How Digital Image Processing Became Really Easy

NASA Astrophysics Data System (ADS)

Cannon, Michael

1988-02-01

In the early and mid-1970s, digital image processing was the subject of intense university and corporate research. The research lay along two lines: (1) developing mathematical techniques for improving the appearance of or analyzing the contents of images represented in digital form, and (2) creating cost-effective hardware to carry out these techniques. The research has been very effective, as evidenced by the continued decline of image processing as a research topic, and the rapid increase of commercial companies to market digital image processing software and hardware.

Image Processing for Teaching.

ERIC Educational Resources Information Center

Greenberg, R.; And Others

1993-01-01

The Image Processing for Teaching project provides a powerful medium to excite students about science and mathematics, especially children from minority groups and others whose needs have not been met by traditional teaching. Using professional-quality software on microcomputers, students explore a variety of scientific data sets, including…

Recent Advances of Malaria Parasites Detection Systems Based on Mathematical Morphology

PubMed Central

Di Ruberto, Cecilia; Kocher, Michel

2018-01-01

Malaria is an epidemic health disease and a rapid, accurate diagnosis is necessary for proper intervention. Generally, pathologists visually examine blood stained slides for malaria diagnosis. Nevertheless, this kind of visual inspection is subjective, error-prone and time-consuming. In order to overcome the issues, numerous methods of automatic malaria diagnosis have been proposed so far. In particular, many researchers have used mathematical morphology as a powerful tool for computer aided malaria detection and classification. Mathematical morphology is not only a theory for the analysis of spatial structures, but also a very powerful technique widely used for image processing purposes and employed successfully in biomedical image analysis, especially in preprocessing and segmentation tasks. Microscopic image analysis and particularly malaria detection and classification can greatly benefit from the use of morphological operators. The aim of this paper is to present a review of recent mathematical morphology based methods for malaria parasite detection and identification in stained blood smears images. PMID:29419781

Recent Advances of Malaria Parasites Detection Systems Based on Mathematical Morphology.

PubMed

Loddo, Andrea; Di Ruberto, Cecilia; Kocher, Michel

2018-02-08

Malaria is an epidemic health disease and a rapid, accurate diagnosis is necessary for proper intervention. Generally, pathologists visually examine blood stained slides for malaria diagnosis. Nevertheless, this kind of visual inspection is subjective, error-prone and time-consuming. In order to overcome the issues, numerous methods of automatic malaria diagnosis have been proposed so far. In particular, many researchers have used mathematical morphology as a powerful tool for computer aided malaria detection and classification. Mathematical morphology is not only a theory for the analysis of spatial structures, but also a very powerful technique widely used for image processing purposes and employed successfully in biomedical image analysis, especially in preprocessing and segmentation tasks. Microscopic image analysis and particularly malaria detection and classification can greatly benefit from the use of morphological operators. The aim of this paper is to present a review of recent mathematical morphology based methods for malaria parasite detection and identification in stained blood smears images.

Synthetic Aperture Radar (SAR) data processing

NASA Technical Reports Server (NTRS)

Beckner, F. L.; Ahr, H. A.; Ausherman, D. A.; Cutrona, L. J.; Francisco, S.; Harrison, R. E.; Heuser, J. S.; Jordan, R. L.; Justus, J.; Manning, B.

1978-01-01

The available and optimal methods for generating SAR imagery for NASA applications were identified. The SAR image quality and data processing requirements associated with these applications were studied. Mathematical operations and algorithms required to process sensor data into SAR imagery were defined. The architecture of SAR image formation processors was discussed, and technology necessary to implement the SAR data processors used in both general purpose and dedicated imaging systems was addressed.

Subband/Transform MATLAB Functions For Processing Images

NASA Technical Reports Server (NTRS)

Glover, D.

1995-01-01

SUBTRANS software is package of routines implementing image-data-processing functions for use with MATLAB*(TM) software. Provides capability to transform image data with block transforms and to produce spatial-frequency subbands of transformed data. Functions cascaded to provide further decomposition into more subbands. Also used in image-data-compression systems. For example, transforms used to prepare data for lossy compression. Written for use in MATLAB mathematical-analysis environment.

Electrophoresis gel image processing and analysis using the KODAK 1D software.

PubMed

Pizzonia, J

2001-06-01

The present article reports on the performance of the KODAK 1D Image Analysis Software for the acquisition of information from electrophoresis experiments and highlights the utility of several mathematical functions for subsequent image processing, analysis, and presentation. Digital images of Coomassie-stained polyacrylamide protein gels containing molecular weight standards and ethidium bromide stained agarose gels containing DNA mass standards are acquired using the KODAK Electrophoresis Documentation and Analysis System 290 (EDAS 290). The KODAK 1D software is used to optimize lane and band identification using features such as isomolecular weight lines. Mathematical functions for mass standard representation are presented, and two methods for estimation of unknown band mass are compared. Given the progressive transition of electrophoresis data acquisition and daily reporting in peer-reviewed journals to digital formats ranging from 8-bit systems such as EDAS 290 to more expensive 16-bit systems, the utility of algorithms such as Gaussian modeling, which can correct geometric aberrations such as clipping due to signal saturation common at lower bit depth levels, is discussed. Finally, image-processing tools that can facilitate image preparation for presentation are demonstrated.

Three-Dimensional Geometric Modeling of Membrane-bound Organelles in Ventricular Myocytes: Bridging the Gap between Microscopic Imaging and Mathematical Simulation

PubMed Central

Yu, Zeyun; Holst, Michael J.; Hayashi, Takeharu; Bajaj, Chandrajit L.; Ellisman, Mark H.; McCammon, J. Andrew; Hoshijima, Masahiko

2009-01-01

A general framework of image-based geometric processing is presented to bridge the gap between three-dimensional (3D) imaging that provides structural details of a biological system and mathematical simulation where high-quality surface or volumetric meshes are required. A 3D density map is processed in the order of image pre-processing (contrast enhancement and anisotropic filtering), feature extraction (boundary segmentation and skeletonization), and high-quality and realistic surface (triangular) and volumetric (tetrahedral) mesh generation. While the tool-chain described is applicable to general types of 3D imaging data, the performance is demonstrated specifically on membrane-bound organelles in ventricular myocytes that are imaged and reconstructed with electron microscopic (EM) tomography and two-photon microscopy (T-PM). Of particular interest in this study are two types of membrane-bound Ca2+-handling organelles, namely, transverse tubules (T-tubules) and junctional sarcoplasmic reticulum (jSR), both of which play an important role in regulating the excitation-contraction (E-C) coupling through dynamic Ca2+ mobilization in cardiomyocytes. PMID:18835449

Three-dimensional geometric modeling of membrane-bound organelles in ventricular myocytes: bridging the gap between microscopic imaging and mathematical simulation.

PubMed

Yu, Zeyun; Holst, Michael J; Hayashi, Takeharu; Bajaj, Chandrajit L; Ellisman, Mark H; McCammon, J Andrew; Hoshijima, Masahiko

2008-12-01

A general framework of image-based geometric processing is presented to bridge the gap between three-dimensional (3D) imaging that provides structural details of a biological system and mathematical simulation where high-quality surface or volumetric meshes are required. A 3D density map is processed in the order of image pre-processing (contrast enhancement and anisotropic filtering), feature extraction (boundary segmentation and skeletonization), and high-quality and realistic surface (triangular) and volumetric (tetrahedral) mesh generation. While the tool-chain described is applicable to general types of 3D imaging data, the performance is demonstrated specifically on membrane-bound organelles in ventricular myocytes that are imaged and reconstructed with electron microscopic (EM) tomography and two-photon microscopy (T-PM). Of particular interest in this study are two types of membrane-bound Ca(2+)-handling organelles, namely, transverse tubules (T-tubules) and junctional sarcoplasmic reticulum (jSR), both of which play an important role in regulating the excitation-contraction (E-C) coupling through dynamic Ca(2+) mobilization in cardiomyocytes.

A Weighted Difference of Anisotropic and Isotropic Total Variation Model for Image Processing

DTIC Science & Technology

2014-09-01

A WEIGHTED DIFFERENCE OF ANISOTROPIC AND ISOTROPIC TOTAL VARIATION MODEL FOR IMAGE PROCESSING YIFEI LOU∗, TIEYONG ZENG† , STANLEY OSHER‡ , AND JACK...grants DMS-0928427 and DMS-1222507. † Department of Mathematics, Hong Kong Baptist University, Kowloon Tong , Hong Kong. Email: zeng@hkbu.edu.hk. TZ is

Distinct and Overlapping Brain Areas Engaged during Value-Based, Mathematical, and Emotional Decision Processing

PubMed Central

Hsu, Chun-Wei; Goh, Joshua O. S.

2016-01-01

When comparing between the values of different choices, human beings can rely on either more cognitive processes, such as using mathematical computation, or more affective processes, such as using emotion. However, the neural correlates of how these two types of processes operate during value-based decision-making remain unclear. In this study, we investigated the extent to which neural regions engaged during value-based decision-making overlap with those engaged during mathematical and emotional processing in a within-subject manner. In a functional magnetic resonance imaging experiment, participants viewed stimuli that always consisted of numbers and emotional faces that depicted two choices. Across tasks, participants decided between the two choices based on the expected value of the numbers, a mathematical result of the numbers, or the emotional face stimuli. We found that all three tasks commonly involved various cortical areas including frontal, parietal, motor, somatosensory, and visual regions. Critically, the mathematical task shared common areas with the value but not emotion task in bilateral striatum. Although the emotion task overlapped with the value task in parietal, motor, and sensory areas, the mathematical task also evoked responses in other areas within these same cortical structures. Minimal areas were uniquely engaged for the value task apart from the other two tasks. The emotion task elicited a more expansive area of neural activity whereas value and mathematical task responses were in more focal regions. Whole-brain spatial correlation analysis showed that valuative processing engaged functional brain responses more similarly to mathematical processing than emotional processing. While decisions on expected value entail both mathematical and emotional processing regions, mathematical processes have a more prominent contribution particularly in subcortical processes. PMID:27375466

Distinct and Overlapping Brain Areas Engaged during Value-Based, Mathematical, and Emotional Decision Processing.

PubMed

Hsu, Chun-Wei; Goh, Joshua O S

2016-01-01

When comparing between the values of different choices, human beings can rely on either more cognitive processes, such as using mathematical computation, or more affective processes, such as using emotion. However, the neural correlates of how these two types of processes operate during value-based decision-making remain unclear. In this study, we investigated the extent to which neural regions engaged during value-based decision-making overlap with those engaged during mathematical and emotional processing in a within-subject manner. In a functional magnetic resonance imaging experiment, participants viewed stimuli that always consisted of numbers and emotional faces that depicted two choices. Across tasks, participants decided between the two choices based on the expected value of the numbers, a mathematical result of the numbers, or the emotional face stimuli. We found that all three tasks commonly involved various cortical areas including frontal, parietal, motor, somatosensory, and visual regions. Critically, the mathematical task shared common areas with the value but not emotion task in bilateral striatum. Although the emotion task overlapped with the value task in parietal, motor, and sensory areas, the mathematical task also evoked responses in other areas within these same cortical structures. Minimal areas were uniquely engaged for the value task apart from the other two tasks. The emotion task elicited a more expansive area of neural activity whereas value and mathematical task responses were in more focal regions. Whole-brain spatial correlation analysis showed that valuative processing engaged functional brain responses more similarly to mathematical processing than emotional processing. While decisions on expected value entail both mathematical and emotional processing regions, mathematical processes have a more prominent contribution particularly in subcortical processes.

The semantic system is involved in mathematical problem solving.

PubMed

Zhou, Xinlin; Li, Mengyi; Li, Leinian; Zhang, Yiyun; Cui, Jiaxin; Liu, Jie; Chen, Chuansheng

2018-02-01

Numerous studies have shown that the brain regions around bilateral intraparietal cortex are critical for number processing and arithmetical computation. However, the neural circuits for more advanced mathematics such as mathematical problem solving (with little routine arithmetical computation) remain unclear. Using functional magnetic resonance imaging (fMRI), this study (N = 24 undergraduate students) compared neural bases of mathematical problem solving (i.e., number series completion, mathematical word problem solving, and geometric problem solving) and arithmetical computation. Direct subject- and item-wise comparisons revealed that mathematical problem solving typically had greater activation than arithmetical computation in all 7 regions of the semantic system (which was based on a meta-analysis of 120 functional neuroimaging studies on semantic processing). Arithmetical computation typically had greater activation in the supplementary motor area and left precentral gyrus. The results suggest that the semantic system in the brain supports mathematical problem solving. Copyright © 2017 Elsevier Inc. All rights reserved.

Statistical Smoothing Methods and Image Analysis

DTIC Science & Technology

1988-12-01

83 - 111. Rosenfeld, A. and Kak, A.C. (1982). Digital Picture Processing. Academic Press,Qrlando. Serra, J. (1982). Image Analysis and Mat hematical ...hypothesis testing. IEEE Trans. Med. Imaging, MI-6, 313-319. Wicksell, S.D. (1925) The corpuscle problem. A mathematical study of a biometric problem

Theoretical foundations of spatially-variant mathematical morphology part ii: gray-level images.

PubMed

Bouaynaya, Nidhal; Schonfeld, Dan

2008-05-01

In this paper, we develop a spatially-variant (SV) mathematical morphology theory for gray-level signals and images in the Euclidean space. The proposed theory preserves the geometrical concept of the structuring function, which provides the foundation of classical morphology and is essential in signal and image processing applications. We define the basic SV gray-level morphological operators (i.e., SV gray-level erosion, dilation, opening, and closing) and investigate their properties. We demonstrate the ubiquity of SV gray-level morphological systems by deriving a kernel representation for a large class of systems, called V-systems, in terms of the basic SV graylevel morphological operators. A V-system is defined to be a gray-level operator, which is invariant under gray-level (vertical) translations. Particular attention is focused on the class of SV flat gray-level operators. The kernel representation for increasing V-systems is a generalization of Maragos' kernel representation for increasing and translation-invariant function-processing systems. A representation of V-systems in terms of their kernel elements is established for increasing and upper-semi-continuous V-systems. This representation unifies a large class of spatially-variant linear and non-linear systems under the same mathematical framework. Finally, simulation results show the potential power of the general theory of gray-level spatially-variant mathematical morphology in several image analysis and computer vision applications.

Applications in Digital Image Processing

ERIC Educational Resources Information Center

Silverman, Jason; Rosen, Gail L.; Essinger, Steve

2013-01-01

Students are immersed in a mathematically intensive, technological world. They engage daily with iPods, HDTVs, and smartphones--technological devices that rely on sophisticated but accessible mathematical ideas. In this article, the authors provide an overview of four lab-type activities that have been used successfully in high school mathematics…

Infrared image enhancement based on the edge detection and mathematical morphology

NASA Astrophysics Data System (ADS)

Zhang, Linlin; Zhao, Yuejin; Dong, Liquan; Liu, Xiaohua; Yu, Xiaomei; Hui, Mei; Chu, Xuhong; Gong, Cheng

2010-11-01

The development of the un-cooled infrared imaging technology from military necessity. At present, It is widely applied in industrial, medicine, scientific and technological research and so on. The infrared radiation temperature distribution of the measured object's surface can be observed visually. The collection of infrared images from our laboratory has following characteristics: Strong spatial correlation, Low contrast , Poor visual effect; Without color or shadows because of gray image , and has low resolution; Low definition compare to the visible light image; Many kinds of noise are brought by the random disturbances of the external environment. Digital image processing are widely applied in many areas, it can now be studied up close and in detail in many research field. It has become one kind of important means of the human visual continuation. Traditional methods for image enhancement cannot capture the geometric information of images and tend to amplify noise. In order to remove noise and improve visual effect. Meanwhile, To overcome the above enhancement issues. The mathematical model of FPA unit was constructed based on matrix transformation theory. According to characteristics of FPA, Image enhancement algorithm which combined with mathematical morphology and edge detection are established. First of all, Image profile is obtained by using the edge detection combine with mathematical morphological operators. And then, through filling the template profile by original image to get the ideal background image, The image noise can be removed on the base of the above method. The experiments show that utilizing the proposed algorithm can enhance image detail and the signal to noise ratio.

The Goddard Profiling Algorithm (GPROF): Description and Current Applications

NASA Technical Reports Server (NTRS)

Olson, William S.; Yang, Song; Stout, John E.; Grecu, Mircea

2004-01-01

Atmospheric scientists use different methods for interpreting satellite data. In the early days of satellite meteorology, the analysis of cloud pictures from satellites was primarily subjective. As computer technology improved, satellite pictures could be processed digitally, and mathematical algorithms were developed and applied to the digital images in different wavelength bands to extract information about the atmosphere in an objective way. The kind of mathematical algorithm one applies to satellite data may depend on the complexity of the physical processes that lead to the observed image, and how much information is contained in the satellite images both spatially and at different wavelengths. Imagery from satellite-borne passive microwave radiometers has limited horizontal resolution, and the observed microwave radiances are the result of complex physical processes that are not easily modeled. For this reason, a type of algorithm called a Bayesian estimation method is utilized to interpret passive microwave imagery in an objective, yet computationally efficient manner.

A Method for Identifying Contours in Processing Digital Images from Computer Tomograph

NASA Astrophysics Data System (ADS)

Roşu, Şerban; Pater, Flavius; Costea, Dan; Munteanu, Mihnea; Roşu, Doina; Fratila, Mihaela

2011-09-01

The first step in digital processing of two-dimensional computed tomography images is to identify the contour of component elements. This paper deals with the collective work of specialists in medicine and applied mathematics in computer science on elaborating new algorithms and methods in medical 2D and 3D imagery.

Image processing and reconstruction

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

Chartrand, Rick

2012-06-15

This talk will examine some mathematical methods for image processing and the solution of underdetermined, linear inverse problems. The talk will have a tutorial flavor, mostly accessible to undergraduates, while still presenting research results. The primary approach is the use of optimization problems. We will find that relaxing the usual assumption of convexity will give us much better results.

The Image of Mathematics Held by Irish Post-Primary Students

ERIC Educational Resources Information Center

Lane, Ciara; Stynes, Martin; O'Donoghue, John

2014-01-01

The image of mathematics held by Irish post-primary students was examined and a model for the image found was constructed. Initially, a definition for "image of mathematics" was adopted with image of mathematics hypothesized as comprising attitudes, beliefs, self-concept, motivation, emotions and past experiences of mathematics. Research…

Basic research planning in mathematical pattern recognition and image analysis

NASA Technical Reports Server (NTRS)

Bryant, J.; Guseman, L. F., Jr.

1981-01-01

Fundamental problems encountered while attempting to develop automated techniques for applications of remote sensing are discussed under the following categories: (1) geometric and radiometric preprocessing; (2) spatial, spectral, temporal, syntactic, and ancillary digital image representation; (3) image partitioning, proportion estimation, and error models in object scene interference; (4) parallel processing and image data structures; and (5) continuing studies in polarization; computer architectures and parallel processing; and the applicability of "expert systems" to interactive analysis.

Introducing Seismic Tomography with Computational Modeling

NASA Astrophysics Data System (ADS)

Neves, R.; Neves, M. L.; Teodoro, V.

2011-12-01

Learning seismic tomography principles and techniques involves advanced physical and computational knowledge. In depth learning of such computational skills is a difficult cognitive process that requires a strong background in physics, mathematics and computer programming. The corresponding learning environments and pedagogic methodologies should then involve sets of computational modelling activities with computer software systems which allow students the possibility to improve their mathematical or programming knowledge and simultaneously focus on the learning of seismic wave propagation and inverse theory. To reduce the level of cognitive opacity associated with mathematical or programming knowledge, several computer modelling systems have already been developed (Neves & Teodoro, 2010). Among such systems, Modellus is particularly well suited to achieve this goal because it is a domain general environment for explorative and expressive modelling with the following main advantages: 1) an easy and intuitive creation of mathematical models using just standard mathematical notation; 2) the simultaneous exploration of images, tables, graphs and object animations; 3) the attribution of mathematical properties expressed in the models to animated objects; and finally 4) the computation and display of mathematical quantities obtained from the analysis of images and graphs. Here we describe virtual simulations and educational exercises which enable students an easy grasp of the fundamental of seismic tomography. The simulations make the lecture more interactive and allow students the possibility to overcome their lack of advanced mathematical or programming knowledge and focus on the learning of seismological concepts and processes taking advantage of basic scientific computation methods and tools.

Neural mechanisms of the mind, Aristotle, Zadeh, and fMRI.

PubMed

Perlovsky, Leonid I

2010-05-01

Processes in the mind: perception, cognition, concepts, instincts, emotions, and higher cognitive abilities for abstract thinking, beautiful music are considered here within a neural modeling fields (NMFs) paradigm. Its fundamental mathematical mechanism is a process "from vague-fuzzy to crisp," called dynamic logic (DL). This paper discusses why this paradigm is necessary mathematically, and relates it to a psychological description of the mind. Surprisingly, the process from "vague to crisp" corresponds to Aristotelian understanding of mental functioning. Recent functional magnetic resonance imaging (fMRI) measurements confirmed this process in neural mechanisms of perception.

Teaching Image-Processing Concepts in Junior High School: Boys' and Girls' Achievements and Attitudes towards Technology

ERIC Educational Resources Information Center

Barak, Moshe; Asad, Khaled

2012-01-01

Background: This research focused on the development, implementation and evaluation of a course on image-processing principles aimed at middle-school students. Purpose: The overarching purpose of the study was that of integrating the learning of subjects in science, technology, engineering and mathematics (STEM), and linking the learning of these…

CT Imaging, Data Reduction, and Visualization of Hardwood Logs

Treesearch

Daniel L. Schmoldt

1996-01-01

Computer tomography (CT) is a mathematical technique that, combined with noninvasive scanning such as x-ray imaging, has become a powerful tool to nondestructively test materials prior to use or to evaluate materials prior to processing. In the current context, hardwood lumber processing can benefit greatly by knowing what a log looks like prior to initial breakdown....

Stochastic processes, estimation theory and image enhancement

NASA Technical Reports Server (NTRS)

Assefi, T.

1978-01-01

An introductory account of stochastic processes, estimation theory, and image enhancement is presented. The book is primarily intended for first-year graduate students and practicing engineers and scientists whose work requires an acquaintance with the theory. Fundamental concepts of probability were reviewed that are required to support the main topics. The appendices discuss the remaining mathematical background.

Analysis of contour images using optics of spiral beams

NASA Astrophysics Data System (ADS)

Volostnikov, V. G.; Kishkin, S. A.; Kotova, S. P.

2018-03-01

An approach is outlined to the recognition of contour images using computer technology based on coherent optics principles. A mathematical description of the recognition process algorithm and the results of numerical modelling are presented. The developed approach to the recognition of contour images using optics of spiral beams is described and justified.

Image analysis and mathematical modelling for the supervision of the dough fermentation process

NASA Astrophysics Data System (ADS)

Zettel, Viktoria; Paquet-Durand, Olivier; Hecker, Florian; Hitzmann, Bernd

2016-10-01

The fermentation (proof) process of dough is one of the quality-determining steps in the production of baking goods. Beside the fluffiness, whose fundaments are built during fermentation, the flavour of the final product is influenced very much during this production stage. However, until now no on-line measurement system is available, which can supervise this important process step. In this investigation the potential of an image analysis system is evaluated, that enables the determination of the volume of fermented dough pieces. The camera is moving around the fermenting pieces and collects images from the objects by means of different angles (360° range). Using image analysis algorithms the volume increase of individual dough pieces is determined. Based on a detailed mathematical description of the volume increase, which based on the Bernoulli equation, carbon dioxide production rate of yeast cells and the diffusion processes of carbon dioxide, the fermentation process is supervised. Important process parameters, like the carbon dioxide production rate of the yeast cells and the dough viscosity can be estimated just after 300 s of proofing. The mean percentage error for forecasting the further evolution of the relative volume of the dough pieces is just 2.3 %. Therefore, a forecast of the further evolution can be performed and used for fault detection.

A low-cost vector processor boosting compute-intensive image processing operations

NASA Technical Reports Server (NTRS)

Adorf, Hans-Martin

1992-01-01

Low-cost vector processing (VP) is within reach of everyone seriously engaged in scientific computing. The advent of affordable add-on VP-boards for standard workstations complemented by mathematical/statistical libraries is beginning to impact compute-intensive tasks such as image processing. A case in point in the restoration of distorted images from the Hubble Space Telescope. A low-cost implementation is presented of the standard Tarasko-Richardson-Lucy restoration algorithm on an Intel i860-based VP-board which is seamlessly interfaced to a commercial, interactive image processing system. First experience is reported (including some benchmarks for standalone FFT's) and some conclusions are drawn.

Numerical image manipulation and display in solar astronomy

NASA Technical Reports Server (NTRS)

Levine, R. H.; Flagg, J. C.

1977-01-01

The paper describes the system configuration and data manipulation capabilities of a solar image display system which allows interactive analysis of visual images and on-line manipulation of digital data. Image processing features include smoothing or filtering of images stored in the display, contrast enhancement, and blinking or flickering images. A computer with a core memory of 28,672 words provides the capacity to perform complex calculations based on stored images, including computing histograms, selecting subsets of images for further analysis, combining portions of images to produce images with physical meaning, and constructing mathematical models of features in an image. Some of the processing modes are illustrated by some image sequences from solar observations.

Spatial/Spectral Identification of Endmembers from AVIRIS Data using Mathematical Morphology

NASA Technical Reports Server (NTRS)

Plaza, Antonio; Martinez, Pablo; Gualtieri, J. Anthony; Perez, Rosa M.

2001-01-01

During the last several years, a number of airborne and satellite hyperspectral sensors have been developed or improved for remote sensing applications. Imaging spectrometry allows the detection of materials, objects and regions in a particular scene with a high degree of accuracy. Hyperspectral data typically consist of hundreds of thousands of spectra, so the analysis of this information is a key issue. Mathematical morphology theory is a widely used nonlinear technique for image analysis and pattern recognition. Although it is especially well suited to segment binary or grayscale images with irregular and complex shapes, its application in the classification/segmentation of multispectral or hyperspectral images has been quite rare. In this paper, we discuss a new completely automated methodology to find endmembers in the hyperspectral data cube using mathematical morphology. The extension of classic morphology to the hyperspectral domain allows us to integrate spectral and spatial information in the analysis process. In Section 3, some basic concepts about mathematical morphology and the technical details of our algorithm are provided. In Section 4, the accuracy of the proposed method is tested by its application to real hyperspectral data obtained from the Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) imaging spectrometer. Some details about these data and reference results, obtained by well-known endmember extraction techniques, are provided in Section 2. Finally, in Section 5 we expose the main conclusions at which we have arrived.

Measuring Leaf Area in Soy Plants by HSI Color Model Filtering and Mathematical Morphology

NASA Astrophysics Data System (ADS)

Benalcázar, M.; Padín, J.; Brun, M.; Pastore, J.; Ballarin, V.; Peirone, L.; Pereyra, G.

2011-12-01

There has been lately a significant progress in automating tasks for the agricultural sector. One of the advances is the development of robots, based on computer vision, applied to care and management of soy crops. In this task, digital image processing plays an important role, but must solve some important problems, like the ones associated to the variations in lighting conditions during image acquisition. Such variations influence directly on the brightness level of the images to be processed. In this paper we propose an algorithm to segment and measure automatically the leaf area of soy plants. This information is used by the specialists to evaluate and compare the growth of different soy genotypes. This algorithm, based on color filtering using the HSI model, detects green objects from the image background. The segmentation of leaves (foliage) was made applying Mathematical Morphology. The foliage area was estimated counting the pixels that belong to the segmented leaves. From several experiments, consisting in applying the algorithm to measure the foliage of about fifty plants of various genotypes of soy, at different growth stages, we obtained successful results, despite the high brightness variations and shadows in the processed images.

An interdisciplinary collaboration between computer engineering and mathematics/bilingual education to develop a curriculum for underrepresented middle school students

NASA Astrophysics Data System (ADS)

Celedón-Pattichis, Sylvia; LópezLeiva, Carlos Alfonso; Pattichis, Marios S.; Llamocca, Daniel

2013-12-01

There is a strong need in the United States to increase the number of students from underrepresented groups who pursue careers in Science, Technology, Engineering, and Mathematics. Drawing from sociocultural theory, we present approaches to establishing collaborations between computer engineering and mathematics/bilingual education faculty to address this need. We describe our work through the Advancing Out-of-School Learning in Mathematics and Engineering project by illustrating how an integrated curriculum that is based on mathematics with applications in image and video processing can be designed and how it can be implemented with middle school students from underrepresented groups.

Vision, healing brush, and fiber bundles

NASA Astrophysics Data System (ADS)

Georgiev, Todor

2005-03-01

The Healing Brush is a tool introduced for the first time in Adobe Photoshop (2002) that removes defects in images by seamless cloning (gradient domain fusion). The Healing Brush algorithms are built on a new mathematical approach that uses Fibre Bundles and Connections to model the representation of images in the visual system. Our mathematical results are derived from first principles of human vision, related to adaptation transforms of von Kries type and Retinex theory. In this paper we present the new result of Healing in arbitrary color space. In addition to supporting image repair and seamless cloning, our approach also produces the exact solution to the problem of high dynamic range compression of17 and can be applied to other image processing algorithms.

3D digital image processing for biofilm quantification from confocal laser scanning microscopy: Multidimensional statistical analysis of biofilm modeling

NASA Astrophysics Data System (ADS)

Zielinski, Jerzy S.

The dramatic increase in number and volume of digital images produced in medical diagnostics, and the escalating demand for rapid access to these relevant medical data, along with the need for interpretation and retrieval has become of paramount importance to a modern healthcare system. Therefore, there is an ever growing need for processed, interpreted and saved images of various types. Due to the high cost and unreliability of human-dependent image analysis, it is necessary to develop an automated method for feature extraction, using sophisticated mathematical algorithms and reasoning. This work is focused on digital image signal processing of biological and biomedical data in one- two- and three-dimensional space. Methods and algorithms presented in this work were used to acquire data from genomic sequences, breast cancer, and biofilm images. One-dimensional analysis was applied to DNA sequences which were presented as a non-stationary sequence and modeled by a time-dependent autoregressive moving average (TD-ARMA) model. Two-dimensional analyses used 2D-ARMA model and applied it to detect breast cancer from x-ray mammograms or ultrasound images. Three-dimensional detection and classification techniques were applied to biofilm images acquired using confocal laser scanning microscopy. Modern medical images are geometrically arranged arrays of data. The broadening scope of imaging as a way to organize our observations of the biophysical world has led to a dramatic increase in our ability to apply new processing techniques and to combine multiple channels of data into sophisticated and complex mathematical models of physiological function and dysfunction. With explosion of the amount of data produced in a field of biomedicine, it is crucial to be able to construct accurate mathematical models of the data at hand. Two main purposes of signal modeling are: data size conservation and parameter extraction. Specifically, in biomedical imaging we have four key problems that were addressed in this work: (i) registration, i.e. automated methods of data acquisition and the ability to align multiple data sets with each other; (ii) visualization and reconstruction, i.e. the environment in which registered data sets can be displayed on a plane or in multidimensional space; (iii) segmentation, i.e. automated and semi-automated methods to create models of relevant anatomy from images; (iv) simulation and prediction, i.e. techniques that can be used to simulate growth end evolution of researched phenomenon. Mathematical models can not only be used to verify experimental findings, but also to make qualitative and quantitative predictions, that might serve as guidelines for the future development of technology and/or treatment.

Designing Image Analysis Pipelines in Light Microscopy: A Rational Approach.

PubMed

Arganda-Carreras, Ignacio; Andrey, Philippe

2017-01-01

With the progress of microscopy techniques and the rapidly growing amounts of acquired imaging data, there is an increased need for automated image processing and analysis solutions in biological studies. Each new application requires the design of a specific image analysis pipeline, by assembling a series of image processing operations. Many commercial or free bioimage analysis software are now available and several textbooks and reviews have presented the mathematical and computational fundamentals of image processing and analysis. Tens, if not hundreds, of algorithms and methods have been developed and integrated into image analysis software, resulting in a combinatorial explosion of possible image processing sequences. This paper presents a general guideline methodology to rationally address the design of image processing and analysis pipelines. The originality of the proposed approach is to follow an iterative, backwards procedure from the target objectives of analysis. The proposed goal-oriented strategy should help biologists to better apprehend image analysis in the context of their research and should allow them to efficiently interact with image processing specialists.

Geometric correction of synchronous scanned Operational Modular Imaging Spectrometer II hyperspectral remote sensing images using spatial positioning data of an inertial navigation system

NASA Astrophysics Data System (ADS)

Zhou, Xiaohu; Neubauer, Franz; Zhao, Dong; Xu, Shichao

2015-01-01

The high-precision geometric correction of airborne hyperspectral remote sensing image processing was a hard nut to crack, and conventional methods of remote sensing image processing by selecting ground control points to correct the images are not suitable in the correction process of airborne hyperspectral image. The optical scanning system of an inertial measurement unit combined with differential global positioning system (IMU/DGPS) is introduced to correct the synchronous scanned Operational Modular Imaging Spectrometer II (OMIS II) hyperspectral remote sensing images. Posture parameters, which were synchronized with the OMIS II, were first obtained from the IMU/DGPS. Second, coordinate conversion and flight attitude parameters' calculations were conducted. Third, according to the imaging principle of OMIS II, mathematical correction was applied and the corrected image pixels were resampled. Then, better image processing results were achieved.

New method of contour image processing based on the formalism of spiral light beams

NASA Astrophysics Data System (ADS)

Volostnikov, Vladimir G.; Kishkin, S. A.; Kotova, S. P.

2013-07-01

The possibility of applying the mathematical formalism of spiral light beams to the problems of contour image recognition is theoretically studied. The advantages and disadvantages of the proposed approach are evaluated; the results of numerical modelling are presented.

Cognitive and Neural Correlates of Mathematical Giftedness in Adults and Children: A Review

PubMed Central

Myers, Timothy; Carey, Emma; Szűcs, Dénes

2017-01-01

Most mathematical cognition research has focused on understanding normal adult function and child development as well as mildly and moderately impaired mathematical skill, often labeled developmental dyscalculia and/or mathematical learning disability. In contrast, much less research is available on cognitive and neural correlates of gifted/excellent mathematical knowledge in adults and children. In order to facilitate further inquiry into this area, here we review 40 available studies, which examine the cognitive and neural basis of gifted mathematics. Studies associated a large number of cognitive factors with gifted mathematics, with spatial processing and working memory being the most frequently identified contributors. However, the current literature suffers from low statistical power, which most probably contributes to variability across findings. Other major shortcomings include failing to establish domain and stimulus specificity of findings, suggesting causation without sufficient evidence and the frequent use of invalid backward inference in neuro-imaging studies. Future studies must increase statistical power and neuro-imaging studies must rely on supporting behavioral data when interpreting findings. Studies should investigate the factors shown to correlate with math giftedness in a more specific manner and determine exactly how individual factors may contribute to gifted math ability. PMID:29118725

Images, Anxieties, and Attitudes toward Mathematics

ERIC Educational Resources Information Center

Belbase, Shashidhar

2013-01-01

The purpose of this paper is to discuss and analyze images, anxieties, and attitudes towards mathematics in order to foster meaningful teaching and learning of mathematics. Images of mathematics seem to be profoundly shaped by epistemological, philosophical, and pedagogical perspectives of one who views mathematics either as priori or a…

Imaging Heterogeneity in Lung Cancer: Techniques, Applications, and Challenges.

PubMed

Bashir, Usman; Siddique, Muhammad Musib; Mclean, Emma; Goh, Vicky; Cook, Gary J

2016-09-01

Texture analysis involves the mathematic processing of medical images to derive sets of numeric quantities that measure heterogeneity. Studies on lung cancer have shown that texture analysis may have a role in characterizing tumors and predicting patient outcome. This article outlines the mathematic basis of and the most recent literature on texture analysis in lung cancer imaging. We also describe the challenges facing the clinical implementation of texture analysis. Texture analysis of lung cancer images has been applied successfully to FDG PET and CT scans. Different texture parameters have been shown to be predictive of the nature of disease and of patient outcome. In general, it appears that more heterogeneous tumors on imaging tend to be more aggressive and to be associated with poorer outcomes and that tumor heterogeneity on imaging decreases with treatment. Despite these promising results, there is a large variation in the reported data and strengths of association.

The image of mathematics held by Irish post-primary students

NASA Astrophysics Data System (ADS)

Lane, Ciara; Stynes, Martin; O'Donoghue, John

2014-08-01

The image of mathematics held by Irish post-primary students was examined and a model for the image found was constructed. Initially, a definition for 'image of mathematics' was adopted with image of mathematics hypothesized as comprising attitudes, beliefs, self-concept, motivation, emotions and past experiences of mathematics. Research focused on students studying ordinary level mathematics for the Irish Leaving Certificate examination - the final examination for students in second-level or post-primary education. Students were aged between 15 and 18 years. A questionnaire was constructed with both quantitative and qualitative aspects. The questionnaire survey was completed by 356 post-primary students. Responses were analysed quantitatively using Statistical Package for the Social Sciences (SPSS) and qualitatively using the constant comparative method of analysis and by reviewing individual responses. Findings provide an insight into Irish post-primary students' images of mathematics and offer a means for constructing a theoretical model of image of mathematics which could be beneficial for future research.

Mathematical model of a DIC position sensing system within an optical trap

NASA Astrophysics Data System (ADS)

Wulff, Kurt D.; Cole, Daniel G.; Clark, Robert L.

