volume (b0), and (iii) diffusion tensor image (DTI). Moreover, we generalize the concept of angular interpolation (AI) to non-linear image registration, and implement it in the FMRIB Software Library (FSL). We demonstrate that AI registration of DW-MRIs is a powerful alternative to volume and tensor-based approaches. In particular, we show that AI improves the registration accuracy in many cases over existing state-of-the-art algorithms, while providing registered raw DW-MRI data, which can be used for any subsequent analysis.

International Geomagnetic Reference Field: the third generation.

USGS Publications Warehouse

Peddie, N.W.

1982-01-01

In August 1981 the International Association of Geomagnetism and Aeronomy revised the International Geomagnetic Reference Field (IGRF). It is the second revision since the inception of the IGRF in 1968. The revision extends the earlier series of IGRF models from 1980 to 1985, introduces a new series of definitive models for 1965-1976, and defines a provisional reference field for 1975- 1980. The revision consists of: 1) a model of the main geomagnetic field at 1980.0, not continuous with the earlier series of IGRF models together with a forecast model of the secular variation of the main field during 1980-1985; 2) definitive models of the main field at 1965.0, 1970.0, and 1975.0, with linear interpolation of the model coefficients specified for intervening dates; and 3) a provisional reference field for 1975-1980, defined as the linear interpolation of the 1975 and 1980 main-field models.-from Author

Statistical assessment and hydrological utility of the latest multi-satellite precipitation analysis IMERG in Ganjiang River basin

NASA Astrophysics Data System (ADS)

Li, Na; Tang, Guoqiang; Zhao, Ping; Hong, Yang; Gou, Yabin; Yang, Kai

2017-01-01

This study aims to statistically and hydrologically assess the hydrological utility of the latest Integrated Multi-satellitE Retrievals from Global Precipitation Measurement (IMERG) multi-satellite constellation over the mid-latitude Ganjiang River basin in China. The investigations are conducted at hourly and 0.1° resolutions throughout the rainy season from March 12 to September 30, 2014. Two high-quality quantitative precipitation estimation (QPE) datasets, i.e., a gauge-corrected radar mosaic QPE product (RQPE) and a highly dense network of 1200 rain gauges, are used as the reference. For the implementation of the study, first, we compare IMERG product and RQPE with rain gauge-interpolated data, respectively. The results indicate that both remote sensing products can estimate precipitation fairly well over the basin, while RQPE significantly outperforms IMERG product in almost all the studied cases. The correlation coefficients of RQPE (CC = 0.98 and CC = 0.67) are much higher than those of IMERG product (CC = 0.80 and CC = 0.33) at basin and grid scales, respectively. Then, the hydrological assessment is conducted with the Coupled Routing and Excess Storage (CREST) model under multiple parameterization scenarios, in which the model is calibrated using the rain gauge-interpolated data, RQPE, and IMERG products respectively. During the calibration period (from March 12 to May 31), the simulated streamflow based on rain gauge-interpolated data shows the highest Nash-Sutcliffe coefficient efficiency (NSCE) value (0.92), closely followed by the RQPE (NSCE = 0.84), while IMERG product performs barely acceptable (NSCE = 0.56). During the validation period (from June 1 to September 30), the three rainfall datasets are used to force the CREST model based on all the three calibrated parameter sets (i.e., nine combinations in total). RQPE outperforms rain gauge-interpolated data and IMERG product in all validation scenarios, possibly due to its advantageous capability in capturing high space-time variability of precipitation systems in the humid climate during the validation period. Overall, RQPE and rain gauge-interpolated data exhibit better performance compared with the newly available IMERG product, and RQPE is better than rain gauge-interpolated data to some extent due to the combination of both radar and rain gauge observations. IMERG-forced hourly CREST hydrologic model based on the Gauge- and RQPE-calibrated parameters performs well over Ganjiang River basin. Future studies should promote the hydrological application of RQPE datasets at global and local scales, and continuously improve IMERG algorithms.

Image interpolation allows accurate quantitative bone morphometry in registered micro-computed tomography scans.

PubMed

Schulte, Friederike A; Lambers, Floor M; Mueller, Thomas L; Stauber, Martin; Müller, Ralph

2014-04-01

Time-lapsed in vivo micro-computed tomography is a powerful tool to analyse longitudinal changes in the bone micro-architecture. Registration can overcome problems associated with spatial misalignment between scans; however, it requires image interpolation which might affect the outcome of a subsequent bone morphometric analysis. The impact of the interpolation error itself, though, has not been quantified to date. Therefore, the purpose of this ex vivo study was to elaborate the effect of different interpolator schemes [nearest neighbour, tri-linear and B-spline (BSP)] on bone morphometric indices. None of the interpolator schemes led to significant differences between interpolated and non-interpolated images, with the lowest interpolation error found for BSPs (1.4%). Furthermore, depending on the interpolator, the processing order of registration, Gaussian filtration and binarisation played a role. Independent from the interpolator, the present findings suggest that the evaluation of bone morphometry should be done with images registered using greyscale information.

Greedy Sampling and Incremental Surrogate Model-Based Tailoring of Aeroservoelastic Model Database for Flexible Aircraft

NASA Technical Reports Server (NTRS)

Wang, Yi; Pant, Kapil; Brenner, Martin J.; Ouellette, Jeffrey A.

2018-01-01

This paper presents a data analysis and modeling framework to tailor and develop linear parameter-varying (LPV) aeroservoelastic (ASE) model database for flexible aircrafts in broad 2D flight parameter space. The Kriging surrogate model is constructed using ASE models at a fraction of grid points within the original model database, and then the ASE model at any flight condition can be obtained simply through surrogate model interpolation. The greedy sampling algorithm is developed to select the next sample point that carries the worst relative error between the surrogate model prediction and the benchmark model in the frequency domain among all input-output channels. The process is iterated to incrementally improve surrogate model accuracy till a pre-determined tolerance or iteration budget is met. The methodology is applied to the ASE model database of a flexible aircraft currently being tested at NASA/AFRC for flutter suppression and gust load alleviation. Our studies indicate that the proposed method can reduce the number of models in the original database by 67%. Even so the ASE models obtained through Kriging interpolation match the model in the original database constructed directly from the physics-based tool with the worst relative error far below 1%. The interpolated ASE model exhibits continuously-varying gains along a set of prescribed flight conditions. More importantly, the selected grid points are distributed non-uniformly in the parameter space, a) capturing the distinctly different dynamic behavior and its dependence on flight parameters, and b) reiterating the need and utility for adaptive space sampling techniques for ASE model database compaction. The present framework is directly extendible to high-dimensional flight parameter space, and can be used to guide the ASE model development, model order reduction, robust control synthesis and novel vehicle design of flexible aircraft.

Frontal Representation as a Metric of Model Performance

NASA Astrophysics Data System (ADS)

Douglass, E.; Mask, A. C.

2017-12-01

Representation of fronts detected by altimetry are used to evaluate the performance of the HYCOM global operational product. Fronts are detected and assessed in daily alongtrack altimetry. Then, modeled sea surface height is interpolated to the locations of the alongtrack observations, and the same frontal detection algorithm is applied to the interpolated model output. The percentage of fronts found in the altimetry and replicated in the model gives a score (0-100) that assesses the model's ability to replicate fronts in the proper location with the proper orientation. Further information can be obtained from determining the number of "extra" fronts found in the model but not in the altimetry, and from assessing the horizontal and vertical dimensions of the front in the model as compared to observations. Finally, the sensitivity of this metric to choices regarding the smoothing of noisy alongtrack altimetry observations, and to the minimum size of fronts being analyzed, is assessed.

Simulation study of axial ultrasound transmission in heterogeneous cortical bone model

NASA Astrophysics Data System (ADS)

Takano, Koki; Nagatani, Yoshiki; Matsukawa, Mami

2017-07-01

Ultrasound propagation in a heterogeneous cortical bone was studied. Using a bovine radius, the longitudinal wave velocity distribution in the axial direction was experimentally measured in the MHz range. The bilinear interpolation and piecewise cubic Hermite interpolation methods were applied to create a three-dimensional (3D) precise velocity model of the bone using experimental data. By assuming the uniaxial anisotropy of the bone, the distributions of all elastic moduli of a 3D heterogeneous model were estimated. The elastic finite-difference time-domain method was used to simulate axial ultrasonic wave propagation. The wave propagation in the initial model was compared with that in the thinner model, where the inner part of the cortical bone model was removed. The wave front of the first arriving signal (FAS) slightly depended on the heterogeneity in each model. Owing to the decrease in bone thickness, the propagation behavior also changed and the FAS velocity clearly decreased.

Empirical modeling of environment-enhanced fatigue crack propagation in structural alloys for component life prediction

NASA Technical Reports Server (NTRS)

Richey, Edward, III

1995-01-01

This research aims to develop the methods and understanding needed to incorporate time and loading variable dependent environmental effects on fatigue crack propagation (FCP) into computerized fatigue life prediction codes such as NASA FLAGRO (NASGRO). In particular, the effect of loading frequency on FCP rates in alpha + beta titanium alloys exposed to an aqueous chloride solution is investigated. The approach couples empirical modeling of environmental FCP with corrosion fatigue experiments. Three different computer models have been developed and incorporated in the DOS executable program. UVAFAS. A multiple power law model is available, and can fit a set of fatigue data to a multiple power law equation. A model has also been developed which implements the Wei and Landes linear superposition model, as well as an interpolative model which can be utilized to interpolate trends in fatigue behavior based on changes in loading characteristics (stress ratio, frequency, and hold times).

AIR QUALITY MODELING OF PM AND AIR TOXICS AT NEIGHBORHOOD SCALES

EPA Science Inventory

The current interest in fine particles and toxics pollutants provide an impetus for extending air quality modeling capability towards improving exposure modeling and assessments. Human exposure models require information on concentration derived from interpolation of observati...

Tutorial: Asteroseismic Stellar Modelling with AIMS

NASA Astrophysics Data System (ADS)

Lund, Mikkel N.; Reese, Daniel R.

The goal of aims (Asteroseismic Inference on a Massive Scale) is to estimate stellar parameters and credible intervals/error bars in a Bayesian manner from a set of asteroseismic frequency data and so-called classical constraints. To achieve reliable parameter estimates and computational efficiency, it searches through a grid of pre-computed models using an MCMC algorithm—interpolation within the grid of models is performed by first tessellating the grid using a Delaunay triangulation and then doing a linear barycentric interpolation on matching simplexes. Inputs for the modelling consist of individual frequencies from peak-bagging, which can be complemented with classical spectroscopic constraints. aims is mostly written in Python with a modular structure to facilitate contributions from the community. Only a few computationally intensive parts have been rewritten in Fortran in order to speed up calculations.

Evaluation of methodologies for interpolation of data for hydrological modeling in glacierized basins with limited information

NASA Astrophysics Data System (ADS)

Muñoz, Randy; Paredes, Javier; Huggel, Christian; Drenkhan, Fabian; García, Javier

2017-04-01

The availability and consistency of data is a determining factor for the reliability of any hydrological model and simulated results. Unfortunately, there are many regions worldwide where data is not available in the desired quantity and quality. The Santa River basin (SRB), located within a complex topographic and climatic setting in the tropical Andes of Peru is a clear example of this challenging situation. A monitoring network of in-situ stations in the SRB recorded series of hydro-meteorological variables which finally ceased to operate in 1999. In the following years, several researchers evaluated and completed many of these series. This database was used by multiple research and policy-oriented projects in the SRB. However, hydroclimatic information remains limited, making it difficult to perform research, especially when dealing with the assessment of current and future water resources. In this context, here the evaluation of different methodologies to interpolate temperature and precipitation data at a monthly time step as well as ice volume data in glacierized basins with limited data is presented. The methodologies were evaluated for the Quillcay River, a tributary of the SRB, where the hydro-meteorological data is available from nearby monitoring stations since 1983. The study period was 1983 - 1999 with a validation period among 1993 - 1999. For temperature series the aim was to extend the observed data and interpolate it. Data from Reanalysis NCEP was used to extend the observed series: 1) using a simple correlation with multiple field stations, or 2) applying the altitudinal correction proposed in previous studies. The interpolation then was applied as a function of altitude. Both methodologies provide very close results, by parsimony simple correlation is shown as a viable choice. For precipitation series, the aim was to interpolate observed data. Two methodologies were evaluated: 1) Inverse Distance Weighting whose results underestimate the amount of precipitation in high-altitudinal zones, and 2) ordinary Kriging (OK) whose variograms were calculated with the multi-annual monthly mean precipitation applying them to the whole study period. OK leads to better results in both low and high altitudinal zones. For ice volume, the aim was to estimate values from historical data: 1) with the GlabTop algorithm which needs digital elevation models, but these are available in an appropriate scale since 2009, 2) with a widely applied but controversially discussed glacier area-volume relation whose parameters were calibrated with results from the GlabTop model. Both methodologies provide reasonable results, but for historical data, the area-volume scaling only requires the glacial area easy to calculate from satellite images since 1986. In conclusion, the simple correlation, the OK and the calibrated relation for ice volume showed the best ways to interpolate glacio-climatic information. However, these methods must be carefully applied and revisited for the specific situation with high complexity. This is a first step in order to identify the most appropriate methods to interpolate and extend observed data in glacierized basins with limited information. New research should be done evaluating another methodologies and meteorological data in order to improve hydrological models and water management policies.

Comparison Study on the Estimation of the Spatial Distribution of Regional Soil Metal(loid)s Pollution Based on Kriging Interpolation and BP Neural Network

PubMed Central

Zhou, Shenglu; Su, Quanlong; Yi, Haomin

2017-01-01

Soil pollution by metal(loid)s resulting from rapid economic development is a major concern. Accurately estimating the spatial distribution of soil metal(loid) pollution has great significance in preventing and controlling soil pollution. In this study, 126 topsoil samples were collected in Kunshan City and the geo-accumulation index was selected as a pollution index. We used Kriging interpolation and BP neural network methods to estimate the spatial distribution of arsenic (As) and cadmium (Cd) pollution in the study area. Additionally, we introduced a cross-validation method to measure the errors of the estimation results by the two interpolation methods and discussed the accuracy of the information contained in the estimation results. The conclusions are as follows: data distribution characteristics, spatial variability, and mean square errors (MSE) of the different methods showed large differences. Estimation results from BP neural network models have a higher accuracy, the MSE of As and Cd are 0.0661 and 0.1743, respectively. However, the interpolation results show significant skewed distribution, and spatial autocorrelation is strong. Using Kriging interpolation, the MSE of As and Cd are 0.0804 and 0.2983, respectively. The estimation results have poorer accuracy. Combining the two methods can improve the accuracy of the Kriging interpolation and more comprehensively represent the spatial distribution characteristics of metal(loid)s in regional soil. The study may provide a scientific basis and technical support for the regulation of soil metal(loid) pollution. PMID:29278363

Optimal interpolation and the Kalman filter. [for analysis of numerical weather predictions

NASA Technical Reports Server (NTRS)

Cohn, S.; Isaacson, E.; Ghil, M.

1981-01-01

The estimation theory of stochastic-dynamic systems is described and used in a numerical study of optimal interpolation. The general form of data assimilation methods is reviewed. The Kalman-Bucy, KB filter, and optimal interpolation (OI) filters are examined for effectiveness in performance as gain matrices using a one-dimensional form of the shallow-water equations. Control runs in the numerical analyses were performed for a ten-day forecast in concert with the OI method. The effects of optimality, initialization, and assimilation were studied. It was found that correct initialization is necessary in order to localize errors, especially near boundary points. Also, the use of small forecast error growth rates over data-sparse areas was determined to offset inaccurate modeling of correlation functions near boundaries.

Simulation of Tracer Concentration Data in the Brush Creek Drainage Flow Using an Integrated Puff Model.

NASA Astrophysics Data System (ADS)

Rao, K. Shankar; Eckman, Richard M.; Hosker, Rayford P., Jr.

1989-07-01

During the 1984 ASCOT field study in Brush Creek Valley, two perfluorocarbon tracers were released into the nocturnal drainage flow at two different heights. The resulting surface concentrations were sampled at 90 sites, and vertical concentration profiles at 11 sites. These detailed tracer measurements provide a valuable dataset for developing and testing models of pollutant transport and dispersion in valleys.In this paper, we present the results of Gaussian puff model simulations of the tracer releases in Brush Creek Valley. The model was modified to account for the restricted lateral dispersion in the valley, and for the gross elevation differences between the release site and the receptors. The variable wind fields needed to transport the puffs were obtained by interpolation between wind profiles measured using tethered balloons at five along-valley sites. Direct turbulence measurements were used to estimate diffusion. Subsidence in the valley flow was included for elevated releases.Two test simulations-covering different nights, tracers, and release heights-were performed. The predicted hourly concentrations were compared with observations at 51 ground-level locations. At most sites, the predicted and observed concentrations agree within a factor of 2 to 6. For the elevated release simulation, the observed mean concentration is 40 pL/L, the predicted mean is 21 pL/L, the correlation coefficient between the observed and predicted concentrations is 0.24, and the index of agreement is 0.46. For the surface release simulation, the observed mean is 85 pL/L, and the predicted mean is 73 pL/L. The correlation coefficient is 0.23, and the index of agreement is 0.42. The results suggest that this modified puff model can be used as a practical tool for simulating pollutant transport and dispersion in deep valleys.

Summary on several key techniques in 3D geological modeling.

PubMed

Mei, Gang

2014-01-01

Several key techniques in 3D geological modeling including planar mesh generation, spatial interpolation, and surface intersection are summarized in this paper. Note that these techniques are generic and widely used in various applications but play a key role in 3D geological modeling. There are two essential procedures in 3D geological modeling: the first is the simulation of geological interfaces using geometric surfaces and the second is the building of geological objects by means of various geometric computations such as the intersection of surfaces. Discrete geometric surfaces that represent geological interfaces can be generated by creating planar meshes first and then spatially interpolating; those surfaces intersect and then form volumes that represent three-dimensional geological objects such as rock bodies. In this paper, the most commonly used algorithms of the key techniques in 3D geological modeling are summarized.

Using the SWAT model to improve process descriptions and define hydrologic partitioning in South Korea

NASA Astrophysics Data System (ADS)

Shope, C. L.; Maharjan, G. R.; Tenhunen, J.; Seo, B.; Kim, K.; Riley, J.; Arnhold, S.; Koellner, T.; Ok, Y. S.; Peiffer, S.; Kim, B.; Park, J.-H.; Huwe, B.

2014-02-01

Watershed-scale modeling can be a valuable tool to aid in quantification of water quality and yield; however, several challenges remain. In many watersheds, it is difficult to adequately quantify hydrologic partitioning. Data scarcity is prevalent, accuracy of spatially distributed meteorology is difficult to quantify, forest encroachment and land use issues are common, and surface water and groundwater abstractions substantially modify watershed-based processes. Our objective is to assess the capability of the Soil and Water Assessment Tool (SWAT) model to capture event-based and long-term monsoonal rainfall-runoff processes in complex mountainous terrain. To accomplish this, we developed a unique quality-control, gap-filling algorithm for interpolation of high-frequency meteorological data. We used a novel multi-location, multi-optimization calibration technique to improve estimations of catchment-wide hydrologic partitioning. The interdisciplinary model was calibrated to a unique combination of statistical, hydrologic, and plant growth metrics. Our results indicate scale-dependent sensitivity of hydrologic partitioning and substantial influence of engineered features. The addition of hydrologic and plant growth objective functions identified the importance of culverts in catchment-wide flow distribution. While this study shows the challenges of applying the SWAT model to complex terrain and extreme environments; by incorporating anthropogenic features into modeling scenarios, we can enhance our understanding of the hydroecological impact.

Spatial and spectral interpolation of ground-motion intensity measure observations

USGS Publications Warehouse

Worden, Charles; Thompson, Eric M.; Baker, Jack W.; Bradley, Brendon A.; Luco, Nicolas; Wilson, David

2018-01-01

Following a significant earthquake, ground‐motion observations are available for a limited set of locations and intensity measures (IMs). Typically, however, it is desirable to know the ground motions for additional IMs and at locations where observations are unavailable. Various interpolation methods are available, but because IMs or their logarithms are normally distributed, spatially correlated, and correlated with each other at a given location, it is possible to apply the conditional multivariate normal (MVN) distribution to the problem of estimating unobserved IMs. In this article, we review the MVN and its application to general estimation problems, and then apply the MVN to the specific problem of ground‐motion IM interpolation. In particular, we present (1) a formulation of the MVN for the simultaneous interpolation of IMs across space and IM type (most commonly, spectral response at different oscillator periods) and (2) the inclusion of uncertain observation data in the MVN formulation. These techniques, in combination with modern empirical ground‐motion models and correlation functions, provide a flexible framework for estimating a variety of IMs at arbitrary locations.

A Comparative Study of Three Spatial Interpolation Methodologies for the Analysis of Air Pollution Concentrations in Athens, Greece

NASA Astrophysics Data System (ADS)

Deligiorgi, Despina; Philippopoulos, Kostas; Thanou, Lelouda; Karvounis, Georgios

2010-01-01

Spatial interpolation in air pollution modeling is the procedure for estimating ambient air pollution concentrations at unmonitored locations based on available observations. The selection of the appropriate methodology is based on the nature and the quality of the interpolated data. In this paper, an assessment of three widely used interpolation methodologies is undertaken in order to estimate the errors involved. For this purpose, air quality data from January 2001 to December 2005, from a network of seventeen monitoring stations, operating at the greater area of Athens in Greece, are used. The Nearest Neighbor and the Liner schemes were applied to the mean hourly observations, while the Inverse Distance Weighted (IDW) method to the mean monthly concentrations. The discrepancies of the estimated and measured values are assessed for every station and pollutant, using the correlation coefficient, the scatter diagrams and the statistical residuals. The capability of the methods to estimate air quality data in an area with multiple land-use types and pollution sources, such as Athens, is discussed.

Using Chebyshev polynomial interpolation to improve the computational efficiency of gravity models near an irregularly-shaped asteroid

NASA Astrophysics Data System (ADS)

Hu, Shou-Cun; Ji, Jiang-Hui

2017-12-01

In asteroid rendezvous missions, the dynamical environment near an asteroid’s surface should be made clear prior to launch of the mission. However, most asteroids have irregular shapes, which lower the efficiency of calculating their gravitational field by adopting the traditional polyhedral method. In this work, we propose a method to partition the space near an asteroid adaptively along three spherical coordinates and use Chebyshev polynomial interpolation to represent the gravitational acceleration in each cell. Moreover, we compare four different interpolation schemes to obtain the best precision with identical initial parameters. An error-adaptive octree division is combined to improve the interpolation precision near the surface. As an example, we take the typical irregularly-shaped near-Earth asteroid 4179 Toutatis to demonstrate the advantage of this method; as a result, we show that the efficiency can be increased by hundreds to thousands of times with our method. Our results indicate that this method can be applicable to other irregularly-shaped asteroids and can greatly improve the evaluation efficiency.

Space Weather Activities of IONOLAB Group: TEC Mapping

NASA Astrophysics Data System (ADS)

Arikan, F.; Yilmaz, A.; Arikan, O.; Sayin, I.; Gurun, M.; Akdogan, K. E.; Yildirim, S. A.

2009-04-01

Being a key player in Space Weather, ionospheric variability affects the performance of both communication and navigation systems. To improve the performance of these systems, ionosphere has to be monitored. Total Electron Content (TEC), line integral of the electron density along a ray path, is an important parameter to investigate the ionospheric variability. A cost-effective way of obtaining TEC is by using dual-frequency GPS receivers. Since these measurements are sparse in space, accurate and robust interpolation techniques are needed to interpolate (or map) the TEC distribution for a given region in space. However, the TEC data derived from GPS measurements contain measurement noise, model and computational errors. Thus, it is necessary to analyze the interpolation performance of the techniques on synthetic data sets that can represent various ionospheric states. By this way, interpolation performance of the techniques can be compared over many parameters that can be controlled to represent the desired ionospheric states. In this study, Multiquadrics, Inverse Distance Weighting (IDW), Cubic Splines, Ordinary and Universal Kriging, Random Field Priors (RFP), Multi-Layer Perceptron Neural Network (MLP-NN), and Radial Basis Function Neural Network (RBF-NN) are employed as the spatial interpolation algorithms. These mapping techniques are initially tried on synthetic TEC surfaces for parameter and coefficient optimization and determination of error bounds. Interpolation performance of these methods are compared on synthetic TEC surfaces over the parameters of sampling pattern, number of samples, the variability of the surface and the trend type in the TEC surfaces. By examining the performance of the interpolation methods, it is observed that both Kriging, RFP and NN have important advantages and possible disadvantages depending on the given constraints. It is also observed that the determining parameter in the error performance is the trend in the Ionosphere. Optimization of the algorithms in terms of their performance parameters (like the choice of the semivariogram function for Kriging algorithms and the hidden layer and neuron numbers for MLP-NN) mostly depend on the behavior of the ionosphere at that given time instant for the desired region. The sampling pattern and number of samples are the other important parameters that may contribute to the higher errors in reconstruction. For example, for all of the above listed algorithms, hexagonal regular sampling of the ionosphere provides the lowest reconstruction error and the performance significantly degrades as the samples in the region become sparse and clustered. The optimized models and coefficients are applied to regional GPS-TEC mapping using the IONOLAB-TEC data (www.ionolab.org). Both Kriging combined with Kalman Filter and dynamic modeling of NN are also implemented as first trials of TEC and space weather predictions.

TDIGG - TWO-DIMENSIONAL, INTERACTIVE GRID GENERATION CODE

NASA Technical Reports Server (NTRS)

Vu, B. T.

1994-01-01

TDIGG is a fast and versatile program for generating two-dimensional computational grids for use with finite-difference flow-solvers. Both algebraic and elliptic grid generation systems are included. The method for grid generation by algebraic transformation is based on an interpolation algorithm and the elliptic grid generation is established by solving the partial differential equation (PDE). Non-uniform grid distributions are carried out using a hyperbolic tangent stretching function. For algebraic grid systems, interpolations in one direction (univariate) and two directions (bivariate) are considered. These interpolations are associated with linear or cubic Lagrangian/Hermite/Bezier polynomial functions. The algebraic grids can subsequently be smoothed using an elliptic solver. For elliptic grid systems, the PDE can be in the form of Laplace (zero forcing function) or Poisson. The forcing functions in the Poisson equation come from the boundary or the entire domain of the initial algebraic grids. A graphics interface procedure using the Silicon Graphics (GL) Library is included to allow users to visualize the grid variations at each iteration. This will allow users to interactively modify the grid to match their applications. TDIGG is written in FORTRAN 77 for Silicon Graphics IRIS series computers running IRIX. This package requires either MIT's X Window System, Version 11 Revision 4 or SGI (Motif) Window System. A sample executable is provided on the distribution medium. It requires 148K of RAM for execution. The standard distribution medium is a .25 inch streaming magnetic IRIX tape cartridge in UNIX tar format. This program was developed in 1992.

A mass-conservative adaptive FAS multigrid solver for cell-centered finite difference methods on block-structured, locally-cartesian grids

NASA Astrophysics Data System (ADS)

Feng, Wenqiang; Guo, Zhenlin; Lowengrub, John S.; Wise, Steven M.

2018-01-01

We present a mass-conservative full approximation storage (FAS) multigrid solver for cell-centered finite difference methods on block-structured, locally cartesian grids. The algorithm is essentially a standard adaptive FAS (AFAS) scheme, but with a simple modification that comes in the form of a mass-conservative correction to the coarse-level force. This correction is facilitated by the creation of a zombie variable, analogous to a ghost variable, but defined on the coarse grid and lying under the fine grid refinement patch. We show that a number of different types of fine-level ghost cell interpolation strategies could be used in our framework, including low-order linear interpolation. In our approach, the smoother, prolongation, and restriction operations need never be aware of the mass conservation conditions at the coarse-fine interface. To maintain global mass conservation, we need only modify the usual FAS algorithm by correcting the coarse-level force function at points adjacent to the coarse-fine interface. We demonstrate through simulations that the solver converges geometrically, at a rate that is h-independent, and we show the generality of the solver, applying it to several nonlinear, time-dependent, and multi-dimensional problems. In several tests, we show that second-order asymptotic (h → 0) convergence is observed for the discretizations, provided that (1) at least linear interpolation of the ghost variables is employed, and (2) the mass conservation corrections are applied to the coarse-level force term.

Design and Testing of a Flexible Inclinometer Probe for Model Tests of Landslide Deep Displacement Measurement.

PubMed

Zhang, Yongquan; Tang, Huiming; Li, Changdong; Lu, Guiying; Cai, Yi; Zhang, Junrong; Tan, Fulin

2018-01-14

The physical model test of landslides is important for studying landslide structural damage, and parameter measurement is key in this process. To meet the measurement requirements for deep displacement in landslide physical models, an automatic flexible inclinometer probe with good coupling and large deformation capacity was designed. The flexible inclinometer probe consists of several gravity acceleration sensing units that are protected and positioned by silicon encapsulation, all the units are connected to a 485-comunication bus. By sensing the two-axis tilt angle, the direction and magnitude of the displacement for a measurement unit can be calculated, then the overall displacement is accumulated according to all units, integrated from bottom to top in turn. In the conversion from angle to displacement, two spline interpolation methods are introduced to correct and resample the data; one is to interpolate the displacement after conversion, and the other is to interpolate the angle before conversion; compared with the result read from checkered paper, the latter is proved to have a better effect, with an additional condition that the displacement curve move up half the length of the unit. The flexible inclinometer is verified with respect to its principle and arrangement by a laboratory physical model test, and the test results are highly consistent with the actual deformation of the landslide model.

Design and Testing of a Flexible Inclinometer Probe for Model Tests of Landslide Deep Displacement Measurement

PubMed Central

Zhang, Yongquan; Tang, Huiming; Li, Changdong; Lu, Guiying; Cai, Yi; Zhang, Junrong; Tan, Fulin

2018-01-01

The physical model test of landslides is important for studying landslide structural damage, and parameter measurement is key in this process. To meet the measurement requirements for deep displacement in landslide physical models, an automatic flexible inclinometer probe with good coupling and large deformation capacity was designed. The flexible inclinometer probe consists of several gravity acceleration sensing units that are protected and positioned by silicon encapsulation, all the units are connected to a 485-comunication bus. By sensing the two-axis tilt angle, the direction and magnitude of the displacement for a measurement unit can be calculated, then the overall displacement is accumulated according to all units, integrated from bottom to top in turn. In the conversion from angle to displacement, two spline interpolation methods are introduced to correct and resample the data; one is to interpolate the displacement after conversion, and the other is to interpolate the angle before conversion; compared with the result read from checkered paper, the latter is proved to have a better effect, with an additional condition that the displacement curve move up half the length of the unit. The flexible inclinometer is verified with respect to its principle and arrangement by a laboratory physical model test, and the test results are highly consistent with the actual deformation of the landslide model. PMID:29342902

A gap-filling model for eddy covariance latent heat flux: Estimating evapotranspiration of a subtropical seasonal evergreen broad-leaved forest as an example

NASA Astrophysics Data System (ADS)

Chen, Yi-Ying; Chu, Chia-Ren; Li, Ming-Hsu

2012-10-01

SummaryIn this paper we present a semi-parametric multivariate gap-filling model for tower-based measurement of latent heat flux (LE). Two statistical techniques, the principal component analysis (PCA) and a nonlinear interpolation approach were integrated into this LE gap-filling model. The PCA was first used to resolve the multicollinearity relationships among various environmental variables, including radiation, soil moisture deficit, leaf area index, wind speed, etc. Two nonlinear interpolation methods, multiple regressions (MRS) and the K-nearest neighbors (KNNs) were examined with random selected flux gaps for both clear sky and nighttime/cloudy data to incorporate into this LE gap-filling model. Experimental results indicated that the KNN interpolation approach is able to provide consistent LE estimations while MRS presents over estimations during nighttime/cloudy. Rather than using empirical regression parameters, the KNN approach resolves the nonlinear relationship between the gap-filled LE flux and principal components with adaptive K values under different atmospheric states. The developed LE gap-filling model (PCA with KNN) works with a RMSE of 2.4 W m-2 (˜0.09 mm day-1) at a weekly time scale by adding 40% artificial flux gaps into original dataset. Annual evapotranspiration at this study site were estimated at 736 mm (1803 MJ) and 728 mm (1785 MJ) for year 2008 and 2009, respectively.

An accurate method for computer-generating tungsten anode x-ray spectra from 30 to 140 kV.

PubMed

Boone, J M; Seibert, J A

1997-11-01

A tungsten anode spectral model using interpolating polynomials (TASMIP) was used to compute x-ray spectra at 1 keV intervals over the range from 30 kV to 140 kV. The TASMIP is not semi-empirical and uses no physical assumptions regarding x-ray production, but rather interpolates measured constant potential x-ray spectra published by Fewell et al. [Handbook of Computed Tomography X-ray Spectra (U.S. Government Printing Office, Washington, D.C., 1981)]. X-ray output measurements (mR/mAs measured at 1 m) were made on a calibrated constant potential generator in our laboratory from 50 kV to 124 kV, and with 0-5 mm added aluminum filtration. The Fewell spectra were slightly modified (numerically hardened) and normalized based on the attenuation and output characteristics of a constant potential generator and metal-insert x-ray tube in our laboratory. Then, using the modified Fewell spectra of different kVs, the photon fluence phi at each 1 keV energy bin (E) over energies from 10 keV to 140 keV was characterized using polynomial functions of the form phi (E) = a0[E] + a1[E] kV + a2[E] kV2 + ... + a(n)[E] kVn. A total of 131 polynomial functions were used to calculate accurate x-ray spectra, each function requiring between two and four terms. The resulting TASMIP algorithm produced x-ray spectra that match both the quality and quantity characteristics of the x-ray system in our laboratory. For photon fluences above 10% of the peak fluence in the spectrum, the average percent difference (and standard deviation) between the modified Fewell spectra and the TASMIP photon fluence was -1.43% (3.8%) for the 50 kV spectrum, -0.89% (1.37%) for the 70 kV spectrum, and for the 80, 90, 100, 110, 120, 130 and 140 kV spectra, the mean differences between spectra were all less than 0.20% and the standard deviations were less than approximately 1.1%. The model was also extended to include the effects of generator-induced kV ripple. Finally, the x-ray photon fluence in the units of photons/mm2 per mR was calculated as a function of HVL, kV, and ripple factor, for various (water-equivalent) patient thicknesses (0, 10, 20, and 30 cm). These values may be useful for computing the detective quantum efficiency, DQE(f), of x-ray detector systems. The TASMIP algorithm and ancillary data are made available on line at http:/(/)www.aip.org/epaps/epaps.html.

Orbital-free bond breaking via machine learning

NASA Astrophysics Data System (ADS)

Snyder, John C.; Rupp, Matthias; Hansen, Katja; Blooston, Leo; Müller, Klaus-Robert; Burke, Kieron

2013-12-01

Using a one-dimensional model, we explore the ability of machine learning to approximate the non-interacting kinetic energy density functional of diatomics. This nonlinear interpolation between Kohn-Sham reference calculations can (i) accurately dissociate a diatomic, (ii) be systematically improved with increased reference data and (iii) generate accurate self-consistent densities via a projection method that avoids directions with no data. With relatively few densities, the error due to the interpolation is smaller than typical errors in standard exchange-correlation functionals.

A new multigrid formulation for high order finite difference methods on summation-by-parts form

NASA Astrophysics Data System (ADS)

Ruggiu, Andrea A.; Weinerfelt, Per; Nordström, Jan

2018-04-01

Multigrid schemes for high order finite difference methods on summation-by-parts form are studied by comparing the effect of different interpolation operators. By using the standard linear prolongation and restriction operators, the Galerkin condition leads to inaccurate coarse grid discretizations. In this paper, an alternative class of interpolation operators that bypass this issue and preserve the summation-by-parts property on each grid level is considered. Clear improvements of the convergence rate for relevant model problems are achieved.

Comparison of Optimum Interpolation and Cressman Analyses

NASA Technical Reports Server (NTRS)

Baker, W. E.; Bloom, S. C.; Nestler, M. S.

1984-01-01

The objective of this investigation is to develop a state-of-the-art optimum interpolation (O/I) objective analysis procedure for use in numerical weather prediction studies. A three-dimensional multivariate O/I analysis scheme has been developed. Some characteristics of the GLAS O/I compared with those of the NMC and ECMWF systems are summarized. Some recent enhancements of the GLAS scheme include a univariate analysis of water vapor mixing ratio, a geographically dependent model prediction error correlation function and a multivariate oceanic surface analysis.

Comparison of Optimum Interpolation and Cressman Analyses

NASA Technical Reports Server (NTRS)

Baker, W. E.; Bloom, S. C.; Nestler, M. S.

1985-01-01

The development of a state of the art optimum interpolation (O/I) objective analysis procedure for use in numerical weather prediction studies was investigated. A three dimensional multivariate O/I analysis scheme was developed. Some characteristics of the GLAS O/I compared with those of the NMC and ECMWF systems are summarized. Some recent enhancements of the GLAS scheme include a univariate analysis of water vapor mixing ratio, a geographically dependent model prediction error correlation function and a multivariate oceanic surface analysis.

An Approach to Co-Channel Talker Interference Suppression Using a Sinusoidal Model for Speech

DTIC Science & Technology

1988-02-05

Massachusetts Institute of Technologp, with the ’Apport of the Department of the Air Force under Contract F19628-85-C-0002. ŕir re-port tniay be...Extracted from Summed Vocalic Waveforms 28 5-1 Failure of the Least Squares Solution with Closely-Spaced Frequencies. (a) Crossing Frequency Tracks, (b... Crossing Pitch Contours. 31 5-2 Multi-Frame Interpolation 33 5-3 Different Forms of Multi-Frame Interpolation 33 5-4 Recovery of Missing Lobe with Multi

Spline-Based Smoothing of Airfoil Curvatures

NASA Technical Reports Server (NTRS)

Li, W.; Krist, S.

2008-01-01

Constrained fitting for airfoil curvature smoothing (CFACS) is a splinebased method of interpolating airfoil surface coordinates (and, concomitantly, airfoil thicknesses) between specified discrete design points so as to obtain smoothing of surface-curvature profiles in addition to basic smoothing of surfaces. CFACS was developed in recognition of the fact that the performance of a transonic airfoil is directly related to both the curvature profile and the smoothness of the airfoil surface. Older methods of interpolation of airfoil surfaces involve various compromises between smoothing of surfaces and exact fitting of surfaces to specified discrete design points. While some of the older methods take curvature profiles into account, they nevertheless sometimes yield unfavorable results, including curvature oscillations near end points and substantial deviations from desired leading-edge shapes. In CFACS as in most of the older methods, one seeks a compromise between smoothing and exact fitting. Unlike in the older methods, the airfoil surface is modified as little as possible from its original specified form and, instead, is smoothed in such a way that the curvature profile becomes a smooth fit of the curvature profile of the original airfoil specification. CFACS involves a combination of rigorous mathematical modeling and knowledge-based heuristics. Rigorous mathematical formulation provides assurance of removal of undesirable curvature oscillations with minimum modification of the airfoil geometry. Knowledge-based heuristics bridge the gap between theory and designers best practices. In CFACS, one of the measures of the deviation of an airfoil surface from smoothness is the sum of squares of the jumps in the third derivatives of a cubicspline interpolation of the airfoil data. This measure is incorporated into a formulation for minimizing an overall deviation- from-smoothness measure of the airfoil data within a specified fitting error tolerance. CFACS has been extensively tested on a number of supercritical airfoil data sets generated by inverse design and optimization computer programs. All of the smoothing results show that CFACS is able to generate unbiased smooth fits of curvature profiles, trading small modifications of geometry for increasing curvature smoothness by eliminating curvature oscillations and bumps (see figure).

Three-dimensional local grid refinement for block-centered finite-difference groundwater models using iteratively coupled shared nodes: A new method of interpolation and analysis of errors

USGS Publications Warehouse

Mehl, S.; Hill, M.C.

2004-01-01

This paper describes work that extends to three dimensions the two-dimensional local-grid refinement method for block-centered finite-difference groundwater models of Mehl and Hill [Development and evaluation of a local grid refinement method for block-centered finite-difference groundwater models using shared nodes. Adv Water Resour 2002;25(5):497-511]. In this approach, the (parent) finite-difference grid is discretized more finely within a (child) sub-region. The grid refinement method sequentially solves each grid and uses specified flux (parent) and specified head (child) boundary conditions to couple the grids. Iteration achieves convergence between heads and fluxes of both grids. Of most concern is how to interpolate heads onto the boundary of the child grid such that the physics of the parent-grid flow is retained in three dimensions. We develop a new two-step, "cage-shell" interpolation method based on the solution of the flow equation on the boundary of the child between nodes shared with the parent grid. Error analysis using a test case indicates that the shared-node local grid refinement method with cage-shell boundary head interpolation is accurate and robust, and the resulting code is used to investigate three-dimensional local grid refinement of stream-aquifer interactions. Results reveal that (1) the parent and child grids interact to shift the true head and flux solution to a different solution where the heads and fluxes of both grids are in equilibrium, (2) the locally refined model provided a solution for both heads and fluxes in the region of the refinement that was more accurate than a model without refinement only if iterations are performed so that both heads and fluxes are in equilibrium, and (3) the accuracy of the coupling is limited by the parent-grid size - A coarse parent grid limits correct representation of the hydraulics in the feedback from the child grid.

EOS Interpolation and Thermodynamic Consistency

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gammel, J. Tinka

2015-11-16

As discussed in LA-UR-08-05451, the current interpolator used by Grizzly, OpenSesame, EOSPAC, and similar routines is the rational function interpolator from Kerley. While the rational function interpolator is well-suited for interpolation on sparse grids with logarithmic spacing and it preserves monotonicity in 1-d, it has some known problems.

Effect of interpolation on parameters extracted from seating interface pressure arrays.

PubMed

Wininger, Michael; Crane, Barbara

2014-01-01

Interpolation is a common data processing step in the study of interface pressure data collected at the wheelchair seating interface. However, there has been no focused study on the effect of interpolation on features extracted from these pressure maps, nor on whether these parameters are sensitive to the manner in which the interpolation is implemented. Here, two different interpolation paradigms, bilinear versus bicubic spline, are tested for their influence on parameters extracted from pressure array data and compared against a conventional low-pass filtering operation. Additionally, analysis of the effect of tandem filtering and interpolation, as well as the interpolation degree (interpolating to 2, 4, and 8 times sampling density), was undertaken. The following recommendations are made regarding approaches that minimized distortion of features extracted from the pressure maps: (1) filter prior to interpolate (strong effect); (2) use of cubic interpolation versus linear (slight effect); and (3) nominal difference between interpolation orders of 2, 4, and 8 times (negligible effect). We invite other investigators to perform similar benchmark analyses on their own data in the interest of establishing a community consensus of best practices in pressure array data processing.

Soil classification based on cone penetration test (CPT) data in Western Central Java

NASA Astrophysics Data System (ADS)

Apriyono, Arwan; Yanto, Santoso, Purwanto Bekti; Sumiyanto

2018-03-01

This study presents a modified friction ratio range for soil classification i.e. gravel, sand, silt & clay and peat, using CPT data in Western Central Java. The CPT data was obtained solely from Soil Mechanic Laboratory of Jenderal Soedirman University that covers more than 300 sites within the study area. About 197 data were produced from data filtering process. IDW method was employed to interpolated friction ratio values in a regular grid point for soil classification map generation. Soil classification map was generated and presented using QGIS software. In addition, soil classification map with respect to modified friction ratio range was validated using 10% of total measurements. The result shows that silt and clay dominate soil type in the study area, which is in agreement with two popular methods namely Begemann and Vos. However, the modified friction ratio range produces 85% similarity with laboratory measurements whereby Begemann and Vos method yields 70% similarity. In addition, modified friction ratio range can effectively distinguish fine and coarse grains, thus useful for soil classification and subsequently for landslide analysis. Therefore, modified friction ratio range proposed in this study can be used to identify soil type for mountainous tropical region.

Coupling Network Computing Applications in Air-cooled Turbine Blades Optimization

NASA Astrophysics Data System (ADS)

Shi, Liang; Yan, Peigang; Xie, Ming; Han, Wanjin

2018-05-01

Through establishing control parameters from blade outside to inside, the parametric design of air-cooled turbine blade based on airfoil has been implemented. On the basis of fast updating structure features and generating solid model, a complex cooling system has been created. Different flow units are modeled into a complex network topology with parallel and serial connection. Applying one-dimensional flow theory, programs have been composed to get pipeline network physical quantities along flow path, including flow rate, pressure, temperature and other parameters. These inner units parameters set as inner boundary conditions for external flow field calculation program HIT-3D by interpolation, thus to achieve full field thermal coupling simulation. Referring the studies in literatures to verify the effectiveness of pipeline network program and coupling algorithm. After that, on the basis of a modified design, and with the help of iSIGHT-FD, an optimization platform had been established. Through MIGA mechanism, the target of enhancing cooling efficiency has been reached, and the thermal stress has been effectively reduced. Research work in this paper has significance for rapid deploying the cooling structure design.

Parametric Grid Information in the DOE Knowledge Base: Data Preparation, Storage, and Access

DOE Office of Scientific and Technical Information (OSTI.GOV)

HIPP,JAMES R.; MOORE,SUSAN G.; MYERS,STEPHEN C.

The parametric grid capability of the Knowledge Base provides an efficient, robust way to store and access interpolatable information which is needed to monitor the Comprehensive Nuclear Test Ban Treaty. To meet both the accuracy and performance requirements of operational monitoring systems, we use a new approach which combines the error estimation of kriging with the speed and robustness of Natural Neighbor Interpolation (NNI). The method involves three basic steps: data preparation (DP), data storage (DS), and data access (DA). The goal of data preparation is to process a set of raw data points to produce a sufficient basis formore » accurate NNI of value and error estimates in the Data Access step. This basis includes a set of nodes and their connectedness, collectively known as a tessellation, and the corresponding values and errors that map to each node, which we call surfaces. In many cases, the raw data point distribution is not sufficiently dense to guarantee accurate error estimates from the NNI, so the original data set must be densified using a newly developed interpolation technique known as Modified Bayesian Kriging. Once appropriate kriging parameters have been determined by variogram analysis, the optimum basis for NNI is determined in a process they call mesh refinement, which involves iterative kriging, new node insertion, and Delauny triangle smoothing. The process terminates when an NNI basis has been calculated which will fir the kriged values within a specified tolerance. In the data storage step, the tessellations and surfaces are stored in the Knowledge Base, currently in a binary flatfile format but perhaps in the future in a spatially-indexed database. Finally, in the data access step, a client application makes a request for an interpolated value, which triggers a data fetch from the Knowledge Base through the libKBI interface, a walking triangle search for the containing triangle, and finally the NNI interpolation.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kolmann, Stephen J.; D'Arcy, Jordan H.; Jordan, Meredith J. T., E-mail: m.jordan@chem.usyd.edu.au

Quantum and anharmonic effects are investigated in H{sub 2}-Li{sup +}-benzene, a model for hydrogen adsorption in metal-organic frameworks and carbon-based materials. Three- and 8-dimensional quantum diffusion Monte Carlo (QDMC) and rigid-body diffusion Monte Carlo (RBDMC) simulations are performed on potential energy surfaces interpolated from electronic structure calculations at the M05-2X/6-31+G(d,p) and M05-2X/6-311+G(2df,p) levels of theory using a three-dimensional spline or a modified Shepard interpolation. These calculations investigate the intermolecular interactions in this system, with three- and 8-dimensional 0 K H{sub 2} binding enthalpy estimates, ΔH{sub bind} (0 K), being 16.5 kJ mol{sup −1} and 12.4 kJ mol{sup −1}, respectively: 0.1 and 0.6more » kJ mol{sup −1} higher than harmonic values. Zero-point energy effects are 35% of the value of ΔH{sub bind} (0 K) at M05-2X/6-311+G(2df,p) and cannot be neglected; uncorrected electronic binding energies overestimate ΔH{sub bind} (0 K) by at least 6 kJ mol{sup −1}. Harmonic intermolecular binding enthalpies can be corrected by treating the H{sub 2} “helicopter” and “ferris wheel” rotations as free and hindered rotations, respectively. These simple corrections yield results within 2% of the 8-dimensional anharmonic calculations. Nuclear ground state probability density histograms obtained from the QDMC and RBDMC simulations indicate the H{sub 2} molecule is delocalized above the Li{sup +}-benzene system at 0 K.« less

Application of data assimilation methods for analysis and integration of observed and modeled Arctic Sea ice motions

NASA Astrophysics Data System (ADS)

Meier, Walter Neil

This thesis demonstrates the applicability of data assimilation methods to improve observed and modeled ice motion fields and to demonstrate the effects of assimilated motion on Arctic processes important to the global climate and of practical concern to human activities. Ice motions derived from 85 GHz and 37 GHz SSM/I imagery and estimated from two-dimensional dynamic-thermodynamic sea ice models are compared to buoy observations. Mean error, error standard deviation, and correlation with buoys are computed for the model domain. SSM/I motions generally have a lower bias, but higher error standard deviations and lower correlation with buoys than model motions. There are notable variations in the statistics depending on the region of the Arctic, season, and ice characteristics. Assimilation methods are investigated and blending and optimal interpolation strategies are implemented. Blending assimilation improves error statistics slightly, but the effect of the assimilation is reduced due to noise in the SSM/I motions and is thus not an effective method to improve ice motion estimates. However, optimal interpolation assimilation reduces motion errors by 25--30% over modeled motions and 40--45% over SSM/I motions. Optimal interpolation assimilation is beneficial in all regions, seasons and ice conditions, and is particularly effective in regimes where modeled and SSM/I errors are high. Assimilation alters annual average motion fields. Modeled ice products of ice thickness, ice divergence, Fram Strait ice volume export, transport across the Arctic and interannual basin averages are also influenced by assimilated motions. Assimilation improves estimates of pollutant transport and corrects synoptic-scale errors in the motion fields caused by incorrect forcings or errors in model physics. The portability of the optimal interpolation assimilation method is demonstrated by implementing the strategy in an ice thickness distribution (ITD) model. This research presents an innovative method of combining a new data set of SSM/I-derived ice motions with three different sea ice models via two data assimilation methods. The work described here is the first example of assimilating remotely-sensed data within high-resolution and detailed dynamic-thermodynamic sea ice models. The results demonstrate that assimilation is a valuable resource for determining accurate ice motion in the Arctic.

An empirical model of electron and ion fluxes derived from observations at geosynchronous orbit

DOE Office of Scientific and Technical Information (OSTI.GOV)

Denton, M. H.; Thomsen, M. F.; Jordanova, V. K.

Knowledge of the plasma fluxes at geosynchronous orbit is important to both scientific and operational investigations. We present a new empirical model of the ion flux and the electron flux at geosynchronous orbit (GEO) in the energy range ~1 eV to ~40 keV. The model is based on a total of 82 satellite-years of observations from the Magnetospheric Plasma Analyzer instruments on Los Alamos National Laboratory satellites at GEO. These data are assigned to a fixed grid of 24 local-times and 40 energies, at all possible values of Kp. Bi-linear interpolation is used between grid points to provide the ionmore » flux and the electron flux values at any energy and local-time, and for given values of geomagnetic activity (proxied by the 3-hour Kp index), and also for given values of solar activity (proxied by the daily F10.7 index). Initial comparison of the electron flux from the model with data from a Compact Environmental Anomaly Sensor II (CEASE-II), also located at geosynchronous orbit, indicate a good match during both quiet and disturbed periods. The model is available for distribution as a FORTRAN code that can be modified to suit user-requirements.« less

Locally adaptive, spatially explicit projection of US population for 2030 and 2050.

PubMed

McKee, Jacob J; Rose, Amy N; Bright, Edward A; Huynh, Timmy; Bhaduri, Budhendra L

2015-02-03

Localized adverse events, including natural hazards, epidemiological events, and human conflict, underscore the criticality of quantifying and mapping current population. Building on the spatial interpolation technique previously developed for high-resolution population distribution data (LandScan Global and LandScan USA), we have constructed an empirically informed spatial distribution of projected population of the contiguous United States for 2030 and 2050, depicting one of many possible population futures. Whereas most current large-scale, spatially explicit population projections typically rely on a population gravity model to determine areas of future growth, our projection model departs from these by accounting for multiple components that affect population distribution. Modeled variables, which included land cover, slope, distances to larger cities, and a moving average of current population, were locally adaptive and geographically varying. The resulting weighted surface was used to determine which areas had the greatest likelihood for future population change. Population projections of county level numbers were developed using a modified version of the US Census's projection methodology, with the US Census's official projection as the benchmark. Applications of our model include incorporating multiple various scenario-driven events to produce a range of spatially explicit population futures for suitability modeling, service area planning for governmental agencies, consequence assessment, mitigation planning and implementation, and assessment of spatially vulnerable populations.

An empirical model of electron and ion fluxes derived from observations at geosynchronous orbit

DOE PAGES

Denton, M. H.; Thomsen, M. F.; Jordanova, V. K.; ...

2015-04-01

Knowledge of the plasma fluxes at geosynchronous orbit is important to both scientific and operational investigations. We present a new empirical model of the ion flux and the electron flux at geosynchronous orbit (GEO) in the energy range ~1 eV to ~40 keV. The model is based on a total of 82 satellite-years of observations from the Magnetospheric Plasma Analyzer instruments on Los Alamos National Laboratory satellites at GEO. These data are assigned to a fixed grid of 24 local-times and 40 energies, at all possible values of Kp. Bi-linear interpolation is used between grid points to provide the ionmore » flux and the electron flux values at any energy and local-time, and for given values of geomagnetic activity (proxied by the 3-hour Kp index), and also for given values of solar activity (proxied by the daily F10.7 index). Initial comparison of the electron flux from the model with data from a Compact Environmental Anomaly Sensor II (CEASE-II), also located at geosynchronous orbit, indicate a good match during both quiet and disturbed periods. The model is available for distribution as a FORTRAN code that can be modified to suit user-requirements.« less

Spherical Harmonics Functions Modelling of Meteorological Parameters in PWV Estimation

NASA Astrophysics Data System (ADS)

Deniz, Ilke; Mekik, Cetin; Gurbuz, Gokhan

2016-08-01

Aim of this study is to derive temperature, pressure and humidity observations using spherical harmonics modelling and to interpolate for the derivation of precipitable water vapor (PWV) of TUSAGA-Active stations in the test area encompassing 38.0°-42.0° northern latitudes and 28.0°-34.0° eastern longitudes of Turkey. In conclusion, the meteorological parameters computed by using GNSS observations for the study area have been modelled with a precision of ±1.74 K in temperature, ±0.95 hPa in pressure and ±14.88 % in humidity. Considering studies on the interpolation of meteorological parameters, the precision of temperature and pressure models provide adequate solutions. This study funded by the Scientific and Technological Research Council of Turkey (TUBITAK) (The Estimation of Atmospheric Water Vapour with GPS Project, Project No: 112Y350).

Simulating hydrodynamics and ice cover in Lake Erie using an unstructured grid model

NASA Astrophysics Data System (ADS)

Fujisaki-Manome, A.; Wang, J.

2016-02-01

An unstructured grid Finite-Volume Coastal Ocean Model (FVCOM) is applied to Lake Erie to simulate seasonal ice cover. The model is coupled with an unstructured-grid, finite-volume version of the Los Alamos Sea Ice Model (UG-CICE). We replaced the original 2-time-step Euler forward scheme in time integration by the central difference (i.e., leapfrog) scheme to assure a neutrally inertial stability. The modified version of FVCOM coupled with the ice model is applied to the shallow freshwater lake in this study using unstructured grids to represent the complicated coastline in the Laurentian Great Lakes and refining the spatial resolution locally. We conducted multi-year simulations in Lake Erie from 2002 to 2013. The results were compared with the observed ice extent, water surface temperature, ice thickness, currents, and water temperature profiles. Seasonal and interannual variation of ice extent and water temperature was captured reasonably, while the modeled thermocline was somewhat diffusive. The modeled ice thickness tends to be systematically thinner than the observed values. The modeled lake currents compared well with measurements obtained from an Acoustic Doppler Current Profiler located in the deep part of the lake, whereas the simulated currents deviated from measurements near the surface, possibly due to the model's inability to reproduce the sharp thermocline during the summer and the lack of detailed representation of offshore wind fields in the interpolated meteorological forcing.

Resilient Sensor Networks with Spatiotemporal Interpolation of Missing Sensors: An Example of Space Weather Forecasting by Multiple Satellites

PubMed Central

Tokumitsu, Masahiro; Hasegawa, Keisuke; Ishida, Yoshiteru

2016-01-01

This paper attempts to construct a resilient sensor network model with an example of space weather forecasting. The proposed model is based on a dynamic relational network. Space weather forecasting is vital for a satellite operation because an operational team needs to make a decision for providing its satellite service. The proposed model is resilient to failures of sensors or missing data due to the satellite operation. In the proposed model, the missing data of a sensor is interpolated by other sensors associated. This paper demonstrates two examples of space weather forecasting that involves the missing observations in some test cases. In these examples, the sensor network for space weather forecasting continues a diagnosis by replacing faulted sensors with virtual ones. The demonstrations showed that the proposed model is resilient against sensor failures due to suspension of hardware failures or technical reasons. PMID:27092508

Summary on Several Key Techniques in 3D Geological Modeling

PubMed Central

2014-01-01

Several key techniques in 3D geological modeling including planar mesh generation, spatial interpolation, and surface intersection are summarized in this paper. Note that these techniques are generic and widely used in various applications but play a key role in 3D geological modeling. There are two essential procedures in 3D geological modeling: the first is the simulation of geological interfaces using geometric surfaces and the second is the building of geological objects by means of various geometric computations such as the intersection of surfaces. Discrete geometric surfaces that represent geological interfaces can be generated by creating planar meshes first and then spatially interpolating; those surfaces intersect and then form volumes that represent three-dimensional geological objects such as rock bodies. In this paper, the most commonly used algorithms of the key techniques in 3D geological modeling are summarized. PMID:24772029

Resilient Sensor Networks with Spatiotemporal Interpolation of Missing Sensors: An Example of Space Weather Forecasting by Multiple Satellites.

PubMed

Tokumitsu, Masahiro; Hasegawa, Keisuke; Ishida, Yoshiteru

2016-04-15

This paper attempts to construct a resilient sensor network model with an example of space weather forecasting. The proposed model is based on a dynamic relational network. Space weather forecasting is vital for a satellite operation because an operational team needs to make a decision for providing its satellite service. The proposed model is resilient to failures of sensors or missing data due to the satellite operation. In the proposed model, the missing data of a sensor is interpolated by other sensors associated. This paper demonstrates two examples of space weather forecasting that involves the missing observations in some test cases. In these examples, the sensor network for space weather forecasting continues a diagnosis by replacing faulted sensors with virtual ones. The demonstrations showed that the proposed model is resilient against sensor failures due to suspension of hardware failures or technical reasons.

Rtop - an R package for interpolation along the stream network

NASA Astrophysics Data System (ADS)

Skøien, J. O.

2009-04-01

Rtop - an R package for interpolation along the stream network Geostatistical methods have been used to a limited extent for estimation along stream networks, with a few exceptions(Gottschalk, 1993; Gottschalk, et al., 2006; Sauquet, et al., 2000; Skøien, et al., 2006). Interpolation of runoff characteristics are more complicated than the traditional random variables estimated by geostatistical methods, as the measurements have a more complicated support, and many catchments are nested. Skøien et al. (2006) presented the model Top-kriging which takes these effects into account for interpolation of stream flow characteristics (exemplified by the 100 year flood). The method has here been implemented as a package in the statistical environment R (R Development Core Team, 2004). Taking advantage of the existing methods in R for working with spatial objects, and the extensive possibilities for visualizing the result, this makes it considerably easier to apply the method on new data sets, in comparison to earlier implementation of the method. Gottschalk, L. 1993. Interpolation of runoff applying objective methods. Stochastic Hydrology and Hydraulics, 7, 269-281. Gottschalk, L., I. Krasovskaia, E. Leblois, and E. Sauquet. 2006. Mapping mean and variance of runoff in a river basin. Hydrology and Earth System Sciences, 10, 469-484. R Development Core Team. 2004. R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing. Sauquet, E., L. Gottschalk, and E. Leblois. 2000. Mapping average annual runoff: a hierarchical approach applying a stochastic interpolation scheme. Hydrological Sciences Journal, 45 (6), 799-815. Skøien, J. O., R. Merz, and G. Blöschl. 2006. Top-kriging - geostatistics on stream networks. Hydrology and Earth System Sciences, 10, 277-287.

Numerical solution of the Hele-Shaw equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Whitaker, N.

1987-04-01

An algorithm is presented for approximating the motion of the interface between two immiscible fluids in a Hele-Shaw cell. The interface is represented by a set of volume fractions. We use the Simple Line Interface Calculation method along with the method of fractional steps to transport the interface. The equation of continuity leads to a Poisson equation for the pressure. The Poisson equation is discretized. Near the interface where the velocity field is discontinuous, the discretization is based on a weak formulation of the continuity equation. Interpolation is used on each side of the interface to increase the accuracy ofmore » the algorithm. The weak formulation as well as the interpolation are based on the computed volume fractions. This treatment of the interface is new. The discretized equations are solved by a modified conjugate gradient method. Surface tension is included and the curvature is computed through the use of osculating circles. For perturbations of small amplitude, a surprisingly good agreement is found between the numerical results and linearized perturbation theory. Numerical results are presented for the finite amplitude growth of unstable fingers. 62 refs., 13 figs.« less

A GENERAL ALGORITHM FOR THE CONSTRUCTION OF CONTOUR PLOTS

NASA Technical Reports Server (NTRS)

Johnson, W.

1994-01-01

The graphical presentation of experimentally or theoretically generated data sets frequently involves the construction of contour plots. A general computer algorithm has been developed for the construction of contour plots. The algorithm provides for efficient and accurate contouring with a modular approach which allows flexibility in modifying the algorithm for special applications. The algorithm accepts as input data values at a set of points irregularly distributed over a plane. The algorithm is based on an interpolation scheme in which the points in the plane are connected by straight line segments to form a set of triangles. In general, the data is smoothed using a least-squares-error fit of the data to a bivariate polynomial. To construct the contours, interpolation along the edges of the triangles is performed, using the bivariable polynomial if data smoothing was performed. Once the contour points have been located, the contour may be drawn. This program is written in FORTRAN IV for batch execution and has been implemented on an IBM 360 series computer with a central memory requirement of approximately 100K of 8-bit bytes. This computer algorithm was developed in 1981.

Autocorrelation Analysis Combined with a Wavelet Transform Method to Detect and Remove Cosmic Rays in a Single Raman Spectrum.

PubMed

Maury, Augusto; Revilla, Reynier I

2015-08-01

Cosmic rays (CRs) occasionally affect charge-coupled device (CCD) detectors, introducing large spikes with very narrow bandwidth in the spectrum. These CR features can distort the chemical information expressed by the spectra. Consequently, we propose here an algorithm to identify and remove significant spikes in a single Raman spectrum. An autocorrelation analysis is first carried out to accentuate the CRs feature as outliers. Subsequently, with an adequate selection of the threshold, a discrete wavelet transform filter is used to identify CR spikes. Identified data points are then replaced by interpolated values using the weighted-average interpolation technique. This approach only modifies the data in a close vicinity of the CRs. Additionally, robust wavelet transform parameters are proposed (a desirable property for automation) after optimizing them with the application of the method in a great number of spectra. However, this algorithm, as well as all the single-spectrum analysis procedures, is limited to the cases in which CRs have much narrower bandwidth than the Raman bands. This might not be the case when low-resolution Raman instruments are used.

Adaptive Radiation within Marine Anisakid Nematodes: A Zoogeographical Modeling of Cosmopolitan, Zoonotic Parasites

PubMed Central

Kuhn, Thomas; García-Màrquez, Jaime; Klimpel, Sven

2011-01-01

Parasites of the nematode genus Anisakis are associated with aquatic organisms. They can be found in a variety of marine hosts including whales, crustaceans, fish and cephalopods and are known to be the cause of the zoonotic disease anisakiasis, a painful inflammation of the gastro-intestinal tract caused by the accidental consumptions of infectious larvae raw or semi-raw fishery products. Since the demand on fish as dietary protein source and the export rates of seafood products in general is rapidly increasing worldwide, the knowledge about the distribution of potential foodborne human pathogens in seafood is of major significance for human health. Studies have provided evidence that a few Anisakis species can cause clinical symptoms in humans. The aim of our study was to interpolate the species range for every described Anisakis species on the basis of the existing occurrence data. We used sequence data of 373 Anisakis larvae from 30 different hosts worldwide and previously published molecular data (n = 584) from 53 field-specific publications to model the species range of Anisakis spp., using a interpolation method that combines aspects of the alpha hull interpolation algorithm as well as the conditional interpolation approach. The results of our approach strongly indicate the existence of species-specific distribution patterns of Anisakis spp. within different climate zones and oceans that are in principle congruent with those of their respective final hosts. Our results support preceding studies that propose anisakid nematodes as useful biological indicators for their final host distribution and abundance as they closely follow the trophic relationships among their successive hosts. The modeling might although be helpful for predicting the likelihood of infection in order to reduce the risk of anisakiasis cases in a given area. PMID:22180787

Precipitation interpolation in mountainous areas

NASA Astrophysics Data System (ADS)

Kolberg, Sjur

2015-04-01

Different precipitation interpolation techniques as well as external drift covariates are tested and compared in a 26000 km2 mountainous area in Norway, using daily data from 60 stations. The main method of assessment is cross-validation. Annual precipitation in the area varies from below 500 mm to more than 2000 mm. The data were corrected for wind-driven undercatch according to operational standards. While temporal evaluation produce seemingly acceptable at-station correlation values (on average around 0.6), the average daily spatial correlation is less than 0.1. Penalising also bias, Nash-Sutcliffe R2 values are negative for spatial correspondence, and around 0.15 for temporal. Despite largely violated assumptions, plain Kriging produces better results than simple inverse distance weighting. More surprisingly, the presumably 'worst-case' benchmark of no interpolation at all, simply averaging all 60 stations for each day, actually outperformed the standard interpolation techniques. For logistic reasons, high altitudes are under-represented in the gauge network. The possible effect of this was investigated by a) fitting a precipitation lapse rate as an external drift, and b) applying a linear model of orographic enhancement (Smith and Barstad, 2004). These techniques improved the results only marginally. The gauge density in the region is one for each 433 km2; higher than the overall density of the Norwegian national network. Admittedly the cross-validation technique reduces the gauge density, still the results suggest that we are far from able to provide hydrological models with adequate data for the main driving force.

Application of Time-Frequency Domain Transform to Three-Dimensional Interpolation of Medical Images.

PubMed

Lv, Shengqing; Chen, Yimin; Li, Zeyu; Lu, Jiahui; Gao, Mingke; Lu, Rongrong

2017-11-01

Medical image three-dimensional (3D) interpolation is an important means to improve the image effect in 3D reconstruction. In image processing, the time-frequency domain transform is an efficient method. In this article, several time-frequency domain transform methods are applied and compared in 3D interpolation. And a Sobel edge detection and 3D matching interpolation method based on wavelet transform is proposed. We combine wavelet transform, traditional matching interpolation methods, and Sobel edge detection together in our algorithm. What is more, the characteristics of wavelet transform and Sobel operator are used. They deal with the sub-images of wavelet decomposition separately. Sobel edge detection 3D matching interpolation method is used in low-frequency sub-images under the circumstances of ensuring high frequency undistorted. Through wavelet reconstruction, it can get the target interpolation image. In this article, we make 3D interpolation of the real computed tomography (CT) images. Compared with other interpolation methods, our proposed method is verified to be effective and superior.