2005-08-01

The quantitative study of displacements and forces of motor proteins and processes that occur at the microscopic level and below require a high level of sensitivity. For optical traps, two techniques for position sensing have been accepted and used quite extensively: quadrant photodiodes and an interferometric position sensing technique based on DIC imaging. While quadrant photodiodes have been studied in depth and mathematically characterized, a mathematical characterization of the interferometric position sensor has not been presented to the authors' knowledge. The interferometric position sensing method works off of the DIC imaging capabilities of a microscope. Circularly polarized light is sent into the microscope and the Wollaston prism used for DIC imaging splits the beam into its orthogonal components, displacing them by a set distance determined by the user. The distance between the axes of the beams is set so the beams overlap at the specimen plane and effectively share the trapped microsphere. A second prism then recombines the light beams and the exiting laser light's polarization is measured and related to position. In this paper we outline the mathematical characterization of a microsphere suspended in an optical trap using a DIC position sensing method. The sensitivity of this mathematical model is then compared to the QPD model. The mathematical model of a microsphere in an optical trap can serve as a calibration curve for an experimental setup.

3-D characterization of weathered building limestones by high resolution synchrotron X-ray microtomography.

PubMed

Rozenbaum, O

2011-04-15

Understanding the weathering processes of building stones and more generally of their transfer properties requires detailed knowledge of the porosity characteristics. This study aims at analyzing three-dimensional images obtained by X-ray microtomography of building stones. In order to validate these new results a weathered limestone previously characterised (Rozenbaum et al., 2007) by two-dimensional image analysis was selected. The 3-D images were analysed by a set of mathematical tools that enable the description of the pore and solid phase distribution. Results show that 3-D image analysis is a powerful technique to characterise the morphological, structural and topological differences due to weathering. The paper also discusses criteria for mathematically determining whether a stone is weathered or not. Copyright © 2011 Elsevier B.V. All rights reserved.

Information, entropy, and fidelity in visual communication

NASA Astrophysics Data System (ADS)

Huck, Friedrich O.; Fales, Carl L.; Alter-Gartenberg, Rachel; Rahman, Zia-ur

1992-10-01

This paper presents an assessment of visual communication that integrates the critical limiting factors of image gathering an display with the digital processing that is used to code and restore images. The approach focuses on two mathematical criteria, information and fidelity, and on their relationships to the entropy of the encoded data and to the visual quality of the restored image.

Information, entropy and fidelity in visual communication

NASA Technical Reports Server (NTRS)

Huck, Friedrich O.; Fales, Carl L.; Alter-Gartenberg, Rachel; Rahman, Zia-Ur

1992-01-01

This paper presents an assessment of visual communication that integrates the critical limiting factors of image gathering and display with the digital processing that is used to code and restore images. The approach focuses on two mathematical criteria, information and fidelity, and on their relationships to the entropy of the encoded data and to the visual quality of the restored image.

A preference for mathematical processing outweighs the selectivity for Arabic numbers in the inferior temporal gyrus.

PubMed

Grotheer, Mareike; Jeska, Brianna; Grill-Spector, Kalanit

2018-03-28

A region in the posterior inferior temporal gyrus (ITG), referred to as the number form area (NFA, here ITG-numbers) has been implicated in the visual processing of Arabic numbers. However, it is unknown if this region is specifically involved in the visual encoding of Arabic numbers per se or in mathematical processing more broadly. Using functional magnetic resonance imaging (fMRI) during experiments that systematically vary tasks and stimuli, we find that mathematical processing, not preference to Arabic numbers, consistently drives both mean and distributed responses in the posterior ITG. While we replicated findings of higher responses in ITG-numbers to numbers than other visual stimuli during a 1-back task, this preference to numbers was abolished when participants engaged in mathematical processing. In contrast, an ITG region (ITG-math) that showed higher responses during an adding task vs. other tasks maintained this preference for mathematical processing across a wide range of stimuli including numbers, number/letter morphs, hands, and dice. Analysis of distributed responses across an anatomically-defined posterior ITG expanse further revealed that mathematical task but not Arabic number form can be successfully and consistently decoded from these distributed responses. Together, our findings suggest that the function of neuronal regions in the posterior ITG goes beyond the specific visual processing of Arabic numbers. We hypothesize that they ascribe numerical content to the visual input, irrespective of the format of the stimulus. Copyright © 2018 Elsevier Inc. All rights reserved.

A Review of Tensors and Tensor Signal Processing

NASA Astrophysics Data System (ADS)

Cammoun, L.; Castaño-Moraga, C. A.; Muñoz-Moreno, E.; Sosa-Cabrera, D.; Acar, B.; Rodriguez-Florido, M. A.; Brun, A.; Knutsson, H.; Thiran, J. P.

Tensors have been broadly used in mathematics and physics, since they are a generalization of scalars or vectors and allow to represent more complex properties. In this chapter we present an overview of some tensor applications, especially those focused on the image processing field. From a mathematical point of view, a lot of work has been developed about tensor calculus, which obviously is more complex than scalar or vectorial calculus. Moreover, tensors can represent the metric of a vector space, which is very useful in the field of differential geometry. In physics, tensors have been used to describe several magnitudes, such as the strain or stress of materials. In solid mechanics, tensors are used to define the generalized Hooke’s law, where a fourth order tensor relates the strain and stress tensors. In fluid dynamics, the velocity gradient tensor provides information about the vorticity and the strain of the fluids. Also an electromagnetic tensor is defined, that simplifies the notation of the Maxwell equations. But tensors are not constrained to physics and mathematics. They have been used, for instance, in medical imaging, where we can highlight two applications: the diffusion tensor image, which represents how molecules diffuse inside the tissues and is broadly used for brain imaging; and the tensorial elastography, which computes the strain and vorticity tensor to analyze the tissues properties. Tensors have also been used in computer vision to provide information about the local structure or to define anisotropic image filters.

The Mathematics of Four or More N-Localizers for Stereotactic Neurosurgery.

PubMed

Brown, Russell A

2015-10-13

The mathematics that were originally developed for the N-localizer apply to three N-localizers that produce three sets of fiducials in a tomographic image. Some applications of the N-localizer use four N-localizers that produce four sets of fiducials; however, the mathematics that apply to three sets of fiducials do not apply to four sets of fiducials. This article presents mathematics that apply to four or more sets of fiducials that all lie within one planar tomographic image. In addition, these mathematics are extended to apply to four or more fiducials that do not all lie within one planar tomographic image, as may be the case with magnetic resonance (MR) imaging where a volume is imaged instead of a series of planar tomographic images. Whether applied to a planar image or a volume image, the mathematics of four or more N-localizers provide a statistical measure of the quality of the image data that may be influenced by factors, such as the nonlinear distortion of MR images.

Hierarchical Heteroclinics in Dynamical Model of Cognitive Processes: Chunking

NASA Astrophysics Data System (ADS)

Afraimovich, Valentin S.; Young, Todd R.; Rabinovich, Mikhail I.

Combining the results of brain imaging and nonlinear dynamics provides a new hierarchical vision of brain network functionality that is helpful in understanding the relationship of the network to different mental tasks. Using these ideas it is possible to build adequate models for the description and prediction of different cognitive activities in which the number of variables is usually small enough for analysis. The dynamical images of different mental processes depend on their temporal organization and, as a rule, cannot be just simple attractors since cognition is characterized by transient dynamics. The mathematical image for a robust transient is a stable heteroclinic channel consisting of a chain of saddles connected by unstable separatrices. We focus here on hierarchical chunking dynamics that can represent several cognitive activities. Chunking is the dynamical phenomenon that means dividing a long information chain into shorter items. Chunking is known to be important in many processes of perception, learning, memory and cognition. We prove that in the phase space of the model that describes chunking there exists a new mathematical object — heteroclinic sequence of heteroclinic cycles — using the technique of slow-fast approximations. This new object serves as a skeleton of motions reflecting sequential features of hierarchical chunking dynamics and is an adequate image of the chunking processing.

Rank-based decompositions of morphological templates.

PubMed

Sussner, P; Ritter, G X

2000-01-01

Methods for matrix decomposition have found numerous applications in image processing, in particular for the problem of template decomposition. Since existing matrix decomposition techniques are mainly concerned with the linear domain, we consider it timely to investigate matrix decomposition techniques in the nonlinear domain with applications in image processing. The mathematical basis for these investigations is the new theory of rank within minimax algebra. Thus far, only minimax decompositions of rank 1 and rank 2 matrices into outer product expansions are known to the image processing community. We derive a heuristic algorithm for the decomposition of matrices having arbitrary rank.

Mathematical methods in medicine: neuroscience, cardiology and pathology

PubMed Central

Amigó, José M.

2017-01-01

The application of mathematics, natural sciences and engineering to medicine is gaining momentum as the mutual benefits of this collaboration become increasingly obvious. This theme issue is intended to highlight the trend in the case of mathematics. Specifically, the scope of this theme issue is to give a general view of the current research in the application of mathematical methods to medicine, as well as to show how mathematics can help in such important aspects as understanding, prediction, treatment and data processing. To this end, three representative specialties have been selected: neuroscience, cardiology and pathology. Concerning the topics, the 12 research papers and one review included in this issue cover biofluids, cardiac and virus dynamics, computational neuroscience, functional magnetic resonance imaging data processing, neural networks, optimization of treatment strategies, time-series analysis and tumour growth. In conclusion, this theme issue contains a collection of fine contributions at the intersection of mathematics and medicine, not as an exercise in applied mathematics but as a multidisciplinary research effort that interests both communities and our society in general. This article is part of the themed issue ‘Mathematical methods in medicine: neuroscience, cardiology and pathology’. PMID:28507240

Mathematical methods in medicine: neuroscience, cardiology and pathology.

PubMed

Amigó, José M; Small, Michael

2017-06-28

The application of mathematics, natural sciences and engineering to medicine is gaining momentum as the mutual benefits of this collaboration become increasingly obvious. This theme issue is intended to highlight the trend in the case of mathematics. Specifically, the scope of this theme issue is to give a general view of the current research in the application of mathematical methods to medicine, as well as to show how mathematics can help in such important aspects as understanding, prediction, treatment and data processing. To this end, three representative specialties have been selected: neuroscience, cardiology and pathology. Concerning the topics, the 12 research papers and one review included in this issue cover biofluids, cardiac and virus dynamics, computational neuroscience, functional magnetic resonance imaging data processing, neural networks, optimization of treatment strategies, time-series analysis and tumour growth. In conclusion, this theme issue contains a collection of fine contributions at the intersection of mathematics and medicine, not as an exercise in applied mathematics but as a multidisciplinary research effort that interests both communities and our society in general.This article is part of the themed issue 'Mathematical methods in medicine: neuroscience, cardiology and pathology'. © 2017 The Author(s).

The Fall of Parity.

ERIC Educational Resources Information Center

Forman, Paul

1982-01-01

Physicists had assumed that the world is distinguishable from its mirror image and constructed theories to ensure that the corresponding mathematical property (parity) is conserved in all subatomic processes. However, a scientific experiment demonstrated an intrinsic handedness to at least one physical process. The experiment, equipment, and…

Software and mathematical support of Kazakhstani star tracker

NASA Astrophysics Data System (ADS)

Akhmedov, D.; Yelubayev, S.; Ten, V.; Bopeyev, T.; Alipbayev, K.; Sukhenko, A.

2016-10-01

Currently the specialists of Kazakhstan have been developing the star tracker that is further planned to use on Kazakhstani satellites of various purposes. At the first stage it has been developed the experimental model of star tracker that has following characteristics: field of view 20°, update frequency 2 Hz, exclusion angle 40°, accuracy of attitude determination of optical axis/around optical axis 15/50 arcsec. Software and mathematical support are the most high technology parts of star tracker. The results of software and mathematical support development of experimental model of Kazakhstani star tracker are represented in this article. In particular, there are described the main mathematical models and algorithms that have been used as a basis for program units of preliminary image processing of starry sky, stars identification and star tracker attitude determination. The results of software and mathematical support testing with the help of program simulation complex using various configurations of defects including image sensor noises, point spread function modeling, optical system distortion up to 2% are presented. Analysis of testing results has shown that accuracy of attitude determination of star tracker is within the permissible range

Investigating Teachers' Images of Mathematics

ERIC Educational Resources Information Center

Sterenberg, Gladys

2008-01-01

Research suggests that understanding new images of mathematics is very challenging and can contribute to teacher resistance. An explicit exploration of personal views of mathematics may be necessary for pedagogical change. One possible way for exploring these images is through mathematical metaphors. As metaphors focus on similarities, they can be…

Promise of new imaging technologies for assessing ovarian function.

PubMed

Singh, Jaswant; Adams, Gregg P; Pierson, Roger A

2003-10-15

Advancements in imaging technologies over the last two decades have ushered a quiet revolution in research approaches to the study of ovarian structure and function. The most significant changes in our understanding of the ovary have resulted from the use of ultrasonography which has enabled sequential analyses in live animals. Computer-assisted image analysis and mathematical modeling of the dynamic changes within the ovary has permitted exciting new avenues of research with readily quantifiable endpoints. Spectral, color-flow and power Doppler imaging now facilitate physiologic interpretations of vascular dynamics over time. Similarly, magnetic resonance imaging (MRI) is emerging as a research tool in ovarian imaging. New technologies, such as three-dimensional ultrasonography and MRI, ultrasound-based biomicroscopy and synchrotron-based techniques each have the potential to enhance our real-time picture of ovarian function to the near-cellular level. Collectively, information available in ultrasonography, MRI, computer-assisted image analysis and mathematical modeling heralds a new era in our understanding of the basic processes of female and male reproduction.

Post-primary students' images of mathematics: findings from a survey of Irish ordinary level mathematics students

NASA Astrophysics Data System (ADS)

Lane, Ciara; Stynes, Martin; O'Donoghue, John

2016-10-01

A questionnaire survey was carried out as part of a PhD research study to investigate the image of mathematics held by post-primary students in Ireland. The study focused on students in fifth year of post-primary education studying ordinary level mathematics for the Irish Leaving Certificate examination - the final examination for students in second-level or post-primary education. At the time this study was conducted, ordinary level mathematics students constituted approximately 72% of Leaving Certificate students. Students were aged between 15 and 18 years. A definition for 'image of mathematics' was adapted from Lim and Wilson, with image of mathematics hypothesized as comprising attitudes, beliefs, self-concept, motivation, emotions and past experiences of mathematics. A questionnaire was composed incorporating 84 fixed-response items chosen from eight pre-established scales by Aiken, Fennema and Sherman, Gourgey and Schoenfeld. This paper focuses on the findings from the questionnaire survey. Students' images of mathematics are compared with regard to gender, type of post-primary school attended and prior mathematical achievement.

An Optimal Partial Differential Equations-based Stopping Criterion for Medical Image Denoising.

PubMed

Khanian, Maryam; Feizi, Awat; Davari, Ali

2014-01-01

Improving the quality of medical images at pre- and post-surgery operations are necessary for beginning and speeding up the recovery process. Partial differential equations-based models have become a powerful and well-known tool in different areas of image processing such as denoising, multiscale image analysis, edge detection and other fields of image processing and computer vision. In this paper, an algorithm for medical image denoising using anisotropic diffusion filter with a convenient stopping criterion is presented. In this regard, the current paper introduces two strategies: utilizing the efficient explicit method due to its advantages with presenting impressive software technique to effectively solve the anisotropic diffusion filter which is mathematically unstable, proposing an automatic stopping criterion, that takes into consideration just input image, as opposed to other stopping criteria, besides the quality of denoised image, easiness and time. Various medical images are examined to confirm the claim.

FRAP Analysis: Accounting for Bleaching during Image Capture

PubMed Central

Wu, Jun; Shekhar, Nandini; Lele, Pushkar P.; Lele, Tanmay P.

2012-01-01

The analysis of Fluorescence Recovery After Photobleaching (FRAP) experiments involves mathematical modeling of the fluorescence recovery process. An important feature of FRAP experiments that tends to be ignored in the modeling is that there can be a significant loss of fluorescence due to bleaching during image capture. In this paper, we explicitly include the effects of bleaching during image capture in the model for the recovery process, instead of correcting for the effects of bleaching using reference measurements. Using experimental examples, we demonstrate the usefulness of such an approach in FRAP analysis. PMID:22912750

Medical Image Segmentation using the HSI color space and Fuzzy Mathematical Morphology

NASA Astrophysics Data System (ADS)

Gasparri, J. P.; Bouchet, A.; Abras, G.; Ballarin, V.; Pastore, J. I.

2011-12-01

Diabetic retinopathy is the most common cause of blindness among the active population in developed countries. An early ophthalmologic examination followed by proper treatment can prevent blindness. The purpose of this work is develop an automated method for segmentation the vasculature in retinal images in order to assist the expert in the evolution of a specific treatment or in the diagnosis of a potential pathology. Since the HSI space has the ability to separate the intensity of the intrinsic color information, its use is recommended for the digital processing images when they are affected by lighting changes, characteristic of the images under study. By the application of color filters, is achieved artificially change the tone of blood vessels, to better distinguish them from the bottom. This technique, combined with the application of fuzzy mathematical morphology tools as the Top-Hat transformation, creates images of the retina, where vascular branches are markedly enhanced over the original. These images provide the visualization of blood vessels by the specialist.

Brain Correlates of Mathematical Competence in Processing Mathematical Representations

PubMed Central

Grabner, Roland H.; Reishofer, Gernot; Koschutnig, Karl; Ebner, Franz

2011-01-01

The ability to extract numerical information from different representation formats (e.g., equations, tables, or diagrams) is a key component of mathematical competence but little is known about its neural correlate. Previous studies comparing mathematically less and more competent adults have focused on mental arithmetic and reported differences in left angular gyrus (AG) activity which were interpreted to reflect differential reliance on arithmetic fact retrieval during problem solving. The aim of the present functional magnetic resonance imaging study was to investigate the brain correlates of mathematical competence in a task requiring the processing of typical mathematical representations. Twenty-eight adults of lower and higher mathematical competence worked on a representation matching task in which they had to evaluate whether the numerical information of a symbolic equation matches that of a bar chart. Two task conditions without and one condition with arithmetic demands were administered. Both competence groups performed equally well in the non-arithmetic conditions and only differed in accuracy in the condition requiring calculation. Activation contrasts between the groups revealed consistently stronger left AG activation in the more competent individuals across all three task conditions. The finding of competence-related activation differences independently of arithmetic demands suggests that more and less competent individuals differ in a cognitive process other than arithmetic fact retrieval. Specifically, it is argued that the stronger left AG activity in the more competent adults may reflect their higher proficiency in processing mathematical symbols. Moreover, the study demonstrates competence-related parietal activation differences that were not accompanied by differential experimental performance. PMID:22069387

Visualization of children's mathematics solving process using near infrared spectroscopic approach

NASA Astrophysics Data System (ADS)

Kuroda, Yasufumi; Okamoto, Naoko; Chance, Britton; Nioka, Shoko; Eda, Hideo; Maesako, Takanori

2009-02-01

Over the past decade, the application of results from brain science research to education research has been a controversial topic. A NIRS imaging system shows images of Hb parameters in the brain. Measurements using NIRS are safe, easy and the equipment is portable, allowing subjects to tolerate longer research periods. The purpose of this research is to examine the characteristics of Hb using NIRS at the moment of understanding. We measured Hb in the prefrontal cortex of children while they were solving mathematical problems (tangram puzzles). As a result of the experiment, we were able to classify the children into three groups based on their solution methods. Hb continually increased in a group which could not develop a problem solving strategy for the tangram puzzles. Hb declined steadily for a group which was able to develop a strategy for the tangram puzzles. Hb was steady for a certain group that had already developed a strategy before solving the problems. Our experiments showed that the brain data from NIRS enables the visualization of children's mathematical solution processes.

Spatial Standard Observer

NASA Technical Reports Server (NTRS)

Watson, Andrw B. (Inventor)

2010-01-01

The present invention relates to devices and methods for the measurement and/or for the specification of the perceptual intensity of a visual image. or the perceptual distance between a pair of images. Grayscale test and reference images are processed to produce test and reference luminance images. A luminance filter function is convolved with the reference luminance image to produce a local mean luminance reference image . Test and reference contrast images are produced from the local mean luminance reference image and the test and reference luminance images respectively, followed by application of a contrast sensitivity filter. The resulting images are combined according to mathematical prescriptions to produce a Just Noticeable Difference, JND value, indicative of a Spatial Standard Observer. SSO. Some embodiments include masking functions. window functions. special treatment for images lying on or near border and pre-processing of test images.

Spatial Standard Observer

NASA Technical Reports Server (NTRS)

Watson, Andrew B. (Inventor)

2012-01-01

The present invention relates to devices and methods for the measurement and/or for the specification of the perceptual intensity of a visual image, or the perceptual distance between a pair of images. Grayscale test and reference images are processed to produce test and reference luminance images. A luminance filter function is convolved with the reference luminance image to produce a local mean luminance reference image. Test and reference contrast images are produced from the local mean luminance reference image and the test and reference luminance images respectively, followed by application of a contrast sensitivity filter. The resulting images are combined according to mathematical prescriptions to produce a Just Noticeable Difference, JND value, indicative of a Spatial Standard Observer, SSO. Some embodiments include masking functions, window functions, special treatment for images lying on or near borders and pre-processing of test images.

Computational and mathematical methods in brain atlasing.

PubMed

Nowinski, Wieslaw L

2017-12-01

Brain atlases have a wide range of use from education to research to clinical applications. Mathematical methods as well as computational methods and tools play a major role in the process of brain atlas building and developing atlas-based applications. Computational methods and tools cover three areas: dedicated editors for brain model creation, brain navigators supporting multiple platforms, and atlas-assisted specific applications. Mathematical methods in atlas building and developing atlas-aided applications deal with problems in image segmentation, geometric body modelling, physical modelling, atlas-to-scan registration, visualisation, interaction and virtual reality. Here I overview computational and mathematical methods in atlas building and developing atlas-assisted applications, and share my contribution to and experience in this field.

Canonical Images

ERIC Educational Resources Information Center

Hewitt, Dave

2007-01-01

In this article, the author offers two well-known mathematical images--that of a dot moving around a circle; and that of the tens chart--and considers their power for developing mathematical thinking. In his opinion, these images each contain the essence of a particular topic of mathematics. They are contrasting images in the sense that they deal…

Cardiovascular imaging and image processing: Theory and practice - 1975; Proceedings of the Conference, Stanford University, Stanford, Calif., July 10-12, 1975

NASA Technical Reports Server (NTRS)

Harrison, D. C.; Sandler, H.; Miller, H. A.

1975-01-01

The present collection of papers outlines advances in ultrasonography, scintigraphy, and commercialization of medical technology as applied to cardiovascular diagnosis in research and clinical practice. Particular attention is given to instrumentation, image processing and display. As necessary concomitants to mathematical analysis, recently improved magnetic recording methods using tape or disks and high-speed computers of large capacity are coming into use. Major topics include Doppler ultrasonic techniques, high-speed cineradiography, three-dimensional imaging of the myocardium with isotopes, sector-scanning echocardiography, and commercialization of the echocardioscope. Individual items are announced in this issue.

Image object recognition based on the Zernike moment and neural networks

NASA Astrophysics Data System (ADS)

Wan, Jianwei; Wang, Ling; Huang, Fukan; Zhou, Liangzhu

1998-03-01

This paper first give a comprehensive discussion about the concept of artificial neural network its research methods and the relations with information processing. On the basis of such a discussion, we expound the mathematical similarity of artificial neural network and information processing. Then, the paper presents a new method of image recognition based on invariant features and neural network by using image Zernike transform. The method not only has the invariant properties for rotation, shift and scale of image object, but also has good fault tolerance and robustness. Meanwhile, it is also compared with statistical classifier and invariant moments recognition method.

Self-aligning and compressed autosophy video databases

NASA Astrophysics Data System (ADS)

Holtz, Klaus E.

1993-04-01

Autosophy, an emerging new science, explains `self-assembling structures,' such as crystals or living trees, in mathematical terms. This research provides a new mathematical theory of `learning' and a new `information theory' which permits the growing of self-assembling data network in a computer memory similar to the growing of `data crystals' or `data trees' without data processing or programming. Autosophy databases are educated very much like a human child to organize their own internal data storage. Input patterns, such as written questions or images, are converted to points in a mathematical omni dimensional hyperspace. The input patterns are then associated with output patterns, such as written answers or images. Omni dimensional information storage will result in enormous data compression because each pattern fragment is only stored once. Pattern recognition in the text or image files is greatly simplified by the peculiar omni dimensional storage method. Video databases will absorb input images from a TV camera and associate them with textual information. The `black box' operations are totally self-aligning where the input data will determine their own hyperspace storage locations. Self-aligning autosophy databases may lead to a new generation of brain-like devices.

Tchebichef moment transform on image dithering for mobile applications

NASA Astrophysics Data System (ADS)

Ernawan, Ferda; Abu, Nur Azman; Rahmalan, Hidayah

2012-04-01

Currently, mobile image applications spend a lot of computing process to display images. A true color raw image contains billions of colors and it consumes high computational power in most mobile image applications. At the same time, mobile devices are only expected to be equipped with lower computing process and minimum storage space. Image dithering is a popular technique to reduce the numbers of bit per pixel at the expense of lower quality image displays. This paper proposes a novel approach on image dithering using 2x2 Tchebichef moment transform (TMT). TMT integrates a simple mathematical framework technique using matrices. TMT coefficients consist of real rational numbers. An image dithering based on TMT has the potential to provide better efficiency and simplicity. The preliminary experiment shows a promising result in term of error reconstructions and image visual textures.

Proceedings of the NASA/MPRIA Workshop: Pattern Recognition

NASA Technical Reports Server (NTRS)

Guseman, L. F., Jr.

1983-01-01

Outlines of talks presented at the workshop conducted at Texas A & M University on February 3 and 4, 1983 are presented. Emphasis was given to the application of Mathematics to image processing and pattern recognition.

Diffusion processes in tumors: A nuclear medicine approach

NASA Astrophysics Data System (ADS)

Amaya, Helman

2016-07-01

The number of counts used in nuclear medicine imaging techniques, only provides physical information about the desintegration of the nucleus present in the the radiotracer molecules that were uptaken in a particular anatomical region, but that information is not a real metabolic information. For this reason a mathematical method was used to find a correlation between number of counts and 18F-FDG mass concentration. This correlation allows a better interpretation of the results obtained in the study of diffusive processes in an agar phantom, and based on it, an image from the PETCETIX DICOM sample image set from OsiriX-viewer software was processed. PET-CT gradient magnitude and Laplacian images could show direct information on diffusive processes for radiopharmaceuticals that enter into the cells by simple diffusion. In the case of the radiopharmaceutical 18F-FDG is necessary to include pharmacokinetic models, to make a correct interpretation of the gradient magnitude and Laplacian of counts images.

The Role of Motion Concepts in Understanding Non-Motion Concepts

PubMed Central

Khatin-Zadeh, Omid; Banaruee, Hassan; Khoshsima, Hooshang; Marmolejo-Ramos, Fernando

2017-01-01

This article discusses a specific type of metaphor in which an abstract non-motion domain is described in terms of a motion event. Abstract non-motion domains are inherently different from concrete motion domains. However, motion domains are used to describe abstract non-motion domains in many metaphors. Three main reasons are suggested for the suitability of motion events in such metaphorical descriptions. Firstly, motion events usually have high degrees of concreteness. Secondly, motion events are highly imageable. Thirdly, components of any motion event can be imagined almost simultaneously within a three-dimensional space. These three characteristics make motion events suitable domains for describing abstract non-motion domains, and facilitate the process of online comprehension throughout language processing. Extending the main point into the field of mathematics, this article discusses the process of transforming abstract mathematical problems into imageable geometric representations within the three-dimensional space. This strategy is widely used by mathematicians to solve highly abstract and complex problems. PMID:29240715

Sensory Information Processing and Symbolic Computation

DTIC Science & Technology

1973-12-31

plague all image deblurring methods when working with high signal to noise ratios, is that of a ringing or ghost image phenomenon which surrounds high...Figure 11 The Impulse Response of an All-Pass Random Phase Filter 24 Figure 12 (a) Unsmoothed Log Spectra of the Sentence "The pipe began to...of automatic deblurring of images, linear predictive coding of speech and the refinement and application of mathematical models of human vision and

Computer-aided light sheet flow visualization using photogrammetry

NASA Technical Reports Server (NTRS)

Stacy, Kathryn; Severance, Kurt; Childers, Brooks A.

1994-01-01

A computer-aided flow visualization process has been developed to analyze video images acquired from rotating and translating light sheet visualization systems. The computer process integrates a mathematical model for image reconstruction, advanced computer graphics concepts, and digital image processing to provide a quantitative and a visual analysis capability. The image reconstruction model, based on photogrammetry, uses knowledge of the camera and light sheet locations and orientations to project two-dimensional light sheet video images into three-dimensional space. A sophisticated computer visualization package, commonly used to analyze computational fluid dynamics (CFD) results, was chosen to interactively display the reconstructed light sheet images with the numerical surface geometry for the model or aircraft under study. The photogrammetric reconstruction technique and the image processing and computer graphics techniques and equipment are described. Results of the computer-aided process applied to both a wind tunnel translating light sheet experiment and an in-flight rotating light sheet experiment are presented. The capability to compare reconstructed experimental light sheet images with CFD solutions in the same graphics environment is also demonstrated.

Computer-Aided Light Sheet Flow Visualization

NASA Technical Reports Server (NTRS)

Stacy, Kathryn; Severance, Kurt; Childers, Brooks A.

1993-01-01

A computer-aided flow visualization process has been developed to analyze video images acquired from rotating and translating light sheet visualization systems. The computer process integrates a mathematical model for image reconstruction, advanced computer graphics concepts, and digital image processing to provide a quantitative and visual analysis capability. The image reconstruction model, based on photogrammetry, uses knowledge of the camera and light sheet locations and orientations to project two-dimensional light sheet video images into three-dimensional space. A sophisticated computer visualization package, commonly used to analyze computational fluid dynamics (CFD) data sets, was chosen to interactively display the reconstructed light sheet images, along with the numerical surface geometry for the model or aircraft under study. A description is provided of the photogrammetric reconstruction technique, and the image processing and computer graphics techniques and equipment. Results of the computer aided process applied to both a wind tunnel translating light sheet experiment and an in-flight rotating light sheet experiment are presented. The capability to compare reconstructed experimental light sheet images and CFD solutions in the same graphics environment is also demonstrated.

Computer-aided light sheet flow visualization

NASA Technical Reports Server (NTRS)

Stacy, Kathryn; Severance, Kurt; Childers, Brooks A.

1993-01-01

A computer-aided flow visualization process has been developed to analyze video images acquired from rotating and translating light sheet visualization systems. The computer process integrates a mathematical model for image reconstruction, advanced computer graphics concepts, and digital image processing to provide a quantitative and visual analysis capability. The image reconstruction model, based on photogrammetry, uses knowledge of the camera and light sheet locations and orientations to project two-dimensional light sheet video images into three-dimensional space. A sophisticated computer visualization package, commonly used to analyze computational fluid dynamics (CFD) data sets, was chosen to interactively display the reconstructed light sheet images, along with the numerical surface geometry for the model or aircraft under study. A description is provided of the photogrammetric reconstruction technique, and the image processing and computer graphics techniques and equipment. Results of the computer aided process applied to both a wind tunnel translating light sheet experiment and an in-flight rotating light sheet experiment are presented. The capability to compare reconstructed experimental light sheet images and CFD solutions in the same graphics environment is also demonstrated.

Optical design and development of a snapshot light-field laryngoscope

NASA Astrophysics Data System (ADS)

Zhu, Shuaishuai; Jin, Peng; Liang, Rongguang; Gao, Liang

2018-02-01

The convergence of recent advances in optical fabrication and digital processing yields a generation of imaging technology-light-field (LF) cameras which bridge the realms of applied mathematics, optics, and high-performance computing. Herein for the first time, we introduce the paradigm of LF imaging into laryngoscopy. The resultant probe can image the three-dimensional shape of vocal folds within a single camera exposure. Furthermore, to improve the spatial resolution, we developed an image fusion algorithm, providing a simple solution to a long-standing problem in LF imaging.

Correlated receptor transport processes buffer single-cell heterogeneity

PubMed Central

Kallenberger, Stefan M.; Unger, Anne L.; Legewie, Stefan; Lymperopoulos, Konstantinos; Eils, Roland

2017-01-01

Cells typically vary in their response to extracellular ligands. Receptor transport processes modulate ligand-receptor induced signal transduction and impact the variability in cellular responses. Here, we quantitatively characterized cellular variability in erythropoietin receptor (EpoR) trafficking at the single-cell level based on live-cell imaging and mathematical modeling. Using ensembles of single-cell mathematical models reduced parameter uncertainties and showed that rapid EpoR turnover, transport of internalized EpoR back to the plasma membrane, and degradation of Epo-EpoR complexes were essential for receptor trafficking. EpoR trafficking dynamics in adherent H838 lung cancer cells closely resembled the dynamics previously characterized by mathematical modeling in suspension cells, indicating that dynamic properties of the EpoR system are widely conserved. Receptor transport processes differed by one order of magnitude between individual cells. However, the concentration of activated Epo-EpoR complexes was less variable due to the correlated kinetics of opposing transport processes acting as a buffering system. PMID:28945754

A novel highly parallel algorithm for linearly unmixing hyperspectral images

NASA Astrophysics Data System (ADS)

Guerra, Raúl; López, Sebastián.; Callico, Gustavo M.; López, Jose F.; Sarmiento, Roberto

2014-10-01

Endmember extraction and abundances calculation represent critical steps within the process of linearly unmixing a given hyperspectral image because of two main reasons. The first one is due to the need of computing a set of accurate endmembers in order to further obtain confident abundance maps. The second one refers to the huge amount of operations involved in these time-consuming processes. This work proposes an algorithm to estimate the endmembers of a hyperspectral image under analysis and its abundances at the same time. The main advantage of this algorithm is its high parallelization degree and the mathematical simplicity of the operations implemented. This algorithm estimates the endmembers as virtual pixels. In particular, the proposed algorithm performs the descent gradient method to iteratively refine the endmembers and the abundances, reducing the mean square error, according with the linear unmixing model. Some mathematical restrictions must be added so the method converges in a unique and realistic solution. According with the algorithm nature, these restrictions can be easily implemented. The results obtained with synthetic images demonstrate the well behavior of the algorithm proposed. Moreover, the results obtained with the well-known Cuprite dataset also corroborate the benefits of our proposal.

A neotropical Miocene pollen database employing image-based search and semantic modeling.

PubMed

Han, Jing Ginger; Cao, Hongfei; Barb, Adrian; Punyasena, Surangi W; Jaramillo, Carlos; Shyu, Chi-Ren

2014-08-01

Digital microscopic pollen images are being generated with increasing speed and volume, producing opportunities to develop new computational methods that increase the consistency and efficiency of pollen analysis and provide the palynological community a computational framework for information sharing and knowledge transfer. • Mathematical methods were used to assign trait semantics (abstract morphological representations) of the images of neotropical Miocene pollen and spores. Advanced database-indexing structures were built to compare and retrieve similar images based on their visual content. A Web-based system was developed to provide novel tools for automatic trait semantic annotation and image retrieval by trait semantics and visual content. • Mathematical models that map visual features to trait semantics can be used to annotate images with morphology semantics and to search image databases with improved reliability and productivity. Images can also be searched by visual content, providing users with customized emphases on traits such as color, shape, and texture. • Content- and semantic-based image searches provide a powerful computational platform for pollen and spore identification. The infrastructure outlined provides a framework for building a community-wide palynological resource, streamlining the process of manual identification, analysis, and species discovery.

Contrasting Cases of Calculus Students' Understanding of Derivative Graphs

ERIC Educational Resources Information Center

Haciomeroglu, Erhan Selcuk; Aspinwall, Leslie; Presmeg, Norma C.

2010-01-01

This study adds momentum to the ongoing discussion clarifying the merits of visualization and analysis in mathematical thinking. Our goal was to gain understanding of three calculus students' mental processes and images used to create meaning for derivative graphs. We contrast the thinking processes of these three students as they attempted to…

Digital techniques for processing Landsat imagery

NASA Technical Reports Server (NTRS)

Green, W. B.

1978-01-01

An overview of the basic techniques used to process Landsat images with a digital computer, and the VICAR image processing software developed at JPL and available to users through the NASA sponsored COSMIC computer program distribution center is presented. Examples of subjective processing performed to improve the information display for the human observer, such as contrast enhancement, pseudocolor display and band rationing, and of quantitative processing using mathematical models, such as classification based on multispectral signatures of different areas within a given scene and geometric transformation of imagery into standard mapping projections are given. Examples are illustrated by Landsat scenes of the Andes mountains and Altyn-Tagh fault zone in China before and after contrast enhancement and classification of land use in Portland, Oregon. The VICAR image processing software system which consists of a language translator that simplifies execution of image processing programs and provides a general purpose format so that imagery from a variety of sources can be processed by the same basic set of general applications programs is described.

Theory of Remote Image Formation

NASA Astrophysics Data System (ADS)

Blahut, Richard E.