An algorithm to generate input data from meteorological and space shuttle observations to validate a CH4-CO model

NASA Technical Reports Server (NTRS)

Peters, L. K.; Yamanis, J.

1981-01-01

Objective procedures to analyze data from meteorological and space shuttle observations to validate a three dimensional model were investigated. The transport and chemistry of carbon monoxide and methane in the troposphere were studied. Four aspects were examined: (1) detailed evaluation of the variational calculus procedure, with the equation of continuity as a strong constraint, for adjustment of global tropospheric wind fields; (2) reduction of the National Meteorological Center (NMC) data tapes for data input to the OSTA-1/MAPS Experiment; (3) interpolation of the NMC Data for input to the CH4-CO model; and (4) temporal and spatial interpolation procedures of the CO measurements from the OSTA-1/MAPS Experiment to generate usable contours of the data.

Charge-based MOSFET model based on the Hermite interpolation polynomial

NASA Astrophysics Data System (ADS)

Colalongo, Luigi; Richelli, Anna; Kovacs, Zsolt

2017-04-01

An accurate charge-based compact MOSFET model is developed using the third order Hermite interpolation polynomial to approximate the relation between surface potential and inversion charge in the channel. This new formulation of the drain current retains the same simplicity of the most advanced charge-based compact MOSFET models such as BSIM, ACM and EKV, but it is developed without requiring the crude linearization of the inversion charge. Hence, the asymmetry and the non-linearity in the channel are accurately accounted for. Nevertheless, the expression of the drain current can be worked out to be analytically equivalent to BSIM, ACM and EKV. Furthermore, thanks to this new mathematical approach the slope factor is rigorously defined in all regions of operation and no empirical assumption is required.

Research progress and hotspot analysis of spatial interpolation

NASA Astrophysics Data System (ADS)

Jia, Li-juan; Zheng, Xin-qi; Miao, Jin-li

2018-02-01

In this paper, the literatures related to spatial interpolation between 1982 and 2017, which are included in the Web of Science core database, are used as data sources, and the visualization analysis is carried out according to the co-country network, co-category network, co-citation network, keywords co-occurrence network. It is found that spatial interpolation has experienced three stages: slow development, steady development and rapid development; The cross effect between 11 clustering groups, the main convergence of spatial interpolation theory research, the practical application and case study of spatial interpolation and research on the accuracy and efficiency of spatial interpolation. Finding the optimal spatial interpolation is the frontier and hot spot of the research. Spatial interpolation research has formed a theoretical basis and research system framework, interdisciplinary strong, is widely used in various fields.

Nearest neighbor, bilinear interpolation and bicubic interpolation geographic correction effects on LANDSAT imagery

NASA Technical Reports Server (NTRS)

Jayroe, R. R., Jr.

1976-01-01

Geographical correction effects on LANDSAT image data are identified, using the nearest neighbor, bilinear interpolation and bicubic interpolation techniques. Potential impacts of registration on image compression and classification are explored.

A Data-Driven, Integrated Flare Model Based on Self-Organized Criticality

NASA Astrophysics Data System (ADS)

Dimitropoulou, M.; Isliker, H.; Vlahos, L.; Georgoulis, M.

2013-09-01

We interpret solar flares as events originating in solar active regions having reached the self-organized critical state, by alternatively using two versions of an "integrated flare model" - one static and one dynamic. In both versions the initial conditions are derived from observations aiming to investigate whether well-known scaling laws observed in the distribution functions of characteristic flare parameters are reproduced after the self-organized critical state has been reached. In the static model, we first apply a nonlinear force-free extrapolation that reconstructs the three-dimensional magnetic fields from two-dimensional vector magnetograms. We then locate magnetic discontinuities exceeding a threshold in the Laplacian of the magnetic field. These discontinuities are relaxed in local diffusion events, implemented in the form of cellular-automaton evolution rules. Subsequent loading and relaxation steps lead the system to self-organized criticality, after which the statistical properties of the simulated events are examined. In the dynamic version we deploy an enhanced driving mechanism, which utilizes the observed evolution of active regions, making use of sequential vector magnetograms. We first apply the static cellular automaton model to consecutive solar vector magnetograms until the self-organized critical state is reached. We then evolve the magnetic field inbetween these processed snapshots through spline interpolation, acting as a natural driver in the dynamic model. The identification of magnetically unstable sites as well as their relaxation follow the same rules as in the static model after each interpolation step. Subsequent interpolation/driving and relaxation steps cover all transitions until the end of the sequence. Physical requirements, such as the divergence-free condition for the magnetic field vector, are approximately satisfied in both versions of the model. We obtain robust power laws in the distribution functions of the modelled flaring events with scaling indices in good agreement with observations. We therefore conclude that well-known statistical properties of flares are reproduced after active regions reach self-organized criticality. The significant enhancement in both the static and the dynamic integrated flare models is that they initiate the simulation from observations, thus facilitating energy calculation in physical units. Especially in the dynamic version of the model, the driving of the system is based on observed, evolving vector magnetograms, allowing for the separation between MHD and kinetic timescales through the assignment of distinct MHD timestamps to each interpolation step.

Flip-avoiding interpolating surface registration for skull reconstruction.

PubMed

Xie, Shudong; Leow, Wee Kheng; Lee, Hanjing; Lim, Thiam Chye

2018-03-30

Skull reconstruction is an important and challenging task in craniofacial surgery planning, forensic investigation and anthropological studies. Existing methods typically reconstruct approximating surfaces that regard corresponding points on the target skull as soft constraints, thus incurring non-zero error even for non-defective parts and high overall reconstruction error. This paper proposes a novel geometric reconstruction method that non-rigidly registers an interpolating reference surface that regards corresponding target points as hard constraints, thus achieving low reconstruction error. To overcome the shortcoming of interpolating a surface, a flip-avoiding method is used to detect and exclude conflicting hard constraints that would otherwise cause surface patches to flip and self-intersect. Comprehensive test results show that our method is more accurate and robust than existing skull reconstruction methods. By incorporating symmetry constraints, it can produce more symmetric and normal results than other methods in reconstructing defective skulls with a large number of defects. It is robust against severe outliers such as radiation artifacts in computed tomography due to dental implants. In addition, test results also show that our method outperforms thin-plate spline for model resampling, which enables the active shape model to yield more accurate reconstruction results. As the reconstruction accuracy of defective parts varies with the use of different reference models, we also study the implication of reference model selection for skull reconstruction. Copyright © 2018 John Wiley & Sons, Ltd.

A characteristics-based method for solving the transport equation and its application to the process of mantle differentiation and continental root growth

NASA Astrophysics Data System (ADS)

de Smet, Jeroen H.; van den Berg, Arie P.; Vlaar, Nico J.; Yuen, David A.

2000-03-01

Purely advective transport of composition is of major importance in the Geosciences, and efficient and accurate solution methods are needed. A characteristics-based method is used to solve the transport equation. We employ a new hybrid interpolation scheme, which allows for the tuning of stability and accuracy through a threshold parameter ɛth. Stability is established by bilinear interpolations, and bicubic splines are used to maintain accuracy. With this scheme, numerical instabilities can be suppressed by allowing numerical diffusion to work in time and locally in space. The scheme can be applied efficiently for preliminary modelling purposes. This can be followed by detailed high-resolution experiments. First, the principal effects of this hybrid interpolation method are illustrated and some tests are presented for numerical solutions of the transport equation. Second, we illustrate that this approach works successfully for a previously developed continental evolution model for the convecting upper mantle. In this model the transport equation contains a source term, which describes the melt production in pressure-released partial melting. In this model, a characteristic phenomenon of small-scale melting diapirs is observed (De Smet et al.1998; De Smet et al. 1999). High-resolution experiments with grid cells down to 700m horizontally and 515m vertically result in highly detailed observations of the diapiric melting phenomenon.

Classical and neural methods of image sequence interpolation

NASA Astrophysics Data System (ADS)

Skoneczny, Slawomir; Szostakowski, Jaroslaw

2001-08-01

An image interpolation problem is often encountered in many areas. Some examples are interpolation for coding/decoding process for transmission purposes, reconstruction a full frame from two interlaced sub-frames in normal TV or HDTV, or reconstruction of missing frames in old destroyed cinematic sequences. In this paper an overview of interframe interpolation methods is presented. Both direct as well as motion compensated interpolation techniques are given by examples. The used methodology can also be either classical or based on neural networks depending on demand of a specific interpolation problem solving person.

A kriging metamodel-assisted robust optimization method based on a reverse model

NASA Astrophysics Data System (ADS)

Zhou, Hui; Zhou, Qi; Liu, Congwei; Zhou, Taotao

2018-02-01

The goal of robust optimization methods is to obtain a solution that is both optimum and relatively insensitive to uncertainty factors. Most existing robust optimization approaches use outer-inner nested optimization structures where a large amount of computational effort is required because the robustness of each candidate solution delivered from the outer level should be evaluated in the inner level. In this article, a kriging metamodel-assisted robust optimization method based on a reverse model (K-RMRO) is first proposed, in which the nested optimization structure is reduced into a single-loop optimization structure to ease the computational burden. Ignoring the interpolation uncertainties from kriging, K-RMRO may yield non-robust optima. Hence, an improved kriging-assisted robust optimization method based on a reverse model (IK-RMRO) is presented to take the interpolation uncertainty of kriging metamodel into consideration. In IK-RMRO, an objective switching criterion is introduced to determine whether the inner level robust optimization or the kriging metamodel replacement should be used to evaluate the robustness of design alternatives. The proposed criterion is developed according to whether or not the robust status of the individual can be changed because of the interpolation uncertainties from the kriging metamodel. Numerical and engineering cases are used to demonstrate the applicability and efficiency of the proposed approach.

A Computational Model of Multidimensional Shape

PubMed Central

Liu, Xiuwen; Shi, Yonggang; Dinov, Ivo

2010-01-01

We develop a computational model of shape that extends existing Riemannian models of curves to multidimensional objects of general topological type. We construct shape spaces equipped with geodesic metrics that measure how costly it is to interpolate two shapes through elastic deformations. The model employs a representation of shape based on the discrete exterior derivative of parametrizations over a finite simplicial complex. We develop algorithms to calculate geodesics and geodesic distances, as well as tools to quantify local shape similarities and contrasts, thus obtaining a formulation that accounts for regional differences and integrates them into a global measure of dissimilarity. The Riemannian shape spaces provide a common framework to treat numerous problems such as the statistical modeling of shapes, the comparison of shapes associated with different individuals or groups, and modeling and simulation of shape dynamics. We give multiple examples of geodesic interpolations and illustrations of the use of the models in brain mapping, particularly, the analysis of anatomical variation based on neuroimaging data. PMID:21057668

MAGIC: A Tool for Combining, Interpolating, and Processing Magnetograms

NASA Technical Reports Server (NTRS)

Allred, Joel

2012-01-01

Transients in the solar coronal magnetic field are ultimately the source of space weather. Models which seek to track the evolution of the coronal field require magnetogram images to be used as boundary conditions. These magnetograms are obtained by numerous instruments with different cadences and resolutions. A tool is required which allows modelers to fmd all available data and use them to craft accurate and physically consistent boundary conditions for their models. We have developed a software tool, MAGIC (MAGnetogram Interpolation and Composition), to perform exactly this function. MAGIC can manage the acquisition of magneto gram data, cast it into a source-independent format, and then perform the necessary spatial and temporal interpolation to provide magnetic field values as requested onto model-defined grids. MAGIC has the ability to patch magneto grams from different sources together providing a more complete picture of the Sun's field than is possible from single magneto grams. In doing this, care must be taken so as not to introduce nonphysical current densities along the seam between magnetograms. We have designed a method which minimizes these spurious current densities. MAGIC also includes a number of post-processing tools which can provide additional information to models. For example, MAGIC includes an interface to the DA VE4VM tool which derives surface flow velocities from the time evolution of surface magnetic field. MAGIC has been developed as an application of the KAMELEON data formatting toolkit which has been developed by the CCMC.

Measurement and modeling of particulate matter concentrations: Applying spatial analysis and regression techniques to assess air quality.

PubMed

Sajjadi, Seyed Ali; Zolfaghari, Ghasem; Adab, Hamed; Allahabadi, Ahmad; Delsouz, Mehri

2017-01-01

This paper presented the levels of PM 2.5 and PM 10 in different stations at the city of Sabzevar, Iran. Furthermore, this study was an attempt to evaluate spatial interpolation methods for determining the PM 2.5 and PM 10 concentrations in the city of Sabzevar. Particulate matters were measured by Haz-Dust EPAM at 48 stations. Then, four interpolating models, including Radial Basis Functions (RBF), Inverse Distance Weighting (IDW), Ordinary Kriging (OK), and Universal Kriging (UK) were used to investigate the status of air pollution in the city. Root Mean Square Error (RMSE), Mean Absolute Error (MAE) and Mean Absolute Percentage Error (MAPE) were employed to compare the four models. The results showed that the PM 2.5 concentrations in the stations were between 10 and 500 μg/m 3 . Furthermore, the PM 10 concentrations for all of 48 stations ranged from 20 to 1500 μg/m 3 . The concentrations obtained for the period of nine months were greater than the standard limits. There was difference in the values of MAPE, RMSE, MBE, and MAE. The results indicated that the MAPE in IDW method was lower than other methods: (41.05 for PM 2.5 and 25.89 for PM 10 ). The best interpolation method for the particulate matter (PM 2.5 and PM 10 ) seemed to be IDW method. •The PM 10 and PM 2.5 concentration measurements were performed in the period of warm and risky in terms of particulate matter at 2016.•Concentrations of PM 2.5 and PM 10 were measured by a monitoring device, environmental dust model Haz-Dust EPAM 5000.•Interpolation is used to convert data from observation points to continuous fields to compare spatial patterns sampled by these measurements with spatial patterns of other spatial entities.

Ortho Image and DTM Generation with Intelligent Methods

NASA Astrophysics Data System (ADS)

Bagheri, H.; Sadeghian, S.

2013-10-01

Nowadays the artificial intelligent algorithms has considered in GIS and remote sensing. Genetic algorithm and artificial neural network are two intelligent methods that are used for optimizing of image processing programs such as edge extraction and etc. these algorithms are very useful for solving of complex program. In this paper, the ability and application of genetic algorithm and artificial neural network in geospatial production process like geometric modelling of satellite images for ortho photo generation and height interpolation in raster Digital Terrain Model production process is discussed. In first, the geometric potential of Ikonos-2 and Worldview-2 with rational functions, 2D & 3D polynomials were tested. Also comprehensive experiments have been carried out to evaluate the viability of the genetic algorithm for optimization of rational function, 2D & 3D polynomials. Considering the quality of Ground Control Points, the accuracy (RMSE) with genetic algorithm and 3D polynomials method for Ikonos-2 Geo image was 0.508 pixel sizes and the accuracy (RMSE) with GA algorithm and rational function method for Worldview-2 image was 0.930 pixel sizes. For more another optimization artificial intelligent methods, neural networks were used. With the use of perceptron network in Worldview-2 image, a result of 0.84 pixel sizes with 4 neurons in middle layer was gained. The final conclusion was that with artificial intelligent algorithms it is possible to optimize the existing models and have better results than usual ones. Finally the artificial intelligence methods, like genetic algorithms as well as neural networks, were examined on sample data for optimizing interpolation and for generating Digital Terrain Models. The results then were compared with existing conventional methods and it appeared that these methods have a high capacity in heights interpolation and that using these networks for interpolating and optimizing the weighting methods based on inverse distance leads to a high accurate estimation of heights.

Timescape: a simple space-time interpolation geostatistical Algorithm

NASA Astrophysics Data System (ADS)

Ciolfi, Marco; Chiocchini, Francesca; Gravichkova, Olga; Pisanelli, Andrea; Portarena, Silvia; Scartazza, Andrea; Brugnoli, Enrico; Lauteri, Marco

2016-04-01

Environmental sciences include both time and space variability in their datasets. Some established tools exist for both spatial interpolation and time series analysis alone, but mixing space and time variability calls for compromise: Researchers are often forced to choose which is the main source of variation, neglecting the other. We propose a simple algorithm, which can be used in many fields of Earth and environmental sciences when both time and space variability must be considered on equal grounds. The algorithm has already been implemented in Java language and the software is currently available at https://sourceforge.net/projects/timescapeglobal/ (it is published under GNU-GPL v3.0 Free Software License). The published version of the software, Timescape Global, is focused on continent- to Earth-wide spatial domains, using global longitude-latitude coordinates for samples localization. The companion Timescape Local software is currently under development ad will be published with an open license as well; it will use projected coordinates for a local to regional space scale. The basic idea of the Timescape Algorithm consists in converting time into a sort of third spatial dimension, with the addition of some causal constraints, which drive the interpolation including or excluding observations according to some user-defined rules. The algorithm is applicable, as a matter of principle, to anything that can be represented with a continuous variable (a scalar field, technically speaking). The input dataset should contain position, time and observed value of all samples. Ancillary data can be included in the interpolation as well. After the time-space conversion, Timescape follows basically the old-fashioned IDW (Inverse Distance Weighted) interpolation Algorithm, although users have a wide choice of customization options that, at least partially, overcome some of the known issues of IDW. The three-dimensional model produced by the Timescape Algorithm can be explored in many ways, including the extraction of time series at fixed locations and GIS layers at constant times, allowing for the inclusion of the model in the users' established workflow. The software requirements are relatively modest since it has been purposely designed for potential users in various research field with a limited computing power at their disposal. Any respectful modern PC or laptop can run it. Users however need a separate database for sample data and models storage because these can be quite bulky in terms of data output: a single model can be composed of several billions of voxels (three-dimensional discrete cells, a sort of 3D pixels). Running times range from a few minutes for sketch models to some days of evaluation for a full-size model, depending on the users' hardware and model size.

The Gaia-ESO Survey: dynamical models of flattened, rotating globular clusters

NASA Astrophysics Data System (ADS)

Jeffreson, S. M. R.; Sanders, J. L.; Evans, N. W.; Williams, A. A.; Gilmore, G. F.; Bayo, A.; Bragaglia, A.; Casey, A. R.; Flaccomio, E.; Franciosini, E.; Hourihane, A.; Jackson, R. J.; Jeffries, R. D.; Jofré, P.; Koposov, S.; Lardo, C.; Lewis, J.; Magrini, L.; Morbidelli, L.; Pancino, E.; Randich, S.; Sacco, G. G.; Worley, C. C.; Zaggia, S.

2017-08-01

We present a family of self-consistent axisymmetric rotating globular cluster models which are fitted to spectroscopic data for NGC 362, NGC 1851, NGC 2808, NGC 4372, NGC 5927 and NGC 6752 to provide constraints on their physical and kinematic properties, including their rotation signals. They are constructed by flattening Modified Plummer profiles, which have the same asymptotic behaviour as classical Plummer models, but can provide better fits to young clusters due to a slower turnover in the density profile. The models are in dynamical equilibrium as they depend solely on the action variables. We employ a fully Bayesian scheme to investigate the uncertainty in our model parameters (including mass-to-light ratios and inclination angles) and evaluate the Bayesian evidence ratio for rotating to non-rotating models. We find convincing levels of rotation only in NGC 2808. In the other clusters, there is just a hint of rotation (in particular, NGC 4372 and NGC 5927), as the data quality does not allow us to draw strong conclusions. Where rotation is present, we find that it is confined to the central regions, within radii of R ≤ 2rh. As part of this work, we have developed a novel q-Gaussian basis expansion of the line-of-sight velocity distributions, from which general models can be constructed via interpolation on the basis coefficients.

Monotonicity preserving splines using rational cubic Timmer interpolation

NASA Astrophysics Data System (ADS)

Zakaria, Wan Zafira Ezza Wan; Alimin, Nur Safiyah; Ali, Jamaludin Md

2017-08-01

In scientific application and Computer Aided Design (CAD), users usually need to generate a spline passing through a given set of data, which preserves certain shape properties of the data such as positivity, monotonicity or convexity. The required curve has to be a smooth shape-preserving interpolant. In this paper a rational cubic spline in Timmer representation is developed to generate interpolant that preserves monotonicity with visually pleasing curve. To control the shape of the interpolant three parameters are introduced. The shape parameters in the description of the rational cubic interpolant are subjected to monotonicity constrained. The necessary and sufficient conditions of the rational cubic interpolant are derived and visually the proposed rational cubic Timmer interpolant gives very pleasing results.

A practical implementation of wave front construction for 3-D isotropic media

NASA Astrophysics Data System (ADS)

Chambers, K.; Kendall, J.-M.

2008-06-01

Wave front construction (WFC) methods are a useful tool for tracking wave fronts and are a natural extension to standard ray shooting methods. Here we describe and implement a simple WFC method that is used to interpolate wavefield properties throughout a 3-D heterogeneous medium. Our approach differs from previous 3-D WFC procedures primarily in the use of a ray interpolation scheme, based on approximating the wave front as a `locally spherical' surface and a `first arrival mode', which reduces computation times, where only first arrivals are required. Both of these features have previously been included in 2-D WFC algorithms; however, until now they have not been extended to 3-D systems. The wave front interpolation scheme allows for rays to be traced from a nearly arbitrary distribution of take-off angles, and the calculation of derivatives with respect to take-off angles is not required for wave front interpolation. However, in regions of steep velocity gradient, the locally spherical approximation is not valid, and it is necessary to backpropagate rays to a sufficiently homogenous region before interpolation of the new ray. Our WFC technique is illustrated using a realistic velocity model, based on a North Sea oil reservoir. We examine wavefield quantities such as traveltimes, ray angles, source take-off angles and geometrical spreading factors, all of which are interpolated on to a regular grid. We compare geometrical spreading factors calculated using two methods: using the ray Jacobian and by taking the ratio of a triangular area of wave front to the corresponding solid angle at the source. The results show that care must be taken when using ray Jacobians to calculate geometrical spreading factors, as the poles of the source coordinate system produce unreliable values, which can be spread over a large area, as only a few initial rays are traced in WFC. We also show that the use of the first arrival mode can reduce computation time by ~65 per cent, with the accuracy of the interpolated traveltimes, ray angles and source take-off angles largely unchanged. However, the first arrival mode does lead to inaccuracies in interpolated angles near caustic surfaces, as well as small variations in geometrical spreading factors for ray tubes that have passed through caustic surfaces.

The analysis of composite laminated beams using a 2D interpolating meshless technique

NASA Astrophysics Data System (ADS)

Sadek, S. H. M.; Belinha, J.; Parente, M. P. L.; Natal Jorge, R. M.; de Sá, J. M. A. César; Ferreira, A. J. M.

2018-02-01

Laminated composite materials are widely implemented in several engineering constructions. For its relative light weight, these materials are suitable for aerospace, military, marine, and automotive structural applications. To obtain safe and economical structures, the modelling analysis accuracy is highly relevant. Since meshless methods in the recent years achieved a remarkable progress in computational mechanics, the present work uses one of the most flexible and stable interpolation meshless technique available in the literature—the Radial Point Interpolation Method (RPIM). Here, a 2D approach is considered to numerically analyse composite laminated beams. Both the meshless formulation and the equilibrium equations ruling the studied physical phenomenon are presented with detail. Several benchmark beam examples are studied and the results are compared with exact solutions available in the literature and the results obtained from a commercial finite element software. The results show the efficiency and accuracy of the proposed numeric technique.

Signal-to-noise ratio estimation using adaptive tuning on the piecewise cubic Hermite interpolation model for images.

PubMed

Sim, K S; Yeap, Z X; Tso, C P

2016-11-01

An improvement to the existing technique of quantifying signal-to-noise ratio (SNR) of scanning electron microscope (SEM) images using piecewise cubic Hermite interpolation (PCHIP) technique is proposed. The new technique uses an adaptive tuning onto the PCHIP, and is thus named as ATPCHIP. To test its accuracy, 70 images are corrupted with noise and their autocorrelation functions are then plotted. The ATPCHIP technique is applied to estimate the uncorrupted noise-free zero offset point from a corrupted image. Three existing methods, the nearest neighborhood, first order interpolation and original PCHIP, are used to compare with the performance of the proposed ATPCHIP method, with respect to their calculated SNR values. Results show that ATPCHIP is an accurate and reliable method to estimate SNR values from SEM images. SCANNING 38:502-514, 2016. © 2015 Wiley Periodicals, Inc. © Wiley Periodicals, Inc.

Direct Validation of the Wall Interference Correction System of the Ames 11-Foot Transonic Wind Tunnel

NASA Technical Reports Server (NTRS)

Ulbrich, Norbert; Boone, Alan R.

2003-01-01

Data from the test of a large semispan model was used to perform a direct validation of a wall interference correction system for a transonic slotted wall wind tunnel. At first, different sets of uncorrected aerodynamic coefficients were generated by physically changing the boundary condition of the test section walls. Then, wall interference corrections were computed and applied to all data points. Finally, an interpolation of the corrected aerodynamic coefficients was performed. This interpolation made sure that the corrected Mach number of a given run would be constant. Overall, the agreement between corresponding interpolated lift, drag, and pitching moment coefficient sets was very good. Buoyancy corrections were also investigated. These studies showed that the accuracy goal of one drag count may only be achieved if reliable estimates of the wall interference induced buoyancy correction are available during a test.

An alternative approach for modeling strength differential effect in sheet metals with symmetric yield functions

NASA Astrophysics Data System (ADS)

Kurukuri, Srihari; Worswick, Michael J.

2013-12-01

An alternative approach is proposed to utilize symmetric yield functions for modeling the tension-compression asymmetry commonly observed in hcp materials. In this work, the strength differential (SD) effect is modeled by choosing separate symmetric plane stress yield functions (for example, Barlat Yld 2000-2d) for the tension i.e., in the first quadrant of principal stress space, and compression i.e., third quadrant of principal stress space. In the second and fourth quadrants, the yield locus is constructed by adopting interpolating functions between uniaxial tensile and compressive stress states. In this work, different interpolating functions are chosen and the predictive capability of each approach is discussed. The main advantage of this proposed approach is that the yield locus parameters are deterministic and relatively easy to identify when compared to the Cazacu family of yield functions commonly used for modeling SD effect observed in hcp materials.

PBPK-Based Probabilistic Risk Assessment for Total Chlorotriazines in Drinking Water

PubMed Central

Breckenridge, Charles B.; Campbell, Jerry L.; Clewell, Harvey J.; Andersen, Melvin E.; Valdez-Flores, Ciriaco; Sielken, Robert L.

2016-01-01

The risk of human exposure to total chlorotriazines (TCT) in drinking water was evaluated using a physiologically based pharmacokinetic (PBPK) model. Daily TCT (atrazine, deethylatrazine, deisopropylatrazine, and diaminochlorotriazine) chemographs were constructed for 17 frequently monitored community water systems (CWSs) using linear interpolation and Krieg estimates between observed TCT values. Synthetic chemographs were created using a conservative bias factor of 3 to generate intervening peaks between measured values. Drinking water consumption records from 24-h diaries were used to calculate daily exposure. Plasma TCT concentrations were updated every 30 minutes using the PBPK model output for each simulated calendar year from 2006 to 2010. Margins of exposure (MOEs) were calculated (MOE = [Human Plasma TCTPOD] ÷ [Human Plasma TCTEXP]) based on the toxicological point of departure (POD) and the drinking water-derived exposure to TCT. MOEs were determined based on 1, 2, 3, 4, 7, 14, 28, or 90 days of rolling average exposures and plasma TCT Cmax, or the area under the curve (AUC). Distributions of MOE were determined and the 99.9th percentile was used for risk assessment. MOEs for all 17 CWSs were >1000 at the 99.9th percentile. The 99.9th percentile of the MOE distribution was 2.8-fold less when the 3-fold synthetic chemograph bias factor was used. MOEs were insensitive to interpolation method, the consumer’s age, the water consumption database used and the duration of time over which the rolling average plasma TCT was calculated, for up to 90 days. MOEs were sensitive to factors that modified the toxicological, or hyphenated appropriately no-observed-effects level (NOEL), including rat strain, endpoint used, method of calculating the NOEL, and the pharmacokinetics of elimination, as well as the magnitude of exposure (CWS, calendar year, and use of bias factors). PMID:26794141

PBPK-Based Probabilistic Risk Assessment for Total Chlorotriazines in Drinking Water.

PubMed

Breckenridge, Charles B; Campbell, Jerry L; Clewell, Harvey J; Andersen, Melvin E; Valdez-Flores, Ciriaco; Sielken, Robert L

2016-04-01

The risk of human exposure to total chlorotriazines (TCT) in drinking water was evaluated using a physiologically based pharmacokinetic (PBPK) model. Daily TCT (atrazine, deethylatrazine, deisopropylatrazine, and diaminochlorotriazine) chemographs were constructed for 17 frequently monitored community water systems (CWSs) using linear interpolation and Krieg estimates between observed TCT values. Synthetic chemographs were created using a conservative bias factor of 3 to generate intervening peaks between measured values. Drinking water consumption records from 24-h diaries were used to calculate daily exposure. Plasma TCT concentrations were updated every 30 minutes using the PBPK model output for each simulated calendar year from 2006 to 2010. Margins of exposure (MOEs) were calculated (MOE = [Human Plasma TCTPOD] ÷ [Human Plasma TCTEXP]) based on the toxicological point of departure (POD) and the drinking water-derived exposure to TCT. MOEs were determined based on 1, 2, 3, 4, 7, 14, 28, or 90 days of rolling average exposures and plasma TCT Cmax, or the area under the curve (AUC). Distributions of MOE were determined and the 99.9th percentile was used for risk assessment. MOEs for all 17 CWSs were >1000 at the 99.9(th)percentile. The 99.9(th)percentile of the MOE distribution was 2.8-fold less when the 3-fold synthetic chemograph bias factor was used. MOEs were insensitive to interpolation method, the consumer's age, the water consumption database used and the duration of time over which the rolling average plasma TCT was calculated, for up to 90 days. MOEs were sensitive to factors that modified the toxicological, or hyphenated appropriately no-observed-effects level (NOEL), including rat strain, endpoint used, method of calculating the NOEL, and the pharmacokinetics of elimination, as well as the magnitude of exposure (CWS, calendar year, and use of bias factors). © The Author 2016. Published by Oxford University Press on behalf of the Society of Toxicology.

Novel view synthesis by interpolation over sparse examples

NASA Astrophysics Data System (ADS)

Liang, Bodong; Chung, Ronald C.

2006-01-01

Novel view synthesis (NVS) is an important problem in image rendering. It involves synthesizing an image of a scene at any specified (novel) viewpoint, given some images of the scene at a few sample viewpoints. The general understanding is that the solution should bypass explicit 3-D reconstruction of the scene. As it is, the problem has a natural tie to interpolation, despite that mainstream efforts on the problem have been adopting formulations otherwise. Interpolation is about finding the output of a function f(x) for any specified input x, given a few input-output pairs {(xi,fi):i=1,2,3,...,n} of the function. If the input x is the viewpoint, and f(x) is the image, the interpolation problem becomes exactly NVS. We treat the NVS problem using the interpolation formulation. In particular, we adopt the example-based everything or interpolation (EBI) mechanism-an established mechanism for interpolating or learning functions from examples. EBI has all the desirable properties of a good interpolation: all given input-output examples are satisfied exactly, and the interpolation is smooth with minimum oscillations between the examples. We point out that EBI, however, has difficulty in interpolating certain classes of functions, including the image function in the NVS problem. We propose an extension of the mechanism for overcoming the limitation. We also present how the extended interpolation mechanism could be used to synthesize images at novel viewpoints. Real image results show that the mechanism has promising performance, even with very few example images.

Spatial interpolation of solar irradiation data over complex orography: Solar map of Canaries Islands

NASA Astrophysics Data System (ADS)

Ortegón Gallego, A.

2010-09-01

In this paper, we describe the calculation methodology we used to determine the spatial structure of solar irradiation over a very complex orography, such as the Canary archipelago, that is broken in seven islands, with only 7500 km2, and with heights in some of the islands upper than 1800 m, that reach to 3718 m in the case of Tenerife island. Starting with the method of Cumulative Semivariograms1, already used to face the irradiation spatial interpolation problem, although not for a complex orography. In this sense, some major modifications are introduced to deal with our needs, which can be summarized as: a) interpolation of clearness index data (Kcd, defined as the division of the global horizontal data, between the corresponding clear sky global horizontal values, obtained from a suitable model) instead of solar irradiation data; b) topographic considerations are included in the clear sky model, such as topographics shadows. This impacts directly over direct component of solar irradiation, and has a minor effect over the diffuse component, arising from a non plane visible horizon; c) the meteorological stations are selected by a criteria of weather proximity, instead of geographic proximity as it was proposed in the original methodology of Cumulative Semivariograms; d) the final result is obtained as the composition of various maps obtained from error minimization within a neighborhood of each available station, instead of using irradiation isolines. A preliminary result with data registered only by Canary Islands Institute of Technology's stations, spread over the whole archipelago, is showed. From our results we can see both, the power of the developed methodology and some limitations due to the extremely complex orography as it is the case of Canary Islands, which consists of a wide variety of microclimate regions. Whenever additional information is available, either in the form of empiric knowledge of the local weather, or in the form of other available radiometric data sources, the results do improve. In the case that all available stations are already used, the empirical knowledge of weather conditions can be introduced in our model by means of a strain parameter that modifies the statistical weight associated to the corresponding station in a given neighborhood. On the other hand, whenever it is possible to increase the spatial density of data sources, that is, to incorporate data from others stations, the result improves provided that data quality is good enough. To validate the results obtained with our methodology, we calculate the error between the estimated solar irradiation at the location of the stations with the records obtained by them.