2004-11-01

In many applications, images, such as ultrasonic or X-ray signals, are recorded and then analyzed with digital or optical processors in order to extract information. Such processing requires the development of algorithms of great precision and sophistication. This book presents a unified treatment of the mathematical methods that underpin the various algorithms used in remote image formation. The author begins with a review of transform and filter theory. He then discusses two- and three-dimensional Fourier transform theory, the ambiguity function, image construction and reconstruction, tomography, baseband surveillance systems, and passive systems (where the signal source might be an earthquake or a galaxy). Information-theoretic methods in image formation are also covered, as are phase errors and phase noise. Throughout the book, practical applications illustrate theoretical concepts, and there are many homework problems. The book is aimed at graduate students of electrical engineering and computer science, and practitioners in industry. Presents a unified treatment of the mathematical methods that underpin the algorithms used in remote image formation Illustrates theoretical concepts with reference to practical applications Provides insights into the design parameters of real systems

Multi-template image matching using alpha-rooted biquaternion phase correlation with application to logo recognition

NASA Astrophysics Data System (ADS)

DelMarco, Stephen

2011-06-01

Hypercomplex approaches are seeing increased application to signal and image processing problems. The use of multicomponent hypercomplex numbers, such as quaternions, enables the simultaneous co-processing of multiple signal or image components. This joint processing capability can provide improved exploitation of the information contained in the data, thereby leading to improved performance in detection and recognition problems. In this paper, we apply hypercomplex processing techniques to the logo image recognition problem. Specifically, we develop an image matcher by generalizing classical phase correlation to the biquaternion case. We further incorporate biquaternion Fourier domain alpha-rooting enhancement to create Alpha-Rooted Biquaternion Phase Correlation (ARBPC). We present the mathematical properties which justify use of ARBPC as an image matcher. We present numerical performance results of a logo verification problem using real-world logo data, demonstrating the performance improvement obtained using the hypercomplex approach. We compare results of the hypercomplex approach to standard multi-template matching approaches.

Visual Depth from Motion Parallax and Eye Pursuit

PubMed Central

Stroyan, Keith; Nawrot, Mark

2012-01-01

A translating observer viewing a rigid environment experiences “motion parallax,” the relative movement upon the observer’s retina of variously positioned objects in the scene. This retinal movement of images provides a cue to the relative depth of objects in the environment, however retinal motion alone cannot mathematically determine relative depth of the objects. Visual perception of depth from lateral observer translation uses both retinal image motion and eye movement. In (Nawrot & Stroyan, 2009, Vision Res. 49, p.1969) we showed mathematically that the ratio of the rate of retinal motion over the rate of smooth eye pursuit mathematically determines depth relative to the fixation point in central vision. We also reported on psychophysical experiments indicating that this ratio is the important quantity for perception. Here we analyze the motion/pursuit cue for the more general, and more complicated, case when objects are distributed across the horizontal viewing plane beyond central vision. We show how the mathematical motion/pursuit cue varies with different points across the plane and with time as an observer translates. If the time varying retinal motion and smooth eye pursuit are the only signals used for this visual process, it is important to know what is mathematically possible to derive about depth and structure. Our analysis shows that the motion/pursuit ratio determines an excellent description of depth and structure in these broader stimulus conditions, provides a detailed quantitative hypothesis of these visual processes for the perception of depth and structure from motion parallax, and provides a computational foundation to analyze the dynamic geometry of future experiments. PMID:21695531

Physics of fractional imaging in biomedicine.

PubMed

Sohail, Ayesha; Bég, O A; Li, Zhiwu; Celik, Sebahattin

2018-03-12

The mathematics of imaging is a growing field of research and is evolving rapidly parallel to evolution in the field of imaging. Imaging, which is a sub-field of biomedical engineering, considers novel approaches to visualize biological tissues with the general goal of improving health. "Medical imaging research provides improved diagnostic tools in clinical settings and supports the development of drugs and other therapies. The data acquisition and diagnostic interpretation with minimum error are the important technical aspects of medical imaging. The image quality and resolution are really important in portraying the internal aspects of patient's body. Although there are several user friendly resources for processing image features, such as enhancement, colour manipulation and compression, the development of new processing methods is still worthy of efforts. In this article we aim to present the role of fractional calculus in imaging with the aid of practical examples. Copyright © 2018 Elsevier Ltd. All rights reserved.

Bio-inspired approach to multistage image processing

NASA Astrophysics Data System (ADS)

Timchenko, Leonid I.; Pavlov, Sergii V.; Kokryatskaya, Natalia I.; Poplavska, Anna A.; Kobylyanska, Iryna M.; Burdenyuk, Iryna I.; Wójcik, Waldemar; Uvaysova, Svetlana; Orazbekov, Zhassulan; Kashaganova, Gulzhan

2017-08-01

Multistage integration of visual information in the brain allows people to respond quickly to most significant stimuli while preserving the ability to recognize small details in the image. Implementation of this principle in technical systems can lead to more efficient processing procedures. The multistage approach to image processing, described in this paper, comprises main types of cortical multistage convergence. One of these types occurs within each visual pathway and the other between the pathways. This approach maps input images into a flexible hierarchy which reflects the complexity of the image data. The procedures of temporal image decomposition and hierarchy formation are described in mathematical terms. The multistage system highlights spatial regularities, which are passed through a number of transformational levels to generate a coded representation of the image which encapsulates, in a computer manner, structure on different hierarchical levels in the image. At each processing stage a single output result is computed to allow a very quick response from the system. The result is represented as an activity pattern, which can be compared with previously computed patterns on the basis of the closest match.

Ethnomathematics elements in Batik Bali using backpropagation method

NASA Astrophysics Data System (ADS)

Lestari, Mei; Irawan, Ari; Rahayu, Wanti; Wayan Parwati, Ni

2018-05-01

Batik is one of traditional arts that has been established by the UNESCO as Indonesia’s cultural heritage. Batik has varieties and motifs, and each motifs has its own uniqueness but seems similar, that makes it difficult to identify. This study aims to develop an application that can identify typical batik Bali with etnomatematics elements on it. Etnomatematics is a study that shows relation between culture and mathematics concepts. Etnomatematics in Batik Bali is more to geometrical concept in line of strong Balinese culture element. The identification process is use backpropagation method. Steps of backpropagation methods are image processing (including scalling and tresholding image process). Next step is insert the processed image to an artificial neural network. This study resulted an accuracy of identification of batik Bali that has Etnomatematics elements on it.

Prototype Images in Mathematics Education: The Case of The Graphical Representation of The Definite Integral

ERIC Educational Resources Information Center

Jones, Steven R.

2018-01-01

Many mathematical concepts may have prototypical images associated with them. While prototypes can be beneficial for efficient thinking or reasoning, they may also have self-attributes that may impact reasoning about the concept. It is essential that mathematics educators understand these prototype images in order to fully recognize their benefits…

Systems Biology-Driven Hypotheses Tested In Vivo: The Need to Advancing Molecular Imaging Tools.

PubMed

Verma, Garima; Palombo, Alessandro; Grigioni, Mauro; La Monaca, Morena; D'Avenio, Giuseppe

2018-01-01

Processing and interpretation of biological images may provide invaluable insights on complex, living systems because images capture the overall dynamics as a "whole." Therefore, "extraction" of key, quantitative morphological parameters could be, at least in principle, helpful in building a reliable systems biology approach in understanding living objects. Molecular imaging tools for system biology models have attained widespread usage in modern experimental laboratories. Here, we provide an overview on advances in the computational technology and different instrumentations focused on molecular image processing and analysis. Quantitative data analysis through various open source software and algorithmic protocols will provide a novel approach for modeling the experimental research program. Besides this, we also highlight the predictable future trends regarding methods for automatically analyzing biological data. Such tools will be very useful to understand the detailed biological and mathematical expressions under in-silico system biology processes with modeling properties.

Wave field restoration using three-dimensional Fourier filtering method.

PubMed

Kawasaki, T; Takai, Y; Ikuta, T; Shimizu, R

2001-11-01

A wave field restoration method in transmission electron microscopy (TEM) was mathematically derived based on a three-dimensional (3D) image formation theory. Wave field restoration using this method together with spherical aberration correction was experimentally confirmed in through-focus images of amorphous tungsten thin film, and the resolution of the reconstructed phase image was successfully improved from the Scherzer resolution limit to the information limit. In an application of this method to a crystalline sample, the surface structure of Au(110) was observed in a profile-imaging mode. The processed phase image showed quantitatively the atomic relaxation of the topmost layer.

Image-based quantification and mathematical modeling of spatial heterogeneity in ESC colonies.

PubMed

Herberg, Maria; Zerjatke, Thomas; de Back, Walter; Glauche, Ingmar; Roeder, Ingo

2015-06-01

Pluripotent embryonic stem cells (ESCs) have the potential to differentiate into cells of all three germ layers. This unique property has been extensively studied on the intracellular, transcriptional level. However, ESCs typically form clusters of cells with distinct size and shape, and establish spatial structures that are vital for the maintenance of pluripotency. Even though it is recognized that the cells' arrangement and local interactions play a role in fate decision processes, the relations between transcriptional and spatial patterns have not yet been studied. We present a systems biology approach which combines live-cell imaging, quantitative image analysis, and multiscale, mathematical modeling of ESC growth. In particular, we develop quantitative measures of the morphology and of the spatial clustering of ESCs with different expression levels and apply them to images of both in vitro and in silico cultures. Using the same measures, we are able to compare model scenarios with different assumptions on cell-cell adhesions and intercellular feedback mechanisms directly with experimental data. Applying our methodology to microscopy images of cultured ESCs, we demonstrate that the emerging colonies are highly variable regarding both morphological and spatial fluorescence patterns. Moreover, we can show that most ESC colonies contain only one cluster of cells with high self-renewing capacity. These cells are preferentially located in the interior of a colony structure. The integrated approach combining image analysis with mathematical modeling allows us to reveal potential transcription factor related cellular and intercellular mechanisms behind the emergence of observed patterns that cannot be derived from images directly. © 2015 International Society for Advancement of Cytometry.

SIproc: an open-source biomedical data processing platform for large hyperspectral images.

PubMed

Berisha, Sebastian; Chang, Shengyuan; Saki, Sam; Daeinejad, Davar; He, Ziqi; Mankar, Rupali; Mayerich, David

2017-04-10

There has recently been significant interest within the vibrational spectroscopy community to apply quantitative spectroscopic imaging techniques to histology and clinical diagnosis. However, many of the proposed methods require collecting spectroscopic images that have a similar region size and resolution to the corresponding histological images. Since spectroscopic images contain significantly more spectral samples than traditional histology, the resulting data sets can approach hundreds of gigabytes to terabytes in size. This makes them difficult to store and process, and the tools available to researchers for handling large spectroscopic data sets are limited. Fundamental mathematical tools, such as MATLAB, Octave, and SciPy, are extremely powerful but require that the data be stored in fast memory. This memory limitation becomes impractical for even modestly sized histological images, which can be hundreds of gigabytes in size. In this paper, we propose an open-source toolkit designed to perform out-of-core processing of hyperspectral images. By taking advantage of graphical processing unit (GPU) computing combined with adaptive data streaming, our software alleviates common workstation memory limitations while achieving better performance than existing applications.

What Mathematical Images Are in a Typical Mathematics Textbook? Implications for Students with Visual Impairments

ERIC Educational Resources Information Center

Emerson, Robert Wall; Anderson, Dawn

2018-01-01

Introduction: Visually impaired students (that is, those who are blind or have low vision) have difficulty accessing curricular material in mathematical textbooks because many mathematics texts have visual images that contain important content information that are not transcribed or described in digital versions of the texts. However, little is…

Target recognition for ladar range image using slice image

NASA Astrophysics Data System (ADS)

Xia, Wenze; Han, Shaokun; Wang, Liang

2015-12-01

A shape descriptor and a complete shape-based recognition system using slice images as geometric feature descriptor for ladar range images are introduced. A slice image is a two-dimensional image generated by three-dimensional Hough transform and the corresponding mathematical transformation. The system consists of two processes, the model library construction and recognition. In the model library construction process, a series of range images are obtained after the model object is sampled at preset attitude angles. Then, all the range images are converted into slice images. The number of slice images is reduced by clustering analysis and finding a representation to reduce the size of the model library. In the recognition process, the slice image of the scene is compared with the slice image in the model library. The recognition results depend on the comparison. Simulated ladar range images are used to analyze the recognition and misjudgment rates, and comparison between the slice image representation method and moment invariants representation method is performed. The experimental results show that whether in conditions without noise or with ladar noise, the system has a high recognition rate and low misjudgment rate. The comparison experiment demonstrates that the slice image has better representation ability than moment invariants.

Thermal Imaging Applied to Cryocrystallography: Cryocooling and Beam Heating (Part I)

NASA Technical Reports Server (NTRS)

Snell, Edward; Bellamy, Henry; Rosenbaum, Gerd; vanderWoerd, Mark; Kazmierczak, Michael

2006-01-01

Thermal imaging provides a non-invasive method to study both the cryocooling process and the heating due to the X-ray beam interaction with a sample. The method has been used successfully to image cryocooling in a number of experimental situations, i.e. cooling as a function of sample volume and as a function of cryostream orientation. Although there are experimental limitations to the method, it has proved a powerful technique to aid cryocrystallography development. Due to the rapid spatial temperature information provided about the sample it is also a powerful tool in the testing of mathematical models. Recently thermal imaging has been used to measure the temperature distribution on both a model and typical crystal samples illuminated with an X-ray beam produced by an undulator. A brief overview of thermal imaging and previous results will be presented. In addition, a detailed description of the calibration and experimental aspects of the beam heating measurements will be described. This will complement the following talk on the mathematical modeling and analysis of the results.

Towards A Complete Model Of Photopic Visual Threshold Performance

NASA Astrophysics Data System (ADS)

Overington, I.

1982-02-01

Based on a wide variety of fragmentary evidence taken from psycho-physics, neurophysiology and electron microscopy, it has been possible to put together a very widely applicable conceptual model of photopic visual threshold performance. Such a model is so complex that a single comprehensive mathematical version is excessively cumbersome. It is, however, possible to set up a suite of related mathematical models, each of limited application but strictly known envelope of usage. Such models may be used for assessment of a variety of facets of visual performance when using display imagery, including effects and interactions of image quality, random and discrete display noise, viewing distance, image motion, etc., both for foveal interrogation tasks and for visual search tasks. The specific model may be selected from the suite according to the assessment task in hand. The paper discusses in some depth the major facets of preperceptual visual processing and their interaction with instrumental image quality and noise. It then highlights the statistical nature of visual performance before going on to consider a number of specific mathematical models of partial visual function. Where appropriate, these are compared with widely popular empirical models of visual function.

Diffusion processes in tumors: A nuclear medicine approach

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

Amaya, Helman, E-mail: haamayae@unal.edu.co

The number of counts used in nuclear medicine imaging techniques, only provides physical information about the desintegration of the nucleus present in the the radiotracer molecules that were uptaken in a particular anatomical region, but that information is not a real metabolic information. For this reason a mathematical method was used to find a correlation between number of counts and {sup 18}F-FDG mass concentration. This correlation allows a better interpretation of the results obtained in the study of diffusive processes in an agar phantom, and based on it, an image from the PETCETIX DICOM sample image set from OsiriX-viewer softwaremore » was processed. PET-CT gradient magnitude and Laplacian images could show direct information on diffusive processes for radiopharmaceuticals that enter into the cells by simple diffusion. In the case of the radiopharmaceutical {sup 18}F-FDG is necessary to include pharmacokinetic models, to make a correct interpretation of the gradient magnitude and Laplacian of counts images.« less

The review on infrared image restoration techniques

NASA Astrophysics Data System (ADS)

Li, Sijian; Fan, Xiang; Zhu, Bin Cheng; Zheng, Dong

2016-11-01

The goal of infrared image restoration is to reconstruct an original scene from a degraded observation. The restoration process in the application of infrared wavelengths, however, still has numerous research possibilities. In order to give people a comprehensive knowledge of infrared image restoration, the degradation factors divided into two major categories of noise and blur. Many kinds of infrared image restoration method were overviewed. Mathematical background and theoretical basis of infrared image restoration technology, and the limitations or insufficiency of existing methods were discussed. After the survey, the direction and prospects of infrared image restoration technology for the future development were forecast and put forward.

Removing Visual Bias in Filament Identification: A New Goodness-of-fit Measure

NASA Astrophysics Data System (ADS)

Green, C.-E.; Cunningham, M. R.; Dawson, J. R.; Jones, P. A.; Novak, G.; Fissel, L. M.

2017-05-01

Different combinations of input parameters to filament identification algorithms, such as disperse and filfinder, produce numerous different output skeletons. The skeletons are a one-pixel-wide representation of the filamentary structure in the original input image. However, these output skeletons may not necessarily be a good representation of that structure. Furthermore, a given skeleton may not be as good of a representation as another. Previously, there has been no mathematical “goodness-of-fit” measure to compare output skeletons to the input image. Thus far this has been assessed visually, introducing visual bias. We propose the application of the mean structural similarity index (MSSIM) as a mathematical goodness-of-fit measure. We describe the use of the MSSIM to find the output skeletons that are the most mathematically similar to the original input image (the optimum, or “best,” skeletons) for a given algorithm, and independently of the algorithm. This measure makes possible systematic parameter studies, aimed at finding the subset of input parameter values returning optimum skeletons. It can also be applied to the output of non-skeleton-based filament identification algorithms, such as the Hessian matrix method. The MSSIM removes the need to visually examine thousands of output skeletons, and eliminates the visual bias, subjectivity, and limited reproducibility inherent in that process, representing a major improvement upon existing techniques. Importantly, it also allows further automation in the post-processing of output skeletons, which is crucial in this era of “big data.”

A neotropical Miocene pollen database employing image-based search and semantic modeling1

PubMed Central

Han, Jing Ginger; Cao, Hongfei; Barb, Adrian; Punyasena, Surangi W.; Jaramillo, Carlos; Shyu, Chi-Ren

2014-01-01

• Premise of the study: Digital microscopic pollen images are being generated with increasing speed and volume, producing opportunities to develop new computational methods that increase the consistency and efficiency of pollen analysis and provide the palynological community a computational framework for information sharing and knowledge transfer. • Methods: Mathematical methods were used to assign trait semantics (abstract morphological representations) of the images of neotropical Miocene pollen and spores. Advanced database-indexing structures were built to compare and retrieve similar images based on their visual content. A Web-based system was developed to provide novel tools for automatic trait semantic annotation and image retrieval by trait semantics and visual content. • Results: Mathematical models that map visual features to trait semantics can be used to annotate images with morphology semantics and to search image databases with improved reliability and productivity. Images can also be searched by visual content, providing users with customized emphases on traits such as color, shape, and texture. • Discussion: Content- and semantic-based image searches provide a powerful computational platform for pollen and spore identification. The infrastructure outlined provides a framework for building a community-wide palynological resource, streamlining the process of manual identification, analysis, and species discovery. PMID:25202648

On the mathematical modeling of wound healing angiogenesis in skin as a reaction-transport process.

PubMed

Flegg, Jennifer A; Menon, Shakti N; Maini, Philip K; McElwain, D L Sean

2015-01-01

Over the last 30 years, numerous research groups have attempted to provide mathematical descriptions of the skin wound healing process. The development of theoretical models of the interlinked processes that underlie the healing mechanism has yielded considerable insight into aspects of this critical phenomenon that remain difficult to investigate empirically. In particular, the mathematical modeling of angiogenesis, i.e., capillary sprout growth, has offered new paradigms for the understanding of this highly complex and crucial step in the healing pathway. With the recent advances in imaging and cell tracking, the time is now ripe for an appraisal of the utility and importance of mathematical modeling in wound healing angiogenesis research. The purpose of this review is to pedagogically elucidate the conceptual principles that have underpinned the development of mathematical descriptions of wound healing angiogenesis, specifically those that have utilized a continuum reaction-transport framework, and highlight the contribution that such models have made toward the advancement of research in this field. We aim to draw attention to the common assumptions made when developing models of this nature, thereby bringing into focus the advantages and limitations of this approach. A deeper integration of mathematical modeling techniques into the practice of wound healing angiogenesis research promises new perspectives for advancing our knowledge in this area. To this end we detail several open problems related to the understanding of wound healing angiogenesis, and outline how these issues could be addressed through closer cross-disciplinary collaboration.

On the mathematical modeling of wound healing angiogenesis in skin as a reaction-transport process

PubMed Central

Flegg, Jennifer A.; Menon, Shakti N.; Maini, Philip K.; McElwain, D. L. Sean

2015-01-01

Over the last 30 years, numerous research groups have attempted to provide mathematical descriptions of the skin wound healing process. The development of theoretical models of the interlinked processes that underlie the healing mechanism has yielded considerable insight into aspects of this critical phenomenon that remain difficult to investigate empirically. In particular, the mathematical modeling of angiogenesis, i.e., capillary sprout growth, has offered new paradigms for the understanding of this highly complex and crucial step in the healing pathway. With the recent advances in imaging and cell tracking, the time is now ripe for an appraisal of the utility and importance of mathematical modeling in wound healing angiogenesis research. The purpose of this review is to pedagogically elucidate the conceptual principles that have underpinned the development of mathematical descriptions of wound healing angiogenesis, specifically those that have utilized a continuum reaction-transport framework, and highlight the contribution that such models have made toward the advancement of research in this field. We aim to draw attention to the common assumptions made when developing models of this nature, thereby bringing into focus the advantages and limitations of this approach. A deeper integration of mathematical modeling techniques into the practice of wound healing angiogenesis research promises new perspectives for advancing our knowledge in this area. To this end we detail several open problems related to the understanding of wound healing angiogenesis, and outline how these issues could be addressed through closer cross-disciplinary collaboration. PMID:26483695

Post-Primary Students' Images of Mathematics: Findings from a Survey of Irish Ordinary Level Mathematics Students

ERIC Educational Resources Information Center

Lane, Ciara; Stynes, Martin; O'Donoghue, John

2016-01-01

A questionnaire survey was carried out as part of a PhD research study to investigate the image of mathematics held by post-primary students in Ireland. The study focused on students in fifth year of post-primary education studying ordinary level mathematics for the Irish Leaving Certificate examination--the final examination for students in…

JIP: Java image processing on the Internet

NASA Astrophysics Data System (ADS)

Wang, Dongyan; Lin, Bo; Zhang, Jun

1998-12-01

In this paper, we present JIP - Java Image Processing on the Internet, a new Internet based application for remote education and software presentation. JIP offers an integrate learning environment on the Internet where remote users not only can share static HTML documents and lectures notes, but also can run and reuse dynamic distributed software components, without having the source code or any extra work of software compilation, installation and configuration. By implementing a platform-independent distributed computational model, local computational resources are consumed instead of the resources on a central server. As an extended Java applet, JIP allows users to selected local image files on their computers or specify any image on the Internet using an URL as input. Multimedia lectures such as streaming video/audio and digital images are integrated into JIP and intelligently associated with specific image processing functions. Watching demonstrations an practicing the functions with user-selected input data dramatically encourages leaning interest, while promoting the understanding of image processing theory. The JIP framework can be easily applied to other subjects in education or software presentation, such as digital signal processing, business, mathematics, physics, or other areas such as employee training and charged software consumption.

A description of a system of programs for mathematically processing on unified series (YeS) computers photographic images of the Earth taken from spacecraft

NASA Technical Reports Server (NTRS)

Zolotukhin, V. G.; Kolosov, B. I.; Usikov, D. A.; Borisenko, V. I.; Mosin, S. T.; Gorokhov, V. N.

1980-01-01

A description of a batch of programs for the YeS-1040 computer combined into an automated system for processing photo (and video) images of the Earth's surface, taken from spacecraft, is presented. Individual programs with the detailed discussion of the algorithmic and programmatic facilities needed by the user are presented. The basic principles for assembling the system, and the control programs are included. The exchange format within whose framework the cataloging of any programs recommended for the system of processing will be activated in the future is displayed.

Generation of synthetic image sequences for the verification of matching and tracking algorithms for deformation analysis

NASA Astrophysics Data System (ADS)

Bethmann, F.; Jepping, C.; Luhmann, T.

2013-04-01

This paper reports on a method for the generation of synthetic image data for almost arbitrary static or dynamic 3D scenarios. Image data generation is based on pre-defined 3D objects, object textures, camera orientation data and their imaging properties. The procedure does not focus on the creation of photo-realistic images under consideration of complex imaging and reflection models as they are used by common computer graphics programs. In contrast, the method is designed with main emphasis on geometrically correct synthetic images without radiometric impact. The calculation process includes photogrammetric distortion models, hence cameras with arbitrary geometric imaging characteristics can be applied. Consequently, image sets can be created that are consistent to mathematical photogrammetric models to be used as sup-pixel accurate data for the assessment of high-precision photogrammetric processing methods. In the first instance the paper describes the process of image simulation under consideration of colour value interpolation, MTF/PSF and so on. Subsequently the geometric quality of the synthetic images is evaluated with ellipse operators. Finally, simulated image sets are used to investigate matching and tracking algorithms as they have been developed at IAPG for deformation measurement in car safety testing.

Vehicle counting system using real-time video processing

NASA Astrophysics Data System (ADS)

Crisóstomo-Romero, Pedro M.

2006-02-01

Transit studies are important for planning a road network with optimal vehicular flow. A vehicular count is essential. This article presents a vehicle counting system based on video processing. An advantage of such system is the greater detail than is possible to obtain, like shape, size and speed of vehicles. The system uses a video camera placed above the street to image transit in real-time. The video camera must be placed at least 6 meters above the street level to achieve proper acquisition quality. Fast image processing algorithms and small image dimensions are used to allow real-time processing. Digital filters, mathematical morphology, segmentation and other techniques allow identifying and counting all vehicles in the image sequences. The system was implemented under Linux in a 1.8 GHz Pentium 4 computer. A successful count was obtained with frame rates of 15 frames per second for images of size 240x180 pixels and 24 frames per second for images of size 180x120 pixels, thus being able to count vehicles whose speeds do not exceed 150 km/h.

Computer analysis of three-dimensional morphological characteristics of the bile duct

NASA Astrophysics Data System (ADS)

Ma, Jinyuan; Chen, Houjin; Peng, Yahui; Shang, Hua

2017-01-01

In this paper, a computer image-processing algorithm for analyzing the morphological characteristics of bile ducts in Magnetic Resonance Cholangiopancreatography (MRCP) images was proposed. The algorithm consisted of mathematical morphology methods including erosion, closing and skeletonization, and a spline curve fitting method to obtain the length and curvature of the center line of the bile duct. Of 10 cases, the average length of the bile duct was 14.56 cm. The maximum curvature was in the range of 0.111 2.339. These experimental results show that using the computer image-processing algorithm to assess the morphological characteristics of the bile duct is feasible and further research is needed to evaluate its potential clinical values.

Imaging model for the scintillator and its application to digital radiography image enhancement.

PubMed

Wang, Qian; Zhu, Yining; Li, Hongwei

2015-12-28

Digital Radiography (DR) images obtained by OCD-based (optical coupling detector) Micro-CT system usually suffer from low contrast. In this paper, a mathematical model is proposed to describe the image formation process in scintillator. By solving the correlative inverse problem, the quality of DR images is improved, i.e. higher contrast and spatial resolution. By analyzing the radiative transfer process of visible light in scintillator, scattering is recognized as the main factor leading to low contrast. Moreover, involved blurring effect is also concerned and described as point spread function (PSF). Based on these physical processes, the scintillator imaging model is then established. When solving the inverse problem, pre-correction to the intensity of x-rays, dark channel prior based haze removing technique, and an effective blind deblurring approach are employed. Experiments on a variety of DR images show that the proposed approach could improve the contrast of DR images dramatically as well as eliminate the blurring vision effectively. Compared with traditional contrast enhancement methods, such as CLAHE, our method could preserve the relative absorption values well.

Architecture of the parallel hierarchical network for fast image recognition

NASA Astrophysics Data System (ADS)

Timchenko, Leonid; Wójcik, Waldemar; Kokriatskaia, Natalia; Kutaev, Yuriy; Ivasyuk, Igor; Kotyra, Andrzej; Smailova, Saule

2016-09-01

Multistage integration of visual information in the brain allows humans to respond quickly to most significant stimuli while maintaining their ability to recognize small details in the image. Implementation of this principle in technical systems can lead to more efficient processing procedures. The multistage approach to image processing includes main types of cortical multistage convergence. The input images are mapped into a flexible hierarchy that reflects complexity of image data. Procedures of the temporal image decomposition and hierarchy formation are described in mathematical expressions. The multistage system highlights spatial regularities, which are passed through a number of transformational levels to generate a coded representation of the image that encapsulates a structure on different hierarchical levels in the image. At each processing stage a single output result is computed to allow a quick response of the system. The result is presented as an activity pattern, which can be compared with previously computed patterns on the basis of the closest match. With regard to the forecasting method, its idea lies in the following. In the results synchronization block, network-processed data arrive to the database where a sample of most correlated data is drawn using service parameters of the parallel-hierarchical network.

Development of 4D mathematical observer models for the task-based evaluation of gated myocardial perfusion SPECT

NASA Astrophysics Data System (ADS)

Lee, Taek-Soo; Frey, Eric C.; Tsui, Benjamin M. W.

2015-04-01

This paper presents two 4D mathematical observer models for the detection of motion defects in 4D gated medical images. Their performance was compared with results from human observers in detecting a regional motion abnormality in simulated 4D gated myocardial perfusion (MP) SPECT images. The first 4D mathematical observer model extends the conventional channelized Hotelling observer (CHO) based on a set of 2D spatial channels and the second is a proposed model that uses a set of 4D space-time channels. Simulated projection data were generated using the 4D NURBS-based cardiac-torso (NCAT) phantom with 16 gates/cardiac cycle. The activity distribution modelled uptake of 99mTc MIBI with normal perfusion and a regional wall motion defect. An analytical projector was used in the simulation and the filtered backprojection (FBP) algorithm was used in image reconstruction followed by spatial and temporal low-pass filtering with various cut-off frequencies. Then, we extracted 2D image slices from each time frame and reorganized them into a set of cine images. For the first model, we applied 2D spatial channels to the cine images and generated a set of feature vectors that were stacked for the images from different slices of the heart. The process was repeated for each of the 1,024 noise realizations, and CHO and receiver operating characteristics (ROC) analysis methodologies were applied to the ensemble of the feature vectors to compute areas under the ROC curves (AUCs). For the second model, a set of 4D space-time channels was developed and applied to the sets of cine images to produce space-time feature vectors to which the CHO methodology was applied. The AUC values of the second model showed better agreement (Spearman’s rank correlation (SRC) coefficient = 0.8) to human observer results than those from the first model (SRC coefficient = 0.4). The agreement with human observers indicates the proposed 4D mathematical observer model provides a good predictor of the performance of human observers in detecting regional motion defects in 4D gated MP SPECT images. The result supports the use of the observer model in the optimization and evaluation of 4D image reconstruction and compensation methods for improving the detection of motion abnormalities in 4D gated MP SPECT images.

Towards intelligent diagnostic system employing integration of mathematical and engineering model

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

Isa, Nor Ashidi Mat

The development of medical diagnostic system has been one of the main research fields during years. The goal of the medical diagnostic system is to place a nosological system that could ease the diagnostic evaluation normally performed by scientists and doctors. Efficient diagnostic evaluation is essentials and requires broad knowledge in order to improve conventional diagnostic system. Several approaches on developing the medical diagnostic system have been designed and tested since the earliest 60s. Attempts on improving their performance have been made which utilizes the fields of artificial intelligence, statistical analyses, mathematical model and engineering theories. With the availability ofmore » the microcomputer and software development as well as the promising aforementioned fields, medical diagnostic prototypes could be developed. In general, the medical diagnostic system consists of several stages, namely the 1) data acquisition, 2) feature extraction, 3) feature selection, and 4) classifications stages. Data acquisition stage plays an important role in converting the inputs measured from the real world physical conditions to the digital numeric values that can be manipulated by the computer system. One of the common medical inputs could be medical microscopic images, radiographic images, magnetic resonance image (MRI) as well as medical signals such as electrocardiogram (ECG) and electroencephalogram (EEG). Normally, the scientist or doctors have to deal with myriad of data and redundant to be processed. In order to reduce the complexity of the diagnosis process, only the significant features of the raw data such as peak value of the ECG signal or size of lesion in the mammogram images will be extracted and considered in the subsequent stages. Mathematical models and statistical analyses will be performed to select the most significant features to be classified. The statistical analyses such as principal component analysis and discriminant analysis as well as mathematical model of clustering technique have been widely used in developing the medical diagnostic systems. The selected features will be classified using mathematical models that embedded engineering theory such as artificial intelligence, support vector machine, neural network and fuzzy-neuro system. These classifiers will provide the diagnostic results without human intervention. Among many publishable researches, several prototypes have been developed namely NeuralPap, Neural Mammo, and Cervix Kit. The former system (NeuralPap) is an automatic intelligent diagnostic system for classifying and distinguishing between the normal and cervical cancerous cells. Meanwhile, the Cervix Kit is a portable Field-programmable gate array (FPGA)-based cervical diagnostic kit that could automatically diagnose the cancerous cell based on the images obtained during sampling test. Besides the cervical diagnostic system, the Neural Mammo system is developed to specifically aid the diagnosis of breast cancer using a fine needle aspiration image.« less

Towards intelligent diagnostic system employing integration of mathematical and engineering model

NASA Astrophysics Data System (ADS)

Isa, Nor Ashidi Mat

2015-05-01

The development of medical diagnostic system has been one of the main research fields during years. The goal of the medical diagnostic system is to place a nosological system that could ease the diagnostic evaluation normally performed by scientists and doctors. Efficient diagnostic evaluation is essentials and requires broad knowledge in order to improve conventional diagnostic system. Several approaches on developing the medical diagnostic system have been designed and tested since the earliest 60s. Attempts on improving their performance have been made which utilizes the fields of artificial intelligence, statistical analyses, mathematical model and engineering theories. With the availability of the microcomputer and software development as well as the promising aforementioned fields, medical diagnostic prototypes could be developed. In general, the medical diagnostic system consists of several stages, namely the 1) data acquisition, 2) feature extraction, 3) feature selection, and 4) classifications stages. Data acquisition stage plays an important role in converting the inputs measured from the real world physical conditions to the digital numeric values that can be manipulated by the computer system. One of the common medical inputs could be medical microscopic images, radiographic images, magnetic resonance image (MRI) as well as medical signals such as electrocardiogram (ECG) and electroencephalogram (EEG). Normally, the scientist or doctors have to deal with myriad of data and redundant to be processed. In order to reduce the complexity of the diagnosis process, only the significant features of the raw data such as peak value of the ECG signal or size of lesion in the mammogram images will be extracted and considered in the subsequent stages. Mathematical models and statistical analyses will be performed to select the most significant features to be classified. The statistical analyses such as principal component analysis and discriminant analysis as well as mathematical model of clustering technique have been widely used in developing the medical diagnostic systems. The selected features will be classified using mathematical models that embedded engineering theory such as artificial intelligence, support vector machine, neural network and fuzzy-neuro system. These classifiers will provide the diagnostic results without human intervention. Among many publishable researches, several prototypes have been developed namely NeuralPap, Neural Mammo, and Cervix Kit. The former system (NeuralPap) is an automatic intelligent diagnostic system for classifying and distinguishing between the normal and cervical cancerous cells. Meanwhile, the Cervix Kit is a portable Field-programmable gate array (FPGA)-based cervical diagnostic kit that could automatically diagnose the cancerous cell based on the images obtained during sampling test. Besides the cervical diagnostic system, the Neural Mammo system is developed to specifically aid the diagnosis of breast cancer using a fine needle aspiration image.

Quantum Analog Computing

NASA Technical Reports Server (NTRS)

Zak, M.

1998-01-01

Quantum analog computing is based upon similarity between mathematical formalism of quantum mechanics and phenomena to be computed. It exploits a dynamical convergence of several competing phenomena to an attractor which can represent an externum of a function, an image, a solution to a system of ODE, or a stochastic process.

Chunky and Smooth Images of Change

ERIC Educational Resources Information Center

Castillo-Garsow, Carlos; Johnson, Heather Lynn; Moore, Kevin C.

2013-01-01

Characterizing how quantities change (or vary) in tandem has been an important historical focus in mathematics that extends into the current teaching of mathematics. Thus, how students conceptualize quantities that change in tandem becomes critical to their mathematical development. In this paper, we propose two images of change: chunky and…

Error propagation in eigenimage filtering.

PubMed

Soltanian-Zadeh, H; Windham, J P; Jenkins, J M

1990-01-01

Mathematical derivation of error (noise) propagation in eigenimage filtering is presented. Based on the mathematical expressions, a method for decreasing the propagated noise given a sequence of images is suggested. The signal-to-noise ratio (SNR) and contrast-to-noise ratio (CNR) of the final composite image are compared to the SNRs and CNRs of the images in the sequence. The consistency of the assumptions and accuracy of the mathematical expressions are investigated using sequences of simulated and real magnetic resonance (MR) images of an agarose phantom and a human brain.

A study of competence in mathematics and mechanics in an engineering curriculum

NASA Astrophysics Data System (ADS)

Munns, Andrew

2017-11-01

Professional bodies expect engineers to show competence in both mathematics and engineering topics such as mechanics, using their abilities in both of these to solve problems. Yet within engineering programmes there is a phenomenon known as 'The Mathematics Problem', with students not demonstrating understanding of the subject. This paper will suggest that students are constructing different concept images in engineering and mathematics, based on their perception of either the use or exchange-value for the topics. Using a mixed methods approach, the paper compares 10 different types of concept image constructed by students, which suggests that familiar procedural images are preferred in mathematics. In contrast strategic and conceptual images develop for mechanics throughout the years of the programme, implying that different forms of competence are being constructed by students between the two subjects. The paper argues that this difference is attributed to the perceived use-value of mechanics in the career of the engineer, compared to the exchange-value associated with mathematics. Questions are raised about the relevance of current definitions of competence given that some routine mathematical operations previously performed by engineers are now being replaced by technology, in the new world of work.

Circular Samples as Objects for Magnetic Resonance Imaging - Mathematical Simulation, Experimental Results

NASA Astrophysics Data System (ADS)

Frollo, Ivan; Krafčík, Andrej; Andris, Peter; Přibil, Jiří; Dermek, Tomáš

2015-12-01

Circular samples are the frequent objects of "in-vitro" investigation using imaging method based on magnetic resonance principles. The goal of our investigation is imaging of thin planar layers without using the slide selection procedure, thus only 2D imaging or imaging of selected layers of samples in circular vessels, eppendorf tubes,.. compulsorily using procedure "slide selection". In spite of that the standard imaging methods was used, some specificity arise when mathematical modeling of these procedure is introduced. In the paper several mathematical models were presented that were compared with real experimental results. Circular magnetic samples were placed into the homogenous magnetic field of a low field imager based on nuclear magnetic resonance. For experimental verification an MRI 0.178 Tesla ESAOTE Opera imager was used.

Incorporating Student Activities into Climate Change Education

NASA Astrophysics Data System (ADS)

Steele, H.; Kelly, K.; Klein, D.; Cadavid, A. C.

2013-12-01

Under a NASA grant, Mathematical and Geospatial Pathways to Climate Change Education, students at California State University, Northridge integrated Geographic Information Systems (GIS), remote sensing, satellite data technologies, and climate modelling into the study of global climate change under a Pathway for studying the Mathematics of Climate Change (PMCC). The PMCC, which is an interdisciplinary option within the BS in Applied Mathematical Sciences, consists of courses offered by the departments of Mathematics, Physics, and Geography and is designed to prepare students for careers and Ph.D. programs in technical fields relevant to global climate change. Under this option students are exposed to the science, mathematics, and applications of climate change science through a variety of methods including hands-on experience with computer modeling and image processing software. In the Geography component of the program, ESRI's ArcGIS and ERDAS Imagine mapping, spatial analysis and image processing software were used to explore NASA satellite data to examine the earth's atmosphere, hydrosphere and biosphere in areas that are affected by climate change or affect climate. These technology tools were incorporated into climate change and remote sensing courses to enhance students' knowledge and understanding of climate change through hands-on application of image processing techniques to NASA data. Several sets of exercises were developed with specific learning objectives in mind. These were (1) to increase student understanding of climate change and climate change processes; (2) to develop student skills in understanding, downloading and processing satellite data; (3) to teach remote sensing technology and GIS through applications to climate change; (4) to expose students to climate data and methods they can apply to solve real world problems and incorporate in future research projects. In the Math and Physics components of the course, students learned about atmospheric circulation with applications of the Lorenz model, explored the land-sea breeze problem with the Dynamics and Thermodynamics Circulation Model (DTDM), and developed simple radiative transfer models. Class projects explored the effects of varying the content of CO2 and CH4 in the atmosphere, as well as the properties of paleoclimates in atmospheric simulations using EdGCM. Initial assessment of student knowledge, attitudes, and behaviors associated with these activities, particularly about climate change, was measured. Pre- and post-course surveys provided student perspectives about the courses and their learning about remote sensing and climate change concepts. Student performance on the tutorials and course projects evaluated students' ability to learn and apply their knowledge about climate change and skills with remote sensing to assigned problems or proposed projects of their choice. Survey and performance data illustrated that the exercises were successful in meeting their intended learning objectives as well as opportunities for further refinement and expansion.

Quantification technology study on flaws in steam-filled pipelines based on image processing

NASA Astrophysics Data System (ADS)

Sun, Lina; Yuan, Peixin

2009-07-01

Starting from exploiting the applied detection system of gas transmission pipeline, a set of X-ray image processing methods and pipeline flaw quantificational evaluation methods are proposed. Defective and non-defective strings and rows in gray image were extracted and oscillogram was obtained. We can distinguish defects in contrast with two gray images division. According to the gray value of defects with different thicknesses, the gray level depth curve is founded. Through exponential and polynomial fitting way to obtain the attenuation mathematical model which the beam penetrates pipeline, thus attain flaw deep dimension. This paper tests on the PPR pipe in the production of simulated holes flaw and cracks flaw, 135KV used the X-ray source on the testing. Test results show that X-ray image processing method, which meet the needs of high efficient flaw detection and provide quality safeguard for thick oil recovery, can be used successfully in detecting corrosion of insulated pipe.

Quantification technology study on flaws in steam-filled pipelines based on image processing

NASA Astrophysics Data System (ADS)

Yuan, Pei-xin; Cong, Jia-hui; Chen, Bo

2008-03-01

Starting from exploiting the applied detection system of gas transmission pipeline, a set of X-ray image processing methods and pipeline flaw quantificational evaluation methods are proposed. Defective and non-defective strings and rows in gray image were extracted and oscillogram was obtained. We can distinguish defects in contrast with two gray images division. According to the gray value of defects with different thicknesses, the gray level depth curve is founded. Through exponential and polynomial fitting way to obtain the attenuation mathematical model which the beam penetrates pipeline, thus attain flaw deep dimension. This paper tests on the PPR pipe in the production of simulated holes flaw and cracks flaw. The X-ray source tube voltage was selected as 130kv and valve current was 1.5mA.Test results show that X-ray image processing methods, which meet the needs of high efficient flaw detection and provide quality safeguard for thick oil recovery, can be used successfully in detecting corrosion of insulated pipe.

Language-Switching Costs in Bilingual Mathematics Learning

ERIC Educational Resources Information Center

Grabner, Roland H.; Saalbach, Henrik; Eckstein, Doris

2012-01-01

Behavioral studies on bilingual learning have revealed cognitive costs (lower accuracy and/or higher processing time) when the language of application differs from the language of learning. The aim of this functional magnetic resonance imaging (fMRI) study was to provide insights into the cognitive underpinnings of these costs (so-called…

[Digital processing and evaluation of ultrasound images].

PubMed

Borchers, J; Klews, P M

1993-10-01

With the help of workstations and PCs, on-site image processing has become possible. If the images are not available in digital form the video signal has to be A/D converted. In the case of colour images the colour channels R (red), G (green) and B (blue) have to be digitized separately. "Truecolour" imaging calls for an 8 bit resolution per channel, leading to 24 bits per pixel. Out of a pool of 2(24) possible values only the relevant 128 gray values and 64 shades of red and blue respectively needed for a colour-coded ultrasound image have to be isolated. Digital images can be changed and evaluated with the help of readily available image evaluation programmes. It is mandatory that during image manipulation the gray scale and colour pixels and LUTs (Look-Up-Table) must be worked on separately. Using relatively simple LUT manipulations astonishing image improvements are possible. Application of simple mathematical operations can lead to completely new clinical results. For example, by subtracting two consecutive colour flow images in time and special LUT operations, local acceleration of blood flow can be visualized (Colour Acceleration Imaging).

Investigation of Primary Mathematics Student Teachers' Concept Images: Cylinder and Cone

ERIC Educational Resources Information Center

Ertekin, Erhan; Yazici, Ersen; Delice, Ali

2014-01-01

The aim of the present study is to determine the influence of concept definitions of cylinder and cone on primary mathematics student teachers' construction of relevant concept images. The study had a relational survey design and the participants were 238 primary mathematics student teachers. Statistical analyses implied the following: mathematics…

Mathematical modeling and fluorescence imaging to study the Ca2+ turnover in skinned muscle fibers.

PubMed Central

Uttenweiler, D; Weber, C; Fink, R H

1998-01-01

A mathematical model was developed for the simulation of the spatial and temporal time course of Ca2+ ion movement in caffeine-induced calcium transients of chemically skinned muscle fiber preparations. Our model assumes cylindrical symmetry and quantifies the radial profile of Ca2+ ion concentration by solving the diffusion equations for Ca2+ ions and various mobile buffers, and the rate equations for Ca2+ buffering (mobile and immobile buffers) and for the release and reuptake of Ca2+ ions by the sarcoplasmic reticulum (SR), with a finite-difference algorithm. The results of the model are compared with caffeine-induced spatial Ca2+ transients obtained from saponin skinned murine fast-twitch fibers by fluorescence photometry and imaging measurements using the ratiometric dye Fura-2. The combination of mathematical modeling and digital image analysis provides a tool for the quantitative description of the total Ca2+ turnover and the different contributions of all interacting processes to the overall Ca2+ transient in skinned muscle fibers. It should thereby strongly improve the usage of skinned fibers as quantitative assay systems for many parameters of the SR and the contractile apparatus helping also to bridge the gap to the intact muscle fiber. PMID:9545029

Visual communication - Information and fidelity. [of images

NASA Technical Reports Server (NTRS)

Huck, Freidrich O.; Fales, Carl L.; Alter-Gartenberg, Rachel; Rahman, Zia-Ur; Reichenbach, Stephen E.

1993-01-01

This assessment of visual communication deals with image gathering, coding, and restoration as a whole rather than as separate and independent tasks. The approach focuses on two mathematical criteria, information and fidelity, and on their relationships to the entropy of the encoded data and to the visual quality of the restored image. Past applications of these criteria to the assessment of image coding and restoration have been limited to the link that connects the output of the image-gathering device to the input of the image-display device. By contrast, the approach presented in this paper explicitly includes the critical limiting factors that constrain image gathering and display. This extension leads to an end-to-end assessment theory of visual communication that combines optical design with digital processing.

Rotationally Symmetric Operators for Surface Interpolation

DTIC Science & Technology

1981-11-01

Computational Geometry for design and rianufacture , Fills Horwood, Chichester UK, 1979. [111 Gladwell 1. and Wait. R. (eds.). Survey of numerical...from an image," Computer Graphics and Image Processing 3(1974), 277-299. 1161 Horn B. K. P. "The curve of least energy," MIT, Al Memo 610, 1981. 117...an object from a single view," Artificial Intelligence 17 (1981), 409-460. [21] Knuth 1). E. "Mathematical typography ," Bull. Amer. Math. Soc. (new

Image model: new perspective for image processing and computer vision

NASA Astrophysics Data System (ADS)

Ziou, Djemel; Allili, Madjid

2004-05-01

We propose a new image model in which the image support and image quantities are modeled using algebraic topology concepts. The image support is viewed as a collection of chains encoding combination of pixels grouped by dimension and linking different dimensions with the boundary operators. Image quantities are encoded using the notion of cochain which associates values for pixels of given dimension that can be scalar, vector, or tensor depending on the problem that is considered. This allows obtaining algebraic equations directly from the physical laws. The coboundary and codual operators, which are generic operations on cochains allow to formulate the classical differential operators as applied for field functions and differential forms in both global and local forms. This image model makes the association between the image support and the image quantities explicit which results in several advantages: it allows the derivation of efficient algorithms that operate in any dimension and the unification of mathematics and physics to solve classical problems in image processing and computer vision. We show the effectiveness of this model by considering the isotropic diffusion.

The museum of unnatural form: a visual and tactile experience of fractals.

PubMed

Della-Bosca, D; Taylor, R P

2009-01-01

A remarkable computer technology is revolutionizing the world of design, allowing intricate patterns to be created with mathematical precision and then 'printed' as physical objects. Contour crafting is a fabrication process capable of assembling physical structures the sizes of houses, firing the imagination of a new generation of architects and artists (Khoshnevisat, 2008). Daniel Della-Bosca has jumped at this opportunity to create the 'Museum of Unnatural Form' at Griffith University. Della-Bosca's museum is populated with fractals sculptures - his own versions of nature's complex objects - that have been printed with the new technology. His sculptures bridge the historical divide in fractal studies between the abstract images of mathematics and the physical objects of Nature (Mandelbrot, 1982). Four of his fractal images will be featured on the cover of NDPLS in 2009.

Validation of a digital mammographic unit model for an objective and highly automated clinical image quality assessment.

PubMed

Perez-Ponce, Hector; Daul, Christian; Wolf, Didier; Noel, Alain

2013-08-01

In mammography, image quality assessment has to be directly related to breast cancer indicator (e.g. microcalcifications) detectability. Recently, we proposed an X-ray source/digital detector (XRS/DD) model leading to such an assessment. This model simulates very realistic contrast-detail phantom (CDMAM) images leading to gold disc (representing microcalcifications) detectability thresholds that are very close to those of real images taken under the simulated acquisition conditions. The detection step was performed with a mathematical observer. The aim of this contribution is to include human observers into the disc detection process in real and virtual images to validate the simulation framework based on the XRS/DD model. Mathematical criteria (contrast-detail curves, image quality factor, etc.) are used to assess and to compare, from the statistical point of view, the cancer indicator detectability in real and virtual images. The quantitative results given in this paper show that the images simulated by the XRS/DD model are useful for image quality assessment in the case of all studied exposure conditions using either human or automated scoring. Also, this paper confirms that with the XRS/DD model the image quality assessment can be automated and the whole time of the procedure can be drastically reduced. Compared to standard quality assessment methods, the number of images to be acquired is divided by a factor of eight. Copyright © 2012 IPEM. Published by Elsevier Ltd. All rights reserved.

An Investigation of K-8 Preservice Teachers' Concept Images and Mathematical Definitions of Polygons

ERIC Educational Resources Information Center

Ward, Robin A.

2004-01-01

In this paper, the author presents a study which explored K-8 preservice teachers' concept images and mathematical definitions of polygons. This study was carried out in which K-8 teacher candidates enrolled in an elementary mathematics content course were asked to sort, identify, and provide definitions of such shapes including triangles,…

Image Schemas in Clock-Reading: Latent Errors and Emerging Expertise

ERIC Educational Resources Information Center

Williams, Robert F.

2012-01-01

An embodied view of mathematical cognition should account not only for how we use our bodies to think and communicate mathematically but also how our bodies equip us to conceive of mathematical ideas. Research in cognitive semantics claims that the human conceptual capacity rests on a foundation of image schemas: topological patterns of spatial…

Gifted Students' Metaphor Images about Mathematics

ERIC Educational Resources Information Center

Arikan, Elif Esra; Unal, Hasan

2015-01-01

The aim of this study is to investigate the metaphors images of gifted students about mathematics. The sample of the study consists of 82 gifted students, which are 2, 3, 4, 5, 6, 7 graders, from Istanbul. Data were collected by asking students to complete the sentence: "Mathematics is as …, because…". In the study content analysis was…

Image-based modelling of skeletal muscle oxygenation

PubMed Central

Clough, G. F.

2017-01-01

The supply of oxygen in sufficient quantity is vital for the correct functioning of all organs in the human body, in particular for skeletal muscle during exercise. Disease is often associated with both an inhibition of the microvascular supply capability and is thought to relate to changes in the structure of blood vessel networks. Different methods exist to investigate the influence of the microvascular structure on tissue oxygenation, varying over a range of application areas, i.e. biological in vivo and in vitro experiments, imaging and mathematical modelling. Ideally, all of these methods should be combined within the same framework in order to fully understand the processes involved. This review discusses the mathematical models of skeletal muscle oxygenation currently available that are based upon images taken of the muscle microvasculature in vivo and ex vivo. Imaging systems suitable for capturing the blood vessel networks are discussed and respective contrasting methods presented. The review further informs the association between anatomical characteristics in health and disease. With this review we give the reader a tool to understand and establish the workflow of developing an image-based model of skeletal muscle oxygenation. Finally, we give an outlook for improvements needed for measurements and imaging techniques to adequately investigate the microvascular capability for oxygen exchange. PMID:28202595

IEEE International Symposium on Biomedical Imaging.

PubMed

2017-01-01

The IEEE International Symposium on Biomedical Imaging (ISBI) is a scientific conference dedicated to mathematical, algorithmic, and computational aspects of biological and biomedical imaging, across all scales of observation. It fosters knowledge transfer among different imaging communities and contributes to an integrative approach to biomedical imaging. ISBI is a joint initiative from the IEEE Signal Processing Society (SPS) and the IEEE Engineering in Medicine and Biology Society (EMBS). The 2018 meeting will include tutorials, and a scientific program composed of plenary talks, invited special sessions, challenges, as well as oral and poster presentations of peer-reviewed papers. High-quality papers are requested containing original contributions to the topics of interest including image formation and reconstruction, computational and statistical image processing and analysis, dynamic imaging, visualization, image quality assessment, and physical, biological, and statistical modeling. Accepted 4-page regular papers will be published in the symposium proceedings published by IEEE and included in IEEE Xplore. To encourage attendance by a broader audience of imaging scientists and offer additional presentation opportunities, ISBI 2018 will continue to have a second track featuring posters selected from 1-page abstract submissions without subsequent archival publication.

Singular value decomposition for photon-processing nuclear imaging systems and applications for reconstruction and computing null functions.

PubMed

Jha, Abhinav K; Barrett, Harrison H; Frey, Eric C; Clarkson, Eric; Caucci, Luca; Kupinski, Matthew A

2015-09-21

Recent advances in technology are enabling a new class of nuclear imaging systems consisting of detectors that use real-time maximum-likelihood (ML) methods to estimate the interaction position, deposited energy, and other attributes of each photon-interaction event and store these attributes in a list format. This class of systems, which we refer to as photon-processing (PP) nuclear imaging systems, can be described by a fundamentally different mathematical imaging operator that allows processing of the continuous-valued photon attributes on a per-photon basis. Unlike conventional photon-counting (PC) systems that bin the data into images, PP systems do not have any binning-related information loss. Mathematically, while PC systems have an infinite-dimensional null space due to dimensionality considerations, PP systems do not necessarily suffer from this issue. Therefore, PP systems have the potential to provide improved performance in comparison to PC systems. To study these advantages, we propose a framework to perform the singular-value decomposition (SVD) of the PP imaging operator. We use this framework to perform the SVD of operators that describe a general two-dimensional (2D) planar linear shift-invariant (LSIV) PP system and a hypothetical continuously rotating 2D single-photon emission computed tomography (SPECT) PP system. We then discuss two applications of the SVD framework. The first application is to decompose the object being imaged by the PP imaging system into measurement and null components. We compare these components to the measurement and null components obtained with PC systems. In the process, we also present a procedure to compute the null functions for a PC system. The second application is designing analytical reconstruction algorithms for PP systems. The proposed analytical approach exploits the fact that PP systems acquire data in a continuous domain to estimate a continuous object function. The approach is parallelizable and implemented for graphics processing units (GPUs). Further, this approach leverages another important advantage of PP systems, namely the possibility to perform photon-by-photon real-time reconstruction. We demonstrate the application of the approach to perform reconstruction in a simulated 2D SPECT system. The results help to validate and demonstrate the utility of the proposed method and show that PP systems can help overcome the aliasing artifacts that are otherwise intrinsically present in PC systems.

Singular value decomposition for photon-processing nuclear imaging systems and applications for reconstruction and computing null functions

NASA Astrophysics Data System (ADS)

Jha, Abhinav K.; Barrett, Harrison H.; Frey, Eric C.; Clarkson, Eric; Caucci, Luca; Kupinski, Matthew A.

2015-09-01

Recent advances in technology are enabling a new class of nuclear imaging systems consisting of detectors that use real-time maximum-likelihood (ML) methods to estimate the interaction position, deposited energy, and other attributes of each photon-interaction event and store these attributes in a list format. This class of systems, which we refer to as photon-processing (PP) nuclear imaging systems, can be described by a fundamentally different mathematical imaging operator that allows processing of the continuous-valued photon attributes on a per-photon basis. Unlike conventional photon-counting (PC) systems that bin the data into images, PP systems do not have any binning-related information loss. Mathematically, while PC systems have an infinite-dimensional null space due to dimensionality considerations, PP systems do not necessarily suffer from this issue. Therefore, PP systems have the potential to provide improved performance in comparison to PC systems. To study these advantages, we propose a framework to perform the singular-value decomposition (SVD) of the PP imaging operator. We use this framework to perform the SVD of operators that describe a general two-dimensional (2D) planar linear shift-invariant (LSIV) PP system and a hypothetical continuously rotating 2D single-photon emission computed tomography (SPECT) PP system. We then discuss two applications of the SVD framework. The first application is to decompose the object being imaged by the PP imaging system into measurement and null components. We compare these components to the measurement and null components obtained with PC systems. In the process, we also present a procedure to compute the null functions for a PC system. The second application is designing analytical reconstruction algorithms for PP systems. The proposed analytical approach exploits the fact that PP systems acquire data in a continuous domain to estimate a continuous object function. The approach is parallelizable and implemented for graphics processing units (GPUs). Further, this approach leverages another important advantage of PP systems, namely the possibility to perform photon-by-photon real-time reconstruction. We demonstrate the application of the approach to perform reconstruction in a simulated 2D SPECT system. The results help to validate and demonstrate the utility of the proposed method and show that PP systems can help overcome the aliasing artifacts that are otherwise intrinsically present in PC systems.

Investigation of Prospective Primary Mathematics Teachers' Perceptions and Images for Quadrilaterals

ERIC Educational Resources Information Center

Turnuklu, Elif; Gundogdu Alayli, Funda; Akkas, Elif Nur

2013-01-01

The object of this study was to show how prospective elementary mathematics teachers define and classify the quadrilaterals and to find out their images. This research was a qualitative study. It was conducted with 36 prospective elementary mathematics teachers studying at 3rd and 4th years in an educational faculty. The data were collected by…

The impact of temporal sampling resolution on parameter inference for biological transport models.

PubMed

Harrison, Jonathan U; Baker, Ruth E

2018-06-25

Imaging data has become an essential tool to explore key biological questions at various scales, for example the motile behaviour of bacteria or the transport of mRNA, and it has the potential to transform our understanding of important transport mechanisms. Often these imaging studies require us to compare biological species or mutants, and to do this we need to quantitatively characterise their behaviour. Mathematical models offer a quantitative description of a system that enables us to perform this comparison, but to relate mechanistic mathematical models to imaging data, we need to estimate their parameters. In this work we study how collecting data at different temporal resolutions impacts our ability to infer parameters of biological transport models; performing exact inference for simple velocity jump process models in a Bayesian framework. The question of how best to choose the frequency with which data is collected is prominent in a host of studies because the majority of imaging technologies place constraints on the frequency with which images can be taken, and the discrete nature of observations can introduce errors into parameter estimates. In this work, we mitigate such errors by formulating the velocity jump process model within a hidden states framework. This allows us to obtain estimates of the reorientation rate and noise amplitude for noisy observations of a simple velocity jump process. We demonstrate the sensitivity of these estimates to temporal variations in the sampling resolution and extent of measurement noise. We use our methodology to provide experimental guidelines for researchers aiming to characterise motile behaviour that can be described by a velocity jump process. In particular, we consider how experimental constraints resulting in a trade-off between temporal sampling resolution and observation noise may affect parameter estimates. Finally, we demonstrate the robustness of our methodology to model misspecification, and then apply our inference framework to a dataset that was generated with the aim of understanding the localization of RNA-protein complexes.

Phase retrieval using regularization method in intensity correlation imaging

NASA Astrophysics Data System (ADS)

Li, Xiyu; Gao, Xin; Tang, Jia; Lu, Changming; Wang, Jianli; Wang, Bin

2014-11-01

Intensity correlation imaging(ICI) method can obtain high resolution image with ground-based low precision mirrors, in the imaging process, phase retrieval algorithm should be used to reconstituted the object's image. But the algorithm now used(such as hybrid input-output algorithm) is sensitive to noise and easy to stagnate. However the signal-to-noise ratio of intensity interferometry is low especially in imaging astronomical objects. In this paper, we build the mathematical model of phase retrieval and simplified it into a constrained optimization problem of a multi-dimensional function. New error function was designed by noise distribution and prior information using regularization method. The simulation results show that the regularization method can improve the performance of phase retrieval algorithm and get better image especially in low SNR condition

Automated segmentation of knee and ankle regions of rats from CT images to quantify bone mineral density for monitoring treatments of rheumatoid arthritis

NASA Astrophysics Data System (ADS)

Cruz, Francisco; Sevilla, Raquel; Zhu, Joe; Vanko, Amy; Lee, Jung Hoon; Dogdas, Belma; Zhang, Weisheng

2014-03-01

Bone mineral density (BMD) obtained from a CT image is an imaging biomarker used pre-clinically for characterizing the Rheumatoid arthritis (RA) phenotype. We use this biomarker in animal studies for evaluating disease progression and for testing various compounds. In the current setting, BMD measurements are obtained manually by selecting the regions of interest from three-dimensional (3-D) CT images of rat legs, which results in a laborious and low-throughput process. Combining image processing techniques, such as intensity thresholding and skeletonization, with mathematical techniques in curve fitting and curvature calculations, we developed an algorithm for quick, consistent, and automatic detection of joints in large CT data sets. The implemented algorithm has reduced analysis time for a study with 200 CT images from 10 days to 3 days and has improved the robust detection of the obtained regions of interest compared with manual segmentation. This algorithm has been used successfully in over 40 studies.

Seeing mathematics: perceptual experience and brain activity in acquired synesthesia.

PubMed

Brogaard, Berit; Vanni, Simo; Silvanto, Juha

2013-01-01

We studied the patient JP who has exceptional abilities to draw complex geometrical images by hand and a form of acquired synesthesia for mathematical formulas and objects, which he perceives as geometrical figures. JP sees all smooth curvatures as discrete lines, similarly regardless of scale. We carried out two preliminary investigations to establish the perceptual nature of synesthetic experience and to investigate the neural basis of this phenomenon. In a functional magnetic resonance imaging (fMRI) study, image-inducing formulas produced larger fMRI responses than non-image inducing formulas in the left temporal, parietal and frontal lobes. Thus our main finding is that the activation associated with his experience of complex geometrical images emerging from mathematical formulas is restricted to the left hemisphere.

Director Field Analysis (DFA): Exploring Local White Matter Geometric Structure in Diffusion MRI.

PubMed

Cheng, Jian; Basser, Peter J

2018-01-01

In Diffusion Tensor Imaging (DTI) or High Angular Resolution Diffusion Imaging (HARDI), a tensor field or a spherical function field (e.g., an orientation distribution function field), can be estimated from measured diffusion weighted images. In this paper, inspired by the microscopic theoretical treatment of phases in liquid crystals, we introduce a novel mathematical framework, called Director Field Analysis (DFA), to study local geometric structural information of white matter based on the reconstructed tensor field or spherical function field: (1) We propose a set of mathematical tools to process general director data, which consists of dyadic tensors that have orientations but no direction. (2) We propose Orientational Order (OO) and Orientational Dispersion (OD) indices to describe the degree of alignment and dispersion of a spherical function in a single voxel or in a region, respectively; (3) We also show how to construct a local orthogonal coordinate frame in each voxel exhibiting anisotropic diffusion; (4) Finally, we define three indices to describe three types of orientational distortion (splay, bend, and twist) in a local spatial neighborhood, and a total distortion index to describe distortions of all three types. To our knowledge, this is the first work to quantitatively describe orientational distortion (splay, bend, and twist) in general spherical function fields from DTI or HARDI data. The proposed DFA and its related mathematical tools can be used to process not only diffusion MRI data but also general director field data, and the proposed scalar indices are useful for detecting local geometric changes of white matter for voxel-based or tract-based analysis in both DTI and HARDI acquisitions. The related codes and a tutorial for DFA will be released in DMRITool. Copyright © 2017 Elsevier B.V. All rights reserved.

Empirical validation of the triple-code model of numerical processing for complex math operations using functional MRI and group Independent Component Analysis of the mental addition and subtraction of fractions.

PubMed

Schmithorst, Vincent J; Brown, Rhonda Douglas

2004-07-01

The suitability of a previously hypothesized triple-code model of numerical processing, involving analog magnitude, auditory verbal, and visual Arabic codes of representation, was investigated for the complex mathematical task of the mental addition and subtraction of fractions. Functional magnetic resonance imaging (fMRI) data from 15 normal adult subjects were processed using exploratory group Independent Component Analysis (ICA). Separate task-related components were found with activation in bilateral inferior parietal, left perisylvian, and ventral occipitotemporal areas. These results support the hypothesized triple-code model corresponding to the activated regions found in the individual components and indicate that the triple-code model may be a suitable framework for analyzing the neuropsychological bases of the performance of complex mathematical tasks. Copyright 2004 Elsevier Inc.

Biological applications of phase-contrast electron microscopy.

PubMed

Nagayama, Kuniaki

2014-01-01

Here, I review the principles and applications of phase-contrast electron microscopy using phase plates. First, I develop the principle of phase contrast based on a minimal model of microscopy, introducing a double Fourier-transform process to mathematically formulate the image formation. Next, I explain four phase-contrast (PC) schemes, defocus PC, Zernike PC, Hilbert differential contrast, and schlieren optics, as image-filtering processes in the context of the minimal model, with particular emphases on the Zernike PC and corresponding Zernike phase plates. Finally, I review applications of Zernike PC cryo-electron microscopy to biological systems such as protein molecules, virus particles, and cells, including single-particle analysis to delineate three-dimensional (3D) structures of protein and virus particles and cryo-electron tomography to reconstruct 3D images of complex protein systems and cells.

Trajectory-based morphological operators: a model for efficient image processing.

PubMed

Jimeno-Morenilla, Antonio; Pujol, Francisco A; Molina-Carmona, Rafael; Sánchez-Romero, José L; Pujol, Mar

2014-01-01

Mathematical morphology has been an area of intensive research over the last few years. Although many remarkable advances have been achieved throughout these years, there is still a great interest in accelerating morphological operations in order for them to be implemented in real-time systems. In this work, we present a new model for computing mathematical morphology operations, the so-called morphological trajectory model (MTM), in which a morphological filter will be divided into a sequence of basic operations. Then, a trajectory-based morphological operation (such as dilation, and erosion) is defined as the set of points resulting from the ordered application of the instant basic operations. The MTM approach allows working with different structuring elements, such as disks, and from the experiments, it can be extracted that our method is independent of the structuring element size and can be easily applied to industrial systems and high-resolution images.

Computations on the massively parallel processor at the Goddard Space Flight Center

NASA Technical Reports Server (NTRS)

Strong, James P.

1991-01-01

Described are four significant algorithms implemented on the massively parallel processor (MPP) at the Goddard Space Flight Center. Two are in the area of image analysis. Of the other two, one is a mathematical simulation experiment and the other deals with the efficient transfer of data between distantly separated processors in the MPP array. The first algorithm presented is the automatic determination of elevations from stereo pairs. The second algorithm solves mathematical logistic equations capable of producing both ordered and chaotic (or random) solutions. This work can potentially lead to the simulation of artificial life processes. The third algorithm is the automatic segmentation of images into reasonable regions based on some similarity criterion, while the fourth is an implementation of a bitonic sort of data which significantly overcomes the nearest neighbor interconnection constraints on the MPP for transferring data between distant processors.

Mathematical Modeling of Protein Misfolding Mechanisms in Neurological Diseases: A Historical Overview.

PubMed

Carbonell, Felix; Iturria-Medina, Yasser; Evans, Alan C

2018-01-01

Protein misfolding refers to a process where proteins become structurally abnormal and lose their specific 3-dimensional spatial configuration. The histopathological presence of misfolded protein (MP) aggregates has been associated as the primary evidence of multiple neurological diseases, including Prion diseases, Alzheimer's disease, Parkinson's disease, and Creutzfeldt-Jacob disease. However, the exact mechanisms of MP aggregation and propagation, as well as their impact in the long-term patient's clinical condition are still not well understood. With this aim, a variety of mathematical models has been proposed for a better insight into the kinetic rate laws that govern the microscopic processes of protein aggregation. Complementary, another class of large-scale models rely on modern molecular imaging techniques for describing the phenomenological effects of MP propagation over the whole brain. Unfortunately, those neuroimaging-based studies do not take full advantage of the tremendous capabilities offered by the chemical kinetics modeling approach. Actually, it has been barely acknowledged that the vast majority of large-scale models have foundations on previous mathematical approaches that describe the chemical kinetics of protein replication and propagation. The purpose of the current manuscript is to present a historical review about the development of mathematical models for describing both microscopic processes that occur during the MP aggregation and large-scale events that characterize the progression of neurodegenerative MP-mediated diseases.

Fitting-free algorithm for efficient quantification of collagen fiber alignment in SHG imaging applications.

PubMed

Hall, Gunnsteinn; Liang, Wenxuan; Li, Xingde

2017-10-01

Collagen fiber alignment derived from second harmonic generation (SHG) microscopy images can be important for disease diagnostics. Image processing algorithms are needed to robustly quantify the alignment in images with high sensitivity and reliability. Fourier transform (FT) magnitude, 2D power spectrum, and image autocorrelation have previously been used to extract fiber information from images by assuming a certain mathematical model (e.g. Gaussian distribution of the fiber-related parameters) and fitting. The fitting process is slow and fails to converge when the data is not Gaussian. Herein we present an efficient constant-time deterministic algorithm which characterizes the symmetricity of the FT magnitude image in terms of a single parameter, named the fiber alignment anisotropy R ranging from 0 (randomized fibers) to 1 (perfect alignment). This represents an important improvement of the technology and may bring us one step closer to utilizing the technology for various applications in real time. In addition, we present a digital image phantom-based framework for characterizing and validating the algorithm, as well as assessing the robustness of the algorithm against different perturbations.

Experiment research on inertia-aided adaptive electronic image stabilization of optical stable platform

NASA Astrophysics Data System (ADS)

Lu, Xiaodong; Wu, Tianze; Zhou, Jun; Zhao, Bin; Ma, Xiaoyuan; Tang, Xiucheng

2016-03-01

An electronic image stabilization method compounded with inertia information, which can compensate the coupling interference caused by the pitch-yaw movement of the optical stable platform system, has been proposed in this paper. Firstly the mechanisms of coning rotation and lever-arm translation of line of sight (LOS) are analyzed during the stabilization process under moving carriers, and the mathematical model which describes the relationship between LOS rotation angle and platform attitude angle are derived. Then the image spin angle caused by coning rotation is estimated by using inertia information. Furthermore, an adaptive block matching method, which based on image edge and angular point, is proposed to smooth the jitter created by the lever-arm translation. This method optimizes the matching process and strategies. Finally, the results of hardware-in-the-loop simulation verified the effectiveness and real-time performance of the proposed method.

Blurred Star Image Processing for Star Sensors under Dynamic Conditions

PubMed Central

Zhang, Weina; Quan, Wei; Guo, Lei

2012-01-01

The precision of star point location is significant to identify the star map and to acquire the aircraft attitude for star sensors. Under dynamic conditions, star images are not only corrupted by various noises, but also blurred due to the angular rate of the star sensor. According to different angular rates under dynamic conditions, a novel method is proposed in this article, which includes a denoising method based on adaptive wavelet threshold and a restoration method based on the large angular rate. The adaptive threshold is adopted for denoising the star image when the angular rate is in the dynamic range. Then, the mathematical model of motion blur is deduced so as to restore the blurred star map due to large angular rate. Simulation results validate the effectiveness of the proposed method, which is suitable for blurred star image processing and practical for attitude determination of satellites under dynamic conditions. PMID:22778666

Robust algebraic image enhancement for intelligent control systems

NASA Technical Reports Server (NTRS)

Lerner, Bao-Ting; Morrelli, Michael

1993-01-01

Robust vision capability for intelligent control systems has been an elusive goal in image processing. The computationally intensive techniques a necessary for conventional image processing make real-time applications, such as object tracking and collision avoidance difficult. In order to endow an intelligent control system with the needed vision robustness, an adequate image enhancement subsystem capable of compensating for the wide variety of real-world degradations, must exist between the image capturing and the object recognition subsystems. This enhancement stage must be adaptive and must operate with consistency in the presence of both statistical and shape-based noise. To deal with this problem, we have developed an innovative algebraic approach which provides a sound mathematical framework for image representation and manipulation. Our image model provides a natural platform from which to pursue dynamic scene analysis, and its incorporation into a vision system would serve as the front-end to an intelligent control system. We have developed a unique polynomial representation of gray level imagery and applied this representation to develop polynomial operators on complex gray level scenes. This approach is highly advantageous since polynomials can be manipulated very easily, and are readily understood, thus providing a very convenient environment for image processing. Our model presents a highly structured and compact algebraic representation of grey-level images which can be viewed as fuzzy sets.

Inverting Image Data For Optical Testing And Alignment

NASA Technical Reports Server (NTRS)

Shao, Michael; Redding, David; Yu, Jeffrey W.; Dumont, Philip J.

1993-01-01

Data from images produced by slightly incorrectly figured concave primary mirror in telescope processed into estimate of spherical aberration of mirror, by use of algorithm finding nonlinear least-squares best fit between actual images and synthetic images produced by multiparameter mathematical model of telescope optical system. Estimated spherical aberration, in turn, converted into estimate of deviation of reflector surface from nominal precise shape. Algorithm devised as part of effort to determine error in surface figure of primary mirror of Hubble space telescope, so corrective lens designed. Modified versions of algorithm also used to find optical errors in other components of telescope or of other optical systems, for purposes of testing, alignment, and/or correction.

Differential morphology and image processing.

PubMed

Maragos, P

1996-01-01

Image processing via mathematical morphology has traditionally used geometry to intuitively understand morphological signal operators and set or lattice algebra to analyze them in the space domain. We provide a unified view and analytic tools for morphological image processing that is based on ideas from differential calculus and dynamical systems. This includes ideas on using partial differential or difference equations (PDEs) to model distance propagation or nonlinear multiscale processes in images. We briefly review some nonlinear difference equations that implement discrete distance transforms and relate them to numerical solutions of the eikonal equation of optics. We also review some nonlinear PDEs that model the evolution of multiscale morphological operators and use morphological derivatives. Among the new ideas presented, we develop some general 2-D max/min-sum difference equations that model the space dynamics of 2-D morphological systems (including the distance computations) and some nonlinear signal transforms, called slope transforms, that can analyze these systems in a transform domain in ways conceptually similar to the application of Fourier transforms to linear systems. Thus, distance transforms are shown to be bandpass slope filters. We view the analysis of the multiscale morphological PDEs and of the eikonal PDE solved via weighted distance transforms as a unified area in nonlinear image processing, which we call differential morphology, and briefly discuss its potential applications to image processing and computer vision.