Theoretical oscillation frequencies for solar-type dwarfs from stellar models with 〈3D〉-atmospheres

NASA Astrophysics Data System (ADS)

Jørgensen, Andreas Christ Sølvsten; Weiss, Achim; Mosumgaard, Jakob Rørsted; Silva Aguirre, Victor; Sahlholdt, Christian Lundsgaard

2017-12-01

We present a new method for replacing the outermost layers of stellar models with interpolated atmospheres based on results from 3D simulations, in order to correct for structural inadequacies of these layers. This replacement is known as patching. Tests, based on 3D atmospheres from three different codes and interior models with different input physics, are performed. Using solar models, we investigate how different patching criteria affect the eigenfrequencies. These criteria include the depth, at which the replacement is performed, the quantity, on which the replacement is based, and the mismatch in Teff and log g between the un-patched model and patched 3D atmosphere. We find the eigenfrequencies to be unaltered by the patching depth deep within the adiabatic region, while changing the patching quantity or the employed atmosphere grid leads to frequency shifts that may exceed 1 μHz. Likewise, the eigenfrequencies are sensitive to mismatches in Teff or log g. A thorough investigation of the accuracy of a new scheme, for interpolating mean 3D stratifications within the atmosphere grids, is furthermore performed. Throughout large parts of the atmosphere grids, our interpolation scheme yields sufficiently accurate results for the purpose of asteroseismology. We apply our procedure in asteroseismic analyses of four Kepler stars and draw the same conclusions as in the solar case: Correcting for structural deficiencies lowers the eigenfrequencies, this correction is slightly sensitive to the patching criteria, and the remaining frequency discrepancy between models and observations is less frequency dependent. Our work shows the applicability and relevance of patching in asteroseismology.

A Thermo-Optic Propagation Modeling Capability.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schrader, Karl; Akau, Ron

2014-10-01

A new theoretical basis is derived for tracing optical rays within a finite-element (FE) volume. The ray-trajectory equations are cast into the local element coordinate frame and the full finite-element interpolation is used to determine instantaneous index gradient for the ray-path integral equation. The FE methodology (FEM) is also used to interpolate local surface deformations and the surface normal vector for computing the refraction angle when launching rays into the volume, and again when rays exit the medium. The method is implemented in the Matlab(TM) environment and compared to closed- form gradient index models. A software architecture is also developedmore » for implementing the algorithms in the Zemax(TM) commercial ray-trace application. A controlled thermal environment was constructed in the laboratory, and measured data was collected to validate the structural, thermal, and optical modeling methods.« less

Restoration of Monotonicity Respecting in Dynamic Regression

PubMed Central

Huang, Yijian

2017-01-01

Dynamic regression models, including the quantile regression model and Aalen’s additive hazards model, are widely adopted to investigate evolving covariate effects. Yet lack of monotonicity respecting with standard estimation procedures remains an outstanding issue. Advances have recently been made, but none provides a complete resolution. In this article, we propose a novel adaptive interpolation method to restore monotonicity respecting, by successively identifying and then interpolating nearest monotonicity-respecting points of an original estimator. Under mild regularity conditions, the resulting regression coefficient estimator is shown to be asymptotically equivalent to the original. Our numerical studies have demonstrated that the proposed estimator is much more smooth and may have better finite-sample efficiency than the original as well as, when available as only in special cases, other competing monotonicity-respecting estimators. Illustration with a clinical study is provided. PMID:29430068

SAR image formation with azimuth interpolation after azimuth transform

DOEpatents

Doerry,; Armin W. , Martin; Grant D. , Holzrichter; Michael, W [Albuquerque, NM

2008-07-08

Two-dimensional SAR data can be processed into a rectangular grid format by subjecting the SAR data to a Fourier transform operation, and thereafter to a corresponding interpolation operation. Because the interpolation operation follows the Fourier transform operation, the interpolation operation can be simplified, and the effect of interpolation errors can be diminished. This provides for the possibility of both reducing the re-grid processing time, and improving the image quality.

Kriging with Unknown Variance Components for Regional Ionospheric Reconstruction.

PubMed

Huang, Ling; Zhang, Hongping; Xu, Peiliang; Geng, Jianghui; Wang, Cheng; Liu, Jingnan

2017-02-27

Ionospheric delay effect is a critical issue that limits the accuracy of precise Global Navigation Satellite System (GNSS) positioning and navigation for single-frequency users, especially in mid- and low-latitude regions where variations in the ionosphere are larger. Kriging spatial interpolation techniques have been recently introduced to model the spatial correlation and variability of ionosphere, which intrinsically assume that the ionosphere field is stochastically stationary but does not take the random observational errors into account. In this paper, by treating the spatial statistical information on ionosphere as prior knowledge and based on Total Electron Content (TEC) semivariogram analysis, we use Kriging techniques to spatially interpolate TEC values. By assuming that the stochastic models of both the ionospheric signals and measurement errors are only known up to some unknown factors, we propose a new Kriging spatial interpolation method with unknown variance components for both the signals of ionosphere and TEC measurements. Variance component estimation has been integrated with Kriging to reconstruct regional ionospheric delays. The method has been applied to data from the Crustal Movement Observation Network of China (CMONOC) and compared with the ordinary Kriging and polynomial interpolations with spherical cap harmonic functions, polynomial functions and low-degree spherical harmonic functions. The statistics of results indicate that the daily ionospheric variations during the experimental period characterized by the proposed approach have good agreement with the other methods, ranging from 10 to 80 TEC Unit (TECU, 1 TECU = 1 × 10 16 electrons/m²) with an overall mean of 28.2 TECU. The proposed method can produce more appropriate estimations whose general TEC level is as smooth as the ordinary Kriging but with a smaller standard deviation around 3 TECU than others. The residual results show that the interpolation precision of the new proposed method is better than the ordinary Kriging and polynomial interpolation by about 1.2 TECU and 0.7 TECU, respectively. The root mean squared error of the proposed new Kriging with variance components is within 1.5 TECU and is smaller than those from other methods under comparison by about 1 TECU. When compared with ionospheric grid points, the mean squared error of the proposed method is within 6 TECU and smaller than Kriging, indicating that the proposed method can produce more accurate ionospheric delays and better estimation accuracy over China regional area.

Kriging with Unknown Variance Components for Regional Ionospheric Reconstruction

PubMed Central

Huang, Ling; Zhang, Hongping; Xu, Peiliang; Geng, Jianghui; Wang, Cheng; Liu, Jingnan

2017-01-01

Ionospheric delay effect is a critical issue that limits the accuracy of precise Global Navigation Satellite System (GNSS) positioning and navigation for single-frequency users, especially in mid- and low-latitude regions where variations in the ionosphere are larger. Kriging spatial interpolation techniques have been recently introduced to model the spatial correlation and variability of ionosphere, which intrinsically assume that the ionosphere field is stochastically stationary but does not take the random observational errors into account. In this paper, by treating the spatial statistical information on ionosphere as prior knowledge and based on Total Electron Content (TEC) semivariogram analysis, we use Kriging techniques to spatially interpolate TEC values. By assuming that the stochastic models of both the ionospheric signals and measurement errors are only known up to some unknown factors, we propose a new Kriging spatial interpolation method with unknown variance components for both the signals of ionosphere and TEC measurements. Variance component estimation has been integrated with Kriging to reconstruct regional ionospheric delays. The method has been applied to data from the Crustal Movement Observation Network of China (CMONOC) and compared with the ordinary Kriging and polynomial interpolations with spherical cap harmonic functions, polynomial functions and low-degree spherical harmonic functions. The statistics of results indicate that the daily ionospheric variations during the experimental period characterized by the proposed approach have good agreement with the other methods, ranging from 10 to 80 TEC Unit (TECU, 1 TECU = 1 × 1016 electrons/m2) with an overall mean of 28.2 TECU. The proposed method can produce more appropriate estimations whose general TEC level is as smooth as the ordinary Kriging but with a smaller standard deviation around 3 TECU than others. The residual results show that the interpolation precision of the new proposed method is better than the ordinary Kriging and polynomial interpolation by about 1.2 TECU and 0.7 TECU, respectively. The root mean squared error of the proposed new Kriging with variance components is within 1.5 TECU and is smaller than those from other methods under comparison by about 1 TECU. When compared with ionospheric grid points, the mean squared error of the proposed method is within 6 TECU and smaller than Kriging, indicating that the proposed method can produce more accurate ionospheric delays and better estimation accuracy over China regional area. PMID:28264424

Task Assignment and Path Planning for Multiple Autonomous Underwater Vehicles Using 3D Dubins Curves †

PubMed Central

Zhang, Meiyan; Zheng, Yahong Rosa

2017-01-01

This paper investigates the task assignment and path planning problem for multiple AUVs in three dimensional (3D) underwater wireless sensor networks where nonholonomic motion constraints of underwater AUVs in 3D space are considered. The multi-target task assignment and path planning problem is modeled by the Multiple Traveling Sales Person (MTSP) problem and the Genetic Algorithm (GA) is used to solve the MTSP problem with Euclidean distance as the cost function and the Tour Hop Balance (THB) or Tour Length Balance (TLB) constraints as the stop criterion. The resulting tour sequences are mapped to 2D Dubins curves in the X−Y plane, and then interpolated linearly to obtain the Z coordinates. We demonstrate that the linear interpolation fails to achieve G1 continuity in the 3D Dubins path for multiple targets. Therefore, the interpolated 3D Dubins curves are checked against the AUV dynamics constraint and the ones satisfying the constraint are accepted to finalize the 3D Dubins curve selection. Simulation results demonstrate that the integration of the 3D Dubins curve with the MTSP model is successful and effective for solving the 3D target assignment and path planning problem. PMID:28696377

Efficient model reduction of parametrized systems by matrix discrete empirical interpolation

NASA Astrophysics Data System (ADS)

Negri, Federico; Manzoni, Andrea; Amsallem, David

2015-12-01

In this work, we apply a Matrix version of the so-called Discrete Empirical Interpolation (MDEIM) for the efficient reduction of nonaffine parametrized systems arising from the discretization of linear partial differential equations. Dealing with affinely parametrized operators is crucial in order to enhance the online solution of reduced-order models (ROMs). However, in many cases such an affine decomposition is not readily available, and must be recovered through (often) intrusive procedures, such as the empirical interpolation method (EIM) and its discrete variant DEIM. In this paper we show that MDEIM represents a very efficient approach to deal with complex physical and geometrical parametrizations in a non-intrusive, efficient and purely algebraic way. We propose different strategies to combine MDEIM with a state approximation resulting either from a reduced basis greedy approach or Proper Orthogonal Decomposition. A posteriori error estimates accounting for the MDEIM error are also developed in the case of parametrized elliptic and parabolic equations. Finally, the capability of MDEIM to generate accurate and efficient ROMs is demonstrated on the solution of two computationally-intensive classes of problems occurring in engineering contexts, namely PDE-constrained shape optimization and parametrized coupled problems.

Generation of Fullspan Leading-Edge 3D Ice Shapes for Swept-Wing Aerodynamic Testing

NASA Technical Reports Server (NTRS)

Camello, Stephanie C.; Lee, Sam; Lum, Christopher; Bragg, Michael B.

2016-01-01

The deleterious effect of ice accretion on aircraft is often assessed through dry-air flight and wind tunnel testing with artificial ice shapes. This paper describes a method to create fullspan swept-wing artificial ice shapes from partial span ice segments acquired in the NASA Glenn Icing Reserch Tunnel for aerodynamic wind-tunnel testing. Full-scale ice accretion segments were laser scanned from the Inboard, Midspan, and Outboard wing station models of the 65% scale Common Research Model (CRM65) aircraft configuration. These were interpolated and extrapolated using a weighted averaging method to generate fullspan ice shapes from the root to the tip of the CRM65 wing. The results showed that this interpolation method was able to preserve many of the highly three dimensional features typically found on swept-wing ice accretions. The interpolated fullspan ice shapes were then scaled to fit the leading edge of a 8.9% scale version of the CRM65 wing for aerodynamic wind-tunnel testing. Reduced fidelity versions of the fullspan ice shapes were also created where most of the local three-dimensional features were removed. The fullspan artificial ice shapes and the reduced fidelity versions were manufactured using stereolithography.

Task Assignment and Path Planning for Multiple Autonomous Underwater Vehicles Using 3D Dubins Curves †.

PubMed

Cai, Wenyu; Zhang, Meiyan; Zheng, Yahong Rosa

2017-07-11

This paper investigates the task assignment and path planning problem for multiple AUVs in three dimensional (3D) underwater wireless sensor networks where nonholonomic motion constraints of underwater AUVs in 3D space are considered. The multi-target task assignment and path planning problem is modeled by the Multiple Traveling Sales Person (MTSP) problem and the Genetic Algorithm (GA) is used to solve the MTSP problem with Euclidean distance as the cost function and the Tour Hop Balance (THB) or Tour Length Balance (TLB) constraints as the stop criterion. The resulting tour sequences are mapped to 2D Dubins curves in the X - Y plane, and then interpolated linearly to obtain the Z coordinates. We demonstrate that the linear interpolation fails to achieve G 1 continuity in the 3D Dubins path for multiple targets. Therefore, the interpolated 3D Dubins curves are checked against the AUV dynamics constraint and the ones satisfying the constraint are accepted to finalize the 3D Dubins curve selection. Simulation results demonstrate that the integration of the 3D Dubins curve with the MTSP model is successful and effective for solving the 3D target assignment and path planning problem.

Holes in the ocean: Filling voids in bathymetric lidar data

NASA Astrophysics Data System (ADS)

Coleman, John B.; Yao, Xiaobai; Jordan, Thomas R.; Madden, Marguertie

2011-04-01

The mapping of coral reefs may be efficiently accomplished by the use of airborne laser bathymetry. However, there are often data holes within the bathymetry data which must be filled in order to produce a complete representation of the coral habitat. This study presents a method to fill these data holes through data merging and interpolation. The method first merges ancillary digital sounding data with airborne laser bathymetry data in order to populate data points in all areas but particularly those of data holes. What follows is to generate an elevation surface by spatial interpolation based on the merged data points obtained in the first step. We conduct a case study of the Dry Tortugas National Park in Florida and produced an enhanced digital elevation model in the ocean with this method. Four interpolation techniques, including Kriging, natural neighbor, spline, and inverse distance weighted, are implemented and evaluated on their ability to accurately and realistically represent the shallow-water bathymetry of the study area. The natural neighbor technique is found to be the most effective. Finally, this enhanced digital elevation model is used in conjunction with Ikonos imagery to produce a complete, three-dimensional visualization of the study area.

Digital elevation modeling via curvature interpolation for lidar data

USDA-ARS?s Scientific Manuscript database

Digital elevation model (DEM) is a three-dimensional (3D) representation of a terrain's surface - for a planet (including Earth), moon, or asteroid - created from point cloud data which measure terrain elevation. Its modeling requires surface reconstruction for the scattered data, which is an ill-p...

A Linear Algebraic Approach to Teaching Interpolation

ERIC Educational Resources Information Center

Tassa, Tamir

2007-01-01

A novel approach for teaching interpolation in the introductory course in numerical analysis is presented. The interpolation problem is viewed as a problem in linear algebra, whence the various forms of interpolating polynomial are seen as different choices of a basis to the subspace of polynomials of the corresponding degree. This approach…

A new ghost-node method for linking different models and initial investigations of heterogeneity and nonmatching grids

USGS Publications Warehouse

Dickinson, J.E.; James, S.C.; Mehl, S.; Hill, M.C.; Leake, S.A.; Zyvoloski, G.A.; Faunt, C.C.; Eddebbarh, A.-A.

2007-01-01

A flexible, robust method for linking parent (regional-scale) and child (local-scale) grids of locally refined models that use different numerical methods is developed based on a new, iterative ghost-node method. Tests are presented for two-dimensional and three-dimensional pumped systems that are homogeneous or that have simple heterogeneity. The parent and child grids are simulated using the block-centered finite-difference MODFLOW and control-volume finite-element FEHM models, respectively. The models are solved iteratively through head-dependent (child model) and specified-flow (parent model) boundary conditions. Boundary conditions for models with nonmatching grids or zones of different hydraulic conductivity are derived and tested against heads and flows from analytical or globally-refined models. Results indicate that for homogeneous two- and three-dimensional models with matched grids (integer number of child cells per parent cell), the new method is nearly as accurate as the coupling of two MODFLOW models using the shared-node method and, surprisingly, errors are slightly lower for nonmatching grids (noninteger number of child cells per parent cell). For heterogeneous three-dimensional systems, this paper compares two methods for each of the two sets of boundary conditions: external heads at head-dependent boundary conditions for the child model are calculated using bilinear interpolation or a Darcy-weighted interpolation; specified-flow boundary conditions for the parent model are calculated using model-grid or hydrogeologic-unit hydraulic conductivities. Results suggest that significantly more accurate heads and flows are produced when both Darcy-weighted interpolation and hydrogeologic-unit hydraulic conductivities are used, while the other methods produce larger errors at the boundary between the regional and local models. The tests suggest that, if posed correctly, the ghost-node method performs well. Additional testing is needed for highly heterogeneous systems. ?? 2007 Elsevier Ltd. All rights reserved.

Spatial Copula Model for Imputing Traffic Flow Data from Remote Microwave Sensors.

PubMed

Ma, Xiaolei; Luan, Sen; Du, Bowen; Yu, Bin

2017-09-21

Issues of missing data have become increasingly serious with the rapid increase in usage of traffic sensors. Analyses of the Beijing ring expressway have showed that up to 50% of microwave sensors pose missing values. The imputation of missing traffic data must be urgently solved although a precise solution that cannot be easily achieved due to the significant number of missing portions. In this study, copula-based models are proposed for the spatial interpolation of traffic flow from remote traffic microwave sensors. Most existing interpolation methods only rely on covariance functions to depict spatial correlation and are unsuitable for coping with anomalies due to Gaussian consumption. Copula theory overcomes this issue and provides a connection between the correlation function and the marginal distribution function of traffic flow. To validate copula-based models, a comparison with three kriging methods is conducted. Results indicate that copula-based models outperform kriging methods, especially on roads with irregular traffic patterns. Copula-based models demonstrate significant potential to impute missing data in large-scale transportation networks.

Zero-point energy conservation in classical trajectory simulations: Application to H2CO

NASA Astrophysics Data System (ADS)

Lee, Kin Long Kelvin; Quinn, Mitchell S.; Kolmann, Stephen J.; Kable, Scott H.; Jordan, Meredith J. T.

2018-05-01

A new approach for preventing zero-point energy (ZPE) violation in quasi-classical trajectory (QCT) simulations is presented and applied to H2CO "roaming" reactions. Zero-point energy may be problematic in roaming reactions because they occur at or near bond dissociation thresholds and these channels may be incorrectly open or closed depending on if, or how, ZPE has been treated. Here we run QCT simulations on a "ZPE-corrected" potential energy surface defined as the sum of the molecular potential energy surface (PES) and the global harmonic ZPE surface. Five different harmonic ZPE estimates are examined with four, on average, giving values within 4 kJ/mol—chemical accuracy—for H2CO. The local harmonic ZPE, at arbitrary molecular configurations, is subsequently defined in terms of "projected" Cartesian coordinates and a global ZPE "surface" is constructed using Shepard interpolation. This, combined with a second-order modified Shepard interpolated PES, V, allows us to construct a proof-of-concept ZPE-corrected PES for H2CO, Veff, at no additional computational cost to the PES itself. Both V and Veff are used to model product state distributions from the H + HCO → H2 + CO abstraction reaction, which are shown to reproduce the literature roaming product state distributions. Our ZPE-corrected PES allows all trajectories to be analysed, whereas, in previous simulations, a significant proportion was discarded because of ZPE violation. We find ZPE has little effect on product rotational distributions, validating previous QCT simulations. Running trajectories on V, however, shifts the product kinetic energy release to higher energy than on Veff and classical simulations of kinetic energy release should therefore be viewed with caution.

Finite difference modelling of dipole acoustic logs in a poroelastic formation with anisotropic permeability

NASA Astrophysics Data System (ADS)

He, Xiao; Hu, Hengshan; Wang, Xiuming

2013-01-01

Sedimentary rocks can exhibit strong permeability anisotropy due to layering, pre-stresses and the presence of aligned microcracks or fractures. In this paper, we develop a modified cylindrical finite-difference algorithm to simulate the borehole acoustic wavefield in a saturated poroelastic medium with transverse isotropy of permeability and tortuosity. A linear interpolation process is proposed to guarantee the leapfrog finite difference scheme for the generalized dynamic equations and Darcy's law for anisotropic porous media. First, the modified algorithm is validated by comparison against the analytical solution when the borehole axis is parallel to the symmetry axis of the formation. The same algorithm is then used to numerically model the dipole acoustic log in a borehole with its axis being arbitrarily deviated from the symmetry axis of transverse isotropy. The simulation results show that the amplitudes of flexural modes vary with the dipole orientation because the permeability tensor of the formation is dependent on the wellbore azimuth. It is revealed that the attenuation of the flexural wave increases approximately linearly with the radial permeability component in the direction of the transmitting dipole. Particularly, when the borehole axis is perpendicular to the symmetry axis of the formation, it is possible to estimate the anisotropy of permeability by evaluating attenuation of the flexural wave using a cross-dipole sonic logging tool according to the results of sensitivity analyses. Finally, the dipole sonic logs in a deviated borehole surrounded by a stratified porous formation are modelled using the proposed finite difference code. Numerical results show that the arrivals and amplitudes of transmitted flexural modes near the layer interface are sensitive to the wellbore inclination.

Automatic elastic image registration by interpolation of 3D rotations and translations from discrete rigid-body transformations.

PubMed

Walimbe, Vivek; Shekhar, Raj

2006-12-01

We present an algorithm for automatic elastic registration of three-dimensional (3D) medical images. Our algorithm initially recovers the global spatial mismatch between the reference and floating images, followed by hierarchical octree-based subdivision of the reference image and independent registration of the floating image with the individual subvolumes of the reference image at each hierarchical level. Global as well as local registrations use the six-parameter full rigid-body transformation model and are based on maximization of normalized mutual information (NMI). To ensure robustness of the subvolume registration with low voxel counts, we calculate NMI using a combination of current and prior mutual histograms. To generate a smooth deformation field, we perform direct interpolation of six-parameter rigid-body subvolume transformations obtained at the last subdivision level. Our interpolation scheme involves scalar interpolation of the 3D translations and quaternion interpolation of the 3D rotational pose. We analyzed the performance of our algorithm through experiments involving registration of synthetically deformed computed tomography (CT) images. Our algorithm is general and can be applied to image pairs of any two modalities of most organs. We have demonstrated successful registration of clinical whole-body CT and positron emission tomography (PET) images using this algorithm. The registration accuracy for this application was evaluated, based on validation using expert-identified anatomical landmarks in 15 CT-PET image pairs. The algorithm's performance was comparable to the average accuracy observed for three expert-determined registrations in the same 15 image pairs.

Gradient-based interpolation method for division-of-focal-plane polarimeters.

PubMed

Gao, Shengkui; Gruev, Viktor

2013-01-14

Recent advancements in nanotechnology and nanofabrication have allowed for the emergence of the division-of-focal-plane (DoFP) polarization imaging sensors. These sensors capture polarization properties of the optical field at every imaging frame. However, the DoFP polarization imaging sensors suffer from large registration error as well as reduced spatial-resolution output. These drawbacks can be improved by applying proper image interpolation methods for the reconstruction of the polarization results. In this paper, we present a new gradient-based interpolation method for DoFP polarimeters. The performance of the proposed interpolation method is evaluated against several previously published interpolation methods by using visual examples and root mean square error (RMSE) comparison. We found that the proposed gradient-based interpolation method can achieve better visual results while maintaining a lower RMSE than other interpolation methods under various dynamic ranges of a scene ranging from dim to bright conditions.

Directional view interpolation for compensation of sparse angular sampling in cone-beam CT.

PubMed

Bertram, Matthias; Wiegert, Jens; Schafer, Dirk; Aach, Til; Rose, Georg

2009-07-01

In flat detector cone-beam computed tomography and related applications, sparse angular sampling frequently leads to characteristic streak artifacts. To overcome this problem, it has been suggested to generate additional views by means of interpolation. The practicality of this approach is investigated in combination with a dedicated method for angular interpolation of 3-D sinogram data. For this purpose, a novel dedicated shape-driven directional interpolation algorithm based on a structure tensor approach is developed. Quantitative evaluation shows that this method clearly outperforms conventional scene-based interpolation schemes. Furthermore, the image quality trade-offs associated with the use of interpolated intermediate views are systematically evaluated for simulated and clinical cone-beam computed tomography data sets of the human head. It is found that utilization of directionally interpolated views significantly reduces streak artifacts and noise, at the expense of small introduced image blur.

Systematic interpolation method predicts protein chromatographic elution with salt gradients, pH gradients and combined salt/pH gradients.

PubMed

Creasy, Arch; Barker, Gregory; Carta, Giorgio

2017-03-01

A methodology is presented to predict protein elution behavior from an ion exchange column using both individual or combined pH and salt gradients based on high-throughput batch isotherm data. The buffer compositions are first optimized to generate linear pH gradients from pH 5.5 to 7 with defined concentrations of sodium chloride. Next, high-throughput batch isotherm data are collected for a monoclonal antibody on the cation exchange resin POROS XS over a range of protein concentrations, salt concentrations, and solution pH. Finally, a previously developed empirical interpolation (EI) method is extended to describe protein binding as a function of the protein and salt concentration and solution pH without using an explicit isotherm model. The interpolated isotherm data are then used with a lumped kinetic model to predict the protein elution behavior. Experimental results obtained for laboratory scale columns show excellent agreement with the predicted elution curves for both individual or combined pH and salt gradients at protein loads up to 45 mg/mL of column. Numerical studies show that the model predictions are robust as long as the isotherm data cover the range of mobile phase compositions where the protein actually elutes from the column. Copyright © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

3-D Interpolation in Object Perception: Evidence from an Objective Performance Paradigm

ERIC Educational Resources Information Center

Kellman, Philip J.; Garrigan, Patrick; Shipley, Thomas F.; Yin, Carol; Machado, Liana

2005-01-01

Object perception requires interpolation processes that connect visible regions despite spatial gaps. Some research has suggested that interpolation may be a 3-D process, but objective performance data and evidence about the conditions leading to interpolation are needed. The authors developed an objective performance paradigm for testing 3-D…

Development and validation of segmentation and interpolation techniques in sinograms for metal artifact suppression in CT.

PubMed

Veldkamp, Wouter J H; Joemai, Raoul M S; van der Molen, Aart J; Geleijns, Jacob

2010-02-01

Metal prostheses cause artifacts in computed tomography (CT) images. The purpose of this work was to design an efficient and accurate metal segmentation in raw data to achieve artifact suppression and to improve CT image quality for patients with metal hip or shoulder prostheses. The artifact suppression technique incorporates two steps: metal object segmentation in raw data and replacement of the segmented region by new values using an interpolation scheme, followed by addition of the scaled metal signal intensity. Segmentation of metal is performed directly in sinograms, making it efficient and different from current methods that perform segmentation in reconstructed images in combination with Radon transformations. Metal signal segmentation is achieved by using a Markov random field model (MRF). Three interpolation methods are applied and investigated. To provide a proof of concept, CT data of five patients with metal implants were included in the study, as well as CT data of a PMMA phantom with Teflon, PVC, and titanium inserts. Accuracy was determined quantitatively by comparing mean Hounsfield (HU) values and standard deviation (SD) as a measure of distortion in phantom images with titanium (original and suppressed) and without titanium insert. Qualitative improvement was assessed by comparing uncorrected clinical images with artifact suppressed images. Artifacts in CT data of a phantom and five patients were automatically suppressed. The general visibility of structures clearly improved. In phantom images, the technique showed reduced SD close to the SD for the case where titanium was not inserted, indicating improved image quality. HU values in corrected images were different from expected values for all interpolation methods. Subtle differences between interpolation methods were found. The new artifact suppression design is efficient, for instance, in terms of preserving spatial resolution, as it is applied directly to original raw data. It successfully reduced artifacts in CT images of five patients and in phantom images. Sophisticated interpolation methods are needed to obtain reliable HU values close to the prosthesis.

Mapping Atmospheric Moisture Climatologies across the Conterminous United States

PubMed Central

Daly, Christopher; Smith, Joseph I.; Olson, Keith V.

2015-01-01

Spatial climate datasets of 1981–2010 long-term mean monthly average dew point and minimum and maximum vapor pressure deficit were developed for the conterminous United States at 30-arcsec (~800m) resolution. Interpolation of long-term averages (twelve monthly values per variable) was performed using PRISM (Parameter-elevation Relationships on Independent Slopes Model). Surface stations available for analysis numbered only 4,000 for dew point and 3,500 for vapor pressure deficit, compared to 16,000 for previously-developed grids of 1981–2010 long-term mean monthly minimum and maximum temperature. Therefore, a form of Climatologically-Aided Interpolation (CAI) was used, in which the 1981–2010 temperature grids were used as predictor grids. For each grid cell, PRISM calculated a local regression function between the interpolated climate variable and the predictor grid. Nearby stations entering the regression were assigned weights based on the physiographic similarity of the station to the grid cell that included the effects of distance, elevation, coastal proximity, vertical atmospheric layer, and topographic position. Interpolation uncertainties were estimated using cross-validation exercises. Given that CAI interpolation was used, a new method was developed to allow uncertainties in predictor grids to be accounted for in estimating the total interpolation error. Local land use/land cover properties had noticeable effects on the spatial patterns of atmospheric moisture content and deficit. An example of this was relatively high dew points and low vapor pressure deficits at stations located in or near irrigated fields. The new grids, in combination with existing temperature grids, enable the user to derive a full suite of atmospheric moisture variables, such as minimum and maximum relative humidity, vapor pressure, and dew point depression, with accompanying assumptions. All of these grids are available online at http://prism.oregonstate.edu, and include 800-m and 4-km resolution data, images, metadata, pedigree information, and station inventory files. PMID:26485026

A Residual Kriging method for the reconstruction of 3D high-resolution meteorological fields from airborne and surface observations

NASA Astrophysics Data System (ADS)

Laiti, Lavinia; Zardi, Dino; de Franceschi, Massimiliano; Rampanelli, Gabriele

2013-04-01

Manned light aircrafts and remotely piloted aircrafts represent very valuable and flexible measurement platforms for atmospheric research, as they are able to provide high temporal and spatial resolution observations of the atmosphere above the ground surface. In the present study the application of a geostatistical interpolation technique called Residual Kriging (RK) is proposed for the mapping of airborne measurements of scalar quantities over regularly spaced 3D grids. In RK the dominant (vertical) trend component underlying the original data is first extracted to filter out local anomalies, then the residual field is separately interpolated and finally added back to the trend; the determination of the interpolation weights relies on the estimate of the characteristic covariance function of the residuals, through the computation and modelling of their semivariogram function. RK implementation also allows for the inference of the characteristic spatial scales of variability of the target field and its isotropization, and for an estimate of the interpolation error. The adopted test-bed database consists in a series of flights of an instrumented motorglider exploring the atmosphere of two valleys near the city of Trento (in the southeastern Italian Alps), performed on fair-weather summer days. RK method is used to reconstruct fully 3D high-resolution fields of potential temperature and mixing ratio for specific vertical slices of the valley atmosphere, integrating also ground-based measurements from the nearest surface weather stations. From RK-interpolated meteorological fields, fine-scale features of the atmospheric boundary layer developing over the complex valley topography in connection with the occurrence of thermally-driven slope and valley winds, are detected. The performance of RK mapping is also tested against two other commonly adopted interpolation methods, i.e. the Inverse Distance Weighting and the Delaunay triangulation methods, comparing the results of a cross-validation procedure.

Real-time Interpolation for True 3-Dimensional Ultrasound Image Volumes

PubMed Central

Ji, Songbai; Roberts, David W.; Hartov, Alex; Paulsen, Keith D.

2013-01-01

We compared trilinear interpolation to voxel nearest neighbor and distance-weighted algorithms for fast and accurate processing of true 3-dimensional ultrasound (3DUS) image volumes. In this study, the computational efficiency and interpolation accuracy of the 3 methods were compared on the basis of a simulated 3DUS image volume, 34 clinical 3DUS image volumes from 5 patients, and 2 experimental phantom image volumes. We show that trilinear interpolation improves interpolation accuracy over both the voxel nearest neighbor and distance-weighted algorithms yet achieves real-time computational performance that is comparable to the voxel nearest neighbor algrorithm (1–2 orders of magnitude faster than the distance-weighted algorithm) as well as the fastest pixel-based algorithms for processing tracked 2-dimensional ultrasound images (0.035 seconds per 2-dimesional cross-sectional image [76,800 pixels interpolated, or 0.46 ms/1000 pixels] and 1.05 seconds per full volume with a 1-mm3 voxel size [4.6 million voxels interpolated, or 0.23 ms/1000 voxels]). On the basis of these results, trilinear interpolation is recommended as a fast and accurate interpolation method for rectilinear sampling of 3DUS image acquisitions, which is required to facilitate subsequent processing and display during operating room procedures such as image-guided neurosurgery. PMID:21266563

Real-time interpolation for true 3-dimensional ultrasound image volumes.

PubMed

Ji, Songbai; Roberts, David W; Hartov, Alex; Paulsen, Keith D

2011-02-01

We compared trilinear interpolation to voxel nearest neighbor and distance-weighted algorithms for fast and accurate processing of true 3-dimensional ultrasound (3DUS) image volumes. In this study, the computational efficiency and interpolation accuracy of the 3 methods were compared on the basis of a simulated 3DUS image volume, 34 clinical 3DUS image volumes from 5 patients, and 2 experimental phantom image volumes. We show that trilinear interpolation improves interpolation accuracy over both the voxel nearest neighbor and distance-weighted algorithms yet achieves real-time computational performance that is comparable to the voxel nearest neighbor algrorithm (1-2 orders of magnitude faster than the distance-weighted algorithm) as well as the fastest pixel-based algorithms for processing tracked 2-dimensional ultrasound images (0.035 seconds per 2-dimesional cross-sectional image [76,800 pixels interpolated, or 0.46 ms/1000 pixels] and 1.05 seconds per full volume with a 1-mm(3) voxel size [4.6 million voxels interpolated, or 0.23 ms/1000 voxels]). On the basis of these results, trilinear interpolation is recommended as a fast and accurate interpolation method for rectilinear sampling of 3DUS image acquisitions, which is required to facilitate subsequent processing and display during operating room procedures such as image-guided neurosurgery.

Directional sinogram interpolation for sparse angular acquisition in cone-beam computed tomography.

PubMed

Zhang, Hua; Sonke, Jan-Jakob

2013-01-01

Cone-beam (CB) computed tomography (CT) is widely used in the field of medical imaging for guidance. Inspired by Betram's directional interpolation (BDI) methods, directional sinogram interpolation (DSI) was implemented to generate more CB projections by optimized (iterative) double-orientation estimation in sinogram space and directional interpolation. A new CBCT was subsequently reconstructed with the Feldkamp algorithm using both the original and interpolated CB projections. The proposed method was evaluated on both phantom and clinical data, and image quality was assessed by correlation ratio (CR) between the interpolated image and a gold standard obtained from full measured projections. Additionally, streak artifact reduction and image blur were assessed. In a CBCT reconstructed by 40 acquired projections over an arc of 360 degree, streak artifacts dropped 20.7% and 6.7% in a thorax phantom, when our method was compared to linear interpolation (LI) and BDI methods. Meanwhile, image blur was assessed by a head-and-neck phantom, where image blur of DSI was 20.1% and 24.3% less than LI and BDI. When our method was compared to LI and DI methods, CR increased by 4.4% and 3.1%. Streak artifacts of sparsely acquired CBCT were decreased by our method and image blur induced by interpolation was constrained to below other interpolation methods.

On the optimal selection of interpolation methods for groundwater contouring: An example of propagation of uncertainty regarding inter-aquifer exchange

NASA Astrophysics Data System (ADS)

Ohmer, Marc; Liesch, Tanja; Goeppert, Nadine; Goldscheider, Nico

2017-11-01

The selection of the best possible method to interpolate a continuous groundwater surface from point data of groundwater levels is a controversial issue. In the present study four deterministic and five geostatistical interpolation methods (global polynomial interpolation, local polynomial interpolation, inverse distance weighting, radial basis function, simple-, ordinary-, universal-, empirical Bayesian and co-Kriging) and six error statistics (ME, MAE, MAPE, RMSE, RMSSE, Pearson R) were examined for a Jurassic karst aquifer and a Quaternary alluvial aquifer. We investigated the possible propagation of uncertainty of the chosen interpolation method on the calculation of the estimated vertical groundwater exchange between the aquifers. Furthermore, we validated the results with eco-hydrogeological data including the comparison between calculated groundwater depths and geographic locations of karst springs, wetlands and surface waters. These results show, that calculated inter-aquifer exchange rates based on different interpolations of groundwater potentials may vary greatly depending on the chosen interpolation method (by factor >10). Therefore, the choice of an interpolation method should be made with care, taking different error measures as well as additional data for plausibility control into account. The most accurate results have been obtained with co-Kriging incorporating secondary data (e.g. topography, river levels).

Sensitivity Analysis of the Static Aeroelastic Response of a Wing

NASA Technical Reports Server (NTRS)

Eldred, Lloyd B.

1993-01-01

A technique to obtain the sensitivity of the static aeroelastic response of a three dimensional wing model is designed and implemented. The formulation is quite general and accepts any aerodynamic and structural analysis capability. A program to combine the discipline level, or local, sensitivities into global sensitivity derivatives is developed. A variety of representations of the wing pressure field are developed and tested to determine the most accurate and efficient scheme for representing the field outside of the aerodynamic code. Chebyshev polynomials are used to globally fit the pressure field. This approach had some difficulties in representing local variations in the field, so a variety of local interpolation polynomial pressure representations are also implemented. These panel based representations use a constant pressure value, a bilinearly interpolated value. or a biquadraticallv interpolated value. The interpolation polynomial approaches do an excellent job of reducing the numerical problems of the global approach for comparable computational effort. Regardless of the pressure representation used. sensitivity and response results with excellent accuracy have been produced for large integrated quantities such as wing tip deflection and trim angle of attack. The sensitivities of such things as individual generalized displacements have been found with fair accuracy. In general, accuracy is found to be proportional to the relative size of the derivatives to the quantity itself.

Morphing of spatial objects in real time with interpolation by functions of radial and orthogonal basis

NASA Astrophysics Data System (ADS)

Kosnikov, Yu N.; Kuzmin, A. V.; Ho, Hoang Thai

2018-05-01

The article is devoted to visualization of spatial objects’ morphing described by the set of unordered reference points. A two-stage model construction is proposed to change object’s form in real time. The first (preliminary) stage is interpolation of the object’s surface by radial basis functions. Initial reference points are replaced by new spatially ordered ones. Reference points’ coordinates change patterns during the process of morphing are assigned. The second (real time) stage is surface reconstruction by blending functions of orthogonal basis. Finite differences formulas are applied to increase the productivity of calculations.

Neural networks for function approximation in nonlinear control

NASA Technical Reports Server (NTRS)

Linse, Dennis J.; Stengel, Robert F.

1990-01-01

Two neural network architectures are compared with a classical spline interpolation technique for the approximation of functions useful in a nonlinear control system. A standard back-propagation feedforward neural network and a cerebellar model articulation controller (CMAC) neural network are presented, and their results are compared with a B-spline interpolation procedure that is updated using recursive least-squares parameter identification. Each method is able to accurately represent a one-dimensional test function. Tradeoffs between size requirements, speed of operation, and speed of learning indicate that neural networks may be practical for identification and adaptation in a nonlinear control environment.

Structure-preserving interpolation of temporal and spatial image sequences using an optical flow-based method.

PubMed

Ehrhardt, J; Säring, D; Handels, H

2007-01-01

Modern tomographic imaging devices enable the acquisition of spatial and temporal image sequences. But, the spatial and temporal resolution of such devices is limited and therefore image interpolation techniques are needed to represent images at a desired level of discretization. This paper presents a method for structure-preserving interpolation between neighboring slices in temporal or spatial image sequences. In a first step, the spatiotemporal velocity field between image slices is determined using an optical flow-based registration method in order to establish spatial correspondence between adjacent slices. An iterative algorithm is applied using the spatial and temporal image derivatives and a spatiotemporal smoothing step. Afterwards, the calculated velocity field is used to generate an interpolated image at the desired time by averaging intensities between corresponding points. Three quantitative measures are defined to evaluate the performance of the interpolation method. The behavior and capability of the algorithm is demonstrated by synthetic images. A population of 17 temporal and spatial image sequences are utilized to compare the optical flow-based interpolation method to linear and shape-based interpolation. The quantitative results show that the optical flow-based method outperforms the linear and shape-based interpolation statistically significantly. The interpolation method presented is able to generate image sequences with appropriate spatial or temporal resolution needed for image comparison, analysis or visualization tasks. Quantitative and qualitative measures extracted from synthetic phantoms and medical image data show that the new method definitely has advantages over linear and shape-based interpolation.

Denoising by coupled partial differential equations and extracting phase by backpropagation neural networks for electronic speckle pattern interferometry.

PubMed

Tang, Chen; Lu, Wenjing; Chen, Song; Zhang, Zhen; Li, Botao; Wang, Wenping; Han, Lin

2007-10-20

We extend and refine previous work [Appl. Opt. 46, 2907 (2007)]. Combining the coupled nonlinear partial differential equations (PDEs) denoising model with the ordinary differential equations enhancement method, we propose the new denoising and enhancing model for electronic speckle pattern interferometry (ESPI) fringe patterns. Meanwhile, we propose the backpropagation neural networks (BPNN) method to obtain unwrapped phase values based on a skeleton map instead of traditional interpolations. We test the introduced methods on the computer-simulated speckle ESPI fringe patterns and experimentally obtained fringe pattern, respectively. The experimental results show that the coupled nonlinear PDEs denoising model is capable of effectively removing noise, and the unwrapped phase values obtained by the BPNN method are much more accurate than those obtained by the well-known traditional interpolation. In addition, the accuracy of the BPNN method is adjustable by changing the parameters of networks such as the number of neurons.

Full Waveform Modeling of Transient Electromagnetic Response Based on Temporal Interpolation and Convolution Method

NASA Astrophysics Data System (ADS)

Qi, Youzheng; Huang, Ling; Wu, Xin; Zhu, Wanhua; Fang, Guangyou; Yu, Gang

2017-07-01

Quantitative modeling of the transient electromagnetic (TEM) response requires consideration of the full transmitter waveform, i.e., not only the specific current waveform in a half cycle but also the bipolar repetition. In this paper, we present a novel temporal interpolation and convolution (TIC) method to facilitate the accurate TEM modeling. We first calculate the temporal basis response on a logarithmic scale using the fast digital-filter-based methods. Then, we introduce a function named hamlogsinc in the framework of discrete signal processing theory to reconstruct the basis function and to make the convolution with the positive half of the waveform. Finally, a superposition procedure is used to take account of the effect of previous bipolar waveforms. Comparisons with the established fast Fourier transform method demonstrate that our TIC method can get the same accuracy with a shorter computing time.

New deconvolution method for microscopic images based on the continuous Gaussian radial basis function interpolation model.

PubMed

Chen, Zhaoxue; Chen, Hao

2014-01-01

A deconvolution method based on the Gaussian radial basis function (GRBF) interpolation is proposed. Both the original image and Gaussian point spread function are expressed as the same continuous GRBF model, thus image degradation is simplified as convolution of two continuous Gaussian functions, and image deconvolution is converted to calculate the weighted coefficients of two-dimensional control points. Compared with Wiener filter and Lucy-Richardson algorithm, the GRBF method has an obvious advantage in the quality of restored images. In order to overcome such a defect of long-time computing, the method of graphic processing unit multithreading or increasing space interval of control points is adopted, respectively, to speed up the implementation of GRBF method. The experiments show that based on the continuous GRBF model, the image deconvolution can be efficiently implemented by the method, which also has a considerable reference value for the study of three-dimensional microscopic image deconvolution.

Grundwasserfließgeschehen Mecklenburg-Vorpommerns - Geohydraulische Modellierung mit Detrended Kriging

NASA Astrophysics Data System (ADS)

Hilgert, Toralf; Hennig, Heiko

2017-03-01

Groundwater heads were mapped for the entire State of Mecklenburg-Western Pomerania by applying a Detrended Kriging method based on a numerical geohydraulic model. The general groundwater flow system (trend surface) was represented by a two-dimensional horizontal flow model. Thus deviations of observed groundwater heads from simulated groundwater heads are no longer subject to a regional trend and can be interpolated by means of Ordinary Kriging. Subsequently, the groundwater heads were obtained from the sum of the simulated trend surface and interpolated residuals. Furthermore, the described procedure allowed a plausibility check of observed groundwater heads by comparing them to results of the hydraulic model. If significant deviations were seen, the observation wells could be allocated to different aquifers. The final results are two hydraulically established groundwater head distributions - one for the regional main aquifer and one for the upper aquifer which may differ locally from the main aquifer.

A Bivariate Chebyshev Spectral Collocation Quasilinearization Method for Nonlinear Evolution Parabolic Equations

PubMed Central

Motsa, S. S.; Magagula, V. M.; Sibanda, P.

2014-01-01

This paper presents a new method for solving higher order nonlinear evolution partial differential equations (NPDEs). The method combines quasilinearisation, the Chebyshev spectral collocation method, and bivariate Lagrange interpolation. In this paper, we use the method to solve several nonlinear evolution equations, such as the modified KdV-Burgers equation, highly nonlinear modified KdV equation, Fisher's equation, Burgers-Fisher equation, Burgers-Huxley equation, and the Fitzhugh-Nagumo equation. The results are compared with known exact analytical solutions from literature to confirm accuracy, convergence, and effectiveness of the method. There is congruence between the numerical results and the exact solutions to a high order of accuracy. Tables were generated to present the order of accuracy of the method; convergence graphs to verify convergence of the method and error graphs are presented to show the excellent agreement between the results from this study and the known results from literature. PMID:25254252

A bivariate Chebyshev spectral collocation quasilinearization method for nonlinear evolution parabolic equations.

PubMed

Motsa, S S; Magagula, V M; Sibanda, P

2014-01-01

This paper presents a new method for solving higher order nonlinear evolution partial differential equations (NPDEs). The method combines quasilinearisation, the Chebyshev spectral collocation method, and bivariate Lagrange interpolation. In this paper, we use the method to solve several nonlinear evolution equations, such as the modified KdV-Burgers equation, highly nonlinear modified KdV equation, Fisher's equation, Burgers-Fisher equation, Burgers-Huxley equation, and the Fitzhugh-Nagumo equation. The results are compared with known exact analytical solutions from literature to confirm accuracy, convergence, and effectiveness of the method. There is congruence between the numerical results and the exact solutions to a high order of accuracy. Tables were generated to present the order of accuracy of the method; convergence graphs to verify convergence of the method and error graphs are presented to show the excellent agreement between the results from this study and the known results from literature.

The Role of Auxiliary Variables in Deterministic and Deterministic-Stochastic Spatial Models of Air Temperature in Poland

NASA Astrophysics Data System (ADS)

Szymanowski, Mariusz; Kryza, Maciej

2017-02-01

Our study examines the role of auxiliary variables in the process of spatial modelling and mapping of climatological elements, with air temperature in Poland used as an example. The multivariable algorithms are the most frequently applied for spatialization of air temperature, and their results in many studies are proved to be better in comparison to those obtained by various one-dimensional techniques. In most of the previous studies, two main strategies were used to perform multidimensional spatial interpolation of air temperature. First, it was accepted that all variables significantly correlated with air temperature should be incorporated into the model. Second, it was assumed that the more spatial variation of air temperature was deterministically explained, the better was the quality of spatial interpolation. The main goal of the paper was to examine both above-mentioned assumptions. The analysis was performed using data from 250 meteorological stations and for 69 air temperature cases aggregated on different levels: from daily means to 10-year annual mean. Two cases were considered for detailed analysis. The set of potential auxiliary variables covered 11 environmental predictors of air temperature. Another purpose of the study was to compare the results of interpolation given by various multivariable methods using the same set of explanatory variables. Two regression models: multiple linear (MLR) and geographically weighted (GWR) method, as well as their extensions to the regression-kriging form, MLRK and GWRK, respectively, were examined. Stepwise regression was used to select variables for the individual models and the cross-validation method was used to validate the results with a special attention paid to statistically significant improvement of the model using the mean absolute error (MAE) criterion. The main results of this study led to rejection of both assumptions considered. Usually, including more than two or three of the most significantly correlated auxiliary variables does not improve the quality of the spatial model. The effects of introduction of certain variables into the model were not climatologically justified and were seen on maps as unexpected and undesired artefacts. The results confirm, in accordance with previous studies, that in the case of air temperature distribution, the spatial process is non-stationary; thus, the local GWR model performs better than the global MLR if they are specified using the same set of auxiliary variables. If only GWR residuals are autocorrelated, the geographically weighted regression-kriging (GWRK) model seems to be optimal for air temperature spatial interpolation.

Hermite-Birkhoff interpolation in the nth roots of unity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cavaretta, A.S. Jr.; Sharma, A.; Varga, R.S.

1980-06-01

Consider, as nodes for polynomial interpolation, the nth roots of unity. For a sufficiently smooth function f(z), we require a polynomial p(z) to interpolate f and certain of its derivatives at each node. It is shown that the so-called Polya conditions, which are necessary for unique interpolation, are in this setting also sufficient.

Empirical performance of interpolation techniques in risk-neutral density (RND) estimation

NASA Astrophysics Data System (ADS)

Bahaludin, H.; Abdullah, M. H.

2017-03-01

The objective of this study is to evaluate the empirical performance of interpolation techniques in risk-neutral density (RND) estimation. Firstly, the empirical performance is evaluated by using statistical analysis based on the implied mean and the implied variance of RND. Secondly, the interpolation performance is measured based on pricing error. We propose using the leave-one-out cross-validation (LOOCV) pricing error for interpolation selection purposes. The statistical analyses indicate that there are statistical differences between the interpolation techniques:second-order polynomial, fourth-order polynomial and smoothing spline. The results of LOOCV pricing error shows that interpolation by using fourth-order polynomial provides the best fitting to option prices in which it has the lowest value error.

A meshless approach to thermomechanics of DC casting of aluminium billets

NASA Astrophysics Data System (ADS)

Mavrič, B.; Šarler, B.

2016-03-01

The ability to model thermomechanics in DC casting is important due to the technological challenges caused by physical phenomena such as different ingot distortions, cracking, hot tearing and residual stress. Many thermomechanical models already exist and usually take into account three contributions: elastic, thermal expansion, and viscoplastic to model the mushy zone. These models are, in a vast majority, solved by the finite element method. In the present work the elastic model that accounts for linear thermal expansion is considered. The method used for solving the model is of a novel meshless type and extends our previous meshless attempts in solving fluid mechanics problems. The solution to the problem is constructed using collocation on the overlapping subdomains, which are composed of computational nodes. Multiquadric radial basis functions, augmented by monomials, are used for the displacement interpolation. The interpolation is constructed in such a manner that it readily satisfies the boundary conditions. The discretization results in construction of a global square sparse matrix representing the system of linear equations for the displacement field. The developed method has many advantages. The system of equations can be easily constructed and efficiently solved. There is no need to perform expensive meshing of the domain and the formulation of the method is similar in two and three dimensions. Since no meshing is required, the nodes can easily be added or removed, which allows for efficient adaption of the node arrangement density. The order of convergence, estimated through an analytically solvable test, can be adjusted through the number of interpolation nodes in the subdomain, with 6 nodes being enough for the second order convergence. Simulations of axisymmetric mechanical problems, associated with low frequency electromagnetic DC casting are presented.

Error analysis and new dual-cosine window for estimating the sensor frequency response function from the step response data

NASA Astrophysics Data System (ADS)

Yang, Shuang-Long; Liang, Li-Ping; Liu, Hou-De; Xu, Ke-Jun

2018-03-01

Aiming at reducing the estimation error of the sensor frequency response function (FRF) estimated by the commonly used window-based spectral estimation method, the error models of interpolation and transient errors are derived in the form of non-parameter models. Accordingly, window effects on the errors are analyzed and reveal that the commonly used hanning window leads to smaller interpolation error which can also be significantly eliminated by the cubic spline interpolation method when estimating the FRF from the step response data, and window with smaller front-end value can restrain more transient error. Thus, a new dual-cosine window with its non-zero discrete Fourier transform bins at -3, -1, 0, 1, and 3 is constructed for FRF estimation. Compared with the hanning window, the new dual-cosine window has the equivalent interpolation error suppression capability and better transient error suppression capability when estimating the FRF from the step response; specifically, it reduces the asymptotic property of the transient error from O(N-2) of the hanning window method to O(N-4) while only increases the uncertainty slightly (about 0.4 dB). Then, one direction of a wind tunnel strain gauge balance which is a high order, small damping, and non-minimum phase system is employed as the example for verifying the new dual-cosine window-based spectral estimation method. The model simulation result shows that the new dual-cosine window method is better than the hanning window method for FRF estimation, and compared with the Gans method and LPM method, it has the advantages of simple computation, less time consumption, and short data requirement; the actual data calculation result of the balance FRF is consistent to the simulation result. Thus, the new dual-cosine window is effective and practical for FRF estimation.

New climatic classification of Nepal

NASA Astrophysics Data System (ADS)

Karki, Ramchandra; Talchabhadel, Rocky; Aalto, Juha; Baidya, Saraju Kumar

2016-08-01

Although it is evident that Nepal has an extremely wide range of climates within a short latitudinal distance, there is a lack of comprehensive research in this field. The climatic zoning in a topographically complex country like Nepal has important implications for the selection of scientific station network design and climate model verification, as well as for studies examining the effects of climate change in terms of shifting climatic boundaries and vegetation in highly sensitive environments. This study presents a new high-resolution climate map of Nepal on the basis of long-term (1981-2010) monthly precipitation data for 240 stations and mean air temperature data for 74 stations, using original and modified Köppen-Geiger climate classification systems. Climatic variables used in Köppen-Geiger system were calculated (i) at each station and (ii) interpolated to 1-km spatial resolution using kriging which accounted for latitude, longitude, and elevation. The original Köppen-Geiger scheme could not identify all five types of climate (including tropical) observed in Nepal. Hence, the original scheme was slightly modified by changing the boundary of coldest month mean air temperature value from 18 °C to 14.5 °C in order to delineate the realistic climatic condition of Nepal. With this modification, all five types of climate (including tropical) were identified. The most common dominant type of climate for Nepal is temperate with dry winter and hot summer (Cwa).

An interpolation method for stream habitat assessments

USGS Publications Warehouse

Sheehan, Kenneth R.; Welsh, Stuart A.

2015-01-01

Interpolation of stream habitat can be very useful for habitat assessment. Using a small number of habitat samples to predict the habitat of larger areas can reduce time and labor costs as long as it provides accurate estimates of habitat. The spatial correlation of stream habitat variables such as substrate and depth improves the accuracy of interpolated data. Several geographical information system interpolation methods (natural neighbor, inverse distance weighted, ordinary kriging, spline, and universal kriging) were used to predict substrate and depth within a 210.7-m2 section of a second-order stream based on 2.5% and 5.0% sampling of the total area. Depth and substrate were recorded for the entire study site and compared with the interpolated values to determine the accuracy of the predictions. In all instances, the 5% interpolations were more accurate for both depth and substrate than the 2.5% interpolations, which achieved accuracies up to 95% and 92%, respectively. Interpolations of depth based on 2.5% sampling attained accuracies of 49–92%, whereas those based on 5% percent sampling attained accuracies of 57–95%. Natural neighbor interpolation was more accurate than that using the inverse distance weighted, ordinary kriging, spline, and universal kriging approaches. Our findings demonstrate the effective use of minimal amounts of small-scale data for the interpolation of habitat over large areas of a stream channel. Use of this method will provide time and cost savings in the assessment of large sections of rivers as well as functional maps to aid the habitat-based management of aquatic species.

Analysis of rainfall distribution in Kelantan river basin, Malaysia

NASA Astrophysics Data System (ADS)

Che Ros, Faizah; Tosaka, Hiroyuki

2018-03-01

Using rainfall gauge on its own as input carries great uncertainties regarding runoff estimation, especially when the area is large and the rainfall is measured and recorded at irregular spaced gauging stations. Hence spatial interpolation is the key to obtain continuous and orderly rainfall distribution at unknown points to be the input to the rainfall runoff processes for distributed and semi-distributed numerical modelling. It is crucial to study and predict the behaviour of rainfall and river runoff to reduce flood damages of the affected area along the Kelantan river. Thus, a good knowledge on rainfall distribution is essential in early flood prediction studies. Forty six rainfall stations and their daily time-series were used to interpolate gridded rainfall surfaces using inverse-distance weighting (IDW), inverse-distance and elevation weighting (IDEW) methods and average rainfall distribution. Sensitivity analysis for distance and elevation parameters were conducted to see the variation produced. The accuracy of these interpolated datasets was examined using cross-validation assessment.

Optimized theory for simple and molecular fluids.

PubMed

Marucho, M; Montgomery Pettitt, B

2007-03-28

An optimized closure approximation for both simple and molecular fluids is presented. A smooth interpolation between Perkus-Yevick and hypernetted chain closures is optimized by minimizing the free energy self-consistently with respect to the interpolation parameter(s). The molecular version is derived from a refinement of the method for simple fluids. In doing so, a method is proposed which appropriately couples an optimized closure with the variant of the diagrammatically proper integral equation recently introduced by this laboratory [K. M. Dyer et al., J. Chem. Phys. 123, 204512 (2005)]. The simplicity of the expressions involved in this proposed theory has allowed the authors to obtain an analytic expression for the approximate excess chemical potential. This is shown to be an efficient tool to estimate, from first principles, the numerical value of the interpolation parameters defining the aforementioned closure. As a preliminary test, representative models for simple fluids and homonuclear diatomic Lennard-Jones fluids were analyzed, obtaining site-site correlation functions in excellent agreement with simulation data.

Combining geostatistics with Moran's I analysis for mapping soil heavy metals in Beijing, China.

PubMed

Huo, Xiao-Ni; Li, Hong; Sun, Dan-Feng; Zhou, Lian-Di; Li, Bao-Guo

2012-03-01

Production of high quality interpolation maps of heavy metals is important for risk assessment of environmental pollution. In this paper, the spatial correlation characteristics information obtained from Moran's I analysis was used to supplement the traditional geostatistics. According to Moran's I analysis, four characteristics distances were obtained and used as the active lag distance to calculate the semivariance. Validation of the optimality of semivariance demonstrated that using the two distances where the Moran's I and the standardized Moran's I, Z(I) reached a maximum as the active lag distance can improve the fitting accuracy of semivariance. Then, spatial interpolation was produced based on the two distances and their nested model. The comparative analysis of estimation accuracy and the measured and predicted pollution status showed that the method combining geostatistics with Moran's I analysis was better than traditional geostatistics. Thus, Moran's I analysis is a useful complement for geostatistics to improve the spatial interpolation accuracy of heavy metals.

Combining Geostatistics with Moran’s I Analysis for Mapping Soil Heavy Metals in Beijing, China

PubMed Central

Huo, Xiao-Ni; Li, Hong; Sun, Dan-Feng; Zhou, Lian-Di; Li, Bao-Guo

2012-01-01

Production of high quality interpolation maps of heavy metals is important for risk assessment of environmental pollution. In this paper, the spatial correlation characteristics information obtained from Moran’s I analysis was used to supplement the traditional geostatistics. According to Moran’s I analysis, four characteristics distances were obtained and used as the active lag distance to calculate the semivariance. Validation of the optimality of semivariance demonstrated that using the two distances where the Moran’s I and the standardized Moran’s I, Z(I) reached a maximum as the active lag distance can improve the fitting accuracy of semivariance. Then, spatial interpolation was produced based on the two distances and their nested model. The comparative analysis of estimation accuracy and the measured and predicted pollution status showed that the method combining geostatistics with Moran’s I analysis was better than traditional geostatistics. Thus, Moran’s I analysis is a useful complement for geostatistics to improve the spatial interpolation accuracy of heavy metals. PMID:22690179

Interpolation of longitudinal shape and image data via optimal mass transport

NASA Astrophysics Data System (ADS)

Gao, Yi; Zhu, Liang-Jia; Bouix, Sylvain; Tannenbaum, Allen

2014-03-01

Longitudinal analysis of medical imaging data has become central to the study of many disorders. Unfortunately, various constraints (study design, patient availability, technological limitations) restrict the acquisition of data to only a few time points, limiting the study of continuous disease/treatment progression. Having the ability to produce a sensible time interpolation of the data can lead to improved analysis, such as intuitive visualizations of anatomical changes, or the creation of more samples to improve statistical analysis. In this work, we model interpolation of medical image data, in particular shape data, using the theory of optimal mass transport (OMT), which can construct a continuous transition from two time points while preserving "mass" (e.g., image intensity, shape volume) during the transition. The theory even allows a short extrapolation in time and may help predict short-term treatment impact or disease progression on anatomical structure. We apply the proposed method to the hippocampus-amygdala complex in schizophrenia, the heart in atrial fibrillation, and full head MR images in traumatic brain injury.

Highly mismatched GaN1-x Sb x alloys: synthesis, structure and electronic properties

NASA Astrophysics Data System (ADS)

Yu, K. M.; Sarney, W. L.; Novikov, S. V.; Segercrantz, N.; Ting, M.; Shaw, M.; Svensson, S. P.; Martin, R. W.; Walukiewicz, W.; Foxon, C. T.

2016-08-01

Highly mismatched alloys (HMAs) is a class of semiconductor alloys whose constituents are distinctly different in terms of size, ionicity and/or electronegativity. Electronic properties of the alloys deviate significantly from an interpolation scheme based on small deviations from the virtual crystal approximation. Most of the HMAs were only studied in a dilute composition limit. Recent advances in understanding of the semiconductor synthesis processes allowed growth of thin films of HMAs under non-equilibrium conditions. Thus reducing the growth temperature allowed synthesis of group III-N-V HMAs over almost the entire composition range. This paper focuses on the GaN x Sb1-x HMA which has been suggested as a potential material for solar water dissociation devices. Here we review our recent work on the synthesis, structural and optical characterization of GaN1-x Sb x HMA. Theoretical modeling studies on its electronic structure based on the band anticrossing (BAC) model are also reviewed. In particular we discuss the effects of growth temperature, Ga flux and Sb flux on the incorporation of Sb, film microstructure and optical properties of the alloys. Results obtained from two separate MBE growths are directly compared. Our work demonstrates that a large range of direct bandgap energies from 3.4 eV to below 1.0 eV can be achieved for this alloy grown at low temperature. We show that the electronic band structure of GaN1-x Sb x HMA over the entire composition range is well described by a modified BAC model which includes the dependence of the host matrix band edges as well as the BAC model coupling parameters on composition. We emphasize that the modified BAC model of the electronic band structure developed for the full composition of GaN x Sb1-x is general and is applicable to any HMA.

Investigation of interpolation techniques for the reconstruction of the first dimension of comprehensive two-dimensional liquid chromatography-diode array detector data.

PubMed

Allen, Robert C; Rutan, Sarah C

2011-10-31

Simulated and experimental data were used to measure the effectiveness of common interpolation techniques during chromatographic alignment of comprehensive two-dimensional liquid chromatography-diode array detector (LC×LC-DAD) data. Interpolation was used to generate a sufficient number of data points in the sampled first chromatographic dimension to allow for alignment of retention times from different injections. Five different interpolation methods, linear interpolation followed by cross correlation, piecewise cubic Hermite interpolating polynomial, cubic spline, Fourier zero-filling, and Gaussian fitting, were investigated. The fully aligned chromatograms, in both the first and second chromatographic dimensions, were analyzed by parallel factor analysis to determine the relative area for each peak in each injection. A calibration curve was generated for the simulated data set. The standard error of prediction and percent relative standard deviation were calculated for the simulated peak for each technique. The Gaussian fitting interpolation technique resulted in the lowest standard error of prediction and average relative standard deviation for the simulated data. However, upon applying the interpolation techniques to the experimental data, most of the interpolation methods were not found to produce statistically different relative peak areas from each other. While most of the techniques were not statistically different, the performance was improved relative to the PARAFAC results obtained when analyzing the unaligned data. Copyright © 2011 Elsevier B.V. All rights reserved.

An efficient interpolation filter VLSI architecture for HEVC standard

NASA Astrophysics Data System (ADS)

Zhou, Wei; Zhou, Xin; Lian, Xiaocong; Liu, Zhenyu; Liu, Xiaoxiang

2015-12-01

The next-generation video coding standard of High-Efficiency Video Coding (HEVC) is especially efficient for coding high-resolution video such as 8K-ultra-high-definition (UHD) video. Fractional motion estimation in HEVC presents a significant challenge in clock latency and area cost as it consumes more than 40 % of the total encoding time and thus results in high computational complexity. With aims at supporting 8K-UHD video applications, an efficient interpolation filter VLSI architecture for HEVC is proposed in this paper. Firstly, a new interpolation filter algorithm based on the 8-pixel interpolation unit is proposed in this paper. It can save 19.7 % processing time on average with acceptable coding quality degradation. Based on the proposed algorithm, an efficient interpolation filter VLSI architecture, composed of a reused data path of interpolation, an efficient memory organization, and a reconfigurable pipeline interpolation filter engine, is presented to reduce the implement hardware area and achieve high throughput. The final VLSI implementation only requires 37.2k gates in a standard 90-nm CMOS technology at an operating frequency of 240 MHz. The proposed architecture can be reused for either half-pixel interpolation or quarter-pixel interpolation, which can reduce the area cost for about 131,040 bits RAM. The processing latency of our proposed VLSI architecture can support the real-time processing of 4:2:0 format 7680 × 4320@78fps video sequences.

A rational interpolation method to compute frequency response

NASA Technical Reports Server (NTRS)

Kenney, Charles; Stubberud, Stephen; Laub, Alan J.

1993-01-01

A rational interpolation method for approximating a frequency response is presented. The method is based on a product formulation of finite differences, thereby avoiding the numerical problems incurred by near-equal-valued subtraction. Also, resonant pole and zero cancellation schemes are developed that increase the accuracy and efficiency of the interpolation method. Selection techniques of interpolation points are also discussed.

Conflict Prediction Through Geo-Spatial Interpolation of Radicalization in Syrian Social Media

DTIC Science & Technology

2015-09-24

TRAC-M-TM-15-031 September 2015 Conflict Prediction Through Geo-Spatial Interpolation of Radicalization in Syrian Social Media ...Spatial Interpolation of Radicalization in Syrian Social Media Authors MAJ Adam Haupt Dr. Camber Warren...Spatial Interpolation of Radicalization in Syrian Social 1RAC Project Code 060114 Media 6. AUTHOR(S) MAJ Haupt, Dr. Warren 7. PERFORMING OR

[An Improved Spectral Quaternion Interpolation Method of Diffusion Tensor Imaging].