A Cognitive Analysis of Students’ Mathematical Communication Ability on Geometry

NASA Astrophysics Data System (ADS)

Sari, D. S.; Kusnandi, K.; Suhendra, S.

2017-09-01

This study aims to analyze the difficulties of mathematical communication ability of students in one of secondary school on “three-dimensional space” topic. This research conducted by using quantitative approach with descriptive method. The population in this research was all students of that school and the sample was thirty students that was chosen by purposive sampling technique. Data of mathematical communication were collected through essay test. Furthermore, the data were analyzed with a descriptive way. The results of this study indicate that the percentage of achievement of student mathematical communication indicators as follows 1) Stating a situation, ideas, and mathematic correlation into images, graphics, or algebraic expressions is 35%; 2) Stating daily experience into a mathematic language / symbol, or a mathematic model is 35%; and 3) Associating images or diagrams into mathematical ideas is 53.3%. Based on the percentage of achievement on each indicator, it can be concluded that the level of achievement of students’ mathematical communication ability is still low. It can be caused the students were not used to convey or write their mathematical ideas systematically. Therefore students’ mathematical communication ability need to be improved.

Conceptions and Images of Mathematics Professors on Teaching Mathematics in School.

ERIC Educational Resources Information Center

Pehkonen, Erkki

1999-01-01

Clarifies what kind of mathematical beliefs are conveyed to student teachers during their studies. Interviews mathematics professors (n=7) from five Finnish universities who were responsible for mathematics teacher education. Professors estimated that teachers' basic knowledge was poor and old-fashioned, requiring improvement, and they emphasized…

A Mathematical Framework for Image Analysis

DTIC Science & Technology

1991-08-01

The results reported here were derived from the research project ’A Mathematical Framework for Image Analysis ’ supported by the Office of Naval...Research, contract N00014-88-K-0289 to Brown University. A common theme for the work reported is the use of probabilistic methods for problems in image ... analysis and image reconstruction. Five areas of research are described: rigid body recognition using a decision tree/combinatorial approach; nonrigid

How concept images affect students' interpretations of Newton's method

NASA Astrophysics Data System (ADS)

Engelke Infante, Nicole; Murphy, Kristen; Glenn, Celeste; Sealey, Vicki

2018-07-01

Knowing when students have the prerequisite knowledge to be able to read and understand a mathematical text is a perennial concern for instructors. Using text describing Newton's method and Vinner's notion of concept image, we exemplify how prerequisite knowledge influences understanding. Through clinical interviews with first-semester calculus students, we determined how evoked concept images of tangent lines and roots contributed to students' interpretation and application of Newton's method. Results show that some students' concept images of root and tangent line developed throughout the interview process, and most students were able to adequately interpret the text on Newton's method. However, students with insufficient concept images of tangent line and students who were unwilling or unable to modify their concept images of tangent line after reading the text were not successful in interpreting Newton's method.

Automated pathologies detection in retina digital images based on complex continuous wavelet transform phase angles.

PubMed

Lahmiri, Salim; Gargour, Christian S; Gabrea, Marcel

2014-10-01

An automated diagnosis system that uses complex continuous wavelet transform (CWT) to process retina digital images and support vector machines (SVMs) for classification purposes is presented. In particular, each retina image is transformed into two one-dimensional signals by concatenating image rows and columns separately. The mathematical norm of phase angles found in each one-dimensional signal at each level of CWT decomposition are relied on to characterise the texture of normal images against abnormal images affected by exudates, drusen and microaneurysms. The leave-one-out cross-validation method was adopted to conduct experiments and the results from the SVM show that the proposed approach gives better results than those obtained by other methods based on the correct classification rate, sensitivity and specificity.

Proceedings of the NASA Symposium on Mathematical Pattern Recognition and Image Analysis

NASA Technical Reports Server (NTRS)

Guseman, L. F., Jr.

1983-01-01

The application of mathematical and statistical analyses techniques to imagery obtained by remote sensors is described by Principal Investigators. Scene-to-map registration, geometric rectification, and image matching are among the pattern recognition aspects discussed.

Parallel asynchronous systems and image processing algorithms

NASA Technical Reports Server (NTRS)

Coon, D. D.; Perera, A. G. U.

1989-01-01

A new hardware approach to implementation of image processing algorithms is described. The approach is based on silicon devices which would permit an independent analog processing channel to be dedicated to evey pixel. A laminar architecture consisting of a stack of planar arrays of the device would form a two-dimensional array processor with a 2-D array of inputs located directly behind a focal plane detector array. A 2-D image data stream would propagate in neuronlike asynchronous pulse coded form through the laminar processor. Such systems would integrate image acquisition and image processing. Acquisition and processing would be performed concurrently as in natural vision systems. The research is aimed at implementation of algorithms, such as the intensity dependent summation algorithm and pyramid processing structures, which are motivated by the operation of natural vision systems. Implementation of natural vision algorithms would benefit from the use of neuronlike information coding and the laminar, 2-D parallel, vision system type architecture. Besides providing a neural network framework for implementation of natural vision algorithms, a 2-D parallel approach could eliminate the serial bottleneck of conventional processing systems. Conversion to serial format would occur only after raw intensity data has been substantially processed. An interesting challenge arises from the fact that the mathematical formulation of natural vision algorithms does not specify the means of implementation, so that hardware implementation poses intriguing questions involving vision science.

Working group organizational meeting

NASA Technical Reports Server (NTRS)

1982-01-01

Scene radiation and atmospheric effects, mathematical pattern recognition and image analysis, information evaluation and utilization, and electromagnetic measurements and signal handling are considered. Research issues in sensors and signals, including radar (SAR) reflectometry, SAR processing speed, registration, including overlay of SAR and optical imagery, entire system radiance calibration, and lack of requirements for both sensors and systems, etc. were discussed.

Neural Connectivity Patterns Underlying Symbolic Number Processing Indicate Mathematical Achievement in Children

ERIC Educational Resources Information Center

Park, Joonkoo; Li, Rosa; Brannon, Elizabeth M.

2014-01-01

In early childhood, humans learn culturally specific symbols for number that allow them entry into the world of complex numerical thinking. Yet little is known about how the brain supports the development of the uniquely human symbolic number system. Here, we use functional magnetic resonance imaging along with an effective connectivity analysis…

Mathematics of gravitational lensing: multiple imaging and magnification

NASA Astrophysics Data System (ADS)

Petters, A. O.; Werner, M. C.

2010-09-01

The mathematical theory of gravitational lensing has revealed many generic and global properties. Beginning with multiple imaging, we review Morse-theoretic image counting formulas and lower bound results, and complex-algebraic upper bounds in the case of single and multiple lens planes. We discuss recent advances in the mathematics of stochastic lensing, discussing a general formula for the global expected number of minimum lensed images as well as asymptotic formulas for the probability densities of the microlensing random time delay functions, random lensing maps, and random shear, and an asymptotic expression for the global expected number of micro-minima. Multiple imaging in optical geometry and a spacetime setting are treated. We review global magnification relation results for model-dependent scenarios and cover recent developments on universal local magnification relations for higher order caustics.

Improving science and mathematics education with computational modelling in interactive engagement environments

NASA Astrophysics Data System (ADS)

Neves, Rui Gomes; Teodoro, Vítor Duarte

2012-09-01

A teaching approach aiming at an epistemologically balanced integration of computational modelling in science and mathematics education is presented. The approach is based on interactive engagement learning activities built around computational modelling experiments that span the range of different kinds of modelling from explorative to expressive modelling. The activities are designed to make a progressive introduction to scientific computation without requiring prior development of a working knowledge of programming, generate and foster the resolution of cognitive conflicts in the understanding of scientific and mathematical concepts and promote performative competency in the manipulation of different and complementary representations of mathematical models. The activities are supported by interactive PDF documents which explain the fundamental concepts, methods and reasoning processes using text, images and embedded movies, and include free space for multimedia enriched student modelling reports and teacher feedback. To illustrate, an example from physics implemented in the Modellus environment and tested in undergraduate university general physics and biophysics courses is discussed.

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.

Feasibility study for automatic reduction of phase change imagery

NASA Technical Reports Server (NTRS)

Nossaman, G. O.

1971-01-01

The feasibility of automatically reducing a form of pictorial aerodynamic heating data is discussed. The imagery, depicting the melting history of a thin coat of fusible temperature indicator painted on an aerodynamically heated model, was previously reduced by manual methods. Careful examination of various lighting theories and approaches led to an experimentally verified illumination concept capable of yielding high-quality imagery. Both digital and video image processing techniques were applied to reduction of the data, and it was demonstrated that either method can be used to develop superimposed contours. Mathematical techniques were developed to find the model-to-image and the inverse image-to-model transformation using six conjugate points, and methods were developed using these transformations to determine heating rates on the model surface. A video system was designed which is able to reduce the imagery rapidly, economically and accurately. Costs for this system were estimated. A study plan was outlined whereby the mathematical transformation techniques developed to produce model coordinate heating data could be applied to operational software, and methods were discussed and costs estimated for obtaining the digital information necessary for this software.

Connectivity inference from neural recording data: Challenges, mathematical bases and research directions.

PubMed

Magrans de Abril, Ildefons; Yoshimoto, Junichiro; Doya, Kenji

2018-06-01

This article presents a review of computational methods for connectivity inference from neural activity data derived from multi-electrode recordings or fluorescence imaging. We first identify biophysical and technical challenges in connectivity inference along the data processing pipeline. We then review connectivity inference methods based on two major mathematical foundations, namely, descriptive model-free approaches and generative model-based approaches. We investigate representative studies in both categories and clarify which challenges have been addressed by which method. We further identify critical open issues and possible research directions. Copyright © 2018 The Author(s). Published by Elsevier Ltd.. All rights reserved.

Mathematical imaging methods for mitosis analysis in live-cell phase contrast microscopy.

PubMed

Grah, Joana Sarah; Harrington, Jennifer Alison; Koh, Siang Boon; Pike, Jeremy Andrew; Schreiner, Alexander; Burger, Martin; Schönlieb, Carola-Bibiane; Reichelt, Stefanie

2017-02-15

In this paper we propose a workflow to detect and track mitotic cells in time-lapse microscopy image sequences. In order to avoid the requirement for cell lines expressing fluorescent markers and the associated phototoxicity, phase contrast microscopy is often preferred over fluorescence microscopy in live-cell imaging. However, common specific image characteristics complicate image processing and impede use of standard methods. Nevertheless, automated analysis is desirable due to manual analysis being subjective, biased and extremely time-consuming for large data sets. Here, we present the following workflow based on mathematical imaging methods. In the first step, mitosis detection is performed by means of the circular Hough transform. The obtained circular contour subsequently serves as an initialisation for the tracking algorithm based on variational methods. It is sub-divided into two parts: in order to determine the beginning of the whole mitosis cycle, a backwards tracking procedure is performed. After that, the cell is tracked forwards in time until the end of mitosis. As a result, the average of mitosis duration and ratios of different cell fates (cell death, no division, division into two or more daughter cells) can be measured and statistics on cell morphologies can be obtained. All of the tools are featured in the user-friendly MATLAB®Graphical User Interface MitosisAnalyser. Copyright © 2017. Published by Elsevier Inc.

Mathematics for What? High School Students Reflect on Mathematics as a Tool for Social Inquiry

ERIC Educational Resources Information Center

Brelias, Anastasia

2015-01-01

This study examines high school students' views of mathematics as a tool for social inquiry in light of their classroom experiences using mathematics to explore social issues. A critical theoretical perspective on mathematics literacy is used to ascertain the ways in which their views challenge or affirm the dominant image of mathematics in…

Parallel-Processing Software for Creating Mosaic Images

NASA Technical Reports Server (NTRS)

Klimeck, Gerhard; Deen, Robert; McCauley, Michael; DeJong, Eric

2008-01-01

A computer program implements parallel processing for nearly real-time creation of panoramic mosaics of images of terrain acquired by video cameras on an exploratory robotic vehicle (e.g., a Mars rover). Because the original images are typically acquired at various camera positions and orientations, it is necessary to warp the images into the reference frame of the mosaic before stitching them together to create the mosaic. [Also see "Parallel-Processing Software for Correlating Stereo Images," Software Supplement to NASA Tech Briefs, Vol. 31, No. 9 (September 2007) page 26.] The warping algorithm in this computer program reflects the considerations that (1) for every pixel in the desired final mosaic, a good corresponding point must be found in one or more of the original images and (2) for this purpose, one needs a good mathematical model of the cameras and a good correlation of individual pixels with respect to their positions in three dimensions. The desired mosaic is divided into slices, each of which is assigned to one of a number of central processing units (CPUs) operating simultaneously. The results from the CPUs are gathered and placed into the final mosaic. The time taken to create the mosaic depends upon the number of CPUs, the speed of each CPU, and whether a local or a remote data-staging mechanism is used.

Single-Scale Fusion: An Effective Approach to Merging Images.

PubMed

Ancuti, Codruta O; Ancuti, Cosmin; De Vleeschouwer, Christophe; Bovik, Alan C

2017-01-01

Due to its robustness and effectiveness, multi-scale fusion (MSF) based on the Laplacian pyramid decomposition has emerged as a popular technique that has shown utility in many applications. Guided by several intuitive measures (weight maps) the MSF process is versatile and straightforward to be implemented. However, the number of pyramid levels increases with the image size, which implies sophisticated data management and memory accesses, as well as additional computations. Here, we introduce a simplified formulation that reduces MSF to only a single level process. Starting from the MSF decomposition, we explain both mathematically and intuitively (visually) a way to simplify the classical MSF approach with minimal loss of information. The resulting single-scale fusion (SSF) solution is a close approximation of the MSF process that eliminates important redundant computations. It also provides insights regarding why MSF is so effective. While our simplified expression is derived in the context of high dynamic range imaging, we show its generality on several well-known fusion-based applications, such as image compositing, extended depth of field, medical imaging, and blending thermal (infrared) images with visible light. Besides visual validation, quantitative evaluations demonstrate that our SSF strategy is able to yield results that are highly competitive with traditional MSF approaches.

A workflow to process 3D+time microscopy images of developing organisms and reconstruct their cell lineage

PubMed Central

Faure, Emmanuel; Savy, Thierry; Rizzi, Barbara; Melani, Camilo; Stašová, Olga; Fabrèges, Dimitri; Špir, Róbert; Hammons, Mark; Čúnderlík, Róbert; Recher, Gaëlle; Lombardot, Benoît; Duloquin, Louise; Colin, Ingrid; Kollár, Jozef; Desnoulez, Sophie; Affaticati, Pierre; Maury, Benoît; Boyreau, Adeline; Nief, Jean-Yves; Calvat, Pascal; Vernier, Philippe; Frain, Monique; Lutfalla, Georges; Kergosien, Yannick; Suret, Pierre; Remešíková, Mariana; Doursat, René; Sarti, Alessandro; Mikula, Karol; Peyriéras, Nadine; Bourgine, Paul

2016-01-01

The quantitative and systematic analysis of embryonic cell dynamics from in vivo 3D+time image data sets is a major challenge at the forefront of developmental biology. Despite recent breakthroughs in the microscopy imaging of living systems, producing an accurate cell lineage tree for any developing organism remains a difficult task. We present here the BioEmergences workflow integrating all reconstruction steps from image acquisition and processing to the interactive visualization of reconstructed data. Original mathematical methods and algorithms underlie image filtering, nucleus centre detection, nucleus and membrane segmentation, and cell tracking. They are demonstrated on zebrafish, ascidian and sea urchin embryos with stained nuclei and membranes. Subsequent validation and annotations are carried out using Mov-IT, a custom-made graphical interface. Compared with eight other software tools, our workflow achieved the best lineage score. Delivered in standalone or web service mode, BioEmergences and Mov-IT offer a unique set of tools for in silico experimental embryology. PMID:26912388

Biological Basis For Computer Vision: Some Perspectives

NASA Astrophysics Data System (ADS)

Gupta, Madan M.

1990-03-01

Using biology as a basis for the development of sensors, devices and computer vision systems is a challenge to systems and vision scientists. It is also a field of promising research for engineering applications. Biological sensory systems, such as vision, touch and hearing, sense different physical phenomena from our environment, yet they possess some common mathematical functions. These mathematical functions are cast into the neural layers which are distributed throughout our sensory regions, sensory information transmission channels and in the cortex, the centre of perception. In this paper, we are concerned with the study of the biological vision system and the emulation of some of its mathematical functions, both retinal and visual cortex, for the development of a robust computer vision system. This field of research is not only intriguing, but offers a great challenge to systems scientists in the development of functional algorithms. These functional algorithms can be generalized for further studies in such fields as signal processing, control systems and image processing. Our studies are heavily dependent on the the use of fuzzy - neural layers and generalized receptive fields. Building blocks of such neural layers and receptive fields may lead to the design of better sensors and better computer vision systems. It is hoped that these studies will lead to the development of better artificial vision systems with various applications to vision prosthesis for the blind, robotic vision, medical imaging, medical sensors, industrial automation, remote sensing, space stations and ocean exploration.

Symbolic Drawings Reveal Changes in Preservice Teacher Mathematics Attitudes after a Mathematics Methods Course

ERIC Educational Resources Information Center

Rule, Audrey C.; Harrell, Mary H.

2006-01-01

A new method of analyzing mathematics attitudes through symbolic drawings, situated within the field of Jungian-oriented analytical psychology, was applied to 52 preservice elementary teachers before and after a mathematics methods course. In this triangulation mixed methods design study, pretest images related to past mathematics experiences…

Brain organization underlying superior mathematical abilities in children with autism.

PubMed

Iuculano, Teresa; Rosenberg-Lee, Miriam; Supekar, Kaustubh; Lynch, Charles J; Khouzam, Amirah; Phillips, Jennifer; Uddin, Lucina Q; Menon, Vinod

2014-02-01

Autism spectrum disorder (ASD) is a neurodevelopmental disorder characterized by social and communication deficits. While such deficits have been the focus of most research, recent evidence suggests that individuals with ASD may exhibit cognitive strengths in domains such as mathematics. Cognitive assessments and functional brain imaging were used to investigate mathematical abilities in 18 children with ASD and 18 age-, gender-, and IQ-matched typically developing (TD) children. Multivariate classification and regression analyses were used to investigate whether brain activity patterns during numerical problem solving were significantly different between the groups and predictive of individual mathematical abilities. Children with ASD showed better numerical problem solving abilities and relied on sophisticated decomposition strategies for single-digit addition problems more frequently than TD peers. Although children with ASD engaged similar brain areas as TD children, they showed different multivariate activation patterns related to arithmetic problem complexity in ventral temporal-occipital cortex, posterior parietal cortex, and medial temporal lobe. Furthermore, multivariate activation patterns in ventral temporal-occipital cortical areas typically associated with face processing predicted individual numerical problem solving abilities in children with ASD but not in TD children. Our study suggests that superior mathematical information processing in children with ASD is characterized by a unique pattern of brain organization and that cortical regions typically involved in perceptual expertise may be utilized in novel ways in ASD. Our findings of enhanced cognitive and neural resources for mathematics have critical implications for educational, professional, and social outcomes for individuals with this lifelong disorder. Copyright © 2014 Society of Biological Psychiatry. Published by Elsevier Inc. All rights reserved.

Assessment of mass detection performance in contrast enhanced digital mammography

NASA Astrophysics Data System (ADS)

Carton, Ann-Katherine; de Carvalho, Pablo M.; Li, Zhijin; Dromain, Clarisse; Muller, Serge

2015-03-01

We address the detectability of contrast-agent enhancing masses for contrast-agent enhanced spectral mammography (CESM), a dual-energy technique providing functional projection images of breast tissue perfusion and vascularity using simulated CESM images. First, the realism of simulated CESM images from anthropomorphic breast software phantoms generated with a software X-ray imaging platform was validated. Breast texture was characterized by power-law coefficients calculated in data sets of real clinical and simulated images. We also performed a 2-alternative forced choice (2-AFC) psychophysical experiment whereby simulated and real images were presented side-by-side to an experienced radiologist to test if real images could be distinguished from the simulated images. It was found that texture in our simulated CESM images has a fairly realistic appearance. Next, the relative performance of human readers and previously developed mathematical observers was assessed for the detection of iodine-enhancing mass lesions containing different contrast agent concentrations. A four alternative-forced-choice (4 AFC) task was designed; the task for the model and human observer was to detect which one of the four simulated DE recombined images contained an iodineenhancing mass. Our results showed that the NPW and NPWE models largely outperform human performance. After introduction of an internal noise component, both observers approached human performance. The CHO observer performs slightly worse than the average human observer. There is still work to be done in improving model observers as predictors of human-observer performance. Larger trials could also improve our test statistics. We hope that in the future, this framework of software breast phantoms, virtual image acquisition and processing, and mathematical observers can be beneficial to optimize CESM imaging techniques.

Phase in Optical Image Processing

NASA Astrophysics Data System (ADS)

Naughton, Thomas J.

2010-04-01

The use of phase has a long standing history in optical image processing, with early milestones being in the field of pattern recognition, such as VanderLugt's practical construction technique for matched filters, and (implicitly) Goodman's joint Fourier transform correlator. In recent years, the flexibility afforded by phase-only spatial light modulators and digital holography, for example, has enabled many processing techniques based on the explicit encoding and decoding of phase. One application area concerns efficient numerical computations. Pushing phase measurement to its physical limits, designs employing the physical properties of phase have ranged from the sensible to the wonderful, in some cases making computationally easy problems easier to solve and in other cases addressing mathematics' most challenging computationally hard problems. Another application area is optical image encryption, in which, typically, a phase mask modulates the fractional Fourier transformed coefficients of a perturbed input image, and the phase of the inverse transform is then sensed as the encrypted image. The inherent linearity that makes the system so elegant mitigates against its use as an effective encryption technique, but we show how a combination of optical and digital techniques can restore confidence in that security. We conclude with the concept of digital hologram image processing, and applications of same that are uniquely suited to optical implementation, where the processing, recognition, or encryption step operates on full field information, such as that emanating from a coherently illuminated real-world three-dimensional object.

The Mathematics of Medical Imaging in the Classroom.

ERIC Educational Resources Information Center

Funkhouser, Charles P.; Jafari, Farhad; Eubank, William B.

2002-01-01

Presents an integrated exposition of aspects of secondary school mathematics and a medical science specialty. Reviews clinical medical practice and theoretical and empirical literature in mathematics education and radiology to develop and pilot model integrative classroom topics and activities. Suggests mathematical applications in numeration and…

Image reconstruction for PET/CT scanners: past achievements and future challenges

PubMed Central

Tong, Shan; Alessio, Adam M; Kinahan, Paul E

2011-01-01

PET is a medical imaging modality with proven clinical value for disease diagnosis and treatment monitoring. The integration of PET and CT on modern scanners provides a synergy of the two imaging modalities. Through different mathematical algorithms, PET data can be reconstructed into the spatial distribution of the injected radiotracer. With dynamic imaging, kinetic parameters of specific biological processes can also be determined. Numerous efforts have been devoted to the development of PET image reconstruction methods over the last four decades, encompassing analytic and iterative reconstruction methods. This article provides an overview of the commonly used methods. Current challenges in PET image reconstruction include more accurate quantitation, TOF imaging, system modeling, motion correction and dynamic reconstruction. Advances in these aspects could enhance the use of PET/CT imaging in patient care and in clinical research studies of pathophysiology and therapeutic interventions. PMID:21339831

Ghost image in enhanced self-heterodyne synthetic aperture imaging ladar

NASA Astrophysics Data System (ADS)

Zhang, Guo; Sun, Jianfeng; Zhou, Yu; Lu, Zhiyong; Li, Guangyuan; Xu, Mengmeng; Zhang, Bo; Lao, Chenzhe; He, Hongyu

2018-03-01

The enhanced self-heterodyne synthetic aperture imaging ladar (SAIL) self-heterodynes two polarization-orthogonal echo signals to eliminate the phase disturbance caused by atmospheric turbulence and mechanical trembling, uses heterodyne receiver instead of self-heterodyne receiver to improve signal-to-noise ratio. The principle and structure of the enhanced self-heterodyne SAIL are presented. The imaging process of enhanced self-heterodyne SAIL for distributed target is also analyzed. In enhanced self-heterodyne SAIL, the phases of two orthogonal-polarization beams are modulated by four cylindrical lenses in transmitter to improve resolutions in orthogonal direction and travel direction, which will generate ghost image. The generation process of ghost image in enhanced self-heterodyne SAIL is mathematically detailed, and a method of eliminating ghost image is also presented, which is significant for far-distance imaging. A number of experiments of enhanced self-heterodyne SAIL for distributed target are presented, these experimental results verify the theoretical analysis of enhanced self-heterodyne SAIL. The enhanced self-heterodyne SAIL has the capability to eliminate the influence from the atmospheric turbulence and mechanical trembling, has high advantage in detecting weak signals, and has promising application for far-distance ladar imaging.

On-Ground Processing of Yaogan-24 Remote Sensing Satellite Attitude Data and Verification Using Geometric Field Calibration

PubMed Central

Wang, Mi; Fan, Chengcheng; Yang, Bo; Jin, Shuying; Pan, Jun

2016-01-01

Satellite attitude accuracy is an important factor affecting the geometric processing accuracy of high-resolution optical satellite imagery. To address the problem whereby the accuracy of the Yaogan-24 remote sensing satellite’s on-board attitude data processing is not high enough and thus cannot meet its image geometry processing requirements, we developed an approach involving on-ground attitude data processing and digital orthophoto (DOM) and the digital elevation model (DEM) verification of a geometric calibration field. The approach focuses on three modules: on-ground processing based on bidirectional filter, overall weighted smoothing and fitting, and evaluation in the geometric calibration field. Our experimental results demonstrate that the proposed on-ground processing method is both robust and feasible, which ensures the reliability of the observation data quality, convergence and stability of the parameter estimation model. In addition, both the Euler angle and quaternion could be used to build a mathematical fitting model, while the orthogonal polynomial fitting model is more suitable for modeling the attitude parameter. Furthermore, compared to the image geometric processing results based on on-board attitude data, the image uncontrolled and relative geometric positioning result accuracy can be increased by about 50%. PMID:27483287

Introduction to the Discrete Fourier Series Considering Both Mathematical and Engineering Aspects--A Linear Algebra Approach

ERIC Educational Resources Information Center

Kohaupt, Ludwig

2015-01-01

The discrete Fourier series is a valuable tool developed and used by mathematicians and engineers alike. One of the most prominent applications is signal processing. Usually, it is important that the signals be transmitted fast, for example, when transmitting images over large distances such as between the moon and the earth or when generating…

Toward Model Building for Visual Aesthetic Perception

PubMed Central

Lughofer, Edwin; Zeng, Xianyi

2017-01-01

Several models of visual aesthetic perception have been proposed in recent years. Such models have drawn on investigations into the neural underpinnings of visual aesthetics, utilizing neurophysiological techniques and brain imaging techniques including functional magnetic resonance imaging, magnetoencephalography, and electroencephalography. The neural mechanisms underlying the aesthetic perception of the visual arts have been explained from the perspectives of neuropsychology, brain and cognitive science, informatics, and statistics. Although corresponding models have been constructed, the majority of these models contain elements that are difficult to be simulated or quantified using simple mathematical functions. In this review, we discuss the hypotheses, conceptions, and structures of six typical models for human aesthetic appreciation in the visual domain: the neuropsychological, information processing, mirror, quartet, and two hierarchical feed-forward layered models. Additionally, the neural foundation of aesthetic perception, appreciation, or judgement for each model is summarized. The development of a unified framework for the neurobiological mechanisms underlying the aesthetic perception of visual art and the validation of this framework via mathematical simulation is an interesting challenge in neuroaesthetics research. This review aims to provide information regarding the most promising proposals for bridging the gap between visual information processing and brain activity involved in aesthetic appreciation. PMID:29270194

New instantaneous frequency estimation method based on the use of image processing techniques

NASA Astrophysics Data System (ADS)

Borda, Monica; Nafornita, Ioan; Isar, Alexandru

2003-05-01

The aim of this paper is to present a new method for the estimation of the instantaneous frequency of a frequency modulated signal, corrupted by additive noise. This method represents an example of fusion of two theories: the time-frequency representations and the mathematical morphology. Any time-frequency representation of a useful signal is concentrated around its instantaneous frequency law and realizes the diffusion of the noise that perturbs the useful signal in the time - frequency plane. In this paper a new time-frequency representation, useful for the estimation of the instantaneous frequency, is proposed. This time-frequency representation is the product of two others time-frequency representations: the Wigner - Ville time-frequency representation and a new one obtained by filtering with a hard thresholding filter the Gabor representation of the signal to be processed. Using the image of this new time-frequency representation the instantaneous frequency of the useful signal can be extracted with the aid of some mathematical morphology operators: the conversion in binary form, the dilation and the skeleton. The simulations of the proposed method have proved its qualities. It is better than other estimation methods, like those based on the use of adaptive notch filters.

Nonuniformity correction of imaging systems with a spatially nonhomogeneous radiation source.

PubMed

Gutschwager, Berndt; Hollandt, Jörg

2015-12-20

We present a novel method of nonuniformity correction of imaging systems in a wide optical spectral range by applying a radiation source with an unknown and spatially nonhomogeneous radiance or radiance temperature distribution. The benefit of this method is that it can be applied with radiation sources of arbitrary spatial radiance or radiance temperature distribution and only requires the sufficient temporal stability of this distribution during the measurement process. The method is based on the recording of several (at least three) images of a radiation source and a purposeful row- and line-shift of these sequent images in relation to the first primary image. The mathematical procedure is explained in detail. Its numerical verification with a source of a predefined nonhomogenous radiance distribution and a thermal imager of a predefined nonuniform focal plane array responsivity is presented.

On use of image quality metrics for perceptual blur modeling: image/video compression case

NASA Astrophysics Data System (ADS)

Cha, Jae H.; Olson, Jeffrey T.; Preece, Bradley L.; Espinola, Richard L.; Abbott, A. Lynn

2018-02-01

Linear system theory is employed to make target acquisition performance predictions for electro-optical/infrared imaging systems where the modulation transfer function (MTF) may be imposed from a nonlinear degradation process. Previous research relying on image quality metrics (IQM) methods, which heuristically estimate perceived MTF has supported that an average perceived MTF can be used to model some types of degradation such as image compression. Here, we discuss the validity of the IQM approach by mathematically analyzing the associated heuristics from the perspective of reliability, robustness, and tractability. Experiments with standard images compressed by x.264 encoding suggest that the compression degradation can be estimated by a perceived MTF within boundaries defined by well-behaved curves with marginal error. Our results confirm that the IQM linearizer methodology provides a credible tool for sensor performance modeling.

Wavelet domain image restoration with adaptive edge-preserving regularization.

PubMed

Belge, M; Kilmer, M E; Miller, E L

2000-01-01

In this paper, we consider a wavelet based edge-preserving regularization scheme for use in linear image restoration problems. Our efforts build on a collection of mathematical results indicating that wavelets are especially useful for representing functions that contain discontinuities (i.e., edges in two dimensions or jumps in one dimension). We interpret the resulting theory in a statistical signal processing framework and obtain a highly flexible framework for adapting the degree of regularization to the local structure of the underlying image. In particular, we are able to adapt quite easily to scale-varying and orientation-varying features in the image while simultaneously retaining the edge preservation properties of the regularizer. We demonstrate a half-quadratic algorithm for obtaining the restorations from observed data.

Scaling of Counter-Current Imbibition Process in Low-Permeability Porous Media, TR-121

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

Kvoscek, A.R.; Zhou, D.; Jia, L.

2001-01-17

This project presents the recent work on imaging imbibition in low permeability porous media (diatomite) with X-ray completed tomography. The viscosity ratio between nonwetting and wetting fluids is varied over several orders of magnitude yielding different levels of imbibition performance. Also performed is mathematical analysis of counter-current imbibition processes and development of a modified scaling group incorporating the mobility ratio. This modified group is physically based and appears to improve scaling accuracy of countercurrent imbibition significantly.

Three-dimensional imaging of flat natural and cultural heritage objects by a Compton scattering modality

NASA Astrophysics Data System (ADS)

Guerrero Prado, Patricio; Nguyen, Mai K.; Dumas, Laurent; Cohen, Serge X.

2017-01-01

Characterization and interpretation of flat ancient material objects, such as those found in archaeology, paleoenvironments, paleontology, and cultural heritage, have remained a challenging task to perform by means of conventional x-ray tomography methods due to their anisotropic morphology and flattened geometry. To overcome the limitations of the mentioned methodologies for such samples, an imaging modality based on Compton scattering is proposed in this work. Classical x-ray tomography treats Compton scattering data as noise in the image formation process, while in Compton scattering tomography the conditions are set such that Compton data become the principal image contrasting agent. Under these conditions, we are able, first, to avoid relative rotations between the sample and the imaging setup, and second, to obtain three-dimensional data even when the object is supported by a dense material by exploiting backscattered photons. Mathematically this problem is addressed by means of a conical Radon transform and its inversion. The image formation process and object reconstruction model are presented. The feasibility of this methodology is supported by numerical simulations.

Mathematics from Still and Moving Images

ERIC Educational Resources Information Center

Pierce, Robyn; Stacey, Kaye; Ball, Lynda

2005-01-01

Digital photos and digital movies offer an excellent way of bringing real world situations into the mathematics classroom. The technologies surveyed here are feasible for everyday classroom use and inexpensive. Examples are drawn from the teaching of Cartesian coordinates, linear functions, ratio and Pythagoras' theorem using still images, and…

Will big data yield new mathematics? An evolving synergy with neuroscience

PubMed Central

Feng, S.; Holmes, P.

2016-01-01

New mathematics has often been inspired by new insights into the natural world. Here we describe some ongoing and possible future interactions among the massive data sets being collected in neuroscience, methods for their analysis and mathematical models of the underlying, still largely uncharted neural substrates that generate these data. We start by recalling events that occurred in turbulence modelling when substantial space-time velocity field measurements and numerical simulations allowed a new perspective on the governing equations of fluid mechanics. While no analogous global mathematical model of neural processes exists, we argue that big data may enable validation or at least rejection of models at cellular to brain area scales and may illuminate connections among models. We give examples of such models and survey some relatively new experimental technologies, including optogenetics and functional imaging, that can report neural activity in live animals performing complex tasks. The search for analytical techniques for these data is already yielding new mathematics, and we believe their multi-scale nature may help relate well-established models, such as the Hodgkin–Huxley equations for single neurons, to more abstract models of neural circuits, brain areas and larger networks within the brain. In brief, we envisage a closer liaison, if not a marriage, between neuroscience and mathematics. PMID:27516705

Will big data yield new mathematics? An evolving synergy with neuroscience.

PubMed

Feng, S; Holmes, P

2016-06-01

New mathematics has often been inspired by new insights into the natural world. Here we describe some ongoing and possible future interactions among the massive data sets being collected in neuroscience, methods for their analysis and mathematical models of the underlying, still largely uncharted neural substrates that generate these data. We start by recalling events that occurred in turbulence modelling when substantial space-time velocity field measurements and numerical simulations allowed a new perspective on the governing equations of fluid mechanics. While no analogous global mathematical model of neural processes exists, we argue that big data may enable validation or at least rejection of models at cellular to brain area scales and may illuminate connections among models. We give examples of such models and survey some relatively new experimental technologies, including optogenetics and functional imaging, that can report neural activity in live animals performing complex tasks. The search for analytical techniques for these data is already yielding new mathematics, and we believe their multi-scale nature may help relate well-established models, such as the Hodgkin-Huxley equations for single neurons, to more abstract models of neural circuits, brain areas and larger networks within the brain. In brief, we envisage a closer liaison, if not a marriage, between neuroscience and mathematics.

Programmability in AIPS++

NASA Technical Reports Server (NTRS)

Hjellming, R. M.

1992-01-01

AIPS++ is an Astronomical Information Processing System being designed and implemented by an international consortium of NRAO and six other radio astronomy institutions in Australia, India, the Netherlands, the United Kingdom, Canada, and the USA. AIPS++ is intended to replace the functionality of AIPS, to be more easily programmable, and will be implemented in C++ using object-oriented techniques. Programmability in AIPS++ is planned at three levels. The first level will be that of a command-line interpreter with characteristics similar to IDL and PV-Wave, but with an intensive set of operations appropriate to telescope data handling, image formation, and image processing. The third level will be in C++ with extensive use of class libraries for both basic operations and advanced applications. The third level will allow input and output of data between external FORTRAN programs and AIPS++ telescope and image databases. In addition to summarizing the above programmability characteristics, this talk will given an overview of the classes currently being designed for telescope data calibration and editing, image formation, and the 'toolkit' of mathematical 'objects' that will perform most of the processing in AIPS++.

The Alchemy of Mathematical Experience: A Psychoanalysis of Student Writings.

ERIC Educational Resources Information Center

Early, Robert E.

1992-01-01

Shares a psychological look at student images of mathematical learning and problem solving through students' writings about mathematical experiences. The analysis is done from a Jungian psychoanalytic orientation with the goal of assisting students develop a deeper perspective from which to view their mathematics experience. (MDH)

Mathematical filtering minimizes metallic halation of titanium implants in MicroCT images.