PubMed

Xu, Yonghong; Gao, Shangce; Hao, Xiaofei

2016-04-01

Diffusion tensor imaging(DTI)is a rapid development technology in recent years of magnetic resonance imaging.The diffusion tensor interpolation is a very important procedure in DTI image processing.The traditional spectral quaternion interpolation method revises the direction of the interpolation tensor and can preserve tensors anisotropy,but the method does not revise the size of tensors.The present study puts forward an improved spectral quaternion interpolation method on the basis of traditional spectral quaternion interpolation.Firstly,we decomposed diffusion tensors with the direction of tensors being represented by quaternion.Then we revised the size and direction of the tensor respectively according to different situations.Finally,we acquired the tensor of interpolation point by calculating the weighted average.We compared the improved method with the spectral quaternion method and the Log-Euclidean method by the simulation data and the real data.The results showed that the improved method could not only keep the monotonicity of the fractional anisotropy(FA)and the determinant of tensors,but also preserve the tensor anisotropy at the same time.In conclusion,the improved method provides a kind of important interpolation method for diffusion tensor image processing.

Minimal norm constrained interpolation. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Irvine, L. D.

1985-01-01

In computational fluid dynamics and in CAD/CAM, a physical boundary is usually known only discreetly and most often must be approximated. An acceptable approximation preserves the salient features of the data such as convexity and concavity. In this dissertation, a smooth interpolant which is locally concave where the data are concave and is locally convex where the data are convex is described. The interpolant is found by posing and solving a minimization problem whose solution is a piecewise cubic polynomial. The problem is solved indirectly by using the Peano Kernal theorem to recast it into an equivalent minimization problem having the second derivative of the interpolant as the solution. This approach leads to the solution of a nonlinear system of equations. It is shown that Newton's method is an exceptionally attractive and efficient method for solving the nonlinear system of equations. Examples of shape-preserving interpolants, as well as convergence results obtained by using Newton's method are also shown. A FORTRAN program to compute these interpolants is listed. The problem of computing the interpolant of minimal norm from a convex cone in a normal dual space is also discussed. An extension of de Boor's work on minimal norm unconstrained interpolation is presented.

Airborne laser scanning for forest health status assessment and radiative transfer modelling

NASA Astrophysics Data System (ADS)

Novotny, Jan; Zemek, Frantisek; Pikl, Miroslav; Janoutova, Ruzena

2013-04-01

Structural parameters of forest stands/ecosystems are an important complementary source of information to spectral signatures obtained from airborne imaging spectroscopy when quantitative assessment of forest stands are in the focus, such as estimation of forest biomass, biochemical properties (e.g. chlorophyll /water content), etc. The parameterization of radiative transfer (RT) models used in latter case requires three-dimensional spatial distribution of green foliage and woody biomass. Airborne LiDAR data acquired over forest sites bears these kinds of 3D information. The main objective of the study was to compare the results from several approaches to interpolation of digital elevation model (DEM) and digital surface model (DSM). We worked with airborne LiDAR data with different density (TopEye Mk II 1,064nm instrument, 1-5 points/m2) acquired over the Norway spruce forests situated in the Beskydy Mountains, the Czech Republic. Three different interpolation algorithms with increasing complexity were tested: i/Nearest neighbour approach implemented in the BCAL software package (Idaho Univ.); ii/Averaging and linear interpolation techniques used in the OPALS software (Vienna Univ. of Technology); iii/Active contour technique implemented in the TreeVis software (Univ. of Freiburg). We defined two spatial resolutions for the resulting coupled raster DEMs and DSMs outputs: 0.4 m and 1 m, calculated by each algorithm. The grids correspond to the same spatial resolutions of hyperspectral imagery data for which the DEMs were used in a/geometrical correction and b/building a complex tree models for radiative transfer modelling. We applied two types of analyses when comparing between results from the different interpolations/raster resolution: 1/calculated DEM or DSM between themselves; 2/comparison with field data: DEM with measurements from referential GPS, DSM - field tree alometric measurements, where tree height was calculated as DSM-DEM. The results of the analyses show that: 1/averaging techniques tend to underestimate the tree height and the generated surface does not follow the first LiDAR echoes both for 1 m and 0.4 m pixel size; 2/we did not find any significant difference between tree heights calculated by nearest neighbour algorithm and the active contour technique for 1 m pixel output but the difference increased with finer resolution (0.4 m); 3/the accuracy of the DEMs calculated by tested algorithms is similar.

Efficient and Adaptive Methods for Computing Accurate Potential Surfaces for Quantum Nuclear Effects: Applications to Hydrogen-Transfer Reactions.

PubMed

DeGregorio, Nicole; Iyengar, Srinivasan S

2018-01-09

We present two sampling measures to gauge critical regions of potential energy surfaces. These sampling measures employ (a) the instantaneous quantum wavepacket density, an approximation to the (b) potential surface, its (c) gradients, and (d) a Shannon information theory based expression that estimates the local entropy associated with the quantum wavepacket. These four criteria together enable a directed sampling of potential surfaces that appears to correctly describe the local oscillation frequencies, or the local Nyquist frequency, of a potential surface. The sampling functions are then utilized to derive a tessellation scheme that discretizes the multidimensional space to enable efficient sampling of potential surfaces. The sampled potential surface is then combined with four different interpolation procedures, namely, (a) local Hermite curve interpolation, (b) low-pass filtered Lagrange interpolation, (c) the monomial symmetrization approximation (MSA) developed by Bowman and co-workers, and (d) a modified Shepard algorithm. The sampling procedure and the fitting schemes are used to compute (a) potential surfaces in highly anharmonic hydrogen-bonded systems and (b) study hydrogen-transfer reactions in biogenic volatile organic compounds (isoprene) where the transferring hydrogen atom is found to demonstrate critical quantum nuclear effects. In the case of isoprene, the algorithm discussed here is used to derive multidimensional potential surfaces along a hydrogen-transfer reaction path to gauge the effect of quantum-nuclear degrees of freedom on the hydrogen-transfer process. Based on the decreased computational effort, facilitated by the optimal sampling of the potential surfaces through the use of sampling functions discussed here, and the accuracy of the associated potential surfaces, we believe the method will find great utility in the study of quantum nuclear dynamics problems, of which application to hydrogen-transfer reactions and hydrogen-bonded systems is demonstrated here.

A robust method of thin plate spline and its application to DEM construction

NASA Astrophysics Data System (ADS)

Chen, Chuanfa; Li, Yanyan

2012-11-01

In order to avoid the ill-conditioning problem of thin plate spline (TPS), the orthogonal least squares (OLS) method was introduced, and a modified OLS (MOLS) was developed. The MOLS of TPS (TPS-M) can not only select significant points, termed knots, from large and dense sampling data sets, but also easily compute the weights of the knots in terms of back-substitution. For interpolating large sampling points, we developed a local TPS-M, where some neighbor sampling points around the point being estimated are selected for computation. Numerical tests indicate that irrespective of sampling noise level, the average performance of TPS-M can advantage with smoothing TPS. Under the same simulation accuracy, the computational time of TPS-M decreases with the increase of the number of sampling points. The smooth fitting results on lidar-derived noise data indicate that TPS-M has an obvious smoothing effect, which is on par with smoothing TPS. The example of constructing a series of large scale DEMs, located in Shandong province, China, was employed to comparatively analyze the estimation accuracies of the two versions of TPS and the classical interpolation methods including inverse distance weighting (IDW), ordinary kriging (OK) and universal kriging with the second-order drift function (UK). Results show that regardless of sampling interval and spatial resolution, TPS-M is more accurate than the classical interpolation methods, except for the smoothing TPS at the finest sampling interval of 20 m, and the two versions of kriging at the spatial resolution of 15 m. In conclusion, TPS-M, which avoids the ill-conditioning problem, is considered as a robust method for DEM construction.

Enhancement of panoramic image resolution based on swift interpolation of Bezier surface

NASA Astrophysics Data System (ADS)

Xiao, Xiao; Yang, Guo-guang; Bai, Jian

2007-01-01

Panoramic annular lens project the view of the entire 360 degrees around the optical axis onto an annular plane based on the way of flat cylinder perspective. Due to the infinite depth of field and the linear mapping relationship between an object and an image, the panoramic imaging system plays important roles in the applications of robot vision, surveillance and virtual reality. An annular image needs to be unwrapped to conventional rectangular image without distortion, in which interpolation algorithm is necessary. Although cubic splines interpolation can enhance the resolution of unwrapped image, it occupies too much time to be applied in practices. This paper adopts interpolation method based on Bezier surface and proposes a swift interpolation algorithm for panoramic image, considering the characteristic of panoramic image. The result indicates that the resolution of the image is well enhanced compared with the image by cubic splines and bilinear interpolation. Meanwhile the time consumed is shortened up by 78% than the time consumed cubic interpolation.

Interpolation problem for the solutions of linear elasticity equations based on monogenic functions

NASA Astrophysics Data System (ADS)

Grigor'ev, Yuri; Gürlebeck, Klaus; Legatiuk, Dmitrii

2017-11-01

Interpolation is an important tool for many practical applications, and very often it is beneficial to interpolate not only with a simple basis system, but rather with solutions of a certain differential equation, e.g. elasticity equation. A typical example for such type of interpolation are collocation methods widely used in practice. It is known, that interpolation theory is fully developed in the framework of the classical complex analysis. However, in quaternionic analysis, which shows a lot of analogies to complex analysis, the situation is more complicated due to the non-commutative multiplication. Thus, a fundamental theorem of algebra is not available, and standard tools from linear algebra cannot be applied in the usual way. To overcome these problems, a special system of monogenic polynomials the so-called Pseudo Complex Polynomials, sharing some properties of complex powers, is used. In this paper, we present an approach to deal with the interpolation problem, where solutions of elasticity equations in three dimensions are used as an interpolation basis.

Signal decomposition for surrogate modeling of a constrained ultrasonic design space

NASA Astrophysics Data System (ADS)

Homa, Laura; Sparkman, Daniel; Wertz, John; Welter, John; Aldrin, John C.

2018-04-01

The U.S. Air Force seeks to improve the methods and measures by which the lifecycle of composite structures are managed. Nondestructive evaluation of damage - particularly internal damage resulting from impact - represents a significant input to that improvement. Conventional ultrasound can detect this damage; however, full 3D characterization has not been demonstrated. A proposed approach for robust characterization uses model-based inversion through fitting of simulated results to experimental data. One challenge with this approach is the high computational expense of the forward model to simulate the ultrasonic B-scans for each damage scenario. A potential solution is to construct a surrogate model using a subset of simulated ultrasonic scans built using a highly accurate, computationally expensive forward model. However, the dimensionality of these simulated B-scans makes interpolating between them a difficult and potentially infeasible problem. Thus, we propose using the chirplet decomposition to reduce the dimensionality of the data, and allow for interpolation in the chirplet parameter space. By applying the chirplet decomposition, we are able to extract the salient features in the data and construct a surrogate forward model.

Nonlinear feedback control for high alpha flight

NASA Technical Reports Server (NTRS)

Stalford, Harold

1990-01-01

Analytical aerodynamic models are derived from a high alpha 6 DOF wind tunnel model. One detail model requires some interpolation between nonlinear functions of alpha. One analytical model requires no interpolation and as such is a completely continuous model. Flight path optimization is conducted on the basic maneuvers: half-loop, 90 degree pitch-up, and level turn. The optimal control analysis uses the derived analytical model in the equations of motion and is based on both moment and force equations. The maximum principle solution for the half-loop is poststall trajectory performing the half-loop in 13.6 seconds. The agility induced by thrust vectoring capability provided a minimum effect on reducing the maneuver time. By means of thrust vectoring control the 90 degrees pitch-up maneuver can be executed in a small place over a short time interval. The agility capability of thrust vectoring is quite beneficial for pitch-up maneuvers. The level turn results are based currently on only outer layer solutions of singular perturbation. Poststall solutions provide high turn rates but generate higher losses of energy than that of classical sustained solutions.

Time optimal control of a jet engine using a quasi-Hermite interpolation model. M.S. Thesis

NASA Technical Reports Server (NTRS)

Comiskey, J. G.

1979-01-01

This work made preliminary efforts to generate nonlinear numerical models of a two-spooled turbofan jet engine, and subject these models to a known method of generating global, nonlinear, time optimal control laws. The models were derived numerically, directly from empirical data, as a first step in developing an automatic modelling procedure.

A Modified LS+AR Model to Improve the Accuracy of the Short-term Polar Motion Prediction

NASA Astrophysics Data System (ADS)

Wang, Z. W.; Wang, Q. X.; Ding, Y. Q.; Zhang, J. J.; Liu, S. S.

2017-03-01

There are two problems of the LS (Least Squares)+AR (AutoRegressive) model in polar motion forecast: the inner residual value of LS fitting is reasonable, but the residual value of LS extrapolation is poor; and the LS fitting residual sequence is non-linear. It is unsuitable to establish an AR model for the residual sequence to be forecasted, based on the residual sequence before forecast epoch. In this paper, we make solution to those two problems with two steps. First, restrictions are added to the two endpoints of LS fitting data to fix them on the LS fitting curve. Therefore, the fitting values next to the two endpoints are very close to the observation values. Secondly, we select the interpolation residual sequence of an inward LS fitting curve, which has a similar variation trend as the LS extrapolation residual sequence, as the modeling object of AR for the residual forecast. Calculation examples show that this solution can effectively improve the short-term polar motion prediction accuracy by the LS+AR model. In addition, the comparison results of the forecast models of RLS (Robustified Least Squares)+AR, RLS+ARIMA (AutoRegressive Integrated Moving Average), and LS+ANN (Artificial Neural Network) confirm the feasibility and effectiveness of the solution for the polar motion forecast. The results, especially for the polar motion forecast in the 1-10 days, show that the forecast accuracy of the proposed model can reach the world level.

Comparing interpolation techniques for annual temperature mapping across Xinjiang region

NASA Astrophysics Data System (ADS)

Ren-ping, Zhang; Jing, Guo; Tian-gang, Liang; Qi-sheng, Feng; Aimaiti, Yusupujiang

2016-11-01

Interpolating climatic variables such as temperature is challenging due to the highly variable nature of meteorological processes and the difficulty in establishing a representative network of stations. In this paper, based on the monthly temperature data which obtained from the 154 official meteorological stations in the Xinjiang region and surrounding areas, we compared five spatial interpolation techniques: Inverse distance weighting (IDW), Ordinary kriging, Cokriging, thin-plate smoothing splines (ANUSPLIN) and Empirical Bayesian kriging(EBK). Error metrics were used to validate interpolations against independent data. Results indicated that, the ANUSPLIN performed best than the other four interpolation methods.

Sandia Unstructured Triangle Tabular Interpolation Package v 0.1 beta

DOE Office of Scientific and Technical Information (OSTI.GOV)

2013-09-24

The software interpolates tabular data, such as for equations of state, provided on an unstructured triangular grid. In particular, interpolation occurs in a two dimensional space by looking up the triangle in which the desired evaluation point resides and then performing a linear interpolation over the n-tuples associated with the nodes of the chosen triangle. The interface to the interpolation routines allows for automated conversion of units from those tabulated to the desired output units. when multiple tables are included in a data file, new tables may be generated by on-the-fly mixing of the provided tables

High degree interpolation polynomial in Newton form

NASA Technical Reports Server (NTRS)

Tal-Ezer, Hillel

1988-01-01

Polynomial interpolation is an essential subject in numerical analysis. Dealing with a real interval, it is well known that even if f(x) is an analytic function, interpolating at equally spaced points can diverge. On the other hand, interpolating at the zeroes of the corresponding Chebyshev polynomial will converge. Using the Newton formula, this result of convergence is true only on the theoretical level. It is shown that the algorithm which computes the divided differences is numerically stable only if: (1) the interpolating points are arranged in a different order, and (2) the size of the interval is 4.

Quasi interpolation with Voronoi splines.

PubMed

Mirzargar, Mahsa; Entezari, Alireza

2011-12-01

We present a quasi interpolation framework that attains the optimal approximation-order of Voronoi splines for reconstruction of volumetric data sampled on general lattices. The quasi interpolation framework of Voronoi splines provides an unbiased reconstruction method across various lattices. Therefore this framework allows us to analyze and contrast the sampling-theoretic performance of general lattices, using signal reconstruction, in an unbiased manner. Our quasi interpolation methodology is implemented as an efficient FIR filter that can be applied online or as a preprocessing step. We present visual and numerical experiments that demonstrate the improved accuracy of reconstruction across lattices, using the quasi interpolation framework. © 2011 IEEE

SU-F-T-315: Comparative Studies of Planar Dose with Different Spatial Resolution for Head and Neck IMRT QA

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hwang, T; Koo, T

Purpose: To quantitatively investigate the planar dose difference and the γ value between the reference fluence map with the 1 mm detector-to-detector distance and the other fluence maps with less spatial resolution for head and neck intensity modulated radiation (IMRT) therapy. Methods: For ten head and neck cancer patients, the IMRT quality assurance (QA) beams were generated using by the commercial radiation treatment planning system, Pinnacle3 (ver. 8.0.d Philips Medical System, Madison, WI). For each beam, ten fluence maps (detector-to-detector distance: 1 mm to 10 mm by 1 mm) were generated. The fluence maps with larger than 1 mm detector-todetectormore » distance were interpolated using MATLAB (R2014a, the Math Works,Natick, MA) by four different interpolation Methods: for the bilinear, the cubic spline, the bicubic, and the nearest neighbor interpolation, respectively. These interpolated fluence maps were compared with the reference one using the γ value (criteria: 3%, 3 mm) and the relative dose difference. Results: As the detector-to-detector distance increases, the dose difference between the two maps increases. For the fluence map with the same resolution, the cubic spline interpolation and the bicubic interpolation are almost equally best interpolation methods while the nearest neighbor interpolation is the worst.For example, for 5 mm distance fluence maps, γ≤1 are 98.12±2.28%, 99.48±0.66%, 99.45±0.65% and 82.23±0.48% for the bilinear, the cubic spline, the bicubic, and the nearest neighbor interpolation, respectively. For 7 mm distance fluence maps, γ≤1 are 90.87±5.91%, 90.22±6.95%, 91.79±5.97% and 71.93±4.92 for the bilinear, the cubic spline, the bicubic, and the nearest neighbor interpolation, respectively. Conclusion: We recommend that the 2-dimensional detector array with high spatial resolution should be used as an IMRT QA tool and that the measured fluence maps should be interpolated using by the cubic spline interpolation or the bicubic interpolation for head and neck IMRT delivery. This work was supported by Radiation Technology R&D program through the National Research Foundation of Korea funded by the Ministry of Science, ICT & Future Planning (No. 2013M2A2A7038291)« less

Construction of Gridded Daily Weather Data and its Use in Central-European Agroclimatic Study

NASA Astrophysics Data System (ADS)

Dubrovsky, M.; Trnka, M.; Skalak, P.

2013-12-01

The regional-scale simulations of weather-sensitive processes (e.g. hydrology, agriculture and forestry) for the present and/or future climate often require high resolution meteorological inputs in terms of the time series of selected surface weather characteristics (typically temperature, precipitation, solar radiation, humidity, wind) for a set of stations or on a regular grid. As even the latest Global and Regional Climate Models (GCMs and RCMs) do not provide realistic representation of statistical structure of the surface weather, the model outputs must be postprocessed (downscaled) to achieve the desired statistical structure of the weather data before being used as an input to the follow-up simulation models. One of the downscaling approaches, which is employed also here, is based on a weather generator (WG), which is calibrated using the observed weather series, interpolated, and then modified according to the GCM- or RCM-based climate change scenarios. The present contribution, in which the parametric daily weather generator M&Rfi is linked to the high-resolution RCM output (ALADIN-Climate/CZ model) and GCM-based climate change scenarios, consists of two parts: The first part focuses on a methodology. Firstly, the gridded WG representing the baseline climate is created by merging information from observations and high resolution RCM outputs. In this procedure, WG is calibrated with RCM-simulated multi-variate weather series, and the grid specific WG parameters are then de-biased by spatially interpolated correction factors based on comparison of WG parameters calibrated with RCM-simulated weather series vs. spatially scarcer observations. To represent the future climate, the WG parameters are modified according to the 'WG-friendly' climate change scenarios. These scenarios are defined in terms of changes in WG parameters and include - apart from changes in the means - changes in WG parameters, which represent the additional characteristics of the weather series (e.g. probability of wet day occurrence and lag-1 autocorrelation of daily mean temperature). The WG-friendly scenarios for the present experiment are based on comparison of future vs baseline surface weather series simulated by GCMs from a CMIP3 database. The second part will present results of climate change impact study based on an above methodology applied to Central Europe. The changes in selected climatic (focusing on the extreme precipitation and temperature characteristics) and agroclimatic (including number of days during vegetation season with heat and drought stresses) characteristics will be analysed. In discussing the results, the emphasis will be put on 'added value' of various aspects of above methodology (e.g. inclusion of changes in 'advanced' WG parameters into the climate change scenarios). Acknowledgements: The present experiment is made within the frame of projects WG4VALUE (project LD12029 sponsored by the Ministry of Education, Youth and Sports of CR), ALARO-Climate (project P209/11/2405 sponsored by the Czech Science Foundation), and VALUE (COST ES 1102 action).

Optimal Interpolation scheme to generate reference crop evapotranspiration

NASA Astrophysics Data System (ADS)

Tomas-Burguera, Miquel; Beguería, Santiago; Vicente-Serrano, Sergio; Maneta, Marco

2018-05-01

We used an Optimal Interpolation (OI) scheme to generate a reference crop evapotranspiration (ETo) grid, forcing meteorological variables, and their respective error variance in the Iberian Peninsula for the period 1989-2011. To perform the OI we used observational data from the Spanish Meteorological Agency (AEMET) and outputs from a physically-based climate model. To compute ETo we used five OI schemes to generate grids for the five observed climate variables necessary to compute ETo using the FAO-recommended form of the Penman-Monteith equation (FAO-PM). The granularity of the resulting grids are less sensitive to variations in the density and distribution of the observational network than those generated by other interpolation methods. This is because our implementation of the OI method uses a physically-based climate model as prior background information about the spatial distribution of the climatic variables, which is critical for under-observed regions. This provides temporal consistency in the spatial variability of the climatic fields. We also show that increases in the density and improvements in the distribution of the observational network reduces substantially the uncertainty of the climatic and ETo estimates. Finally, a sensitivity analysis of observational uncertainties and network densification suggests the existence of a trade-off between quantity and quality of observations.

A Method for Extracting Road Boundary Information from Crowdsourcing Vehicle GPS Trajectories.

PubMed

Yang, Wei; Ai, Tinghua; Lu, Wei

2018-04-19

Crowdsourcing trajectory data is an important approach for accessing and updating road information. In this paper, we present a novel approach for extracting road boundary information from crowdsourcing vehicle traces based on Delaunay triangulation (DT). First, an optimization and interpolation method is proposed to filter abnormal trace segments from raw global positioning system (GPS) traces and interpolate the optimization segments adaptively to ensure there are enough tracking points. Second, constructing the DT and the Voronoi diagram within interpolated tracking lines to calculate road boundary descriptors using the area of Voronoi cell and the length of triangle edge. Then, the road boundary detection model is established integrating the boundary descriptors and trajectory movement features (e.g., direction) by DT. Third, using the boundary detection model to detect road boundary from the DT constructed by trajectory lines, and a regional growing method based on seed polygons is proposed to extract the road boundary. Experiments were conducted using the GPS traces of taxis in Beijing, China, and the results show that the proposed method is suitable for extracting the road boundary from low-frequency GPS traces, multi-type road structures, and different time intervals. Compared with two existing methods, the automatically extracted boundary information was proved to be of higher quality.

A Method for Extracting Road Boundary Information from Crowdsourcing Vehicle GPS Trajectories

PubMed Central

Yang, Wei

2018-01-01

Crowdsourcing trajectory data is an important approach for accessing and updating road information. In this paper, we present a novel approach for extracting road boundary information from crowdsourcing vehicle traces based on Delaunay triangulation (DT). First, an optimization and interpolation method is proposed to filter abnormal trace segments from raw global positioning system (GPS) traces and interpolate the optimization segments adaptively to ensure there are enough tracking points. Second, constructing the DT and the Voronoi diagram within interpolated tracking lines to calculate road boundary descriptors using the area of Voronoi cell and the length of triangle edge. Then, the road boundary detection model is established integrating the boundary descriptors and trajectory movement features (e.g., direction) by DT. Third, using the boundary detection model to detect road boundary from the DT constructed by trajectory lines, and a regional growing method based on seed polygons is proposed to extract the road boundary. Experiments were conducted using the GPS traces of taxis in Beijing, China, and the results show that the proposed method is suitable for extracting the road boundary from low-frequency GPS traces, multi-type road structures, and different time intervals. Compared with two existing methods, the automatically extracted boundary information was proved to be of higher quality. PMID:29671792

Measurement and tricubic interpolation of the magnetic field for the OLYMPUS experiment

NASA Astrophysics Data System (ADS)

Bernauer, J. C.; Diefenbach, J.; Elbakian, G.; Gavrilov, G.; Goerrissen, N.; Hasell, D. K.; Henderson, B. S.; Holler, Y.; Karyan, G.; Ludwig, J.; Marukyan, H.; Naryshkin, Y.; O'Connor, C.; Russell, R. L.; Schmidt, A.; Schneekloth, U.; Suvorov, K.; Veretennikov, D.

2016-07-01

The OLYMPUS experiment used a 0.3 T toroidal magnetic spectrometer to measure the momenta of outgoing charged particles. In order to accurately determine particle trajectories, knowledge of the magnetic field was needed throughout the spectrometer volume. For that purpose, the magnetic field was measured at over 36,000 positions using a three-dimensional Hall probe actuated by a system of translation tables. We used these field data to fit a numerical magnetic field model, which could be employed to calculate the magnetic field at any point in the spectrometer volume. Calculations with this model were computationally intensive; for analysis applications where speed was crucial, we pre-computed the magnetic field and its derivatives on an evenly spaced grid so that the field could be interpolated between grid points. We developed a spline-based interpolation scheme suitable for SIMD implementations, with a memory layout chosen to minimize space and optimize the cache behavior to quickly calculate field values. This scheme requires only one-eighth of the memory needed to store necessary coefficients compared with a previous scheme (Lekien and Marsden, 2005 [1]). This method was accurate for the vast majority of the spectrometer volume, though special fits and representations were needed to improve the accuracy close to the magnet coils and along the toroidal axis.

Rtop - an R package for interpolation of data with a variable spatial support - examples from river networks

NASA Astrophysics Data System (ADS)

Olav Skøien, Jon; Laaha, Gregor; Koffler, Daniel; Blöschl, Günter; Pebesma, Edzer; Parajka, Juraj; Viglione, Alberto

2013-04-01

Geostatistical methods have been applied only to a limited extent for spatial interpolation in applications where the observations have an irregular support, such as runoff characteristics or population health data. Several studies have shown the potential of such methods (Gottschalk 1993, Sauquet et al. 2000, Gottschalk et al. 2006, Skøien et al. 2006, Goovaerts 2008), but these developments have so far not led to easily accessible, versatile, easy to apply and open source software. Based on the top-kriging approach suggested by Skøien et al. (2006), we will here present the package rtop, which has been implemented in the statistical environment R (R Core Team 2012). Taking advantage of the existing methods in R for analysis of spatial objects (Bivand et al. 2008), and the extensive possibilities for visualizing the results, rtop makes it easy to apply geostatistical interpolation methods when observations have a non-point spatial support. Although the package is flexible regarding data input, the main application so far has been for interpolation along river networks. We will present some examples showing how the package can easily be used for such interpolation. The model will soon be uploaded to CRAN, but is in the meantime also available from R-forge and can be installed by: > install.packages("rtop", repos="http://R-Forge.R-project.org") Bivand, R.S., Pebesma, E.J. & Gómez-Rubio, V., 2008. Applied spatial data analysis with r: Springer. Goovaerts, P., 2008. Kriging and semivariogram deconvolution in the presence of irregular geographical units. Mathematical Geosciences, 40 (1), 101-128. Gottschalk, L., 1993. Interpolation of runoff applying objective methods. Stochastic Hydrology and Hydraulics, 7, 269-281. Gottschalk, L., Krasovskaia, I., Leblois, E. & Sauquet, E., 2006. Mapping mean and variance of runoff in a river basin. Hydrology and Earth System Sciences, 10, 469-484. R Core Team, 2012. R: A language and environment for statistical computing. Vienna, Austria, ISBN 3-900051-07-0. Sauquet, E., Gottschalk, L. & Leblois, E., 2000. Mapping average annual runoff: A hierarchical approach applying a stochastic interpolation scheme. Hydrological Sciences Journal, 45 (6), 799-815. Skøien, J.O., Merz, R. & Blöschl, G., 2006. Top-kriging - geostatistics on stream networks. Hydrology and Earth System Sciences, 10, 277-287.

On the Quality of Velocity Interpolation Schemes for Marker-In-Cell Methods on 3-D Staggered Grids

NASA Astrophysics Data System (ADS)

Kaus, B.; Pusok, A. E.; Popov, A.

2015-12-01

The marker-in-cell method is generally considered to be a flexible and robust method to model advection of heterogenous non-diffusive properties (i.e. rock type or composition) in geodynamic problems or incompressible Stokes problems. In this method, Lagrangian points carrying compositional information are advected with the ambient velocity field on an immobile, Eulerian grid. However, velocity interpolation from grid points to marker locations is often performed without preserving the zero divergence of the velocity field at the interpolated locations (i.e. non-conservative). Such interpolation schemes can induce non-physical clustering of markers when strong velocity gradients are present (Jenny et al., 2001) and this may, eventually, result in empty grid cells, a serious numerical violation of the marker-in-cell method. Solutions to this problem include: using larger mesh resolutions and/or marker densities, or repeatedly controlling the marker distribution (i.e. inject/delete), but which does not have an established physical background. To remedy this at low computational costs, Jenny et al. (2001) and Meyer and Jenny (2004) proposed a simple, conservative velocity interpolation (CVI) scheme for 2-D staggered grid, while Wang et al. (2015) extended the formulation to 3-D finite element methods. Here, we follow up with these studies and report on the quality of velocity interpolation methods for 2-D and 3-D staggered grids. We adapt the formulations from both Jenny et al. (2001) and Wang et al. (2015) for use on 3-D staggered grids, where the velocity components have different node locations as compared to finite element, where they share the same node location. We test the different interpolation schemes (CVI and non-CVI) in combination with different advection schemes (Euler, RK2 and RK4) and with/out marker control on Stokes problems with strong velocity gradients, which are discretized using a finite difference method. We show that a conservative formulation reduces the dispersion or clustering of markers and that the density of markers remains steady over time without the need of additional marker control. Jenny et al. (2001, J Comp Phys, 166, 218-252 Meyer and Jenny (2004), Proc Appl Math Mech, 4, 466-467 Wang et al. (2015), G3, Vol.16 Funding was provided by the ERC Starting Grant #258830.

Reconstruction of reflectance data using an interpolation technique.

PubMed

Abed, Farhad Moghareh; Amirshahi, Seyed Hossein; Abed, Mohammad Reza Moghareh

2009-03-01

A linear interpolation method is applied for reconstruction of reflectance spectra of Munsell as well as ColorChecker SG color chips from the corresponding colorimetric values under a given set of viewing conditions. Hence, different types of lookup tables (LUTs) have been created to connect the colorimetric and spectrophotometeric data as the source and destination spaces in this approach. To optimize the algorithm, different color spaces and light sources have been used to build different types of LUTs. The effects of applied color datasets as well as employed color spaces are investigated. Results of recovery are evaluated by the mean and the maximum color difference values under other sets of standard light sources. The mean and the maximum values of root mean square (RMS) error between the reconstructed and the actual spectra are also calculated. Since the speed of reflectance reconstruction is a key point in the LUT algorithm, the processing time spent for interpolation of spectral data has also been measured for each model. Finally, the performance of the suggested interpolation technique is compared with that of the common principal component analysis method. According to the results, using the CIEXYZ tristimulus values as a source space shows priority over the CIELAB color space. Besides, the colorimetric position of a desired sample is a key point that indicates the success of the approach. In fact, because of the nature of the interpolation technique, the colorimetric position of the desired samples should be located inside the color gamut of available samples in the dataset. The resultant spectra that have been reconstructed by this technique show considerable improvement in terms of RMS error between the actual and the reconstructed reflectance spectra as well as CIELAB color differences under the other light source in comparison with those obtained from the standard PCA technique.

Daily air temperature interpolated at high spatial resolution over a large mountainous region

USGS Publications Warehouse

Dodson, R.; Marks, D.

1997-01-01

Two methods are investigated for interpolating daily minimum and maximum air temperatures (Tmin and Tmax) at a 1 km spatial resolution over a large mountainous region (830 000 km2) in the U.S. Pacific Northwest. The methods were selected because of their ability to (1) account for the effect of elevation on temperature and (2) efficiently handle large volumes of data. The first method, the neutral stability algorithm (NSA), used the hydrostatic and potential temperature equations to convert measured temperatures and elevations to sea-level potential temperatures. The potential temperatures were spatially interpolated using an inverse-squared-distance algorithm and then mapped to the elevation surface of a digital elevation model (DEM). The second method, linear lapse rate adjustment (LLRA), involved the same basic procedure as the NSA, but used a constant linear lapse rate instead of the potential temperature equation. Cross-validation analyses were performed using the NSA and LLRA methods to interpolate Tmin and Tmax each day for the 1990 water year, and the methods were evaluated based on mean annual interpolation error (IE). The NSA method showed considerable bias for sites associated with vertical extrapolation. A correction based on climate station/grid cell elevation differences was developed and found to successfully remove the bias. The LLRA method was tested using 3 lapse rates, none of which produced a serious extrapolation bias. The bias-adjusted NSA and the 3 LLRA methods produced almost identical levels of accuracy (mean absolute errors between 1.2 and 1.3??C), and produced very similar temperature surfaces based on image difference statistics. In terms of accuracy, speed, and ease of implementation, LLRA was chosen as the best of the methods tested.

Contrast-guided image interpolation.

PubMed

Wei, Zhe; Ma, Kai-Kuang

2013-11-01

In this paper a contrast-guided image interpolation method is proposed that incorporates contrast information into the image interpolation process. Given the image under interpolation, four binary contrast-guided decision maps (CDMs) are generated and used to guide the interpolation filtering through two sequential stages: 1) the 45(°) and 135(°) CDMs for interpolating the diagonal pixels and 2) the 0(°) and 90(°) CDMs for interpolating the row and column pixels. After applying edge detection to the input image, the generation of a CDM lies in evaluating those nearby non-edge pixels of each detected edge for re-classifying them possibly as edge pixels. This decision is realized by solving two generalized diffusion equations over the computed directional variation (DV) fields using a derived numerical approach to diffuse or spread the contrast boundaries or edges, respectively. The amount of diffusion or spreading is proportional to the amount of local contrast measured at each detected edge. The diffused DV fields are then thresholded for yielding the binary CDMs, respectively. Therefore, the decision bands with variable widths will be created on each CDM. The two CDMs generated in each stage will be exploited as the guidance maps to conduct the interpolation process: for each declared edge pixel on the CDM, a 1-D directional filtering will be applied to estimate its associated to-be-interpolated pixel along the direction as indicated by the respective CDM; otherwise, a 2-D directionless or isotropic filtering will be used instead to estimate the associated missing pixels for each declared non-edge pixel. Extensive simulation results have clearly shown that the proposed contrast-guided image interpolation is superior to other state-of-the-art edge-guided image interpolation methods. In addition, the computational complexity is relatively low when compared with existing methods; hence, it is fairly attractive for real-time image applications.

Hydrologic Implications of Dynamical and Statistical Approaches to Downscaling Climate Model Outputs

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wood, Andrew W; Leung, Lai R; Sridhar, V

Six approaches for downscaling climate model outputs for use in hydrologic simulation were evaluated, with particular emphasis on each method's ability to produce precipitation and other variables used to drive a macroscale hydrology model applied at much higher spatial resolution than the climate model. Comparisons were made on the basis of a twenty-year retrospective (1975–1995) climate simulation produced by the NCAR-DOE Parallel Climate Model (PCM), and the implications of the comparison for a future (2040–2060) PCM climate scenario were also explored. The six approaches were made up of three relatively simple statistical downscaling methods – linear interpolation (LI), spatial disaggregationmore » (SD), and bias-correction and spatial disaggregation (BCSD) – each applied to both PCM output directly (at T42 spatial resolution), and after dynamical downscaling via a Regional Climate Model (RCM – at ½-degree spatial resolution), for downscaling the climate model outputs to the 1/8-degree spatial resolution of the hydrological model. For the retrospective climate simulation, results were compared to an observed gridded climatology of temperature and precipitation, and gridded hydrologic variables resulting from forcing the hydrologic model with observations. The most significant findings are that the BCSD method was successful in reproducing the main features of the observed hydrometeorology from the retrospective climate simulation, when applied to both PCM and RCM outputs. Linear interpolation produced better results using RCM output than PCM output, but both methods (PCM-LI and RCM-LI) lead to unacceptably biased hydrologic simulations. Spatial disaggregation of the PCM output produced results similar to those achieved with the RCM interpolated output; nonetheless, neither PCM nor RCM output was useful for hydrologic simulation purposes without a bias-correction step. For the future climate scenario, only the BCSD-method (using PCM or RCM) was able to produce hydrologically plausible results. With the BCSD method, the RCM-derived hydrology was more sensitive to climate change than the PCM-derived hydrology.« less

Model Order Reduction of Aeroservoelastic Model of Flexible Aircraft

NASA Technical Reports Server (NTRS)

Wang, Yi; Song, Hongjun; Pant, Kapil; Brenner, Martin J.; Suh, Peter

2016-01-01

This paper presents a holistic model order reduction (MOR) methodology and framework that integrates key technological elements of sequential model reduction, consistent model representation, and model interpolation for constructing high-quality linear parameter-varying (LPV) aeroservoelastic (ASE) reduced order models (ROMs) of flexible aircraft. The sequential MOR encapsulates a suite of reduction techniques, such as truncation and residualization, modal reduction, and balanced realization and truncation to achieve optimal ROMs at grid points across the flight envelope. The consistence in state representation among local ROMs is obtained by the novel method of common subspace reprojection. Model interpolation is then exploited to stitch ROMs at grid points to build a global LPV ASE ROM feasible to arbitrary flight condition. The MOR method is applied to the X-56A MUTT vehicle with flexible wing being tested at NASA/AFRC for flutter suppression and gust load alleviation. Our studies demonstrated that relative to the fullorder model, our X-56A ROM can accurately and reliably capture vehicles dynamics at various flight conditions in the target frequency regime while the number of states in ROM can be reduced by 10X (from 180 to 19), and hence, holds great promise for robust ASE controller synthesis and novel vehicle design.

Uncertainty quantification of resonant ultrasound spectroscopy for material property and single crystal orientation estimation on a complex part

NASA Astrophysics Data System (ADS)

Aldrin, John C.; Mayes, Alexander; Jauriqui, Leanne; Biedermann, Eric; Heffernan, Julieanne; Livings, Richard; Goodlet, Brent; Mazdiyasni, Siamack

2018-04-01

A case study is presented evaluating uncertainty in Resonance Ultrasound Spectroscopy (RUS) inversion for a single crystal (SX) Ni-based superalloy Mar-M247 cylindrical dog-bone specimens. A number of surrogate models were developed with FEM model solutions, using different sampling schemes (regular grid, Monte Carlo sampling, Latin Hyper-cube sampling) and model approaches, N-dimensional cubic spline interpolation and Kriging. Repeated studies were used to quantify the well-posedness of the inversion problem, and the uncertainty was assessed in material property and crystallographic orientation estimates given typical geometric dimension variability in aerospace components. Surrogate model quality was found to be an important factor in inversion results when the model more closely represents the test data. One important discovery was when the model matches well with test data, a Kriging surrogate model using un-sorted Latin Hypercube sampled data performed as well as the best results from an N-dimensional interpolation model using sorted data. However, both surrogate model quality and mode sorting were found to be less critical when inverting properties from either experimental data or simulated test cases with uncontrolled geometric variation.

WRF-Fire: coupled weather-wildland fire modeling with the weather research and forecasting model

Treesearch

Janice L. Coen; Marques Cameron; John Michalakes; Edward G. Patton; Philip J. Riggan; Kara M. Yedinak

2012-01-01

A wildland fire behavior module (WRF-Fire) was integrated into the Weather Research and Forecasting (WRF) public domain numerical weather prediction model. The fire module is a surface fire behavior model that is two-way coupled with the atmospheric model. Near-surface winds from the atmospheric model are interpolated to a finer fire grid and used, with fuel properties...

The Interpolation Theory of Radial Basis Functions

NASA Astrophysics Data System (ADS)

Baxter, Brad

2010-06-01

In this dissertation, it is first shown that, when the radial basis function is a p-norm and 1 < p < 2, interpolation is always possible when the points are all different and there are at least two of them. We then show that interpolation is not always possible when p > 2. Specifically, for every p > 2, we construct a set of different points in some Rd for which the interpolation matrix is singular. The greater part of this work investigates the sensitivity of radial basis function interpolants to changes in the function values at the interpolation points. Our early results show that it is possible to recast the work of Ball, Narcowich and Ward in the language of distributional Fourier transforms in an elegant way. We then use this language to study the interpolation matrices generated by subsets of regular grids. In particular, we are able to extend the classical theory of Toeplitz operators to calculate sharp bounds on the spectra of such matrices. Applying our understanding of these spectra, we construct preconditioners for the conjugate gradient solution of the interpolation equations. Our main result is that the number of steps required to achieve solution of the linear system to within a required tolerance can be independent of the number of interpolation points. The Toeplitz structure allows us to use fast Fourier transform techniques, which imp lies that the total number of operations is a multiple of n log n, where n is the number of interpolation points. Finally, we use some of our methods to study the behaviour of the multiquadric when its shape parameter increases to infinity. We find a surprising link with the sinus cardinalis or sinc function of Whittaker. Consequently, it can be highly useful to use a large shape parameter when approximating band-limited functions.

An algorithm for treating flat areas and depressions in digital elevation models using linear interpolation

EPA Science Inventory

Digital elevation model (DEM) data are essential to hydrological applications and have been widely used to calculate a variety of useful topographic characteristics, e.g., slope, flow direction, flow accumulation area, stream channel network, topographic index, and others. Excep...

Dynamic data-driven integrated flare model based on self-organized criticality

NASA Astrophysics Data System (ADS)

Dimitropoulou, M.; Isliker, H.; Vlahos, L.; Georgoulis, M. K.

2013-05-01

Context. We interpret solar flares as events originating in active regions that have reached the self-organized critical state. We describe them with a dynamic integrated flare model whose initial conditions and driving mechanism are derived from observations. Aims: We investigate whether well-known scaling laws observed in the distribution functions of characteristic flare parameters are reproduced after the self-organized critical state has been reached. Methods: To investigate whether the distribution functions of total energy, peak energy, and event duration follow the expected scaling laws, we first applied the previously reported static cellular automaton model to a time series of seven solar vector magnetograms of the NOAA active region 8210 recorded by the Imaging Vector Magnetograph on May 1 1998 between 18:59 UT and 23:16 UT until the self-organized critical state was reached. We then evolved the magnetic field between these processed snapshots through spline interpolation, mimicking a natural driver in our dynamic model. We identified magnetic discontinuities that exceeded a threshold in the Laplacian of the magnetic field after each interpolation step. These discontinuities were relaxed in local diffusion events, implemented in the form of cellular automaton evolution rules. Subsequent interpolation and relaxation steps covered all transitions until the end of the processed magnetograms' sequence. We additionally advanced each magnetic configuration that has reached the self-organized critical state (SOC configuration) by the static model until 50 more flares were triggered, applied the dynamic model again to the new sequence, and repeated the same process sufficiently often to generate adequate statistics. Physical requirements, such as the divergence-free condition for the magnetic field, were approximately imposed. Results: We obtain robust power laws in the distribution functions of the modeled flaring events with scaling indices that agree well with observations. Peak and total flare energy obey single power laws with indices -1.65 ± 0.11 and -1.47 ± 0.13, while the flare duration is best fitted with a double power law (-2.15 ± 0.15 and -3.60 ± 0.09 for the flatter and steeper parts, respectively). Conclusions: We conclude that well-known statistical properties of flares are reproduced after active regions reach the state of self-organized criticality. A significant enhancement of our refined cellular automaton model is that it initiates and further drives the simulation from observed evolving vector magnetograms, thus facilitating energy calculation in physical units, while a separation between MHD and kinetic timescales is possible by assigning distinct MHD timestamps to each interpolation step.

Interpolation and analyses of EURO-Cordex data for the characterization of local and regional climate change impact

NASA Astrophysics Data System (ADS)

Fink, Manfred; Pfannschmidt, Kai; Knevels, Raphel; Fischer, Christian; Brenning, Alexander

2017-04-01

Decisions on measures for adapting to possible climate impacts are critical at both regional and local levels of authority. Currently, the data from EURO-CORDEX is only provided at resolutions (0.11 and 0.44 degrees) that are sufficient for climate analysis in larger scale regions. Therefore, there is a need for more detailed climate information that can assist decision making at the county and town levels. To tackle this challenge, we have developed a tool for the Just Another Modelling System (JAMS; Kralisch et al. 2007) that produces approx. 50 climate characterizing parameters (e.g. average temperature, ice days, climatic water balance, among others) for different time intervals. This tool is combined within the JAMS environment with the J2000g distributed conceptual hydrological model (Krause and Hanisch 2009) to additionally calculate hydro-meteorological parameters, such as actual evapotranspiration, ground water recharge and runoff generation. The resolution of the data was transformed to a higher resolution (250 m) by applying an inverse distance weights (IDW) interpolation. The IDW was combined with an altitude regression approach using digital elevation model data to represent more detailed information of the land surface. We applied this downscaling approach for the federal state of Thuringia, Germany, which is represented by 371206 model units. An ensemble of 10 different EURO-CORDEX models (0.11 degree resolution) in a time period from 1961 to 2100 and measured data from 1960 to 1990 were analyzed. The climate change impacts were estimated by analyzing the changes between historical periods (1960 - 1990) and future periods (2020 - 2050, 2070 -2100) within the modeled EURO-CORDEX ensemble members. We also improved our interpolation approach by replacing IDW with kriging; this approach was especially an advantage for the interpolation of irregularly distributed measurement stations. The results were used to estimate the effects of climate change for the federal state of Thuringia and to support Thuringian climate-change mitigation and adaptation strategies. Future work will concentrate on bias correction of the ensemble members using the measured data. References Kralisch, S., P. Krause, M. Fink, C. Fischer, and W. Flügel (2007): Component based environmental modelling using the JAMS framework, in Proceedings of the MODSIM 2007 International Congress on Modelling and Simulation, edited by D. Kulasiri and L. Oxley, Christchurch, New Zealand Krause P, Hanisch S (2009): Simulation and analysis of the impact of projected climate change on the spatially distributed water balance in Thuringia, Germany. Adv Geosci 21:33-48. doi:10.5194/adgeo-21-33-2009

Locally-Adaptive, Spatially-Explicit Projection of U.S. Population for 2030 and 2050

DOE PAGES

McKee, Jacob J.; Rose, Amy N.; Bright, Eddie A.; ...

2015-02-03

Localized adverse events, including natural hazards, epidemiological events, and human conflict, underscore the criticality of quantifying and mapping current population. Moreover, knowing the spatial distribution of future population allows for increased preparation in the event of an emergency. Building on the spatial interpolation technique previously developed for high resolution population distribution data (LandScan Global and LandScan USA), we have constructed an empirically-informed spatial distribution of the projected population of the contiguous U.S. for 2030 and 2050. Whereas most current large-scale, spatially explicit population projections typically rely on a population gravity model to determine areas of future growth, our projection modelmore » departs from these by accounting for multiple components that affect population distribution. Modelled variables, which included land cover, slope, distances to larger cities, and a moving average of current population, were locally adaptive and geographically varying. The resulting weighted surface was used to determine which areas had the greatest likelihood for future population change. Population projections of county level numbers were developed using a modified version of the U.S. Census s projection methodology with the U.S. Census s official projection as the benchmark. Applications of our model include, but are not limited to, suitability modelling, service area planning for governmental agencies, consequence assessment, mitigation planning and implementation, and assessment of spatially vulnerable populations.« less

Locally-Adaptive, Spatially-Explicit Projection of U.S. Population for 2030 and 2050

DOE Office of Scientific and Technical Information (OSTI.GOV)

McKee, Jacob J.; Rose, Amy N.; Bright, Eddie A.

Localized adverse events, including natural hazards, epidemiological events, and human conflict, underscore the criticality of quantifying and mapping current population. Moreover, knowing the spatial distribution of future population allows for increased preparation in the event of an emergency. Building on the spatial interpolation technique previously developed for high resolution population distribution data (LandScan Global and LandScan USA), we have constructed an empirically-informed spatial distribution of the projected population of the contiguous U.S. for 2030 and 2050. Whereas most current large-scale, spatially explicit population projections typically rely on a population gravity model to determine areas of future growth, our projection modelmore » departs from these by accounting for multiple components that affect population distribution. Modelled variables, which included land cover, slope, distances to larger cities, and a moving average of current population, were locally adaptive and geographically varying. The resulting weighted surface was used to determine which areas had the greatest likelihood for future population change. Population projections of county level numbers were developed using a modified version of the U.S. Census s projection methodology with the U.S. Census s official projection as the benchmark. Applications of our model include, but are not limited to, suitability modelling, service area planning for governmental agencies, consequence assessment, mitigation planning and implementation, and assessment of spatially vulnerable populations.« less

Investigations of interpolation errors of angle encoders for high precision angle metrology

NASA Astrophysics Data System (ADS)

Yandayan, Tanfer; Geckeler, Ralf D.; Just, Andreas; Krause, Michael; Asli Akgoz, S.; Aksulu, Murat; Grubert, Bernd; Watanabe, Tsukasa

2018-06-01

Interpolation errors at small angular scales are caused by the subdivision of the angular interval between adjacent grating lines into smaller intervals when radial gratings are used in angle encoders. They are often a major error source in precision angle metrology and better approaches for determining them at low levels of uncertainty are needed. Extensive investigations of interpolation errors of different angle encoders with various interpolators and interpolation schemes were carried out by adapting the shearing method to the calibration of autocollimators with angle encoders. The results of the laboratories with advanced angle metrology capabilities are presented which were acquired by the use of four different high precision angle encoders/interpolators/rotary tables. State of the art uncertainties down to 1 milliarcsec (5 nrad) were achieved for the determination of the interpolation errors using the shearing method which provides simultaneous access to the angle deviations of the autocollimator and of the angle encoder. Compared to the calibration and measurement capabilities (CMC) of the participants for autocollimators, the use of the shearing technique represents a substantial improvement in the uncertainty by a factor of up to 5 in addition to the precise determination of interpolation errors or their residuals (when compensated). A discussion of the results is carried out in conjunction with the equipment used.

EBSDinterp 1.0: A MATLAB® Program to Perform Microstructurally Constrained Interpolation of EBSD Data.

PubMed

Pearce, Mark A

2015-08-01

EBSDinterp is a graphic user interface (GUI)-based MATLAB® program to perform microstructurally constrained interpolation of nonindexed electron backscatter diffraction data points. The area available for interpolation is restricted using variations in pattern quality or band contrast (BC). Areas of low BC are not available for interpolation, and therefore cannot be erroneously filled by adjacent grains "growing" into them. Points with the most indexed neighbors are interpolated first and the required number of neighbors is reduced with each successive round until a minimum number of neighbors is reached. Further iterations allow more data points to be filled by reducing the BC threshold. This method ensures that the best quality points (those with high BC and most neighbors) are interpolated first, and that the interpolation is restricted to grain interiors before adjacent grains are grown together to produce a complete microstructure. The algorithm is implemented through a GUI, taking advantage of MATLAB®'s parallel processing toolbox to perform the interpolations rapidly so that a variety of parameters can be tested to ensure that the final microstructures are robust and artifact-free. The software is freely available through the CSIRO Data Access Portal (doi:10.4225/08/5510090C6E620) as both a compiled Windows executable and as source code.

The natural neighbor series manuals and source codes

NASA Astrophysics Data System (ADS)

Watson, Dave

1999-05-01

This software series is concerned with reconstruction of spatial functions by interpolating a set of discrete observations having two or three independent variables. There are three components in this series: (1) nngridr: an implementation of natural neighbor interpolation, 1994, (2) modemap: an implementation of natural neighbor interpolation on the sphere, 1998 and (3) orebody: an implementation of natural neighbor isosurface generation (publication incomplete). Interpolation is important to geologists because it can offer graphical insights into significant geological structure and behavior, which, although inherent in the data, may not be otherwise apparent. It also is the first step in numerical integration, which provides a primary avenue to detailed quantification of the observed spatial function. Interpolation is implemented by selecting a surface-generating rule that controls the form of a `bridge' built across the interstices between adjacent observations. The cataloging and classification of the many such rules that have been reported is a subject in itself ( Watson, 1992), and the merits of various approaches have been debated at length. However, for practical purposes, interpolation methods are usually judged on how satisfactorily they handle problematic data sets. Sparse scattered data or traverse data, especially if the functional values are highly variable, generally tests interpolation methods most severely; but one method, natural neighbor interpolation, usually does produce preferable results for such data.

Interpolation for de-Dopplerisation

NASA Astrophysics Data System (ADS)

Graham, W. R.

2018-05-01

'De-Dopplerisation' is one aspect of a problem frequently encountered in experimental acoustics: deducing an emitted source signal from received data. It is necessary when source and receiver are in relative motion, and requires interpolation of the measured signal. This introduces error. In acoustics, typical current practice is to employ linear interpolation and reduce error by over-sampling. In other applications, more advanced approaches with better performance have been developed. Associated with this work is a large body of theoretical analysis, much of which is highly specialised. Nonetheless, a simple and compact performance metric is available: the Fourier transform of the 'kernel' function underlying the interpolation method. Furthermore, in the acoustics context, it is a more appropriate indicator than other, more abstract, candidates. On this basis, interpolators from three families previously identified as promising - - piecewise-polynomial, windowed-sinc, and B-spline-based - - are compared. The results show that significant improvements over linear interpolation can straightforwardly be obtained. The recommended approach is B-spline-based interpolation, which performs best irrespective of accuracy specification. Its only drawback is a pre-filtering requirement, which represents an additional implementation cost compared to other methods. If this cost is unacceptable, and aliasing errors (on re-sampling) up to approximately 1% can be tolerated, a family of piecewise-cubic interpolators provides the best alternative.

Quantum realization of the nearest neighbor value interpolation method for INEQR

NASA Astrophysics Data System (ADS)

Zhou, RiGui; Hu, WenWen; Luo, GaoFeng; Liu, XingAo; Fan, Ping

2018-07-01

This paper presents the nearest neighbor value (NNV) interpolation algorithm for the improved novel enhanced quantum representation of digital images (INEQR). It is necessary to use interpolation in image scaling because there is an increase or a decrease in the number of pixels. The difference between the proposed scheme and nearest neighbor interpolation is that the concept applied, to estimate the missing pixel value, is guided by the nearest value rather than the distance. Firstly, a sequence of quantum operations is predefined, such as cyclic shift transformations and the basic arithmetic operations. Then, the feasibility of the nearest neighbor value interpolation method for quantum image of INEQR is proven using the previously designed quantum operations. Furthermore, quantum image scaling algorithm in the form of circuits of the NNV interpolation for INEQR is constructed for the first time. The merit of the proposed INEQR circuit lies in their low complexity, which is achieved by utilizing the unique properties of quantum superposition and entanglement. Finally, simulation-based experimental results involving different classical images and ratios (i.e., conventional or non-quantum) are simulated based on the classical computer's MATLAB 2014b software, which demonstrates that the proposed interpolation method has higher performances in terms of high resolution compared to the nearest neighbor and bilinear interpolation.

Spatially continuous interpolation of water stage and water depths using the Everglades depth estimation network (EDEN)

USGS Publications Warehouse

Pearlstine, Leonard; Higer, Aaron; Palaseanu, Monica; Fujisaki, Ikuko; Mazzotti, Frank

2007-01-01

The Everglades Depth Estimation Network (EDEN) is an integrated network of real-time water-level monitoring, ground-elevation modeling, and water-surface modeling that provides scientists and managers with current (2000-present), online water-stage and water-depth information for the entire freshwater portion of the Greater Everglades. Continuous daily spatial interpolations of the EDEN network stage data are presented on a 400-square-meter grid spacing. EDEN offers a consistent and documented dataset that can be used by scientists and managers to (1) guide large-scale field operations, (2) integrate hydrologic and ecological responses, and (3) support biological and ecological assessments that measure ecosystem responses to the implementation of the Comprehensive Everglades Restoration Plan (CERP) The target users are biologists and ecologists examining trophic level responses to hydrodynamic changes in the Everglades.

Path Integral Computation of Quantum Free Energy Differences Due to Alchemical Transformations Involving Mass and Potential.

PubMed

Pérez, Alejandro; von Lilienfeld, O Anatole

2011-08-09

Thermodynamic integration, perturbation theory, and λ-dynamics methods were applied to path integral molecular dynamics calculations to investigate free energy differences due to "alchemical" transformations. Several estimators were formulated to compute free energy differences in solvable model systems undergoing changes in mass and/or potential. Linear and nonlinear alchemical interpolations were used for the thermodynamic integration. We find improved convergence for the virial estimators, as well as for the thermodynamic integration over nonlinear interpolation paths. Numerical results for the perturbative treatment of changes in mass and electric field strength in model systems are presented. We used thermodynamic integration in ab initio path integral molecular dynamics to compute the quantum free energy difference of the isotope transformation in the Zundel cation. The performance of different free energy methods is discussed.

Retina-like sensor image coordinates transformation and display

NASA Astrophysics Data System (ADS)

Cao, Fengmei; Cao, Nan; Bai, Tingzhu; Song, Shengyu

2015-03-01

For a new kind of retina-like senor camera, the image acquisition, coordinates transformation and interpolation need to be realized. Both of the coordinates transformation and interpolation are computed in polar coordinate due to the sensor's particular pixels distribution. The image interpolation is based on sub-pixel interpolation and its relative weights are got in polar coordinates. The hardware platform is composed of retina-like senor camera, image grabber and PC. Combined the MIL and OpenCV library, the software program is composed in VC++ on VS 2010. Experience results show that the system can realizes the real-time image acquisition, coordinate transformation and interpolation.

[Spatial distribution prediction of surface soil Pb in a battery contaminated site].

PubMed

Liu, Geng; Niu, Jun-Jie; Zhang, Chao; Zhao, Xin; Guo, Guan-Lin

2014-12-01

In order to enhance the reliability of risk estimation and to improve the accuracy of pollution scope determination in a battery contaminated site with the soil characteristic pollutant Pb, four spatial interpolation models, including Combination Prediction Model (OK(LG) + TIN), kriging model (OK(BC)), Inverse Distance Weighting model (IDW), and Spline model were employed to compare their effects on the spatial distribution and pollution assessment of soil Pb. The results showed that Pb concentration varied significantly and the data was severely skewed. The variation coefficient of the site was higher in the local region. OK(LG) + TIN was found to be more accurate than the other three models in predicting the actual pollution situations of the contaminated site. The prediction accuracy of other models was lower, due to the effect of the principle of different models and datum feature. The interpolation results of OK(BC), IDW and Spline could not reflect the detailed characteristics of seriously contaminated areas, and were not suitable for mapping and spatial distribution prediction of soil Pb in this site. This study gives great contributions and provides useful references for defining the remediation boundary and making remediation decision of contaminated sites.

Procedures for offline grid nesting in regional ocean models

NASA Astrophysics Data System (ADS)

Mason, Evan; Molemaker, Jeroen; Shchepetkin, Alexander F.; Colas, Francois; McWilliams, James C.; Sangrà, Pablo

One-way offline nesting of a primitive-equation regional ocean numerical model (ROMS) is investigated, with special attention to the boundary forcing file creation process. The model has a modified open boundary condition which minimises false wave reflections, and is optimised to utilise high-frequency boundary updates. The model configuration features a previously computed solution which supplies boundary forcing data to an interior domain with an increased grid resolution. At the open boundaries of the interior grid (the child) the topography is matched to that of the outer grid (the parent), over a narrow transition region. A correction is applied to the normal baroclinic and barotropic velocities at the open boundaries of the child to ensure volume conservation. It is shown that these steps, together with a carefully constructed interpolation of the parent data, lead to a high-quality child solution, with minimal artifacts such as persistent rim currents and wave reflections at the boundaries. Sensitivity experiments provide information about the robustness of the model open boundary condition to perturbations in the surface wind stress forcing field, to the perturbation of the volume conservation enforcement in the boundary forcing, and to perturbation of the vertical density structure in the boundary forcing. This knowledge is important when extending the nesting technique to include external data from alien sources, such as ocean models with physics and/or numerics different from ROMS, or from observed climatologies of temperature, salinity and sea level.

Correlation-based motion vector processing with adaptive interpolation scheme for motion-compensated frame interpolation.

PubMed

Huang, Ai-Mei; Nguyen, Truong

2009-04-01

In this paper, we address the problems of unreliable motion vectors that cause visual artifacts but cannot be detected by high residual energy or bidirectional prediction difference in motion-compensated frame interpolation. A correlation-based motion vector processing method is proposed to detect and correct those unreliable motion vectors by explicitly considering motion vector correlation in the motion vector reliability classification, motion vector correction, and frame interpolation stages. Since our method gradually corrects unreliable motion vectors based on their reliability, we can effectively discover the areas where no motion is reliable to be used, such as occlusions and deformed structures. We also propose an adaptive frame interpolation scheme for the occlusion areas based on the analysis of their surrounding motion distribution. As a result, the interpolated frames using the proposed scheme have clearer structure edges and ghost artifacts are also greatly reduced. Experimental results show that our interpolated results have better visual quality than other methods. In addition, the proposed scheme is robust even for those video sequences that contain multiple and fast motions.

Accurate B-spline-based 3-D interpolation scheme for digital volume correlation

NASA Astrophysics Data System (ADS)

Ren, Maodong; Liang, Jin; Wei, Bin

2016-12-01

An accurate and efficient 3-D interpolation scheme, based on sampling theorem and Fourier transform technique, is proposed to reduce the sub-voxel matching error caused by intensity interpolation bias in digital volume correlation. First, the influence factors of the interpolation bias are investigated theoretically using the transfer function of an interpolation filter (henceforth filter) in the Fourier domain. A law that the positional error of a filter can be expressed as a function of fractional position and wave number is found. Then, considering the above factors, an optimized B-spline-based recursive filter, combining B-spline transforms and least squares optimization method, is designed to virtually eliminate the interpolation bias in the process of sub-voxel matching. Besides, given each volumetric image containing different wave number ranges, a Gaussian weighting function is constructed to emphasize or suppress certain of wave number ranges based on the Fourier spectrum analysis. Finally, a novel software is developed and series of validation experiments were carried out to verify the proposed scheme. Experimental results show that the proposed scheme can reduce the interpolation bias to an acceptable level.

Spatial Copula Model for Imputing Traffic Flow Data from Remote Microwave Sensors

PubMed Central

Ma, Xiaolei; Du, Bowen; Yu, Bin

2017-01-01

Issues of missing data have become increasingly serious with the rapid increase in usage of traffic sensors. Analyses of the Beijing ring expressway have showed that up to 50% of microwave sensors pose missing values. The imputation of missing traffic data must be urgently solved although a precise solution that cannot be easily achieved due to the significant number of missing portions. In this study, copula-based models are proposed for the spatial interpolation of traffic flow from remote traffic microwave sensors. Most existing interpolation methods only rely on covariance functions to depict spatial correlation and are unsuitable for coping with anomalies due to Gaussian consumption. Copula theory overcomes this issue and provides a connection between the correlation function and the marginal distribution function of traffic flow. To validate copula-based models, a comparison with three kriging methods is conducted. Results indicate that copula-based models outperform kriging methods, especially on roads with irregular traffic patterns. Copula-based models demonstrate significant potential to impute missing data in large-scale transportation networks. PMID:28934164

An artificial intelligence tool for complex age-depth models

NASA Astrophysics Data System (ADS)

Bradley, E.; Anderson, K. A.; de Vesine, L. R.; Lai, V.; Thomas, M.; Nelson, T. H.; Weiss, I.; White, J. W. C.

2017-12-01

CSciBox is an integrated software system for age modeling of paleoenvironmental records. It incorporates an array of data-processing and visualization facilities, ranging from 14C calibrations to sophisticated interpolation tools. Using CSciBox's GUI, a scientist can build custom analysis pipelines by composing these built-in components or adding new ones. Alternatively, she can employ CSciBox's automated reasoning engine, Hobbes, which uses AI techniques to perform an in-depth, autonomous exploration of the space of possible age-depth models and presents the results—both the models and the reasoning that was used in constructing and evaluating them—to the user for her inspection. Hobbes accomplishes this using a rulebase that captures the knowledge of expert geoscientists, which was collected over the course of more than 100 hours of interviews. It works by using these rules to generate arguments for and against different age-depth model choices for a given core. Given a marine-sediment record containing uncalibrated 14C dates, for instance, Hobbes tries CALIB-style calibrations using a choice of IntCal curves, with reservoir age correction values chosen from the 14CHRONO database using the lat/long information provided with the core, and finally composes the resulting age points into a full age model using different interpolation methods. It evaluates each model—e.g., looking for outliers or reversals—and uses that information to guide the next steps of its exploration, and presents the results to the user in human-readable form. The most powerful of CSciBox's built-in interpolation methods is BACON, a Bayesian sedimentation-rate algorithm—a powerful but complex tool that can be difficult to use. Hobbes adjusts BACON's many parameters autonomously to match the age model to the expectations of expert geoscientists, as captured in its rulebase. It then checks the model against the data and iteratively re-calculates until it is a good fit to the data.

An image morphing technique based on optimal mass preserving mapping.

PubMed

Zhu, Lei; Yang, Yan; Haker, Steven; Tannenbaum, Allen

2007-06-01

Image morphing, or image interpolation in the time domain, deals with the metamorphosis of one image into another. In this paper, a new class of image morphing algorithms is proposed based on the theory of optimal mass transport. The L(2) mass moving energy functional is modified by adding an intensity penalizing term, in order to reduce the undesired double exposure effect. It is an intensity-based approach and, thus, is parameter free. The optimal warping function is computed using an iterative gradient descent approach. This proposed morphing method is also extended to doubly connected domains using a harmonic parameterization technique, along with finite-element methods.

An Image Morphing Technique Based on Optimal Mass Preserving Mapping

PubMed Central

Zhu, Lei; Yang, Yan; Haker, Steven; Tannenbaum, Allen

2013-01-01

Image morphing, or image interpolation in the time domain, deals with the metamorphosis of one image into another. In this paper, a new class of image morphing algorithms is proposed based on the theory of optimal mass transport. The L2 mass moving energy functional is modified by adding an intensity penalizing term, in order to reduce the undesired double exposure effect. It is an intensity-based approach and, thus, is parameter free. The optimal warping function is computed using an iterative gradient descent approach. This proposed morphing method is also extended to doubly connected domains using a harmonic parameterization technique, along with finite-element methods. PMID:17547128

The isentropic quantum drift-diffusion model in two or three space dimensions

NASA Astrophysics Data System (ADS)

Chen, Xiuqing

2009-05-01

We investigate the isentropic quantum drift-diffusion model, a fourth order parabolic system, in space dimensions d = 2, 3. First, we establish the global weak solutions with large initial value and periodic boundary conditions. Then we show the semiclassical limit by delicate interpolation estimates and compactness argument.