PubMed

Ha, Jee; Osher, Stanley J; Nishimura, Ichiro

2013-01-01

Microcomputed tomography (MicroCT) images containing titanium implant suffer from x-rays scattering, artifact and the implant surface is critically affected by metallic halation. To improve the metallic halation artifact, a nonlinear Total Variation denoising algorithm such as Split Bregman algorithm was applied to the digital data set of MicroCT images. This study demonstrated that the use of a mathematical filter could successfully reduce metallic halation, facilitating the osseointegration evaluation at the bone implant interface in the reconstructed images.

Enhancing the Teaching and Learning of Mathematical Visual Images

ERIC Educational Resources Information Center

Quinnell, Lorna

2014-01-01

The importance of mathematical visual images is indicated by the introductory paragraph in the Statistics and Probability content strand of the Australian Curriculum, which draws attention to the importance of learners developing skills to analyse and draw inferences from data and "represent, summarise and interpret data and undertake…

Semantic Processing of Mathematical Gestures

ERIC Educational Resources Information Center

Lim, Vanessa K.; Wilson, Anna J.; Hamm, Jeff P.; Phillips, Nicola; Iwabuchi, Sarina J.; Corballis, Michael C.; Arzarello, Ferdinando; Thomas, Michael O. J.

2009-01-01

Objective: To examine whether or not university mathematics students semantically process gestures depicting mathematical functions (mathematical gestures) similarly to the way they process action gestures and sentences. Semantic processing was indexed by the N400 effect. Results: The N400 effect elicited by words primed with mathematical gestures…

Processing electronic photos of Mercury produced by ground based observation

NASA Astrophysics Data System (ADS)

Ksanfomality, Leonid

New images of Mercury have been obtained by processing of ground based observations that were carried out using the short exposure technique. The disk of the planet extendeds usually from 6 to 7 arc seconds, with the linear size of the image in a focal plane of the telescope about 0.3-0.5 mm on the average. Processing initial millisecond electronic photos of the planet is very labour-consuming. Some features of processing of initial millisecond electronic photos by methods of correlation stacking were considered in (Ksanfomality et al., 2005; Ksanfomality and Sprague, 2007). The method uses manual selection of good photos including a so-called pilot- file, the search for which usually must be done manually. The pilot-file is the most successful one, in opinion of the operator. It defines the future result of the stacking. To change pilot-files increases the labor of processing many times. Programs of processing analyze the contents of a sample, find in it any details, and search for recurrence of these almost imperceptible details in thousand of other stacking electronic pictures. If, proceeding from experience, the form and position of a pilot-file still can be estimated, the estimation of a reality of barely distinct details in it is somewhere in between the imaging and imagination. In 2006-07 some programs of automatic processing have been created. Unfortunately, the efficiency of all automatic programs is not as good as manual selection. Together with the selection, some other known methods are used. The point spread function (PSF) is described by a known mathematical function which in its central part decreases smoothly from the center. Usually the width of this function is accepted at a level 0.7 or 0.5 of the maxima. If many thousands of initial electronic pictures are acquired, it is possible during their processing to take advantage of known statistics of random variables and to choose the width of the function at a level, say, 0.9 maxima. Then the resolution of the image improves appreciably. The essential element of processing is the mathematical model of unsharp mask. But this is a two-edged instrument. The result depends on a choice of the size of the mask. If the size is too small, all low spatial frequencies will be lost, and the image becomes grey uniformly; on the contrary, if the size of the unsharp mask is too great, all fine details disappear. In some cases the compromise in selection of parameters of the unsharp mask becomes critical.

Adaptive multifocus image fusion using block compressed sensing with smoothed projected Landweber integration in the wavelet domain.

PubMed

V S, Unni; Mishra, Deepak; Subrahmanyam, G R K S

2016-12-01

The need for image fusion in current image processing systems is increasing mainly due to the increased number and variety of image acquisition techniques. Image fusion is the process of combining substantial information from several sensors using mathematical techniques in order to create a single composite image that will be more comprehensive and thus more useful for a human operator or other computer vision tasks. This paper presents a new approach to multifocus image fusion based on sparse signal representation. Block-based compressive sensing integrated with a projection-driven compressive sensing (CS) recovery that encourages sparsity in the wavelet domain is used as a method to get the focused image from a set of out-of-focus images. Compression is achieved during the image acquisition process using a block compressive sensing method. An adaptive thresholding technique within the smoothed projected Landweber recovery process reconstructs high-resolution focused images from low-dimensional CS measurements of out-of-focus images. Discrete wavelet transform and dual-tree complex wavelet transform are used as the sparsifying basis for the proposed fusion. The main finding lies in the fact that sparsification enables a better selection of the fusion coefficients and hence better fusion. A Laplacian mixture model fit is done in the wavelet domain and estimation of the probability density function (pdf) parameters by expectation maximization leads us to the proper selection of the coefficients of the fused image. Using the proposed method compared with the fusion scheme without employing the projected Landweber (PL) scheme and the other existing CS-based fusion approaches, it is observed that with fewer samples itself, the proposed method outperforms other approaches.

V-Sipal - a Virtual Laboratory for Satellite Image Processing and Analysis

NASA Astrophysics Data System (ADS)

Buddhiraju, K. M.; Eeti, L.; Tiwari, K. K.

2011-09-01

In this paper a virtual laboratory for the Satellite Image Processing and Analysis (v-SIPAL) being developed at the Indian Institute of Technology Bombay is described. v-SIPAL comprises a set of experiments that are normally carried out by students learning digital processing and analysis of satellite images using commercial software. Currently, the experiments that are available on the server include Image Viewer, Image Contrast Enhancement, Image Smoothing, Edge Enhancement, Principal Component Transform, Texture Analysis by Co-occurrence Matrix method, Image Indices, Color Coordinate Transforms, Fourier Analysis, Mathematical Morphology, Unsupervised Image Classification, Supervised Image Classification and Accuracy Assessment. The virtual laboratory includes a theory module for each option of every experiment, a description of the procedure to perform each experiment, the menu to choose and perform the experiment, a module on interpretation of results when performed with a given image and pre-specified options, bibliography, links to useful internet resources and user-feedback. The user can upload his/her own images for performing the experiments and can also reuse outputs of one experiment in another experiment where applicable. Some of the other experiments currently under development include georeferencing of images, data fusion, feature evaluation by divergence andJ-M distance, image compression, wavelet image analysis and change detection. Additions to the theory module include self-assessment quizzes, audio-video clips on selected concepts, and a discussion of elements of visual image interpretation. V-SIPAL is at the satge of internal evaluation within IIT Bombay and will soon be open to selected educational institutions in India for evaluation.

In Silico Neuro-Oncology: Brownian Motion-Based Mathematical Treatment as a Potential Platform for Modeling the Infiltration of Glioma Cells into Normal Brain Tissue.

PubMed

Antonopoulos, Markos; Stamatakos, Georgios

2015-01-01

Intensive glioma tumor infiltration into the surrounding normal brain tissues is one of the most critical causes of glioma treatment failure. To quantitatively understand and mathematically simulate this phenomenon, several diffusion-based mathematical models have appeared in the literature. The majority of them ignore the anisotropic character of diffusion of glioma cells since availability of pertinent truly exploitable tomographic imaging data is limited. Aiming at enriching the anisotropy-enhanced glioma model weaponry so as to increase the potential of exploiting available tomographic imaging data, we propose a Brownian motion-based mathematical analysis that could serve as the basis for a simulation model estimating the infiltration of glioblastoma cells into the surrounding brain tissue. The analysis is based on clinical observations and exploits diffusion tensor imaging (DTI) data. Numerical simulations and suggestions for further elaboration are provided.

Fisher information theory for parameter estimation in single molecule microscopy: tutorial

PubMed Central

Chao, Jerry; Ward, E. Sally; Ober, Raimund J.

2016-01-01

Estimation of a parameter of interest from image data represents a task that is commonly carried out in single molecule microscopy data analysis. The determination of the positional coordinates of a molecule from its image, for example, forms the basis of standard applications such as single molecule tracking and localization-based superresolution image reconstruction. Assuming that the estimator used recovers, on average, the true value of the parameter, its accuracy, or standard deviation, is then at best equal to the square root of the Cramér-Rao lower bound. The Cramér-Rao lower bound can therefore be used as a benchmark in the evaluation of the accuracy of an estimator. Additionally, as its value can be computed and assessed for different experimental settings, it is useful as an experimental design tool. This tutorial demonstrates a mathematical framework that has been specifically developed to calculate the Cramér-Rao lower bound for estimation problems in single molecule microscopy and, more broadly, fluorescence microscopy. The material includes a presentation of the photon detection process that underlies all image data, various image data models that describe images acquired with different detector types, and Fisher information expressions that are necessary for the calculation of the lower bound. Throughout the tutorial, examples involving concrete estimation problems are used to illustrate the effects of various factors on the accuracy of parameter estimation, and more generally, to demonstrate the flexibility of the mathematical framework. PMID:27409706

Theory and applications of structured light single pixel imaging

NASA Astrophysics Data System (ADS)

Stokoe, Robert J.; Stockton, Patrick A.; Pezeshki, Ali; Bartels, Randy A.

2018-02-01

Many single-pixel imaging techniques have been developed in recent years. Though the methods of image acquisition vary considerably, the methods share unifying features that make general analysis possible. Furthermore, the methods developed thus far are based on intuitive processes that enable simple and physically-motivated reconstruction algorithms, however, this approach may not leverage the full potential of single-pixel imaging. We present a general theoretical framework of single-pixel imaging based on frame theory, which enables general, mathematically rigorous analysis. We apply our theoretical framework to existing single-pixel imaging techniques, as well as provide a foundation for developing more-advanced methods of image acquisition and reconstruction. The proposed frame theoretic framework for single-pixel imaging results in improved noise robustness, decrease in acquisition time, and can take advantage of special properties of the specimen under study. By building on this framework, new methods of imaging with a single element detector can be developed to realize the full potential associated with single-pixel imaging.

Dynamic cardiac PET imaging: extraction of time-activity curves using ICA and a generalized Gaussian distribution model.

PubMed

Mabrouk, Rostom; Dubeau, François; Bentabet, Layachi

2013-01-01

Kinetic modeling of metabolic and physiologic cardiac processes in small animals requires an input function (IF) and a tissue time-activity curves (TACs). In this paper, we present a mathematical method based on independent component analysis (ICA) to extract the IF and the myocardium's TACs directly from dynamic positron emission tomography (PET) images. The method assumes a super-Gaussian distribution model for the blood activity, and a sub-Gaussian distribution model for the tissue activity. Our appreach was applied on 22 PET measurement sets of small animals, which were obtained from the three most frequently used cardiac radiotracers, namely: desoxy-fluoro-glucose ((18)F-FDG), [(13)N]-ammonia, and [(11)C]-acetate. Our study was extended to PET human measurements obtained with the Rubidium-82 ((82) Rb) radiotracer. The resolved mathematical IF values compare favorably to those derived from curves extracted from regions of interest (ROI), suggesting that the procedure presents a reliable alternative to serial blood sampling for small-animal cardiac PET studies.

Mathematics Undergraduates' Responses to Semantic Abbreviations, 'Geometric' Images and Multi-Level Abstractions in Group Theory.

ERIC Educational Resources Information Center

Nardi, Elena

2000-01-01

Identifies and explores the difficulties in the novice mathematician's encounter with mathematical abstraction. Observes 20 first-year mathematics undergraduates and extracts sets of episodes from the transcripts of the tutorials and interviews within five topics in pure mathematics. Discusses issues related to the learning of one mathematical…

Loving and Loathing: Portrayals of School Mathematics in Young Adult Fiction

ERIC Educational Resources Information Center

Darragh, Lisa

2018-01-01

Images of mathematics and mathematicians are often negative and stereotyped. These portrayals may work to construct our impressions of mathematics and influence students' identity with and future participation in the subject. This study examined young adult fiction as a context in which school mathematics is portrayed and constructed. I used…

Machine processing of remotely sensed data; Proceedings of the Conference, Purdue University, West Lafayette, Ind., October 16-18, 1973

NASA Technical Reports Server (NTRS)

1973-01-01

Topics discussed include the management and processing of earth resources information, special-purpose processors for the machine processing of remotely sensed data, digital image registration by a mathematical programming technique, the use of remote-sensor data in land classification (in particular, the use of ERTS-1 multispectral scanning data), the use of remote-sensor data in geometrical transformations and mapping, earth resource measurement with the aid of ERTS-1 multispectral scanning data, the use of remote-sensor data in the classification of turbidity levels in coastal zones and in the identification of ecological anomalies, the problem of feature selection and the classification of objects in multispectral images, the estimation of proportions of certain categories of objects, and a number of special systems and techniques. Individual items are announced in this issue.

On-line object feature extraction for multispectral scene representation

NASA Technical Reports Server (NTRS)

Ghassemian, Hassan; Landgrebe, David

1988-01-01

A new on-line unsupervised object-feature extraction method is presented that reduces the complexity and costs associated with the analysis of the multispectral image data and data transmission, storage, archival and distribution. The ambiguity in the object detection process can be reduced if the spatial dependencies, which exist among the adjacent pixels, are intelligently incorporated into the decision making process. The unity relation was defined that must exist among the pixels of an object. Automatic Multispectral Image Compaction Algorithm (AMICA) uses the within object pixel-feature gradient vector as a valuable contextual information to construct the object's features, which preserve the class separability information within the data. For on-line object extraction the path-hypothesis and the basic mathematical tools for its realization are introduced in terms of a specific similarity measure and adjacency relation. AMICA is applied to several sets of real image data, and the performance and reliability of features is evaluated.

Looking for Science and Mathematics in All the Right Places: Using Mobile Technologies as Culturally-Sensitive Pedagogical Tools to Capture Generative Images

ERIC Educational Resources Information Center

Arreguin-Anderson, Maria G.; Ruiz, Elsa Cantu

2013-01-01

The exploration into cultural practices occurring in households has become more fluid and transparent process thanks to the presence of mobile technologies that allow members of a group to capture daily occurrences. This case study explored ways in which three Latino preservice teachers used mobile devices to discover connections between…

Mathematical modeling and SAR simulation multifunction SAR technology efforts

NASA Technical Reports Server (NTRS)

Griffin, C. R.; Estes, J. M.

1981-01-01

The orbital SAR (synthetic aperture radar) simulation data was used in several simulation efforts directed toward advanced SAR development. Efforts toward simulating an operational radar, simulation of antenna polarization effects, and simulation of SAR images at serveral different wavelengths are discussed. Avenues for improvements in the orbital SAR simulation and its application to the development of advanced digital radar data processing schemes are indicated.

Fundamental remote sensing science research program. Part 1: Status report of the mathematical pattern recognition and image analysis project

NASA Technical Reports Server (NTRS)

Heydorn, R. D.

1984-01-01

The Mathematical Pattern Recognition and Image Analysis (MPRIA) Project is concerned with basic research problems related to the study of the Earth from remotely sensed measurement of its surface characteristics. The program goal is to better understand how to analyze the digital image that represents the spatial, spectral, and temporal arrangement of these measurements for purposing of making selected inference about the Earth.

"Mathematicians Would Say It This Way": An Investigation of Teachers' Framings of Mathematicians

ERIC Educational Resources Information Center

Cirillo, Michelle; Herbel-Eisenmann, Beth

2011-01-01

Although popular media often provides negative images of mathematicians, we contend that mathematics classroom practices can also contribute to students' images of mathematicians. In this study, we examined eight mathematics teachers' framings of mathematicians in their classrooms. Here, we analyze classroom observations to explore some of the…

EISCAT Aperture Synthesis Imaging (EASI _3D) for the EISCAT_3D Project

NASA Astrophysics Data System (ADS)

La Hoz, Cesar; Belyey, Vasyl

2012-07-01

Aperture Synthesis Imaging Radar (ASIR) is one of the technologies adopted by the EISCAT_3D project to endow it with imaging capabilities in 3-dimensions that includes sub-beam resolution. Complemented by pulse compression, it will provide 3-dimensional images of certain types of incoherent scatter radar targets resolved to about 100 metres at 100 km range, depending on the signal-to-noise ratio. This ability will open new research opportunities to map small structures associated with non-homogeneous, unstable processes such as aurora, summer and winter polar radar echoes (PMSE and PMWE), Natural Enhanced Ion Acoustic Lines (NEIALs), structures excited by HF ionospheric heating, meteors, space debris, and others. The underlying physico-mathematical principles of the technique are the same as the technique employed in radioastronomy to image stellar objects; both require sophisticated inversion techniques to obtain reliable images.

Image Segmentation Method Using Fuzzy C Mean Clustering Based on Multi-Objective Optimization

NASA Astrophysics Data System (ADS)

Chen, Jinlin; Yang, Chunzhi; Xu, Guangkui; Ning, Li

2018-04-01

Image segmentation is not only one of the hottest topics in digital image processing, but also an important part of computer vision applications. As one kind of image segmentation algorithms, fuzzy C-means clustering is an effective and concise segmentation algorithm. However, the drawback of FCM is that it is sensitive to image noise. To solve the problem, this paper designs a novel fuzzy C-mean clustering algorithm based on multi-objective optimization. We add a parameter λ to the fuzzy distance measurement formula to improve the multi-objective optimization. The parameter λ can adjust the weights of the pixel local information. In the algorithm, the local correlation of neighboring pixels is added to the improved multi-objective mathematical model to optimize the clustering cent. Two different experimental results show that the novel fuzzy C-means approach has an efficient performance and computational time while segmenting images by different type of noises.

Label-free assessment of endothelial cell metabolic state using autofluorescent microscopy

NASA Astrophysics Data System (ADS)

Pullen, Benjamin J.; Nguyen, Tam; Gosnell, Martin; Anwer, Ayad G.; Goldys, Ewa; Nicholls, Stephen J.; Psaltis, Peter J.

2016-12-01

To examine the process of endothelial cell aging we utilised hyperspectral imaging to collect broad autofluorescence emission at the individual cellular level and mathematically isolate the characteristic spectra of nicotinamide and flavin adenine dinucleotides (NADH and FAD, respectively). Quantitative analysis of this data provides the basis for a non-destructive spatial imaging method for cells and tissue. FAD and NADH are important factors in cellular metabolism and have been shown to be involved with the redox state of the cell; with the ratio between the two providing the basis for an `optical redox ratio'.

Detecting perceptual groupings in textures by continuity considerations

NASA Technical Reports Server (NTRS)

Greene, Richard J.

1990-01-01

A generalization is presented for the second derivative of a Gaussian D(sup 2)G operator to apply to problems of perceptual organization involving textures. Extensions to other problems of perceptual organization are evident and a new research direction can be established. The technique presented is theoretically pleasing since it has the potential of unifying the entire area of image segmentation under the mathematical notion of continuity and presents a single algorithm to form perceptual groupings where many algorithms existed previously. The eventual impact on both the approach and technique of image processing segmentation operations could be significant.

Simulation of noise involved in synthetic aperture radar

NASA Astrophysics Data System (ADS)

Grandchamp, Myriam; Cavassilas, Jean-Francois

1996-08-01

The synthetic aperture radr (SAR) returns from a linear distribution of scatterers are simulated and processed in order to estimate the reflectivity coefficients of the ground. An original expression of this estimate is given, which establishes the relation between the terms of signal and noise. Both are compared. One application of this formulation consists of detecting a surface ship wake on a complex SAR image. A smoothing is first accomplished on the complex image. The choice of the integration area is determined by the preceding mathematical formulation. Then a differential filter is applied, and results are shown for two parts of the wake.

Basic research and data analysis for the earth and ocean physics applications program and for the National Geodetic Satellite program

NASA Technical Reports Server (NTRS)

1975-01-01

Data acquisition using single image and seven image data processing is used to provide a precise and accurate geometric description of the earth's surface. Transformation parameters and network distortions are determined, Sea slope along the continental boundaries of the U.S. and earth rotation are examined, along with close grid geodynamic satellite system. Data are derived for a mathematical description of the earth's gravitational field; time variations are determined for geometry of the ocean surface, the solid earth, gravity field, and other geophysical parameters.

Imaging quality evaluation method of pixel coupled electro-optical imaging system

NASA Astrophysics Data System (ADS)

He, Xu; Yuan, Li; Jin, Chunqi; Zhang, Xiaohui

2017-09-01

With advancements in high-resolution imaging optical fiber bundle fabrication technology, traditional photoelectric imaging system have become ;flexible; with greatly reduced volume and weight. However, traditional image quality evaluation models are limited by the coupling discrete sampling effect of fiber-optic image bundles and charge-coupled device (CCD) pixels. This limitation substantially complicates the design, optimization, assembly, and evaluation image quality of the coupled discrete sampling imaging system. Based on the transfer process of grayscale cosine distribution optical signal in the fiber-optic image bundle and CCD, a mathematical model of coupled modulation transfer function (coupled-MTF) is established. This model can be used as a basis for following studies on the convergence and periodically oscillating characteristics of the function. We also propose the concept of the average coupled-MTF, which is consistent with the definition of traditional MTF. Based on this concept, the relationships among core distance, core layer radius, and average coupled-MTF are investigated.

An interactive medical image segmentation framework using iterative refinement.

PubMed

Kalshetti, Pratik; Bundele, Manas; Rahangdale, Parag; Jangra, Dinesh; Chattopadhyay, Chiranjoy; Harit, Gaurav; Elhence, Abhay

2017-04-01

Segmentation is often performed on medical images for identifying diseases in clinical evaluation. Hence it has become one of the major research areas. Conventional image segmentation techniques are unable to provide satisfactory segmentation results for medical images as they contain irregularities. They need to be pre-processed before segmentation. In order to obtain the most suitable method for medical image segmentation, we propose MIST (Medical Image Segmentation Tool), a two stage algorithm. The first stage automatically generates a binary marker image of the region of interest using mathematical morphology. This marker serves as the mask image for the second stage which uses GrabCut to yield an efficient segmented result. The obtained result can be further refined by user interaction, which can be done using the proposed Graphical User Interface (GUI). Experimental results show that the proposed method is accurate and provides satisfactory segmentation results with minimum user interaction on medical as well as natural images. Copyright © 2017 Elsevier Ltd. All rights reserved.

Evaluation of area-based collagen scoring by nonlinear microscopy in chronic hepatitis C-induced liver fibrosis

PubMed Central

Sevrain, David; Dubreuil, Matthieu; Dolman, Grace Elizabeth; Zaitoun, Abed; Irving, William; Guha, Indra Neil; Odin, Christophe; Le Grand, Yann

2015-01-01

In this paper we analyze a fibrosis scoring method based on measurement of the fibrillar collagen area from second harmonic generation (SHG) microscopy images of unstained histological slices from human liver biopsies. The study is conducted on a cohort of one hundred chronic hepatitis C patients with intermediate to strong Metavir and Ishak stages of liver fibrosis. We highlight a key parameter of our scoring method to discriminate between high and low fibrosis stages. Moreover, according to the intensity histograms of the SHG images and simple mathematical arguments, we show that our area-based method is equivalent to an intensity-based method, despite saturation of the images. Finally we propose an improvement of our scoring method using very simple image processing tools. PMID:25909005

Evaluation of area-based collagen scoring by nonlinear microscopy in chronic hepatitis C-induced liver fibrosis.

PubMed

Sevrain, David; Dubreuil, Matthieu; Dolman, Grace Elizabeth; Zaitoun, Abed; Irving, William; Guha, Indra Neil; Odin, Christophe; Le Grand, Yann

2015-04-01

In this paper we analyze a fibrosis scoring method based on measurement of the fibrillar collagen area from second harmonic generation (SHG) microscopy images of unstained histological slices from human liver biopsies. The study is conducted on a cohort of one hundred chronic hepatitis C patients with intermediate to strong Metavir and Ishak stages of liver fibrosis. We highlight a key parameter of our scoring method to discriminate between high and low fibrosis stages. Moreover, according to the intensity histograms of the SHG images and simple mathematical arguments, we show that our area-based method is equivalent to an intensity-based method, despite saturation of the images. Finally we propose an improvement of our scoring method using very simple image processing tools.

Laser Speckle Imaging to Monitor Microvascular Blood Flow: A Review.

PubMed

Vaz, Pedro G; Humeau-Heurtier, Anne; Figueiras, Edite; Correia, Carlos; Cardoso, Joao

2016-01-01

Laser speckle is a complex interference phenomenon that can easily be understood, in concept, but is difficult to predict mathematically, because it is a stochastic process. The use of laser speckle to produce images, which can carry many types of information, is called laser speckle imaging (LSI). The biomedical applications of LSI started in 1981 and, since then, many scientists have improved the laser speckle theory and developed different imaging techniques. During this process, some inconsistencies have been propagated up to now. These inconsistencies should be clarified in order to avoid errors in future works. This review presents a review of the laser speckle theory used in biomedical applications. Moreover, we also make a review of the practical concepts that are useful in the construction of laser speckle imagers. This study is not only an exposition of the concepts that can be found in the literature but also a critical analysis of the investigations presented so far. Concepts like scatterers velocity distribution, effect of static scatterers, optimal speckle size, light penetration angle, and contrast computation algorithms are discussed in detail.

Laser marking as a result of applying reverse engineering

NASA Astrophysics Data System (ADS)

Mihalache, Andrei; Nagîţ, Gheorghe; Rîpanu, Marius Ionuţ; Slǎtineanu, Laurenţiu; Dodun, Oana; Coteaţǎ, Margareta

2018-05-01

The elaboration of a modern manufacturing technology needs a certain quantum of information concerning the part to be obtained. When it is necessary to elaborate the technology for an existing object, such an information could be ensured by using the principles specific to the reverse engineering. Essentially, in the case of this method, the analysis of the surfaces and of other characteristics of the part must offer enough information for the elaboration of the part manufacturing technology. On the other hand, it is known that the laser marking is a processing method able to ensure the transfer of various inscriptions or drawings on a part. Sometimes, the laser marking could be based on the analysis of an existing object, whose image could be used to generate the same object or an improved object. There are many groups of factors able to affect the results of applying the laser marking process. A theoretical analysis was proposed to show that the heights of triangles obtained by means of a CNC marking equipment depend on the width of the line generated by the laser spot on the workpiece surface. An experimental research was thought and materialized to highlight the influence exerted by the line with and the angle of lines intersections on the accuracy of the marking process. By mathematical processing of the experimental results, empirical mathematical models were determined. The power type model and the graphical representation elaborated on the base of this model offered an image concerning the influences exerted by the considered input factors on the marking process accuracy.

Preliminary Evaluation Report on the Los Angeles City Schools, SB 28 Demonstration Program in Mathematics.

ERIC Educational Resources Information Center

Gordon, C. Wayne

The purpose of this preliminary report is to describe and evaluate the Los Angeles Model Mathematics Project (LAMMP). The objectives of this project include the improvement of mathematical skills and understanding of mathematical concepts, the improvement of students' self-image, the development of instructional materials and the assessment of…

Universal gestational age effects on cognitive and basic mathematic processing: 2 cohorts in 2 countries.

PubMed

Wolke, Dieter; Strauss, Vicky Yu-Chun; Johnson, Samantha; Gilmore, Camilla; Marlow, Neil; Jaekel, Julia

2015-06-01

To determine whether general cognitive ability, basic mathematic processing, and mathematic attainment are universally affected by gestation at birth, as well as whether mathematic attainment is more strongly associated with cohort-specific factors such as schooling than basic cognitive and mathematical abilities. The Bavarian Longitudinal Study (BLS, 1289 children, 27-41 weeks gestational age [GA]) was used to estimate effects of GA on IQ, basic mathematic processing, and mathematic attainment. These estimations were used to predict IQ, mathematic processing, and mathematic attainment in the EPICure Study (171 children <26 weeks GA). For children born <34 weeks GA, each lower week decreased IQ and mathematic attainment scores by 2.34 (95% CI: -2.99, -1.70) and 2.76 (95% CI: -3.40, -2.11) points, respectively. There were no differences among children born 34-41 weeks GA. Similarly, for children born <36 weeks GA, mathematic processing scores decreased by 1.77 (95% CI: -2.20, -1.34) points with each lower GA week. The prediction function generated using BLS data accurately predicted the effect of GA on IQ and mathematic processing among EPICure children. However, these children had better attainment than predicted by BLS. Prematurity has adverse effects on basic mathematic processing following birth at all gestations <36 weeks and on IQ and mathematic attainment <34 weeks GA. The ability to predict IQ and mathematic processing scores from one cohort to another among children cared for in different eras and countries suggests that universal neurodevelopmental factors may explain the effects of gestation at birth. In contrast, mathematic attainment may be improved by schooling. Copyright © 2015 The Authors. Published by Elsevier Inc. All rights reserved.

Universal Gestational Age Effects on Cognitive and Basic Mathematic Processing: 2 Cohorts in 2 Countries

PubMed Central

Wolke, Dieter; Strauss, Vicky Yu-Chun; Johnson, Samantha; Gilmore, Camilla; Marlow, Neil; Jaekel, Julia

2015-01-01

Objective To determine whether general cognitive ability, basic mathematic processing, and mathematic attainment are universally affected by gestation at birth, as well as whether mathematic attainment is more strongly associated with cohort-specific factors such as schooling than basic cognitive and mathematical abilities. Study design The Bavarian Longitudinal Study (BLS, 1289 children, 27-41 weeks gestational age [GA]) was used to estimate effects of GA on IQ, basic mathematic processing, and mathematic attainment. These estimations were used to predict IQ, mathematic processing, and mathematic attainment in the EPICure Study (171 children <26 weeks GA). Results For children born <34 weeks GA, each lower week decreased IQ and mathematic attainment scores by 2.34 (95% CI: −2.99, −1.70) and 2.76 (95% CI: −3.40, −2.11) points, respectively. There were no differences among children born 34-41 weeks GA. Similarly, for children born <36 weeks GA, mathematic processing scores decreased by 1.77 (95% CI: −2.20, −1.34) points with each lower GA week. The prediction function generated using BLS data accurately predicted the effect of GA on IQ and mathematic processing among EPICure children. However, these children had better attainment than predicted by BLS. Conclusions Prematurity has adverse effects on basic mathematic processing following birth at all gestations <36 weeks and on IQ and mathematic attainment <34 weeks GA. The ability to predict IQ and mathematic processing scores from one cohort to another among children cared for in different eras and countries suggests that universal neurodevelopmental factors may explain the effects of gestation at birth. In contrast, mathematic attainment may be improved by schooling. PMID:25842966

The experience of mathematical beauty and its neural correlates

PubMed Central

Zeki, Semir; Romaya, John Paul; Benincasa, Dionigi M. T.; Atiyah, Michael F.

2014-01-01

Many have written of the experience of mathematical beauty as being comparable to that derived from the greatest art. This makes it interesting to learn whether the experience of beauty derived from such a highly intellectual and abstract source as mathematics correlates with activity in the same part of the emotional brain as that derived from more sensory, perceptually based, sources. To determine this, we used functional magnetic resonance imaging (fMRI) to image the activity in the brains of 15 mathematicians when they viewed mathematical formulae which they had individually rated as beautiful, indifferent or ugly. Results showed that the experience of mathematical beauty correlates parametrically with activity in the same part of the emotional brain, namely field A1 of the medial orbito-frontal cortex (mOFC), as the experience of beauty derived from other sources. PMID:24592230

Mathematics, anxiety, and the brain.

PubMed

Moustafa, Ahmed A; Tindle, Richard; Ansari, Zaheda; Doyle, Margery J; Hewedi, Doaa H; Eissa, Abeer

2017-05-24

Given that achievement in learning mathematics at school correlates with work and social achievements, it is important to understand the cognitive processes underlying abilities to learn mathematics efficiently as well as reasons underlying the occurrence of mathematics anxiety (i.e. feelings of tension and fear upon facing mathematical problems or numbers) among certain individuals. Over the last two decades, many studies have shown that learning mathematical and numerical concepts relies on many cognitive processes, including working memory, spatial skills, and linguistic abilities. In this review, we discuss the relationship between mathematical learning and cognitive processes as well as the neural substrates underlying successful mathematical learning and problem solving. More importantly, we also discuss the relationship between these cognitive processes, mathematics anxiety, and mathematics learning disabilities (dyscalculia). Our review shows that mathematical cognition relies on a complex brain network, and dysfunction to different segments of this network leads to varying manifestations of mathematical learning disabilities.

Multistage morphological segmentation of bright-field and fluorescent microscopy images

NASA Astrophysics Data System (ADS)

Korzyńska, A.; Iwanowski, M.

2012-06-01

This paper describes the multistage morphological segmentation method (MSMA) for microscopic cell images. The proposed method enables us to study the cell behaviour by using a sequence of two types of microscopic images: bright field images and/or fluorescent images. The proposed method is based on two types of information: the cell texture coming from the bright field images and intensity of light emission, done by fluorescent markers. The method is dedicated to the image sequences segmentation and it is based on mathematical morphology methods supported by other image processing techniques. The method allows for detecting cells in image independently from a degree of their flattening and from presenting structures which produce the texture. It makes use of some synergic information from the fluorescent light emission image as the support information. The MSMA method has been applied to images acquired during the experiments on neural stem cells as well as to artificial images. In order to validate the method, two types of errors have been considered: the error of cell area detection and the error of cell position using artificial images as the "gold standard".

Using image processing technology and mathematical algorithm in the automatic selection of vocal cord opening and closing images from the larynx endoscopy video.

PubMed

Kuo, Chung-Feng Jeffrey; Chu, Yueng-Hsiang; Wang, Po-Chun; Lai, Chun-Yu; Chu, Wen-Lin; Leu, Yi-Shing; Wang, Hsing-Won

2013-12-01

The human larynx is an important organ for voice production and respiratory mechanisms. The vocal cord is approximated for voice production and open for breathing. The videolaryngoscope is widely used for vocal cord examination. At present, physicians usually diagnose vocal cord diseases by manually selecting the image of the vocal cord opening to the largest extent (abduction), thus maximally exposing the vocal cord lesion. On the other hand, the severity of diseases such as vocal palsy, atrophic vocal cord is largely dependent on the vocal cord closing to the smallest extent (adduction). Therefore, diseases can be assessed by the image of the vocal cord opening to the largest extent, and the seriousness of breathy voice is closely correlated to the gap between vocal cords when closing to the smallest extent. The aim of the study was to design an automatic vocal cord image selection system to improve the conventional selection process by physicians and enhance diagnosis efficiency. Also, due to the unwanted fuzzy images resulting from examination process caused by human factors as well as the non-vocal cord images, texture analysis is added in this study to measure image entropy to establish a screening and elimination system to effectively enhance the accuracy of selecting the image of the vocal cord closing to the smallest extent. Copyright © 2013 Elsevier Ireland Ltd. All rights reserved.

Developing Physics E-Scaffolding Teaching Media to Increase the Eleventh-Grade Students' Problem Solving Ability and Scientific Attitude

ERIC Educational Resources Information Center

Saputri, Affa Ardhi; Wilujeng, Insih

2017-01-01

This research aims at revealing (1) the suitability of physics e-scaffolding teaching media with mathematical and image/diagrammatic representation, as well as (2) the effectiveness of the e-scaffolding teaching media with mathematical and image/diagrammatic representation to improve students' problem solving ability and scientific attitude. It is…

Image gathering and restoration - Information and visual quality

NASA Technical Reports Server (NTRS)

Mccormick, Judith A.; Alter-Gartenberg, Rachel; Huck, Friedrich O.

1989-01-01

A method is investigated for optimizing the end-to-end performance of image gathering and restoration for visual quality. To achieve this objective, one must inevitably confront the problems that the visual quality of restored images depends on perceptual rather than mathematical considerations and that these considerations vary with the target, the application, and the observer. The method adopted in this paper is to optimize image gathering informationally and to restore images interactively to obtain the visually preferred trade-off among fidelity resolution, sharpness, and clarity. The results demonstrate that this method leads to significant improvements in the visual quality obtained by the traditional digital processing methods. These traditional methods allow a significant loss of visual quality to occur because they treat the design of the image-gathering system and the formulation of the image-restoration algorithm as two separate tasks and fail to account for the transformations between the continuous and the discrete representations in image gathering and reconstruction.

The Cognitive Differences According to Regionality and Mathematical Minds

NASA Astrophysics Data System (ADS)

Park, Inchan; Igarashi, Hiroya; Yamanaka, Toshimasa

The purpose of this research is to explore factors that create cognitive diversity. We studied two different ways of recognizing images in our preliminary experiment: attribute-oriented thoughts and relationship-oriented thoughts. We examined whether we could observe the divergences in recognition processes between Asian and European cultures. From the result, we found that European (Dutch and British) subjects had stronger tendencies in attribute-oriented thoughts than the Korean subjects. However, in spite of their regional similarity, the Japanese subjects had greater tendencies in attribute-oriented thoughts than Korean subjects when comparing two Asian countries. This result made us question if there would be any other factors that could create the cognitive differences. Through the consideration of the participants' educational background, we found a possibility that the mathematical thoughts of the European and Japanese subjects were greater than the Korean subjects. Furthermore, in our subsequent study, we discovered that mathematical minds (skill and interest) effected on creating attribute-oriented thoughts as factors. We found the interesting discovery of the Japanese male participants, who had different cognitive tendencies with their mathematical skills and interests; the male subjects who had high-leveled mathematical skills, and who liked mathematics showed stronger tendencies of Attribute-oriented thoughts than those who did not. Based on the result, a possibility was suggested that the Japanese males' strong mathematical minds might be one of the factors that create the cognitive difference between Japanese and Korean subjects in the preliminary experiment.