40 CFR 86.094-16 - Prohibition of defeat devices.

Code of Federal Regulations, 2010 CFR

2010-07-01

... Provisions for Emission Regulations for 1977 and Later Model Year New Light-Duty Vehicles, Light-Duty Trucks and Heavy-Duty Engines, and for 1985 and Later Model Year New Gasoline Fueled, Natural Gas-Fueled... congruity across the intermediate temperature range is the linear interpolation between the CO standard...

Generalized Reduced Order Modeling of Aeroservoelastic Systems

NASA Astrophysics Data System (ADS)

Gariffo, James Michael

Transonic aeroelastic and aeroservoelastic (ASE) modeling presents a significant technical and computational challenge. Flow fields with a mixture of subsonic and supersonic flow, as well as moving shock waves, can only be captured through high-fidelity CFD analysis. With modern computing power, it is realtively straightforward to determine the flutter boundary for a single structural configuration at a single flight condition, but problems of larger scope remain quite costly. Some such problems include characterizing a vehicle's flutter boundary over its full flight envelope, optimizing its structural weight subject to aeroelastic constraints, and designing control laws for flutter suppression. For all of these applications, reduced-order models (ROMs) offer substantial computational savings. ROM techniques in general have existed for decades, and the methodology presented in this dissertation builds on successful previous techniques to create a powerful new scheme for modeling aeroelastic systems, and predicting and interpolating their transonic flutter boundaries. In this method, linear ASE state-space models are constructed from modal structural and actuator models coupled to state-space models of the linearized aerodynamic forces through feedback loops. Flutter predictions can be made from these models through simple eigenvalue analysis of their state-transition matrices for an appropriate set of dynamic pressures. Moreover, this analysis returns the frequency and damping trend of every aeroelastic branch. In contrast, determining the critical dynamic pressure by direct time-marching CFD requires a separate run for every dynamic pressure being analyzed simply to obtain the trend for the critical branch. The present ROM methodology also includes a new model interpolation technique that greatly enhances the benefits of these ROMs. This enables predictions of the dynamic behavior of the system for flight conditions where CFD analysis has not been explicitly performed, thus making it possible to characterize the overall flutter boundary with far fewer CFD runs. A major challenge of this research is that transonic flutter boundaries can involve multiple unstable modes of different types. Multiple ROM-based studies on the ONERA M6 wing are shown indicating that in addition to classic bending-torsion (BT) flutter modes. which become unstable above a threshold dynamic pressure after two natural modes become aerodynamically coupled, some natural modes are able to extract energy from the air and become unstable by themselves. These single-mode instabilities tend to be weaker than the BT instabilities, but have near-zero flutter boundaries (exactly zero in the absence of structural damping). Examples of hump modes, which behave like natural mode instabilities before stabilizing, are also shown, as are cases where multiple instabilities coexist at a single flight condition. The result of all these instabilities is a highly sensitive flutter boundary, where small changes in Mach number, structural stiffness, and structural damping can substantially alter not only the stability of individual aeroelastic branches, but also which branch is critical. Several studies are shown presenting how the flutter boundary varies with respect to all three of these parameters, as well as the number of structural modes used to construct the ROMs. Finally, an investigation of the effectiveness and limitations of the interpolation scheme is presented. It is found that in regions where the flutter boundary is relatively smooth, the interpolation method produces ROMs that predict the flutter characteristics of the corresponding directly computed models to a high degree of accuracy, even for relatively coarsely spaced data. On the other hand, in the transonic dip region, the interpolated ROMs show significant errors at points where the boundary changes rapidly; however, they still give a good qualitative estimate of where the largest jumps occur.

Preliminary results of spatial modeling of selected forest health variables in Georgia

Treesearch

Brock Stewart; Chris J. Cieszewski

2009-01-01

Variables relating to forest health monitoring, such as mortality, are difficult to predict and model. We present here the results of fitting various spatial regression models to these variables. We interpolate plot-level values compiled from the Forest Inventory and Analysis National Information Management System (FIA-NIMS) data that are related to forest health....

Fast digital zooming system using directionally adaptive image interpolation and restoration.

PubMed

Kang, Wonseok; Jeon, Jaehwan; Yu, Soohwan; Paik, Joonki

2014-01-01

This paper presents a fast digital zooming system for mobile consumer cameras using directionally adaptive image interpolation and restoration methods. The proposed interpolation algorithm performs edge refinement along the initially estimated edge orientation using directionally steerable filters. Either the directionally weighted linear or adaptive cubic-spline interpolation filter is then selectively used according to the refined edge orientation for removing jagged artifacts in the slanted edge region. A novel image restoration algorithm is also presented for removing blurring artifacts caused by the linear or cubic-spline interpolation using the directionally adaptive truncated constrained least squares (TCLS) filter. Both proposed steerable filter-based interpolation and the TCLS-based restoration filters have a finite impulse response (FIR) structure for real time processing in an image signal processing (ISP) chain. Experimental results show that the proposed digital zooming system provides high-quality magnified images with FIR filter-based fast computational structure.

Quantum realization of the bilinear interpolation method for NEQR.

PubMed

Zhou, Ri-Gui; Hu, Wenwen; Fan, Ping; Ian, Hou

2017-05-31

In recent years, quantum image processing is one of the most active fields in quantum computation and quantum information. Image scaling as a kind of image geometric transformation has been widely studied and applied in the classical image processing, however, the quantum version of which does not exist. This paper is concerned with the feasibility of the classical bilinear interpolation based on novel enhanced quantum image representation (NEQR). Firstly, the feasibility of the bilinear interpolation for NEQR is proven. Then the concrete quantum circuits of the bilinear interpolation including scaling up and scaling down for NEQR are given by using the multiply Control-Not operation, special adding one operation, the reverse parallel adder, parallel subtractor, multiplier and division operations. Finally, the complexity analysis of the quantum network circuit based on the basic quantum gates is deduced. Simulation result shows that the scaled-up image using bilinear interpolation is clearer and less distorted than nearest interpolation.

Quantum realization of the nearest-neighbor interpolation method for FRQI and NEQR

NASA Astrophysics Data System (ADS)

Sang, Jianzhi; Wang, Shen; Niu, Xiamu

2016-01-01

This paper is concerned with the feasibility of the classical nearest-neighbor interpolation based on flexible representation of quantum images (FRQI) and novel enhanced quantum representation (NEQR). Firstly, the feasibility of the classical image nearest-neighbor interpolation for quantum images of FRQI and NEQR is proven. Then, by defining the halving operation and by making use of quantum rotation gates, the concrete quantum circuit of the nearest-neighbor interpolation for FRQI is designed for the first time. Furthermore, quantum circuit of the nearest-neighbor interpolation for NEQR is given. The merit of the proposed NEQR circuit lies in their low complexity, which is achieved by utilizing the halving operation and the quantum oracle operator. Finally, in order to further improve the performance of the former circuits, new interpolation circuits for FRQI and NEQR are presented by using Control-NOT gates instead of a halving operation. Simulation results show the effectiveness of the proposed circuits.

Application of spatial methods to identify areas with lime requirement in eastern Croatia

NASA Astrophysics Data System (ADS)

Bogunović, Igor; Kisic, Ivica; Mesic, Milan; Zgorelec, Zeljka; Percin, Aleksandra; Pereira, Paulo

2016-04-01

With more than 50% of acid soils in all agricultural land in Croatia, soil acidity is recognized as a big problem. Low soil pH leads to a series of negative phenomena in plant production and therefore as a compulsory measure for reclamation of acid soils is liming, recommended on the base of soil analysis. The need for liming is often erroneously determined only on the basis of the soil pH, because the determination of cation exchange capacity, the hydrolytic acidity and base saturation is a major cost to producers. Therefore, in Croatia, as well as some other countries, the amount of liming material needed to ameliorate acid soils is calculated by considering their hydrolytic acidity. For this research, several interpolation methods were tested to identify the best spatial predictor of hidrolitic acidity. The purpose of this study was to: test several interpolation methods to identify the best spatial predictor of hidrolitic acidity; and to determine the possibility of using multivariate geostatistics in order to reduce the number of needed samples for determination the hydrolytic acidity, all with an aim that the accuracy of the spatial distribution of liming requirement is not significantly reduced. Soil pH (in KCl) and hydrolytic acidity (Y1) is determined in the 1004 samples (from 0-30 cm) randomized collected in agricultural fields near Orahovica in eastern Croatia. This study tested 14 univariate interpolation models (part of ArcGIS software package) in order to provide most accurate spatial map of hydrolytic acidity on a base of: all samples (Y1 100%), and the datasets with 15% (Y1 85%), 30% (Y1 70%) and 50% fewer samples (Y1 50%). Parallel to univariate interpolation methods, the precision of the spatial distribution of the Y1 was tested by the co-kriging method with exchangeable acidity (pH in KCl) as a covariate. The soils at studied area had an average pH (KCl) 4,81, while the average Y1 10,52 cmol+ kg-1. These data suggest that liming is necessary agrotechnical measure for soil conditioning. The results show that ordinary kriging was most accurate univariate interpolation method with smallest error (RMSE) in all four data sets, while the least precise showed Radial Basis Functions (Thin Plate Spline and Inverse Multiquadratic). Furthermore, it is noticeable a trend of increasing errors (RMSE) with a reduced number of samples tested on the most accurate univariate interpolation model: 3,096 (Y1 100%), 3,258 (Y1 85%), 3,317 (Y1 70%), 3,546 (Y1 50%). The best-fit semivariograms show a strong spatial dependence in Y1 100% (Nugget/Sill 20.19) and Y1 85% (Nugget/Sill 23.83), while a further reduction of the number of samples resulted with moderate spatial dependence (Y1 70% -35,85% and Y1 50% - 32,01). Co-kriging method resulted in a reduction in RMSE compared with univariate interpolation methods for each data set with: 2,054, 1,731 and 1,734 for Y1 85%, Y1 70%, Y1 50%, respectively. The results show the possibility for reducing sampling costs by using co-kriging method which is useful from the practical viewpoint. Reduced number of samples by half for determination of hydrolytic acidity in the interaction with the soil pH provides a higher precision for variable liming compared to the univariate interpolation methods of the entire set of data. These data provide new opportunities to reduce costs in the practical plant production in Croatia.

Virtual Seismic Observation (VSO) with Sparsity-Promotion Inversion

NASA Astrophysics Data System (ADS)

Tiezhao, B.; Ning, J.; Jianwei, M.

2017-12-01

Large station interval leads to low resolution images, sometimes prevents people from obtaining images in concerned regions. Sparsity-promotion inversion, a useful method to recover missing data in industrial field acquisition, can be lent to interpolate seismic data on none-sampled sites, forming Virtual Seismic Observation (VSO). Traditional sparsity-promotion inversion suffers when coming up with large time difference in adjacent sites, which we concern most and use shift method to improve it. The procedure of the interpolation is that we first employ low-pass filter to get long wavelength waveform data and shift the waveforms of the same wave in different seismograms to nearly same arrival time. Then we use wavelet-transform-based sparsity-promotion inversion to interpolate waveform data on none-sampled sites and filling a phase in each missing trace. Finally, we shift back the waveforms to their original arrival times. We call our method FSIS (Filtering, Shift, Interpolation, Shift) interpolation. By this way, we can insert different virtually observed seismic phases into none-sampled sites and get dense seismic observation data. For testing our method, we randomly hide the real data in a site and use the rest to interpolate the observation on that site, using direct interpolation or FSIS method. Compared with directly interpolated data, interpolated data with FSIS can keep amplitude better. Results also show that the arrival times and waveforms of those VSOs well express the real data, which convince us that our method to form VSOs are applicable. In this way, we can provide needed data for some advanced seismic technique like RTM to illuminate shallow structures.

Coherent Doppler Lidar for Boundary Layer Studies and Wind Energy

NASA Astrophysics Data System (ADS)

Choukulkar, Aditya

This thesis outlines the development of a vector retrieval technique, based on data assimilation, for a coherent Doppler LIDAR (Light Detection and Ranging). A detailed analysis of the Optimal Interpolation (OI) technique for vector retrieval is presented. Through several modifications to the OI technique, it is shown that the modified technique results in significant improvement in velocity retrieval accuracy. These modifications include changes to innovation covariance portioning, covariance binning, and analysis increment calculation. It is observed that the modified technique is able to make retrievals with better accuracy, preserves local information better, and compares well with tower measurements. In order to study the error of representativeness and vector retrieval error, a lidar simulator was constructed. Using the lidar simulator a thorough sensitivity analysis of the lidar measurement process and vector retrieval is carried out. The error of representativeness as a function of scales of motion and sensitivity of vector retrieval to look angle is quantified. Using the modified OI technique, study of nocturnal flow in Owens' Valley, CA was carried out to identify and understand uncharacteristic events on the night of March 27th 2006. Observations from 1030 UTC to 1230 UTC (0230 hr local time to 0430 hr local time) on March 27 2006 are presented. Lidar observations show complex and uncharacteristic flows such as sudden bursts of westerly cross-valley wind mixing with the dominant up-valley wind. Model results from Coupled Ocean/Atmosphere Mesoscale Prediction System (COAMPS RTM) and other in-situ instrumentations are used to corroborate and complement these observations. The modified OI technique is used to identify uncharacteristic and extreme flow events at a wind development site. Estimates of turbulence and shear from this technique are compared to tower measurements. A formulation for equivalent wind speed in the presence of variations in wind speed and direction, combined with shear is developed and used to determine wind energy content in presence of turbulence.

A Final Approach Trajectory Model for Current Operations

NASA Technical Reports Server (NTRS)

Gong, Chester; Sadovsky, Alexander

2010-01-01

Predicting accurate trajectories with limited intent information is a challenge faced by air traffic management decision support tools in operation today. One such tool is the FAA's Terminal Proximity Alert system which is intended to assist controllers in maintaining safe separation of arrival aircraft during final approach. In an effort to improve the performance of such tools, two final approach trajectory models are proposed; one based on polynomial interpolation, the other on the Fourier transform. These models were tested against actual traffic data and used to study effects of the key final approach trajectory modeling parameters of wind, aircraft type, and weight class, on trajectory prediction accuracy. Using only the limited intent data available to today's ATM system, both the polynomial interpolation and Fourier transform models showed improved trajectory prediction accuracy over a baseline dead reckoning model. Analysis of actual arrival traffic showed that this improved trajectory prediction accuracy leads to improved inter-arrival separation prediction accuracy for longer look ahead times. The difference in mean inter-arrival separation prediction error between the Fourier transform and dead reckoning models was 0.2 nmi for a look ahead time of 120 sec, a 33 percent improvement, with a corresponding 32 percent improvement in standard deviation.

Computationally efficient real-time interpolation algorithm for non-uniform sampled biosignals

PubMed Central

Eftekhar, Amir; Kindt, Wilko; Constandinou, Timothy G.

2016-01-01

This Letter presents a novel, computationally efficient interpolation method that has been optimised for use in electrocardiogram baseline drift removal. In the authors’ previous Letter three isoelectric baseline points per heartbeat are detected, and here utilised as interpolation points. As an extension from linear interpolation, their algorithm segments the interpolation interval and utilises different piecewise linear equations. Thus, the algorithm produces a linear curvature that is computationally efficient while interpolating non-uniform samples. The proposed algorithm is tested using sinusoids with different fundamental frequencies from 0.05 to 0.7 Hz and also validated with real baseline wander data acquired from the Massachusetts Institute of Technology University and Boston's Beth Israel Hospital (MIT-BIH) Noise Stress Database. The synthetic data results show an root mean square (RMS) error of 0.9 μV (mean), 0.63 μV (median) and 0.6 μV (standard deviation) per heartbeat on a 1 mVp–p 0.1 Hz sinusoid. On real data, they obtain an RMS error of 10.9 μV (mean), 8.5 μV (median) and 9.0 μV (standard deviation) per heartbeat. Cubic spline interpolation and linear interpolation on the other hand shows 10.7 μV, 11.6 μV (mean), 7.8 μV, 8.9 μV (median) and 9.8 μV, 9.3 μV (standard deviation) per heartbeat. PMID:27382478

Computationally efficient real-time interpolation algorithm for non-uniform sampled biosignals.

PubMed

Guven, Onur; Eftekhar, Amir; Kindt, Wilko; Constandinou, Timothy G

2016-06-01

This Letter presents a novel, computationally efficient interpolation method that has been optimised for use in electrocardiogram baseline drift removal. In the authors' previous Letter three isoelectric baseline points per heartbeat are detected, and here utilised as interpolation points. As an extension from linear interpolation, their algorithm segments the interpolation interval and utilises different piecewise linear equations. Thus, the algorithm produces a linear curvature that is computationally efficient while interpolating non-uniform samples. The proposed algorithm is tested using sinusoids with different fundamental frequencies from 0.05 to 0.7 Hz and also validated with real baseline wander data acquired from the Massachusetts Institute of Technology University and Boston's Beth Israel Hospital (MIT-BIH) Noise Stress Database. The synthetic data results show an root mean square (RMS) error of 0.9 μV (mean), 0.63 μV (median) and 0.6 μV (standard deviation) per heartbeat on a 1 mVp-p 0.1 Hz sinusoid. On real data, they obtain an RMS error of 10.9 μV (mean), 8.5 μV (median) and 9.0 μV (standard deviation) per heartbeat. Cubic spline interpolation and linear interpolation on the other hand shows 10.7 μV, 11.6 μV (mean), 7.8 μV, 8.9 μV (median) and 9.8 μV, 9.3 μV (standard deviation) per heartbeat.

An integral conservative gridding--algorithm using Hermitian curve interpolation.

PubMed

Volken, Werner; Frei, Daniel; Manser, Peter; Mini, Roberto; Born, Ernst J; Fix, Michael K

2008-11-07

The problem of re-sampling spatially distributed data organized into regular or irregular grids to finer or coarser resolution is a common task in data processing. This procedure is known as 'gridding' or 're-binning'. Depending on the quantity the data represents, the gridding-algorithm has to meet different requirements. For example, histogrammed physical quantities such as mass or energy have to be re-binned in order to conserve the overall integral. Moreover, if the quantity is positive definite, negative sampling values should be avoided. The gridding process requires a re-distribution of the original data set to a user-requested grid according to a distribution function. The distribution function can be determined on the basis of the given data by interpolation methods. In general, accurate interpolation with respect to multiple boundary conditions of heavily fluctuating data requires polynomial interpolation functions of second or even higher order. However, this may result in unrealistic deviations (overshoots or undershoots) of the interpolation function from the data. Accordingly, the re-sampled data may overestimate or underestimate the given data by a significant amount. The gridding-algorithm presented in this work was developed in order to overcome these problems. Instead of a straightforward interpolation of the given data using high-order polynomials, a parametrized Hermitian interpolation curve was used to approximate the integrated data set. A single parameter is determined by which the user can control the behavior of the interpolation function, i.e. the amount of overshoot and undershoot. Furthermore, it is shown how the algorithm can be extended to multidimensional grids. The algorithm was compared to commonly used gridding-algorithms using linear and cubic interpolation functions. It is shown that such interpolation functions may overestimate or underestimate the source data by about 10-20%, while the new algorithm can be tuned to significantly reduce these interpolation errors. The accuracy of the new algorithm was tested on a series of x-ray CT-images (head and neck, lung, pelvis). The new algorithm significantly improves the accuracy of the sampled images in terms of the mean square error and a quality index introduced by Wang and Bovik (2002 IEEE Signal Process. Lett. 9 81-4).

Efficient Implementation of an Optimal Interpolator for Large Spatial Data Sets

NASA Technical Reports Server (NTRS)

Memarsadeghi, Nargess; Mount, David M.

2007-01-01

Scattered data interpolation is a problem of interest in numerous areas such as electronic imaging, smooth surface modeling, and computational geometry. Our motivation arises from applications in geology and mining, which often involve large scattered data sets and a demand for high accuracy. The method of choice is ordinary kriging. This is because it is a best unbiased estimator. Unfortunately, this interpolant is computationally very expensive to compute exactly. For n scattered data points, computing the value of a single interpolant involves solving a dense linear system of size roughly n x n. This is infeasible for large n. In practice, kriging is solved approximately by local approaches that are based on considering only a relatively small'number of points that lie close to the query point. There are many problems with this local approach, however. The first is that determining the proper neighborhood size is tricky, and is usually solved by ad hoc methods such as selecting a fixed number of nearest neighbors or all the points lying within a fixed radius. Such fixed neighborhood sizes may not work well for all query points, depending on local density of the point distribution. Local methods also suffer from the problem that the resulting interpolant is not continuous. Meyer showed that while kriging produces smooth continues surfaces, it has zero order continuity along its borders. Thus, at interface boundaries where the neighborhood changes, the interpolant behaves discontinuously. Therefore, it is important to consider and solve the global system for each interpolant. However, solving such large dense systems for each query point is impractical. Recently a more principled approach to approximating kriging has been proposed based on a technique called covariance tapering. The problems arise from the fact that the covariance functions that are used in kriging have global support. Our implementations combine, utilize, and enhance a number of different approaches that have been introduced in literature for solving large linear systems for interpolation of scattered data points. For very large systems, exact methods such as Gaussian elimination are impractical since they require 0(n(exp 3)) time and 0(n(exp 2)) storage. As Billings et al. suggested, we use an iterative approach. In particular, we use the SYMMLQ method, for solving the large but sparse ordinary kriging systems that result from tapering. The main technical issue that need to be overcome in our algorithmic solution is that the points' covariance matrix for kriging should be symmetric positive definite. The goal of tapering is to obtain a sparse approximate representation of the covariance matrix while maintaining its positive definiteness. Furrer et al. used tapering to obtain a sparse linear system of the form Ax = b, where A is the tapered symmetric positive definite covariance matrix. Thus, Cholesky factorization could be used to solve their linear systems. They implemented an efficient sparse Cholesky decomposition method. They also showed if these tapers are used for a limited class of covariance models, the solution of the system converges to the solution of the original system. Matrix A in the ordinary kriging system, while symmetric, is not positive definite. Thus, their approach is not applicable to the ordinary kriging system. Therefore, we use tapering only to obtain a sparse linear system. Then, we use SYMMLQ to solve the ordinary kriging system. We show that solving large kriging systems becomes practical via tapering and iterative methods, and results in lower estimation errors compared to traditional local approaches, and significant memory savings compared to the original global system. We also developed a more efficient variant of the sparse SYMMLQ method for large ordinary kriging systems. This approach adaptively finds the correct local neighborhood for each query point in the interpolation process.

Uncertainty Analysis Based on Sparse Grid Collocation and Quasi-Monte Carlo Sampling with Application in Groundwater Modeling

NASA Astrophysics Data System (ADS)

Zhang, G.; Lu, D.; Ye, M.; Gunzburger, M.

2011-12-01

Markov Chain Monte Carlo (MCMC) methods have been widely used in many fields of uncertainty analysis to estimate the posterior distributions of parameters and credible intervals of predictions in the Bayesian framework. However, in practice, MCMC may be computationally unaffordable due to slow convergence and the excessive number of forward model executions required, especially when the forward model is expensive to compute. Both disadvantages arise from the curse of dimensionality, i.e., the posterior distribution is usually a multivariate function of parameters. Recently, sparse grid method has been demonstrated to be an effective technique for coping with high-dimensional interpolation or integration problems. Thus, in order to accelerate the forward model and avoid the slow convergence of MCMC, we propose a new method for uncertainty analysis based on sparse grid interpolation and quasi-Monte Carlo sampling. First, we construct a polynomial approximation of the forward model in the parameter space by using the sparse grid interpolation. This approximation then defines an accurate surrogate posterior distribution that can be evaluated repeatedly at minimal computational cost. Second, instead of using MCMC, a quasi-Monte Carlo method is applied to draw samples in the parameter space. Then, the desired probability density function of each prediction is approximated by accumulating the posterior density values of all the samples according to the prediction values. Our method has the following advantages: (1) the polynomial approximation of the forward model on the sparse grid provides a very efficient evaluation of the surrogate posterior distribution; (2) the quasi-Monte Carlo method retains the same accuracy in approximating the PDF of predictions but avoids all disadvantages of MCMC. The proposed method is applied to a controlled numerical experiment of groundwater flow modeling. The results show that our method attains the same accuracy much more efficiently than traditional MCMC.

Hand skin reconstruction from skeletal landmarks.

PubMed

Lefèvre, P; Van Sint Jan, S; Beauthier, J P; Rooze, M

2007-11-01

Many studies related to three-dimensional facial reconstruction have been previously reported. On the other hand, no extensive work has been found in the literature about hand reconstruction as an identification method. In this paper, the feasibility of virtual reconstruction of hand skin based on (1) its skeleton and (2) another hand skin and skeleton used as template was assessed. One cadaver hand and one volunteer's hand have been used. For the two hands, computer models of the bones and skin were obtained from computerized tomography. A customized software allowed locating spatial coordinates of bony anatomical landmarks on the models. From these landmarks, the spatial relationships between the models were determined and used to interpolate the missing hand skin. The volume of the interpolated skin was compared to the real skin obtained from medical imaging for validation. Results seem to indicate that such a method is of interest to give forensic investigators morphological clues related to an individual hand skin based on its skeleton. Further work is in progress to finalize the method.

An operational global-scale ocean thermal analysis system

DOE Office of Scientific and Technical Information (OSTI.GOV)

Clancy, R. M.; Pollak, K.D.; Phoebus, P.A.

1990-04-01

The Optimum Thermal Interpolation System (OTIS) is an ocean thermal analysis system designed for operational use at FNOC. It is based on the optimum interpolation of the assimilation technique and functions in an analysis-prediction-analysis data assimilation cycle with the TOPS mixed-layer model. OTIS provides a rigorous framework for combining real-time data, climatology, and predictions from numerical ocean prediction models to produce a large-scale synoptic representation of ocean thermal structure. The techniques and assumptions used in OTIS are documented and results of operational tests of global scale OTIS at FNOC are presented. The tests involved comparisons of OTIS against an existingmore » operational ocean thermal structure model and were conducted during February, March, and April 1988. Qualitative comparison of the two products suggests that OTIS gives a more realistic representation of subsurface anomalies and horizontal gradients and that it also gives a more accurate analysis of the thermal structure, with improvements largest below the mixed layer. 37 refs.« less

New Mass-Conserving Bedrock Topography for Pine Island Glacier Impacts Simulated Decadal Rates of Mass Loss

NASA Astrophysics Data System (ADS)

Nias, I. J.; Cornford, S. L.; Payne, A. J.

2018-04-01

High-resolution ice flow modeling requires bedrock elevation and ice thickness data, consistent with one another and with modeled physics. Previous studies have shown that gridded ice thickness products that rely on standard interpolation techniques (such as Bedmap2) can be inconsistent with the conservation of mass, given observed velocity, surface elevation change, and surface mass balance, for example, near the grounding line of Pine Island Glacier, West Antarctica. Using the BISICLES ice flow model, we compare results of simulations using both Bedmap2 bedrock and thickness data, and a new interpolation method that respects mass conservation. We find that simulations using the new geometry result in higher sea level contribution than Bedmap2 and reveal decadal-scale trends in the ice stream dynamics. We test the impact of several sliding laws and find that it is at least as important to accurately represent the bedrock and initial ice thickness as the choice of sliding law.

Performance of signal-to-noise ratio estimation for scanning electron microscope using autocorrelation Levinson-Durbin recursion model.

PubMed

Sim, K S; Lim, M S; Yeap, Z X

2016-07-01

A new technique to quantify signal-to-noise ratio (SNR) value of the scanning electron microscope (SEM) images is proposed. This technique is known as autocorrelation Levinson-Durbin recursion (ACLDR) model. To test the performance of this technique, the SEM image is corrupted with noise. The autocorrelation function of the original image and the noisy image are formed. The signal spectrum based on the autocorrelation function of image is formed. ACLDR is then used as an SNR estimator to quantify the signal spectrum of noisy image. The SNR values of the original image and the quantified image are calculated. The ACLDR is then compared with the three existing techniques, which are nearest neighbourhood, first-order linear interpolation and nearest neighbourhood combined with first-order linear interpolation. It is shown that ACLDR model is able to achieve higher accuracy in SNR estimation. © 2016 The Authors Journal of Microscopy © 2016 Royal Microscopical Society.

A refined characterization of the alluvial geology of yucca flat and its effect on bulk hydraulic conductivity

USGS Publications Warehouse

Phelps, G.A.; Halford, K.J.

2011-01-01

In Yucca Flat, on the Nevada National Security Site in southern Nevada, the migration of radionuclides from tests located in the alluvial deposits into the Paleozoic carbonate aquifer involves passage through a thick, heterogeneous section of late Tertiary and Quaternary alluvial sediments. An understanding of the lateral and vertical changes in the material properties of the alluvial sediments will aid in the further development of the hydrogeologic framework and the delineation of hydrostratigraphic units and hydraulic properties required for simulating groundwater flow in the Yucca Flat area. Previously published geologic models for the alluvial sediments within Yucca Flat are based on extensive examination and categorization of drill-hole data, combined with a simple, data-driven interpolation scheme. The U.S. Geological Survey, in collaboration with Stanford University, is researching improvements to the modeling of the alluvial section, incorporating prior knowledge of geologic structure into the interpolation method and estimating the uncertainty of the modeled hydrogeologic units.

Spatial interpolation techniques using R

EPA Science Inventory

Interpolation techniques are used to predict the cell values of a raster based on sample data points. For example, interpolation can be used to predict the distribution of sediment particle size throughout an estuary based on discrete sediment samples. We demonstrate some inter...

Ground-state properties of anyons in a one-dimensional lattice

NASA Astrophysics Data System (ADS)

Tang, Guixin; Eggert, Sebastian; Pelster, Axel

2015-12-01

Using the Anyon-Hubbard Hamiltonian, we analyze the ground-state properties of anyons in a one-dimensional lattice. To this end we map the hopping dynamics of correlated anyons to an occupation-dependent hopping Bose-Hubbard model using the fractional Jordan-Wigner transformation. In particular, we calculate the quasi-momentum distribution of anyons, which interpolates between Bose-Einstein and Fermi-Dirac statistics. Analytically, we apply a modified Gutzwiller mean-field approach, which goes beyond a classical one by including the influence of the fractional phase of anyons within the many-body wavefunction. Numerically, we use the density-matrix renormalization group by relying on the ansatz of matrix product states. As a result it turns out that the anyonic quasi-momentum distribution reveals both a peak-shift and an asymmetry which mainly originates from the nonlocal string property. In addition, we determine the corresponding quasi-momentum distribution of the Jordan-Wigner transformed bosons, where, in contrast to the hard-core case, we also observe an asymmetry for the soft-core case, which strongly depends on the particle number density.

Propeller performance and weight predictions appended to the Navy/NASA engine program

NASA Technical Reports Server (NTRS)

Plencner, R. M.; Senty, P.; Wickenheiser, T. J.

1983-01-01

The Navy/NASA Engine Performance (NNEP) is a general purpose computer program currently employed by government, industry and university personnel to simulate the thermodynamic cycles of turbine engines. NNEP is a modular program which has the ability to evaluate the performance of an arbitrary engine configuration defined by the user. In 1979, a program to calculate engine weight (WATE-2) was developed by Boeing's Military Division under NASA contract. This program uses a preliminary design approach to determine engine weights and dimensions. Because the thermodynamic and configuration information required by the weight code was available in NNEP, the weight code was appended to NNEP. Due to increased emphasis on fuel economy, a renewed interest has developed in propellers. This report describes the modifications developed by NASA to both NNEP and WATE-2 to determine the performance, weight and dimensions of propellers and the corresponding gearbox. The propeller performance model has three options, two of which are based on propeller map interpolation. Propeller and gearbox weights are obtained from empirical equations which may easily be modified by the user.

Volumetric three-dimensional intravascular ultrasound visualization using shape-based nonlinear interpolation

PubMed Central

2013-01-01

Background Intravascular ultrasound (IVUS) is a standard imaging modality for identification of plaque formation in the coronary and peripheral arteries. Volumetric three-dimensional (3D) IVUS visualization provides a powerful tool to overcome the limited comprehensive information of 2D IVUS in terms of complex spatial distribution of arterial morphology and acoustic backscatter information. Conventional 3D IVUS techniques provide sub-optimal visualization of arterial morphology or lack acoustic information concerning arterial structure due in part to low quality of image data and the use of pixel-based IVUS image reconstruction algorithms. In the present study, we describe a novel volumetric 3D IVUS reconstruction algorithm to utilize IVUS signal data and a shape-based nonlinear interpolation. Methods We developed an algorithm to convert a series of IVUS signal data into a fully volumetric 3D visualization. Intermediary slices between original 2D IVUS slices were generated utilizing the natural cubic spline interpolation to consider the nonlinearity of both vascular structure geometry and acoustic backscatter in the arterial wall. We evaluated differences in image quality between the conventional pixel-based interpolation and the shape-based nonlinear interpolation methods using both virtual vascular phantom data and in vivo IVUS data of a porcine femoral artery. Volumetric 3D IVUS images of the arterial segment reconstructed using the two interpolation methods were compared. Results In vitro validation and in vivo comparative studies with the conventional pixel-based interpolation method demonstrated more robustness of the shape-based nonlinear interpolation algorithm in determining intermediary 2D IVUS slices. Our shape-based nonlinear interpolation demonstrated improved volumetric 3D visualization of the in vivo arterial structure and more realistic acoustic backscatter distribution compared to the conventional pixel-based interpolation method. Conclusions This novel 3D IVUS visualization strategy has the potential to improve ultrasound imaging of vascular structure information, particularly atheroma determination. Improved volumetric 3D visualization with accurate acoustic backscatter information can help with ultrasound molecular imaging of atheroma component distribution. PMID:23651569