A simple and robust method for artifacts correction on X-ray microtomography images

NASA Astrophysics Data System (ADS)

Timofey, Sizonenko; Marina, Karsanina; Dina, Gilyazetdinova; Irina, Bayuk; Kirill, Gerke

2017-04-01

X-ray microtomography images of rock material often have some kinds of distortion due to different reasons such as X-ray attenuation, beam hardening, irregularity of distribution of liquid/solid phases. Several kinds of distortion can arise from further image processing and stitching of images from different measurements. Beam-hardening is a well-known and studied distortion which is relative easy to be described, fitted and corrected using a number of equations. However, this is not the case for other grey scale intensity distortions. Shading by irregularity of distribution of liquid phases, incorrect scanner operating/parameters choosing, as well as numerous artefacts from mathematical reconstructions from projections, including stitching from separate scans cannot be described using single mathematical model. To correct grey scale intensities on large 3D images we developed a package Traditional method for removing the beam hardening [1] has been modified in order to find the center of distortion. The main contribution of this work is in development of a method for arbitrary image correction. This method is based on fitting the distortion by Bezier curve using image histogram. The distortion along the image is represented by a number of Bezier curves and one base line that characterizes the natural distribution of gray value along the image. All of these curves are set manually by the operator. We have tested our approaches on different X-ray microtomography images of porous media. Arbitrary correction removes all principal distortion. After correction the images has been binarized with subsequent pore-network extracted. Equal distribution of pore-network elements along the image was the criteria to verify the proposed technique to correct grey scale intensities. [1] Iassonov, P. and Tuller, M., 2010. Application of segmentation for correction of intensity bias in X-ray computed tomography images. Vadose Zone Journal, 9(1), pp.187-191.

Thermal imaging measurement of lateral diffusivity and non-invasive material defect detection

DOEpatents

Sun, Jiangang; Deemer, Chris

2003-01-01

A system and method for determining lateral thermal diffusivity of a material sample using a heat pulse; a sample oriented within an orthogonal coordinate system; an infrared camera; and a computer that has a digital frame grabber, and data acquisition and processing software. The mathematical model used within the data processing software is capable of determining the lateral thermal diffusivity of a sample of finite boundaries. The system and method may also be used as a nondestructive method for detecting and locating cracks within the material sample.

The Development of a Mathematical Foundation for Cellular Image Processing.

DTIC Science & Technology

1984-02-01

PERFORMING ORGANIZATION REPORT NUMBERIS) 5. MONITORING ORGANIZATION REPORT NUMBER(S) AFOSR-TR. 407 6&. NAME OF PERFORMING ORGANIZATION 5b. OFFICE...SYMBOL 7s. NAME OF MONITORING ORGANIZATION University of Florida (it appicable) Air Force Office of Scientific Research 6c. ADDRESS (City. State and ZIP...Bolling AFB DC 20332 84. NAME OF FUNDING/SPONSORING IBb. OFFICE SYMBOL 9. PROCUREMENT INSTRUMENT IDENTIFICATION NUMBER ORGANIZATION J(If applicablej FS

Unpacking the Logic of Mathematical Statements.

ERIC Educational Resources Information Center

Selden, John; Selden, Annie

1995-01-01

Investigated (n=61) undergraduates' ability to unpack informally written mathematical statements into the language of predicate calculus in an introduction to proofs and mathematical reasoning. Found that students were unable to construct proofs or validate them. Appendices are "A Sample Validation" and "Building a Statement Image." (MKR)

Teaching image-processing concepts in junior high school: boys' and girls' achievements and attitudes towards technology

NASA Astrophysics Data System (ADS)

Barak, Moshe; Asad, Khaled

2012-04-01

Background : This research focused on the development, implementation and evaluation of a course on image-processing principles aimed at middle-school students. Purpose : The overarching purpose of the study was that of integrating the learning of subjects in science, technology, engineering and mathematics (STEM), and linking the learning of these subjects to the children's world and to the digital culture characterizing society today. Sample : The participants were 60 junior high-school students (9th grade). Design and method : Data collection included observations in the classes, administering an attitude questionnaire before and after the course, giving an achievement exam and analyzing the students' final projects. Results and conclusions : The findings indicated that boys' and girls' achievements were similar throughout the course, and all managed to handle the mathematical knowledge without any particular difficulties. Learners' motivation to engage in the subject was high in the project-based learning part of the course in which they dealt, for instance, with editing their own pictures and experimenting with a facial recognition method. However, the students were less interested in learning the theory at the beginning of the course. The course increased the girls', more than the boys', interest in learning scientific-technological subjects in school, and the gender gap in this regard was bridged.

New formulation for interferometric synthetic aperture radar for terrain mapping

NASA Astrophysics Data System (ADS)

Jakowatz, Charles V., Jr.; Wahl, Daniel E.; Eichel, Paul H.; Thompson, Paul A.

1994-06-01

The subject of interferometric synthetic aperture radar (IFSAR) for high-accuracy terrain elevation mapping continues to gain importance in the arena of radar signal processing. Applications to problems in precision terrain-aided guidance and automatic target recognition, as well as a variety of civil applications, are being studied by a number of researchers. Not unlike many other areas of SAR processing, the subject of IFSAR can, at first glance, appear to be somewhat mysterious. In this paper we show how the mathematics of IFSAR for terrain elevation mapping using a pair of spotlight mode SAR collections can be derived in a very straightforward manner. Here, we employ an approach that relies entirely on Fourier transforms, and utilizes no reference to range equations or Doppler concepts. The result is a simplified explanation of the fundamentals of interferometry, including an easily-seen link between image domain phase difference and terrain elevation height. The derivation builds upon previous work by the authors in which a framework for spotlight mode SAR image formation based on an analogy to 3D computerized axial tomography (CAT) was developed. After outlining the major steps in the mathematics, we show how a computer simulator which utilizes 3D Fourier transforms can be constructed that demonstrates all of the major aspects of IFSAR from spotlight mode collections.

How predictive quantitative modelling of tissue organisation can inform liver disease pathogenesis.

PubMed

Drasdo, Dirk; Hoehme, Stefan; Hengstler, Jan G

2014-10-01

From the more than 100 liver diseases described, many of those with high incidence rates manifest themselves by histopathological changes, such as hepatitis, alcoholic liver disease, fatty liver disease, fibrosis, and, in its later stages, cirrhosis, hepatocellular carcinoma, primary biliary cirrhosis and other disorders. Studies of disease pathogeneses are largely based on integrating -omics data pooled from cells at different locations with spatial information from stained liver structures in animal models. Even though this has led to significant insights, the complexity of interactions as well as the involvement of processes at many different time and length scales constrains the possibility to condense disease processes in illustrations, schemes and tables. The combination of modern imaging modalities with image processing and analysis, and mathematical models opens up a promising new approach towards a quantitative understanding of pathologies and of disease processes. This strategy is discussed for two examples, ammonia metabolism after drug-induced acute liver damage, and the recovery of liver mass as well as architecture during the subsequent regeneration process. This interdisciplinary approach permits integration of biological mechanisms and models of processes contributing to disease progression at various scales into mathematical models. These can be used to perform in silico simulations to promote unravelling the relation between architecture and function as below illustrated for liver regeneration, and bridging from the in vitro situation and animal models to humans. In the near future novel mechanisms will usually not be directly elucidated by modelling. However, models will falsify hypotheses and guide towards the most informative experimental design. Copyright © 2014 European Association for the Study of the Liver. Published by Elsevier B.V. All rights reserved.

Signal dependence of inter-pixel capacitance in hybridized HgCdTe H2RG arrays for use in James Webb space telescope's NIRcam

NASA Astrophysics Data System (ADS)

Donlon, Kevan; Ninkov, Zoran; Baum, Stefi

2016-08-01

Interpixel capacitance (IPC) is a deterministic electronic coupling by which signal generated in one pixel is measured in neighboring pixels. Examination of dark frames from test NIRcam arrays corroborates earlier results and simulations illustrating a signal dependent coupling. When the signal on an individual pixel is larger, the fractional coupling to nearest neighbors is lesser than when the signal is lower. Frames from test arrays indicate a drop in average coupling from approximately 1.0% at low signals down to approximately 0.65% at high signals depending on the particular array in question. The photometric ramifications for this non-uniformity are not fully understood. This non-uniformity intro-duces a non-linearity in the current mathematical model for IPC coupling. IPC coupling has been mathematically formalized as convolution by a blur kernel. Signal dependence requires that the blur kernel be locally defined as a function of signal intensity. Through application of a signal dependent coupling kernel, the IPC coupling can be modeled computationally. This method allows for simultaneous knowledge of the intrinsic parameters of the image scene, the result of applying a constant IPC, and the result of a signal dependent IPC. In the age of sub-pixel precision in astronomy these effects must be properly understood and accounted for in order for the data to accurately represent the object of observation. Implementation of this method is done through python scripted processing of images. The introduction of IPC into simulated frames is accomplished through convolution of the image with a blur kernel whose parameters are themselves locally defined functions of the image. These techniques can be used to enhance the data processing pipeline for NIRcam.

Segmentation-based retrospective shading correction in fluorescence microscopy E. coli images for quantitative analysis

NASA Astrophysics Data System (ADS)

Mai, Fei; Chang, Chunqi; Liu, Wenqing; Xu, Weichao; Hung, Yeung S.

2009-10-01

Due to the inherent imperfections in the imaging process, fluorescence microscopy images often suffer from spurious intensity variations, which is usually referred to as intensity inhomogeneity, intensity non uniformity, shading or bias field. In this paper, a retrospective shading correction method for fluorescence microscopy Escherichia coli (E. Coli) images is proposed based on segmentation result. Segmentation and shading correction are coupled together, so we iteratively correct the shading effects based on segmentation result and refine the segmentation by segmenting the image after shading correction. A fluorescence microscopy E. Coli image can be segmented (based on its intensity value) into two classes: the background and the cells, where the intensity variation within each class is close to zero if there is no shading. Therefore, we make use of this characteristics to correct the shading in each iteration. Shading is mathematically modeled as a multiplicative component and an additive noise component. The additive component is removed by a denoising process, and the multiplicative component is estimated using a fast algorithm to minimize the intra-class intensity variation. We tested our method on synthetic images and real fluorescence E.coli images. It works well not only for visual inspection, but also for numerical evaluation. Our proposed method should be useful for further quantitative analysis especially for protein expression value comparison.

Extended wavelet transformation to digital holographic reconstruction: application to the elliptical, astigmatic Gaussian beams.

PubMed

Remacha, Clément; Coëtmellec, Sébastien; Brunel, Marc; Lebrun, Denis

2013-02-01

Wavelet analysis provides an efficient tool in numerous signal processing problems and has been implemented in optical processing techniques, such as in-line holography. This paper proposes an improvement of this tool for the case of an elliptical, astigmatic Gaussian (AEG) beam. We show that this mathematical operator allows reconstructing an image of a spherical particle without compression of the reconstructed image, which increases the accuracy of the 3D location of particles and of their size measurement. To validate the performance of this operator we have studied the diffraction pattern produced by a particle illuminated by an AEG beam. This study used mutual intensity propagation, and the particle is defined as a chirped Gaussian sum. The proposed technique was applied and the experimental results are presented.

Surge of Bering Glacier and Bagley Ice Field: Parameterization of surge characteristics based on automated analysis of crevasse image data and laser altimeter data

NASA Astrophysics Data System (ADS)

Stachura, M.; Herzfeld, U. C.; McDonald, B.; Weltman, A.; Hale, G.; Trantow, T.

2012-12-01

The dynamical processes that occur during the surge of a large, complex glacier system are far from being understood. The aim of this paper is to derive a parameterization of surge characteristics that captures the principle processes and can serve as the basis for a dynamic surge model. Innovative mathematical methods are introduced that facilitate derivation of such a parameterization from remote-sensing observations. Methods include automated geostatistical characterization and connectionist-geostatistical classification of dynamic provinces and deformation states, using the vehicle of crevasse patterns. These methods are applied to analyze satellite and airborne image and laser altimeter data collected during the current surge of Bering Glacier and Bagley Ice Field, Alaska.

Age-related changes in the activation of the intraparietal sulcus during nonsymbolic magnitude processing: an event-related functional magnetic resonance imaging study.

PubMed

Ansari, Daniel; Dhital, Bibek

2006-11-01

Numerical magnitude processing is an essential everyday skill. Functional brain imaging studies with human adults have repeatedly revealed that bilateral regions of the intraparietal sulcus are correlated with various numerical and mathematical skills. Surprisingly little, however, is known about the development of these brain representations. In the present study, we used functional neuroimaging to compare the neural correlates of nonsymbolic magnitude judgments between children and adults. Although behavioral performance was similar across groups, in comparison to the group of children the adult participants exhibited greater effects of numerical distance on the left intraparietal sulcus. Our findings are the first to reveal that even the most basic aspects of numerical cognition are subject to age-related changes in functional neuroanatomy. We propose that developmental impairments of number may be associated with atypical specialization of cortical regions underlying magnitude processing.

A mathematical model for computer image tracking.

PubMed

Legters, G R; Young, T Y

1982-06-01

A mathematical model using an operator formulation for a moving object in a sequence of images is presented. Time-varying translation and rotation operators are derived to describe the motion. A variational estimation algorithm is developed to track the dynamic parameters of the operators. The occlusion problem is alleviated by using a predictive Kalman filter to keep the tracking on course during severe occlusion. The tracking algorithm (variational estimation in conjunction with Kalman filter) is implemented to track moving objects with occasional occlusion in computer-simulated binary images.

Avoiding math on a rapid timescale: Emotional responsivity and anxious attention in math anxiety.

PubMed

Pizzie, Rachel G; Kraemer, David J M

2017-11-01

Math anxiety (MA) is characterized by negative feelings towards mathematics, resulting in avoidance of math classes and of careers that rely on mathematical skills. Focused on a long timescale, this research may miss important cognitive and affective processes that operate moment-to-moment, changing rapid reactions even when a student simply sees a math problem. Here, using fMRI with an attentional deployment paradigm, we show that MA influences rapid spontaneous emotional and attentional responses to mathematical stimuli upon brief presentation. Critically, participants viewed but did not attempt to solve the problems. Indicating increased threat reactivity to even brief presentations of math problems, increased MA was associated with increased amygdala response during math viewing trials. Functionally and anatomically defined amygdala ROIs yielded similar results, indicating robustness of the finding. Similar to the pattern of vigilance and avoidance observed in specific phobia, behavioral results of the attentional paradigm demonstrated that MA is associated with attentional disengagement for mathematical symbols. This attentional avoidance is specific to math stimuli; when viewing negatively-valenced images, MA is correlated with attentional engagement, similar to other forms of anxiety. These results indicate that even brief exposure to mathematics triggers a neural response related to threat avoidance in highly MA individuals. Copyright © 2017 Elsevier Inc. All rights reserved.

Go With the Flow, on Jupiter and Snow. Coherence from Model-Free Video Data Without Trajectories

NASA Astrophysics Data System (ADS)

AlMomani, Abd AlRahman R.; Bollt, Erik

2018-06-01

Viewing a data set such as the clouds of Jupiter, coherence is readily apparent to human observers, especially the Great Red Spot, but also other great storms and persistent structures. There are now many different definitions and perspectives mathematically describing coherent structures, but we will take an image processing perspective here. We describe an image processing perspective inference of coherent sets from a fluidic system directly from image data, without attempting to first model underlying flow fields, related to a concept in image processing called motion tracking. In contrast to standard spectral methods for image processing which are generally related to a symmetric affinity matrix, leading to standard spectral graph theory, we need a not symmetric affinity which arises naturally from the underlying arrow of time. We develop an anisotropic, directed diffusion operator corresponding to flow on a directed graph, from a directed affinity matrix developed with coherence in mind, and corresponding spectral graph theory from the graph Laplacian. Our methodology is not offered as more accurate than other traditional methods of finding coherent sets, but rather our approach works with alternative kinds of data sets, in the absence of vector field. Our examples will include partitioning the weather and cloud structures of Jupiter, and a local to Potsdam, NY, lake effect snow event on Earth, as well as the benchmark test double-gyre system.

Using wavelet denoising and mathematical morphology in the segmentation technique applied to blood cells images.

PubMed

Boix, Macarena; Cantó, Begoña

2013-04-01

Accurate image segmentation is used in medical diagnosis since this technique is a noninvasive pre-processing step for biomedical treatment. In this work we present an efficient segmentation method for medical image analysis. In particular, with this method blood cells can be segmented. For that, we combine the wavelet transform with morphological operations. Moreover, the wavelet thresholding technique is used to eliminate the noise and prepare the image for suitable segmentation. In wavelet denoising we determine the best wavelet that shows a segmentation with the largest area in the cell. We study different wavelet families and we conclude that the wavelet db1 is the best and it can serve for posterior works on blood pathologies. The proposed method generates goods results when it is applied on several images. Finally, the proposed algorithm made in MatLab environment is verified for a selected blood cells.

Image-algebraic design of multispectral target recognition algorithms

NASA Astrophysics Data System (ADS)

Schmalz, Mark S.; Ritter, Gerhard X.

1994-06-01

In this paper, we discuss methods for multispectral ATR (Automated Target Recognition) of small targets that are sensed under suboptimal conditions, such as haze, smoke, and low light levels. In particular, we discuss our ongoing development of algorithms and software that effect intelligent object recognition by selecting ATR filter parameters according to ambient conditions. Our algorithms are expressed in terms of IA (image algebra), a concise, rigorous notation that unifies linear and nonlinear mathematics in the image processing domain. IA has been implemented on a variety of parallel computers, with preprocessors available for the Ada and FORTRAN languages. An image algebra C++ class library has recently been made available. Thus, our algorithms are both feasible implementationally and portable to numerous machines. Analyses emphasize the aspects of image algebra that aid the design of multispectral vision algorithms, such as parameterized templates that facilitate the flexible specification of ATR filters.

Experience With Bayesian Image Based Surface Modeling

NASA Technical Reports Server (NTRS)

Stutz, John C.

2005-01-01

Bayesian surface modeling from images requires modeling both the surface and the image generation process, in order to optimize the models by comparing actual and generated images. Thus it differs greatly, both conceptually and in computational difficulty, from conventional stereo surface recovery techniques. But it offers the possibility of using any number of images, taken under quite different conditions, and by different instruments that provide independent and often complementary information, to generate a single surface model that fuses all available information. I describe an implemented system, with a brief introduction to the underlying mathematical models and the compromises made for computational efficiency. I describe successes and failures achieved on actual imagery, where we went wrong and what we did right, and how our approach could be improved. Lastly I discuss how the same approach can be extended to distinct types of instruments, to achieve true sensor fusion.

Optimization of a hardware implementation for pulse coupled neural networks for image applications

NASA Astrophysics Data System (ADS)

Gimeno Sarciada, Jesús; Lamela Rivera, Horacio; Warde, Cardinal

2010-04-01

Pulse Coupled Neural Networks are a very useful tool for image processing and visual applications, since it has the advantages of being invariant to image changes as rotation, scale, or certain distortion. Among other characteristics, the PCNN changes a given image input into a temporal representation which can be easily later analyzed for pattern recognition. The structure of a PCNN though, makes it necessary to determine all of its parameters very carefully in order to function optimally, so that the responses to the kind of inputs it will be subjected are clearly discriminated allowing for an easy and fast post-processing yielding useful results. This tweaking of the system is a taxing process. In this paper we analyze and compare two methods for modeling PCNNs. A purely mathematical model is programmed and a similar circuital model is also designed. Both are then used to determine the optimal values of the several parameters of a PCNN: gain, threshold, time constants for feed-in and threshold and linking leading to an optimal design for image recognition. The results are compared for usefulness, accuracy and speed, as well as the performance and time requirements for fast and easy design, thus providing a tool for future ease of management of a PCNN for different tasks.

The Mathematics of Medical Imaging in the Classroom

ERIC Educational Resources Information Center

Funkhouser, Charles P.; Jafari, Farhad; Eubank, William B.

2002-01-01

The article presents an integrated exposition of aspects of secondary school mathematics and a medical science specialty together with related classroom activities. Clinical medical practice and theoretical and empirical literature in mathematics education and radiology were reviewed to develop and pilot model integrative classroom topics and…

Workbook, Basic Mathematics and Wastewater Processing Calculations.

ERIC Educational Resources Information Center

New York State Dept. of Environmental Conservation, Albany.

This workbook serves as a self-learning guide to basic mathematics and treatment plant calculations and also as a reference and source book for the mathematics of sewage treatment and processing. In addition to basic mathematics, the workbook discusses processing and process control, laboratory calculations and efficiency calculations necessary in…

Imaging and applied optics: introduction to the feature issue.

PubMed

Zalevsky, Zeev; Arnison, Matthew R; Javidi, Bahram; Testorf, Markus

2018-03-01

This special issue of Applied Optics contains selected papers from OSA's Imaging Congress with particular emphasis on work from mathematics in imaging, computational optical sensing and imaging, imaging systems and applications, and 3D image acquisition and display.

Super-resolved refocusing with a plenoptic camera

NASA Astrophysics Data System (ADS)

Zhou, Zhiliang; Yuan, Yan; Bin, Xiangli; Qian, Lulu

2011-03-01

This paper presents an approach to enhance the resolution of refocused images by super resolution methods. In plenoptic imaging, we demonstrate that the raw sensor image can be divided to a number of low-resolution angular images with sub-pixel shifts between each other. The sub-pixel shift, which defines the super-resolving ability, is mathematically derived by considering the plenoptic camera as equivalent camera arrays. We implement simulation to demonstrate the imaging process of a plenoptic camera. A high-resolution image is then reconstructed using maximum a posteriori (MAP) super resolution algorithms. Without other degradation effects in simulation, the super resolved image achieves a resolution as high as predicted by the proposed model. We also build an experimental setup to acquire light fields. With traditional refocusing methods, the image is rendered at a rather low resolution. In contrast, we implement the super-resolved refocusing methods and recover an image with more spatial details. To evaluate the performance of the proposed method, we finally compare the reconstructed images using image quality metrics like peak signal to noise ratio (PSNR).

Image Science and Analysis Group Spacecraft Damage Detection/Characterization

NASA Technical Reports Server (NTRS)

Wheaton, Ira M., Jr.

2010-01-01

This project consisted of several tasks that could be served by an intern to assist the ISAG in detecting damage to spacecrafts during missions. First, this project focused on supporting the Micrometeoroid Orbital Debris (MMOD) damage detection and assessment for the Hubble Space Telescope (HST) using imagery from the last two HST Shuttle servicing missions. In this project, we used coordinates of two windows on the Shuttle Aft flight deck from where images were taken and the coordinates of three ID points in order to calculate the distance from each window to the three points. Then, using the specifications from the camera used, we calculated the image scale in pixels per inch for planes parallel to and planes in the z-direction to the image plane (shown in Table 1). This will help in the future for calculating measurements of objects in the images. Next, tabulation and statistical analysis were conducted for screening results (shown in Table 2) of imagery with Orion Thermal Protection System (TPS) damage. Using the Microsoft Excel CRITBINOM function and Goal Seek, the probabilities of detection of damage to different shuttle tiles were calculated as shown in Table 3. Using developed measuring tools, volume and area measurements will be created from 3D models of Orion TPS damage. Last, mathematical expertise was provided to the Photogrammetry Team. These mathematical tasks consisted of developing elegant image space error equations for observations along 3D lines, circles, planes, etc. and checking proofs for minimal sets of sufficient multi-linear constraints. Some of the processes and resulting equations are displayed in Figure 1.

Aberrant Functional Activation in School Age Children At-Risk for Mathematical Disability: A Functional Imaging Study of Simple Arithmetic Skill

ERIC Educational Resources Information Center

Davis, Nicole; Cannistraci, Christopher J.; Rogers, Baxter P.; Gatenby, J. Christopher; Fuchs, Lynn S.; Anderson, Adam W.; Gore, John C.

2009-01-01

We used functional magnetic resonance imaging (fMRI) to explore the patterns of brain activation associated with different levels of performance in exact and approximate calculation tasks in well-defined cohorts of children with mathematical calculation difficulties (MD) and typically developing controls. Both groups of children activated the same…

An image overall complexity evaluation method based on LSD line detection

NASA Astrophysics Data System (ADS)

Li, Jianan; Duan, Jin; Yang, Xu; Xiao, Bo

2017-04-01

In the artificial world, whether it is the city's traffic roads or engineering buildings contain a lot of linear features. Therefore, the research on the image complexity of linear information has become an important research direction in digital image processing field. This paper, by detecting the straight line information in the image and using the straight line as the parameter index, establishing the quantitative and accurate mathematics relationship. In this paper, we use LSD line detection algorithm which has good straight-line detection effect to detect the straight line, and divide the detected line by the expert consultation strategy. Then we use the neural network to carry on the weight training and get the weight coefficient of the index. The image complexity is calculated by the complexity calculation model. The experimental results show that the proposed method is effective. The number of straight lines in the image, the degree of dispersion, uniformity and so on will affect the complexity of the image.

Aircraft geometry verification with enhanced computer generated displays

NASA Technical Reports Server (NTRS)

Cozzolongo, J. V.

1982-01-01

A method for visual verification of aerodynamic geometries using computer generated, color shaded images is described. The mathematical models representing aircraft geometries are created for use in theoretical aerodynamic analyses and in computer aided manufacturing. The aerodynamic shapes are defined using parametric bi-cubic splined patches. This mathematical representation is then used as input to an algorithm that generates a color shaded image of the geometry. A discussion of the techniques used in the mathematical representation of the geometry and in the rendering of the color shaded display is presented. The results include examples of color shaded displays, which are contrasted with wire frame type displays. The examples also show the use of mapped surface pressures in terms of color shaded images of V/STOL fighter/attack aircraft and advanced turboprop aircraft.

Modeling birds on wires.

PubMed

Aydoğdu, A; Frasca, P; D'Apice, C; Manzo, R; Thornton, J M; Gachomo, B; Wilson, T; Cheung, B; Tariq, U; Saidel, W; Piccoli, B

2017-02-21

In this paper we introduce a mathematical model to study the group dynamics of birds resting on wires. The model is agent-based and postulates attraction-repulsion forces between the interacting birds: the interactions are "topological", in the sense that they involve a given number of neighbors irrespective of their distance. The model is first mathematically analyzed and then simulated to study its main properties: we observe that the model predicts birds to be more widely spaced near the borders of each group. We compare the results from the model with experimental data, derived from the analysis of pictures of pigeons and starlings taken in New Jersey: two different image elaboration protocols allow us to establish a good agreement with the model and to quantify its main parameters. We also discuss the potential handedness of the birds, by analyzing the group organization features and the group dynamics at the arrival of new birds. Finally, we propose a more refined mathematical model that describes landing and departing birds by suitable stochastic processes. Copyright © 2016 Elsevier Ltd. All rights reserved.

The use of algorithmic behavioural transfer functions in parametric EO system performance models

NASA Astrophysics Data System (ADS)

Hickman, Duncan L.; Smith, Moira I.

2015-10-01

The use of mathematical models to predict the overall performance of an electro-optic (EO) system is well-established as a methodology and is used widely to support requirements definition, system design, and produce performance predictions. Traditionally these models have been based upon cascades of transfer functions based on established physical theory, such as the calculation of signal levels from radiometry equations, as well as the use of statistical models. However, the performance of an EO system is increasing being dominated by the on-board processing of the image data and this automated interpretation of image content is complex in nature and presents significant modelling challenges. Models and simulations of EO systems tend to either involve processing of image data as part of a performance simulation (image-flow) or else a series of mathematical functions that attempt to define the overall system characteristics (parametric). The former approach is generally more accurate but statistically and theoretically weak in terms of specific operational scenarios, and is also time consuming. The latter approach is generally faster but is unable to provide accurate predictions of a system's performance under operational conditions. An alternative and novel architecture is presented in this paper which combines the processing speed attributes of parametric models with the accuracy of image-flow representations in a statistically valid framework. An additional dimension needed to create an effective simulation is a robust software design whose architecture reflects the structure of the EO System and its interfaces. As such, the design of the simulator can be viewed as a software prototype of a new EO System or an abstraction of an existing design. This new approach has been used successfully to model a number of complex military systems and has been shown to combine improved performance estimation with speed of computation. Within the paper details of the approach and architecture are described in detail, and example results based on a practical application are then given which illustrate the performance benefits. Finally, conclusions are drawn and comments given regarding the benefits and uses of the new approach.

Hybrid model based unified scheme for endoscopic Cerenkov and radio-luminescence tomography: Simulation demonstration

NASA Astrophysics Data System (ADS)

Wang, Lin; Cao, Xin; Ren, Qingyun; Chen, Xueli; He, Xiaowei

2018-05-01

Cerenkov luminescence imaging (CLI) is an imaging method that uses an optical imaging scheme to probe a radioactive tracer. Application of CLI with clinically approved radioactive tracers has opened an opportunity for translating optical imaging from preclinical to clinical applications. Such translation was further improved by developing an endoscopic CLI system. However, two-dimensional endoscopic imaging cannot identify accurate depth and obtain quantitative information. Here, we present an imaging scheme to retrieve the depth and quantitative information from endoscopic Cerenkov luminescence tomography, which can also be applied for endoscopic radio-luminescence tomography. In the scheme, we first constructed a physical model for image collection, and then a mathematical model for characterizing the luminescent light propagation from tracer to the endoscopic detector. The mathematical model is a hybrid light transport model combined with the 3rd order simplified spherical harmonics approximation, diffusion, and radiosity equations to warrant accuracy and speed. The mathematical model integrates finite element discretization, regularization, and primal-dual interior-point optimization to retrieve the depth and the quantitative information of the tracer. A heterogeneous-geometry-based numerical simulation was used to explore the feasibility of the unified scheme, which demonstrated that it can provide a satisfactory balance between imaging accuracy and computational burden.

Mathematization Competencies of Pre-Service Elementary Mathematics Teachers in the Mathematical Modelling Process

ERIC Educational Resources Information Center

Yilmaz, Suha; Tekin-Dede, Ayse

2016-01-01

Mathematization competency is considered in the field as the focus of modelling process. Considering the various definitions, the components of the mathematization competency are determined as identifying assumptions, identifying variables based on the assumptions and constructing mathematical model/s based on the relations among identified…

Study of Tissue Phantoms, Tissues, and Contrast Agent with the Biophotoacoustic Radar and Comparison to Ultrasound Imaging for Deep Subsurface Imaging

NASA Astrophysics Data System (ADS)

Alwi, R.; Telenkov, S.; Mandelis, A.; Gu, F.

2012-11-01

In this study, the imaging capability of our wide-spectrum frequency-domain photoacoustic (FD-PA) imaging alias "photoacoustic radar" methodology for imaging of soft tissues is explored. A practical application of the mathematical correlation processing method with relatively long (1 ms) frequency-modulated optical excitation is demonstrated for reconstruction of the spatial location of the PA sources. Image comparison with ultrasound (US) modality was investigated to see the complementarity between the two techniques. The obtained results with a phased array probe on tissue phantoms and their comparison to US images demonstrated that the FD-PA technique has strong potential for deep subsurface imaging with excellent contrast and high signal-to-noise ratio. FD-PA images of blood vessels in a human wrist and an in vivo subcutaneous tumor in a rat model are presented. As in other imaging modalities, the employment of contrast agents is desirable to improve the capability of medical diagnostics. Therefore, this study also evaluated and characterized the use of Food and Drug Administration (FDA)-approved superparamagnetic iron oxide nanoparticles (SPION) as PA contrast agents.

Alignment theory of parallel-beam computed tomography image reconstruction for elastic-type objects using virtual focusing method.

PubMed

Jun, Kyungtaek; Kim, Dongwook

2018-01-01

X-ray computed tomography has been studied in various fields. Considerable effort has been focused on reconstructing the projection image set from a rigid-type specimen. However, reconstruction of images projected from an object showing elastic motion has received minimal attention. In this paper, a mathematical solution to reconstructing the projection image set obtained from an object with specific elastic motions-periodically, regularly, and elliptically expanded or contracted specimens-is proposed. To reconstruct the projection image set from expanded or contracted specimens, methods are presented for detection of the sample's motion modes, mathematical rescaling of pixel values, and conversion of the projection angle for a common layer.

Modelling the influence of noise of the image sensor for blood cells recognition in computer microscopy

NASA Astrophysics Data System (ADS)

Nikitaev, V. G.; Nagornov, O. V.; Pronichev, A. N.; Polyakov, E. V.; Dmitrieva, V. V.

2017-12-01

The first stage of diagnostics of blood cancer is the analysis of blood smears. The application of decision-making support systems would reduce the subjectivity of the diagnostic process and avoid errors, resulting in often irreversible changes in the patient's condition. In this regard, the solution of this problem requires the use of modern technology. One of the tools of the program classification of blood cells are texture features, and the task of finding informative among them is promising. The paper investigates the effect of noise of the image sensor to informative texture features with application of methods of mathematical modelling.

Stack of Layers at 'Payson' in Meridiani Planum

NASA Technical Reports Server (NTRS)

2006-01-01

The stack of fine layers exposed at a ledge called 'Payson' on the western edge of 'Erebus Crater' in Mars' Meridiani Planum shows a diverse range of primary and secondary sedimentary textures formed billions of years ago. These structures likely result from an interplay between windblown and water-involved processes.

The panoramic camera (Pancam) on NASA's Mars Exploration Rover Opportunity acquired the exposures for this image on the rover's 749th Martian day (March 3, 2006) This view is an approximately true-color rendering mathematically generated from separate images taken through all of the left Pancam's 432-nanometer to 753-nanometer filters.

Computer Modeling of Basic Physico-Chemical Processes for DSEC Composites of System LaB6-MeB2(MeTi, Zr, Hf) at Macro-, Meso- and Microstructure Scales

DTIC Science & Technology

2010-07-15

operations of mathematical morphology applied for analysis of images are ways to extract information of image. The approach early developed [52] to use...1,2568 57 VB2 5,642; 5,804; 5,67; 5,784 0,5429 0,2338 0,04334 0,45837 CrB2 5,62; 5,779; 5,61; 5,783 0,53276 0,23482...maxT For VB2 - has min value if compare with other composite materials on the base of LaB6 and diborides of transitive metals [3], = Joule and

A domain-knowledge-inspired mathematical framework for the description and classification of H&E stained histopathology images.

PubMed

Massar, Melody L; Bhagavatula, Ramamurthy; Ozolek, John A; Castro, Carlos A; Fickus, Matthew; Kovačević, Jelena

2011-10-19

We present the current state of our work on a mathematical framework for identification and delineation of histopathology images-local histograms and occlusion models. Local histograms are histograms computed over defined spatial neighborhoods whose purpose is to characterize an image locally. This unit of description is augmented by our occlusion models that describe a methodology for image formation. In the context of this image formation model, the power of local histograms with respect to appropriate families of images will be shown through various proved statements about expected performance. We conclude by presenting a preliminary study to demonstrate the power of the framework in the context of histopathology image classification tasks that, while differing greatly in application, both originate from what is considered an appropriate class of images for this framework.

Networks for image acquisition, processing and display

NASA Technical Reports Server (NTRS)

Ahumada, Albert J., Jr.

1990-01-01

The human visual system comprises layers of networks which sample, process, and code images. Understanding these networks is a valuable means of understanding human vision and of designing autonomous vision systems based on network processing. Ames Research Center has an ongoing program to develop computational models of such networks. The models predict human performance in detection of targets and in discrimination of displayed information. In addition, the models are artificial vision systems sharing properties with biological vision that has been tuned by evolution for high performance. Properties include variable density sampling, noise immunity, multi-resolution coding, and fault-tolerance. The research stresses analysis of noise in visual networks, including sampling, photon, and processing unit noises. Specific accomplishments include: models of sampling array growth with variable density and irregularity comparable to that of the retinal cone mosaic; noise models of networks with signal-dependent and independent noise; models of network connection development for preserving spatial registration and interpolation; multi-resolution encoding models based on hexagonal arrays (HOP transform); and mathematical procedures for simplifying analysis of large networks.

Cognitive correlates of performance in advanced mathematics.

PubMed

Wei, Wei; Yuan, Hongbo; Chen, Chuansheng; Zhou, Xinlin

2012-03-01

Much research has been devoted to understanding cognitive correlates of elementary mathematics performance, but little such research has been done for advanced mathematics (e.g., modern algebra, statistics, and mathematical logic). To promote mathematical knowledge among college students, it is necessary to understand what factors (including cognitive factors) are important for acquiring advanced mathematics. We recruited 80 undergraduates from four universities in Beijing. The current study investigated the associations between students' performance on a test of advanced mathematics and a battery of 17 cognitive tasks on basic numerical processing, complex numerical processing, spatial abilities, language abilities, and general cognitive processing. The results showed that spatial abilities were significantly correlated with performance in advanced mathematics after controlling for other factors. In addition, certain language abilities (i.e., comprehension of words and sentences) also made unique contributions. In contrast, basic numerical processing and computation were generally not correlated with performance in advanced mathematics. Results suggest that spatial abilities and language comprehension, but not basic numerical processing, may play an important role in advanced mathematics. These results are discussed in terms of their theoretical significance and practical implications. ©2011 The British Psychological Society.

The role of picture of process (pp) on senior high school students’ collision concept learning activities and multirepresentation ability

NASA Astrophysics Data System (ADS)

Sutarto; Indrawati; Wicaksono, I.

2018-04-01

The objectives of the study are to describe the effect of PP collision concepts to high school students’ learning activities and multirepresentation abilities. This study was a quasi experimental with non- equivalent post-test only control group design. The population of this study were students who will learn the concept of collision in three state Senior High Schools in Indonesia, with a sample of each school 70 students, 35 students as an experimental group and 35 students as a control group. Technique of data collection were observation and test. The data were analized by descriptive and inferensial statistic. Student learning activities were: group discussions, describing vectors of collision events, and formulating problem-related issues of impact. Multirepresentation capabilities were student ability on image representation, verbal, mathematics, and graph. The results showed that the learning activities in the three aspects for the three high school average categorized good. The impact of using PP on students’ ability on image and graph representation were a significant impact, but for verbal and mathematical skills there are differences but not significant.

Active learning in camera calibration through vision measurement application

NASA Astrophysics Data System (ADS)

Li, Xiaoqin; Guo, Jierong; Wang, Xianchun; Liu, Changqing; Cao, Binfang

2017-08-01

Since cameras are increasingly more used in scientific application as well as in the applications requiring precise visual information, effective calibration of such cameras is getting more important. There are many reasons why the measurements of objects are not accurate. The largest reason is that the lens has a distortion. Another detrimental influence on the evaluation accuracy is caused by the perspective distortions in the image. They happen whenever we cannot mount the camera perpendicularly to the objects we want to measure. In overall, it is very important for students to understand how to correct lens distortions, that is camera calibration. If the camera is calibrated, the images are rectificated, and then it is possible to obtain undistorted measurements in world coordinates. This paper presents how the students should develop a sense of active learning for mathematical camera model besides the theoretical scientific basics. The authors will present the theoretical and practical lectures which have the goal of deepening the students understanding of the mathematical models of area scan cameras and building some practical vision measurement process by themselves.

3-Dimensional stereo implementation of photoacoustic imaging based on a new image reconstruction algorithm without using discrete Fourier transform

NASA Astrophysics Data System (ADS)

Ham, Woonchul; Song, Chulgyu

2017-05-01

In this paper, we propose a new three-dimensional stereo image reconstruction algorithm for a photoacoustic medical imaging system. We also introduce and discuss a new theoretical algorithm by using the physical concept of Radon transform. The main key concept of proposed theoretical algorithm is to evaluate the existence possibility of the acoustic source within a searching region by using the geometric distance between each sensor element of acoustic detector and the corresponding searching region denoted by grid. We derive the mathematical equation for the magnitude of the existence possibility which can be used for implementing a new proposed algorithm. We handle and derive mathematical equations of proposed algorithm for the one-dimensional sensing array case as well as two dimensional sensing array case too. A mathematical k-wave simulation data are used for comparing the image quality of the proposed algorithm with that of general conventional algorithm in which the FFT should be necessarily used. From the k-wave Matlab simulation results, we can prove the effectiveness of the proposed reconstruction algorithm.

Parallel algorithm of real-time infrared image restoration based on total variation theory

NASA Astrophysics Data System (ADS)

Zhu, Ran; Li, Miao; Long, Yunli; Zeng, Yaoyuan; An, Wei

2015-10-01

Image restoration is a necessary preprocessing step for infrared remote sensing applications. Traditional methods allow us to remove the noise but penalize too much the gradients corresponding to edges. Image restoration techniques based on variational approaches can solve this over-smoothing problem for the merits of their well-defined mathematical modeling of the restore procedure. The total variation (TV) of infrared image is introduced as a L1 regularization term added to the objective energy functional. It converts the restoration process to an optimization problem of functional involving a fidelity term to the image data plus a regularization term. Infrared image restoration technology with TV-L1 model exploits the remote sensing data obtained sufficiently and preserves information at edges caused by clouds. Numerical implementation algorithm is presented in detail. Analysis indicates that the structure of this algorithm can be easily implemented in parallelization. Therefore a parallel implementation of the TV-L1 filter based on multicore architecture with shared memory is proposed for infrared real-time remote sensing systems. Massive computation of image data is performed in parallel by cooperating threads running simultaneously on multiple cores. Several groups of synthetic infrared image data are used to validate the feasibility and effectiveness of the proposed parallel algorithm. Quantitative analysis of measuring the restored image quality compared to input image is presented. Experiment results show that the TV-L1 filter can restore the varying background image reasonably, and that its performance can achieve the requirement of real-time image processing.

Hadamard multimode optical imaging transceiver

DOEpatents

Cooke, Bradly J; Guenther, David C; Tiee, Joe J; Kellum, Mervyn J; Olivas, Nicholas L; Weisse-Bernstein, Nina R; Judd, Stephen L; Braun, Thomas R

2012-10-30

Disclosed is a method and system for simultaneously acquiring and producing results for multiple image modes using a common sensor without optical filtering, scanning, or other moving parts. The system and method utilize the Walsh-Hadamard correlation detection process (e.g., functions/matrix) to provide an all-binary structure that permits seamless bridging between analog and digital domains. An embodiment may capture an incoming optical signal at an optical aperture, convert the optical signal to an electrical signal, pass the electrical signal through a Low-Noise Amplifier (LNA) to create an LNA signal, pass the LNA signal through one or more correlators where each correlator has a corresponding Walsh-Hadamard (WH) binary basis function, calculate a correlation output coefficient for each correlator as a function of the corresponding WH binary basis function in accordance with Walsh-Hadamard mathematical principles, digitize each of the correlation output coefficient by passing each correlation output coefficient through an Analog-to-Digital Converter (ADC), and performing image mode processing on the digitized correlation output coefficients as desired to produce one or more image modes. Some, but not all, potential image modes include: multi-channel access, temporal, range, three-dimensional, and synthetic aperture.

The Social Context of Mathematics Teaching. Perspectives 37.

ERIC Educational Resources Information Center

Ernest, Paul, Ed.

This publication contains seven papers by the staff of the University of Exeter School of Education and by invited outside contributors. The focus is on issues that consider the social context of mathematics. The papers are: (1) "Images of Mathematics" (Leone Burton); (2) "Of Course You Could be an Engineer, Dear, but Wouldn't You…

New Mathematical Dimensions: Adam's Story

ERIC Educational Resources Information Center

Manizade, Agida

2009-01-01

Adam, an 11th grader, was identified as gifted and accepted into a two week summer enrichment program. He signed up for "Geometry with Flash Programming." He had no prior programming experience but had a strong and healthy self-image as mathematics student. Although Adam had a positive attitude toward mathematics and saw himself as a successful…

Infographics and Mathematics: A Mechanism for Effective Learning in the Classroom

ERIC Educational Resources Information Center

Sudakov, Ivan; Bellsky, Thomas; Usenyuk, Svetlana; Polyakova, Victoria V.

2016-01-01

This work discusses the creation and use of infographics in an undergraduate mathematics course. Infographics are a visualization of information that combines data, formulas, and images. This article discusses how to form an infographic and uses infographics on topics within mathematics and climate as examples. It concludes with survey data from…

Suppressing the image smear of the vibration modulation transfer function for remote-sensing optical cameras.

PubMed

Li, Jin; Liu, Zilong; Liu, Si

2017-02-20

In on-board photographing processes of satellite cameras, the platform vibration can generate image motion, distortion, and smear, which seriously affect the image quality and image positioning. In this paper, we create a mathematical model of a vibrating modulate transfer function (VMTF) for a remote-sensing camera. The total MTF of a camera is reduced by the VMTF, which means the image quality is degraded. In order to avoid the degeneration of the total MTF caused by vibrations, we use an Mn-20Cu-5Ni-2Fe (M2052) manganese copper alloy material to fabricate a vibration-isolation mechanism (VIM). The VIM can transform platform vibration energy into irreversible thermal energy with its internal twin crystals structure. Our experiment shows the M2052 manganese copper alloy material is good enough to suppress image motion below 125 Hz, which is the vibration frequency of satellite platforms. The camera optical system has a higher MTF after suppressing the vibration of the M2052 material than before.

Adaptive and automatic red blood cell counting method based on microscopic hyperspectral imaging technology

NASA Astrophysics Data System (ADS)

Liu, Xi; Zhou, Mei; Qiu, Song; Sun, Li; Liu, Hongying; Li, Qingli; Wang, Yiting

2017-12-01

Red blood cell counting, as a routine examination, plays an important role in medical diagnoses. Although automated hematology analyzers are widely used, manual microscopic examination by a hematologist or pathologist is still unavoidable, which is time-consuming and error-prone. This paper proposes a full-automatic red blood cell counting method which is based on microscopic hyperspectral imaging of blood smears and combines spatial and spectral information to achieve high precision. The acquired hyperspectral image data of the blood smear in the visible and near-infrared spectral range are firstly preprocessed, and then a quadratic blind linear unmixing algorithm is used to get endmember abundance images. Based on mathematical morphological operation and an adaptive Otsu’s method, a binaryzation process is performed on the abundance images. Finally, the connected component labeling algorithm with magnification-based parameter setting is applied to automatically select the binary images of red blood cell cytoplasm. Experimental results show that the proposed method can perform well and has potential for clinical applications.

Method of passive ranging from infrared image sequence based on equivalent area

NASA Astrophysics Data System (ADS)

Yang, Weiping; Shen, Zhenkang

2007-11-01

The information of range between missile and targets is important not only to missile controlling component, but also to automatic target recognition, so studying the technique of passive ranging from infrared images has important theoretic and practical meanings. Here we tried to get the range between guided missile and target and help to identify targets or dodge a hit. The issue of distance between missile and target is currently a hot and difficult research content. As all know, infrared imaging detector can not range so that it restricts the functions of the guided information processing system based on infrared images. In order to break through the technical puzzle, we investigated the principle of the infrared imaging, after analysing the imaging geometric relationship between the guided missile and the target, we brought forward the method of passive ranging based on equivalent area and provided mathematical analytic formulas. Validating Experiments demonstrate that the presented method has good effect, the lowest relative error can reach 10% in some circumstances.

Spatially variant morphological restoration and skeleton representation.

PubMed

Bouaynaya, Nidhal; Charif-Chefchaouni, Mohammed; Schonfeld, Dan

2006-11-01

The theory of spatially variant (SV) mathematical morphology is used to extend and analyze two important image processing applications: morphological image restoration and skeleton representation of binary images. For morphological image restoration, we propose the SV alternating sequential filters and SV median filters. We establish the relation of SV median filters to the basic SV morphological operators (i.e., SV erosions and SV dilations). For skeleton representation, we present a general framework for the SV morphological skeleton representation of binary images. We study the properties of the SV morphological skeleton representation and derive conditions for its invertibility. We also develop an algorithm for the implementation of the SV morphological skeleton representation of binary images. The latter algorithm is based on the optimal construction of the SV structuring element mapping designed to minimize the cardinality of the SV morphological skeleton representation. Experimental results show the dramatic improvement in the performance of the SV morphological restoration and SV morphological skeleton representation algorithms in comparison to their translation-invariant counterparts.

Real-Time Feature Tracking Using Homography

NASA Technical Reports Server (NTRS)

Clouse, Daniel S.; Cheng, Yang; Ansar, Adnan I.; Trotz, David C.; Padgett, Curtis W.

2010-01-01

This software finds feature point correspondences in sequences of images. It is designed for feature matching in aerial imagery. Feature matching is a fundamental step in a number of important image processing operations: calibrating the cameras in a camera array, stabilizing images in aerial movies, geo-registration of images, and generating high-fidelity surface maps from aerial movies. The method uses a Shi-Tomasi corner detector and normalized cross-correlation. This process is likely to result in the production of some mismatches. The feature set is cleaned up using the assumption that there is a large planar patch visible in both images. At high altitude, this assumption is often reasonable. A mathematical transformation, called an homography, is developed that allows us to predict the position in image 2 of any point on the plane in image 1. Any feature pair that is inconsistent with the homography is thrown out. The output of the process is a set of feature pairs, and the homography. The algorithms in this innovation are well known, but the new implementation improves the process in several ways. It runs in real-time at 2 Hz on 64-megapixel imagery. The new Shi-Tomasi corner detector tries to produce the requested number of features by automatically adjusting the minimum distance between found features. The homography-finding code now uses an implementation of the RANSAC algorithm that adjusts the number of iterations automatically to achieve a pre-set probability of missing a set of inliers. The new interface allows the caller to pass in a set of predetermined points in one of the images. This allows the ability to track the same set of points through multiple frames.

Intentional and automatic numerical processing as predictors of mathematical abilities in primary school children

PubMed Central

Pina, Violeta; Castillo, Alejandro; Cohen Kadosh, Roi; Fuentes, Luis J.

2015-01-01

Previous studies have suggested that numerical processing relates to mathematical performance, but it seems that such relationship is more evident for intentional than for automatic numerical processing. In the present study we assessed the relationship between the two types of numerical processing and specific mathematical abilities in a sample of 109 children in grades 1–6. Participants were tested in an ample range of mathematical tests and also performed both a numerical and a size comparison task. The results showed that numerical processing related to mathematical performance only when inhibitory control was involved in the comparison tasks. Concretely, we found that intentional numerical processing, as indexed by the numerical distance effect in the numerical comparison task, was related to mathematical reasoning skills only when the task-irrelevant dimension (the physical size) was incongruent; whereas automatic numerical processing, indexed by the congruency effect in the size comparison task, was related to mathematical calculation skills only when digits were separated by small distance. The observed double dissociation highlights the relevance of both intentional and automatic numerical processing in mathematical skills, but when inhibitory control is also involved. PMID:25873909

The effects of geometric uncertainties on computational modelling of knee biomechanics

NASA Astrophysics Data System (ADS)

Meng, Qingen; Fisher, John; Wilcox, Ruth

2017-08-01

The geometry of the articular components of the knee is an important factor in predicting joint mechanics in computational models. There are a number of uncertainties in the definition of the geometry of cartilage and meniscus, and evaluating the effects of these uncertainties is fundamental to understanding the level of reliability of the models. In this study, the sensitivity of knee mechanics to geometric uncertainties was investigated by comparing polynomial-based and image-based knee models and varying the size of meniscus. The results suggested that the geometric uncertainties in cartilage and meniscus resulting from the resolution of MRI and the accuracy of segmentation caused considerable effects on the predicted knee mechanics. Moreover, even if the mathematical geometric descriptors can be very close to the imaged-based articular surfaces, the detailed contact pressure distribution produced by the mathematical geometric descriptors was not the same as that of the image-based model. However, the trends predicted by the models based on mathematical geometric descriptors were similar to those of the imaged-based models.

Mathematical Model of Seasonal Influenza with Treatment in Constant Population

NASA Astrophysics Data System (ADS)

Kharis, M.; Arifudin, R.

2017-04-01

Seasonal Influenza is one of disease that outbreaks periodically at least once every year. This disease caused many people hospitalized. Many hospitalized people as employers would infect production quantities, distribution time, and some economic aspects. It will infect economic growth. Infected people need treatments to reduce infection period and cure the infection. In this paper, we discussed about a mathematical model of seasonal influenza with treatment. Factually, the disease was held in short period, less than one year. Hence, we can assume that the population is constant at the disease outbreak time. In this paper, we analyzed the existence of the equilibrium points of the model and their stability. We also give some simulation to give a geometric image about the results of the analysis process.

Mathematical analysis of the 1D model and reconstruction schemes for magnetic particle imaging

NASA Astrophysics Data System (ADS)

Erb, W.; Weinmann, A.; Ahlborg, M.; Brandt, C.; Bringout, G.; Buzug, T. M.; Frikel, J.; Kaethner, C.; Knopp, T.; März, T.; Möddel, M.; Storath, M.; Weber, A.

2018-05-01

Magnetic particle imaging (MPI) is a promising new in vivo medical imaging modality in which distributions of super-paramagnetic nanoparticles are tracked based on their response in an applied magnetic field. In this paper we provide a mathematical analysis of the modeled MPI operator in the univariate situation. We provide a Hilbert space setup, in which the MPI operator is decomposed into simple building blocks and in which these building blocks are analyzed with respect to their mathematical properties. In turn, we obtain an analysis of the MPI forward operator and, in particular, of its ill-posedness properties. We further get that the singular values of the MPI core operator decrease exponentially. We complement our analytic results by some numerical studies which, in particular, suggest a rapid decay of the singular values of the MPI operator.

Artificial retina model for the retinally blind based on wavelet transform

NASA Astrophysics Data System (ADS)

Zeng, Yan-an; Song, Xin-qiang; Jiang, Fa-gang; Chang, Da-ding

2007-01-01

Artificial retina is aimed for the stimulation of remained retinal neurons in the patients with degenerated photoreceptors. Microelectrode arrays have been developed for this as a part of stimulator. Design such microelectrode arrays first requires a suitable mathematical method for human retinal information processing. In this paper, a flexible and adjustable human visual information extracting model is presented, which is based on the wavelet transform. With the flexible of wavelet transform to image information processing and the consistent to human visual information extracting, wavelet transform theory is applied to the artificial retina model for the retinally blind. The response of the model to synthetic image is shown. The simulated experiment demonstrates that the model behaves in a manner qualitatively similar to biological retinas and thus may serve as a basis for the development of an artificial retina.

Multistage Spatial Property Based Segmentation for Quantification of Fluorescence Distribution in Cells

NASA Astrophysics Data System (ADS)

Zhang, Guangyun; Jia, Xiuping; Pham, Tuan D.; Crane, Denis I.

2010-01-01

The interpretation of the distribution of fluorescence in cells is often by simple visualization of microscope-derived images for qualitative studies. In other cases, however, it is desirable to be able to quantify the distribution of fluorescence using digital image processing techniques. In this paper, the challenges of fluorescence segmentation due to the noise present in the data are addressed. We report that intensity measurements alone do not allow separation of overlapping data between target and background. Consequently, spatial properties derived from neighborhood profile were included. Mathematical Morphological operations were implemented for cell boundary extraction and a window based contrast measure was developed for fluorescence puncta identification. All of these operations were applied in the proposed multistage processing scheme. The testing results show that the spatial measures effectively enhance the target separability.

Smart sensors and virtual physiology human approach as a basis of personalized therapies in diabetes mellitus.

PubMed

Fernández Peruchena, Carlos M; Prado-Velasco, Manuel

2010-01-01

Diabetes mellitus (DM) has a growing incidence and prevalence in modern societies, pushed by the aging and change of life styles. Despite the huge resources dedicated to improve their quality of life, mortality and morbidity rates, these are still very poor. In this work, DM pathology is revised from clinical and metabolic points of view, as well as mathematical models related to DM, with the aim of justifying an evolution of DM therapies towards the correction of the physiological metabolic loops involved. We analyze the reliability of mathematical models, under the perspective of virtual physiological human (VPH) initiatives, for generating and integrating customized knowledge about patients, which is needed for that evolution. Wearable smart sensors play a key role in this frame, as they provide patient's information to the models.A telehealthcare computational architecture based on distributed smart sensors (first processing layer) and personalized physiological mathematical models integrated in Human Physiological Images (HPI) computational components (second processing layer), is presented. This technology was designed for a renal disease telehealthcare in earlier works and promotes crossroads between smart sensors and the VPH initiative. We suggest that it is able to support a truly personalized, preventive, and predictive healthcare model for the delivery of evolved DM therapies.

Smart Sensors and Virtual Physiology Human Approach as a Basis of Personalized Therapies in Diabetes Mellitus

PubMed Central

Fernández Peruchena, Carlos M; Prado-Velasco, Manuel

2010-01-01

Diabetes mellitus (DM) has a growing incidence and prevalence in modern societies, pushed by the aging and change of life styles. Despite the huge resources dedicated to improve their quality of life, mortality and morbidity rates, these are still very poor. In this work, DM pathology is revised from clinical and metabolic points of view, as well as mathematical models related to DM, with the aim of justifying an evolution of DM therapies towards the correction of the physiological metabolic loops involved. We analyze the reliability of mathematical models, under the perspective of virtual physiological human (VPH) initiatives, for generating and integrating customized knowledge about patients, which is needed for that evolution. Wearable smart sensors play a key role in this frame, as they provide patient’s information to the models. A telehealthcare computational architecture based on distributed smart sensors (first processing layer) and personalized physiological mathematical models integrated in Human Physiological Images (HPI) computational components (second processing layer), is presented. This technology was designed for a renal disease telehealthcare in earlier works and promotes crossroads between smart sensors and the VPH initiative. We suggest that it is able to support a truly personalized, preventive, and predictive healthcare model for the delivery of evolved DM therapies. PMID:21625646

An approach to separating the levels of hierarchical structure building in language and mathematics.

PubMed

Makuuchi, Michiru; Bahlmann, Jörg; Friederici, Angela D

2012-07-19

We aimed to dissociate two levels of hierarchical structure building in language and mathematics, namely 'first-level' (the build-up of hierarchical structure with externally given elements) and 'second-level' (the build-up of hierarchical structure with internally represented elements produced by first-level processes). Using functional magnetic resonance imaging, we investigated these processes in three domains: sentence comprehension, arithmetic calculation (using Reverse Polish notation, which gives two operands followed by an operator) and a working memory control task. All tasks required the build-up of hierarchical structures at the first- and second-level, resulting in a similar computational hierarchy across language and mathematics, as well as in a working memory control task. Using a novel method that estimates the difference in the integration cost for conditions of different trial durations, we found an anterior-to-posterior functional organization in the prefrontal cortex, according to the level of hierarchy. Common to all domains, the ventral premotor cortex (PMv) supports first-level hierarchy building, while the dorsal pars opercularis (POd) subserves second-level hierarchy building, with lower activation for language compared with the other two tasks. These results suggest that the POd and the PMv support domain-general mechanisms for hierarchical structure building, with the POd being uniquely efficient for language.

Breast cancer evaluation by fluorescent dot detection using combined mathematical morphology and multifractal techniques

PubMed Central

2011-01-01

Background Fluorescence in situ hybridization (FISH) is very accurate method for measuring HER2 gene copies, as a sign of potential breast cancer. This method requires small tissue samples, and has a high sensitivity to detect abnormalities from a histological section. By using multiple colors, this method allows the detection of multiple targets simultaneously. The target parts in the cells become visible as colored dots. The HER-2 probes are visible as orange stained spots under a fluorescent microscope while probes for centromere 17 (CEP-17), the chromosome on which the gene HER-2/neu is located, are visible as green spots. Methods The conventional analysis involves the scoring of the ratio of HER-2/neu over CEP 17 dots within each cell nucleus and then averaging the scores for a number of 60 cells. A ratio of 2.0 of HER-2/neu to CEP 17 copy number denotes amplification. Several methods have been proposed for the detection and automated evaluation (dot counting) of FISH signals. In this paper the combined method based on the mathematical morphology (MM) and inverse multifractal (IMF) analysis is suggested. Similar method was applied recently in detection of microcalcifications in digital mammograms, and was very successful. Results The combined MM using top-hat and bottom-hat filters, and the IMF method was applied to FISH images from Molecular Biology Lab, Department of Pathology, Wielkoposka Cancer Center, Poznan. Initial results indicate that this method can be applied to FISH images for the evaluation of HER2/neu status. Conclusions Mathematical morphology and multifractal approach are used for colored dot detection and counting in FISH images. Initial results derived on clinical cases are promising. Note that the overlapping of colored dots, particularly red/orange dots, needs additional improvements in post-processing. PMID:21489192

Diderot: a Domain-Specific Language for Portable Parallel Scientific Visualization and Image Analysis.

PubMed

Kindlmann, Gordon; Chiw, Charisee; Seltzer, Nicholas; Samuels, Lamont; Reppy, John

2016-01-01

Many algorithms for scientific visualization and image analysis are rooted in the world of continuous scalar, vector, and tensor fields, but are programmed in low-level languages and libraries that obscure their mathematical foundations. Diderot is a parallel domain-specific language that is designed to bridge this semantic gap by providing the programmer with a high-level, mathematical programming notation that allows direct expression of mathematical concepts in code. Furthermore, Diderot provides parallel performance that takes advantage of modern multicore processors and GPUs. The high-level notation allows a concise and natural expression of the algorithms and the parallelism allows efficient execution on real-world datasets.

NASA-HBCU Space Science and Engineering Research Forum Proceedings

NASA Technical Reports Server (NTRS)

Sanders, Yvonne D. (Editor); Freeman, Yvonne B. (Editor); George, M. C. (Editor)

1989-01-01

The proceedings of the Historically Black Colleges and Universities (HBCU) forum are presented. A wide range of research topics from plant science to space science and related academic areas was covered. The sessions were divided into the following subject areas: Life science; Mathematical modeling, image processing, pattern recognition, and algorithms; Microgravity processing, space utilization and application; Physical science and chemistry; Research and training programs; Space science (astronomy, planetary science, asteroids, moon); Space technology (engineering, structures and systems for application in space); Space technology (physics of materials and systems for space applications); and Technology (materials, techniques, measurements).

Iterative Self-Dual Reconstruction on Radar Image Recovery

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

Martins, Charles; Medeiros, Fatima; Ushizima, Daniela

2010-05-21

Imaging systems as ultrasound, sonar, laser and synthetic aperture radar (SAR) are subjected to speckle noise during image acquisition. Before analyzing these images, it is often necessary to remove the speckle noise using filters. We combine properties of two mathematical morphology filters with speckle statistics to propose a signal-dependent noise filter to multiplicative noise. We describe a multiscale scheme that preserves sharp edges while it smooths homogeneous areas, by combining local statistics with two mathematical morphology filters: the alternating sequential and the self-dual reconstruction algorithms. The experimental results show that the proposed approach is less sensitive to varying window sizesmore » when applied to simulated and real SAR images in comparison with standard filters.« less

Point spread function and depth-invariant focal sweep point spread function for plenoptic camera 2.0.

PubMed

Jin, Xin; Liu, Li; Chen, Yanqin; Dai, Qionghai

2017-05-01

This paper derives a mathematical point spread function (PSF) and a depth-invariant focal sweep point spread function (FSPSF) for plenoptic camera 2.0. Derivation of PSF is based on the Fresnel diffraction equation and image formation analysis of a self-built imaging system which is divided into two sub-systems to reflect the relay imaging properties of plenoptic camera 2.0. The variations in PSF, which are caused by changes of object's depth and sensor position variation, are analyzed. A mathematical model of FSPSF is further derived, which is verified to be depth-invariant. Experiments on the real imaging systems demonstrate the consistency between the proposed PSF and the actual imaging results.

Image Algebra Matlab language version 2.3 for image processing and compression research

NASA Astrophysics Data System (ADS)

Schmalz, Mark S.; Ritter, Gerhard X.; Hayden, Eric

2010-08-01

Image algebra is a rigorous, concise notation that unifies linear and nonlinear mathematics in the image domain. Image algebra was developed under DARPA and US Air Force sponsorship at University of Florida for over 15 years beginning in 1984. Image algebra has been implemented in a variety of programming languages designed specifically to support the development of image processing and computer vision algorithms and software. The University of Florida has been associated with development of the languages FORTRAN, Ada, Lisp, and C++. The latter implementation involved a class library, iac++, that supported image algebra programming in C++. Since image processing and computer vision are generally performed with operands that are array-based, the Matlab™ programming language is ideal for implementing the common subset of image algebra. Objects include sets and set operations, images and operations on images, as well as templates and image-template convolution operations. This implementation, called Image Algebra Matlab (IAM), has been found to be useful for research in data, image, and video compression, as described herein. Due to the widespread acceptance of the Matlab programming language in the computing community, IAM offers exciting possibilities for supporting a large group of users. The control over an object's computational resources provided to the algorithm designer by Matlab means that IAM programs can employ versatile representations for the operands and operations of the algebra, which are supported by the underlying libraries written in Matlab. In a previous publication, we showed how the functionality of IAC++ could be carried forth into a Matlab implementation, and provided practical details of a prototype implementation called IAM Version 1. In this paper, we further elaborate the purpose and structure of image algebra, then present a maturing implementation of Image Algebra Matlab called IAM Version 2.3, which extends the previous implementation of IAM to include polymorphic operations over different point sets, as well as recursive convolution operations and functional composition. We also show how image algebra and IAM can be employed in image processing and compression research, as well as algorithm development and analysis.

Measurement of glucose concentration by image processing of thin film slides

NASA Astrophysics Data System (ADS)

Piramanayagam, Sankaranaryanan; Saber, Eli; Heavner, David

2012-02-01

Measurement of glucose concentration is important for diagnosis and treatment of diabetes mellitus and other medical conditions. This paper describes a novel image-processing based approach for measuring glucose concentration. A fluid drop (patient sample) is placed on a thin film slide. Glucose, present in the sample, reacts with reagents on the slide to produce a color dye. The color intensity of the dye formed varies with glucose at different concentration levels. Current methods use spectrophotometry to determine the glucose level of the sample. Our proposed algorithm uses an image of the slide, captured at a specific wavelength, to automatically determine glucose concentration. The algorithm consists of two phases: training and testing. Training datasets consist of images at different concentration levels. The dye-occupied image region is first segmented using a Hough based technique and then an intensity based feature is calculated from the segmented region. Subsequently, a mathematical model that describes a relationship between the generated feature values and the given concentrations is obtained. During testing, the dye region of a test slide image is segmented followed by feature extraction. These two initial steps are similar to those done in training. However, in the final step, the algorithm uses the model (feature vs. concentration) obtained from the training and feature generated from test image to predict the unknown concentration. The performance of the image-based analysis was compared with that of a standard glucose analyzer.

The method of parallel-hierarchical transformation for rapid recognition of dynamic images using GPGPU technology

NASA Astrophysics Data System (ADS)

Timchenko, Leonid; Yarovyi, Andrii; Kokriatskaya, Nataliya; Nakonechna, Svitlana; Abramenko, Ludmila; Ławicki, Tomasz; Popiel, Piotr; Yesmakhanova, Laura

2016-09-01

The paper presents a method of parallel-hierarchical transformations for rapid recognition of dynamic images using GPU technology. Direct parallel-hierarchical transformations based on cluster CPU-and GPU-oriented hardware platform. Mathematic models of training of the parallel hierarchical (PH) network for the transformation are developed, as well as a training method of the PH network for recognition of dynamic images. This research is most topical for problems on organizing high-performance computations of super large arrays of information designed to implement multi-stage sensing and processing as well as compaction and recognition of data in the informational structures and computer devices. This method has such advantages as high performance through the use of recent advances in parallelization, possibility to work with images of ultra dimension, ease of scaling in case of changing the number of nodes in the cluster, auto scan of local network to detect compute nodes.

Enhancement of low visibility aerial images using histogram truncation and an explicit Retinex representation for balancing contrast and color consistency

NASA Astrophysics Data System (ADS)

Liu, Changjiang; Cheng, Irene; Zhang, Yi; Basu, Anup

2017-06-01

This paper presents an improved multi-scale Retinex (MSR) based enhancement for ariel images under low visibility. For traditional multi-scale Retinex, three scales are commonly employed, which limits its application scenarios. We extend our research to a general purpose enhanced method, and design an MSR with more than three scales. Based on the mathematical analysis and deductions, an explicit multi-scale representation is proposed that balances image contrast and color consistency. In addition, a histogram truncation technique is introduced as a post-processing strategy to remap the multi-scale Retinex output to the dynamic range of the display. Analysis of experimental results and comparisons with existing algorithms demonstrate the effectiveness and generality of the proposed method. Results on image quality assessment proves the accuracy of the proposed method with respect to both objective and subjective criteria.

Image processing with the radial Hilbert transform of photo-thermal imaging for carious detection

NASA Astrophysics Data System (ADS)

El-Sharkawy, Yasser H.

2014-03-01

Knowledge of heat transfer in biological bodies has many diagnostic and therapeutic applications involving either raising or lowering of temperature, and often requires precise monitoring of the spatial distribution of thermal histories that are produced during a treatment protocol. The present paper therefore aims to design and implementation of laser therapeutic and imaging system used for carious tracking and drilling by develop a mathematical algorithm using Hilbert transform for edge detection of photo-thermal imaging. photothermal imaging has the ability to penetrate and yield information about an opaque medium well beyond the range of conventional optical imaging. Owing to this ability, Q- switching Nd:YAG laser at wavelength 1064 nm has been extensively used in human teeth to study the sub-surface deposition of laser radiation. The high absorption coefficient of the carious rather than normal region rise its temperature generating IR thermal radiation captured by high resolution thermal camera. Changing the pulse repetition frequency of the laser pulses affects the penetration depth of the laser, which can provide three-dimensional (3D) images in arbitrary planes and allow imaging deep within a solid tissue.

Multiscale morphological filtering for analysis of noisy and complex images

NASA Astrophysics Data System (ADS)

Kher, A.; Mitra, S.

Images acquired with passive sensing techniques suffer from illumination variations and poor local contrasts that create major difficulties in interpretation and identification tasks. On the other hand, images acquired with active sensing techniques based on monochromatic illumination are degraded with speckle noise. Mathematical morphology offers elegant techniques to handle a wide range of image degradation problems. Unlike linear filters, morphological filters do not blur the edges and hence maintain higher image resolution. Their rich mathematical framework facilitates the design and analysis of these filters as well as their hardware implementation. Morphological filters are easier to implement and are more cost effective and efficient than several conventional linear filters. Morphological filters to remove speckle noise while maintaining high resolution and preserving thin image regions that are particularly vulnerable to speckle noise were developed and applied to SAR imagery. These filters used combination of linear (one-dimensional) structuring elements in different (typically four) orientations. Although this approach preserves more details than the simple morphological filters using two-dimensional structuring elements, the limited orientations of one-dimensional elements approximate the fine details of the region boundaries. A more robust filter designed recently overcomes the limitation of the fixed orientations. This filter uses a combination of concave and convex structuring elements. Morphological operators are also useful in extracting features from visible and infrared imagery. A multiresolution image pyramid obtained with successive filtering and a subsampling process aids in the removal of the illumination variations and enhances local contrasts. A morphology-based interpolation scheme was also introduced to reduce intensity discontinuities created in any morphological filtering task. The generality of morphological filtering techniques in extracting information from a wide variety of images obtained with active and passive sensing techniques is discussed. Such techniques are particularly useful in obtaining more information from fusion of complex images by different sensors such as SAR, visible, and infrared.

Multiscale Morphological Filtering for Analysis of Noisy and Complex Images

NASA Technical Reports Server (NTRS)

Kher, A.; Mitra, S.

1993-01-01

Images acquired with passive sensing techniques suffer from illumination variations and poor local contrasts that create major difficulties in interpretation and identification tasks. On the other hand, images acquired with active sensing techniques based on monochromatic illumination are degraded with speckle noise. Mathematical morphology offers elegant techniques to handle a wide range of image degradation problems. Unlike linear filters, morphological filters do not blur the edges and hence maintain higher image resolution. Their rich mathematical framework facilitates the design and analysis of these filters as well as their hardware implementation. Morphological filters are easier to implement and are more cost effective and efficient than several conventional linear filters. Morphological filters to remove speckle noise while maintaining high resolution and preserving thin image regions that are particularly vulnerable to speckle noise were developed and applied to SAR imagery. These filters used combination of linear (one-dimensional) structuring elements in different (typically four) orientations. Although this approach preserves more details than the simple morphological filters using two-dimensional structuring elements, the limited orientations of one-dimensional elements approximate the fine details of the region boundaries. A more robust filter designed recently overcomes the limitation of the fixed orientations. This filter uses a combination of concave and convex structuring elements. Morphological operators are also useful in extracting features from visible and infrared imagery. A multiresolution image pyramid obtained with successive filtering and a subsampling process aids in the removal of the illumination variations and enhances local contrasts. A morphology-based interpolation scheme was also introduced to reduce intensity discontinuities created in any morphological filtering task. The generality of morphological filtering techniques in extracting information from a wide variety of images obtained with active and passive sensing techniques is discussed. Such techniques are particularly useful in obtaining more information from fusion of complex images by different sensors such as SAR, visible, and infrared.

A new three-dimensional nonscanning laser imaging system based on the illumination pattern of a point-light-source array

NASA Astrophysics Data System (ADS)

Xia, Wenze; Ma, Yayun; Han, Shaokun; Wang, Yulin; Liu, Fei; Zhai, Yu

2018-06-01

One of the most important goals of research on three-dimensional nonscanning laser imaging systems is the improvement of the illumination system. In this paper, a new three-dimensional nonscanning laser imaging system based on the illumination pattern of a point-light-source array is proposed. This array is obtained using a fiber array connected to a laser array with each unit laser having independent control circuits. This system uses a point-to-point imaging process, which is realized using the exact corresponding optical relationship between the point-light-source array and a linear-mode avalanche photodiode array detector. The complete working process of this system is explained in detail, and the mathematical model of this system containing four equations is established. A simulated contrast experiment and two real contrast experiments which use the simplified setup without a laser array are performed. The final results demonstrate that unlike a conventional three-dimensional nonscanning laser imaging system, the proposed system meets all the requirements of an eligible illumination system. Finally, the imaging performance of this system is analyzed under defocusing situations, and analytical results show that the system has good defocusing robustness and can be easily adjusted in real applications.

Image denoising by a direct variational minimization

NASA Astrophysics Data System (ADS)

Janev, Marko; Atanacković, Teodor; Pilipović, Stevan; Obradović, Radovan

2011-12-01

In this article we introduce a novel method for the image de-noising which combines a mathematically well-posdenes of the variational modeling with the efficiency of a patch-based approach in the field of image processing. It based on a direct minimization of an energy functional containing a minimal surface regularizer that uses fractional gradient. The minimization is obtained on every predefined patch of the image, independently. By doing so, we avoid the use of an artificial time PDE model with its inherent problems of finding optimal stopping time, as well as the optimal time step. Moreover, we control the level of image smoothing on each patch (and thus on the whole image) by adapting the Lagrange multiplier using the information on the level of discontinuities on a particular patch, which we obtain by pre-processing. In order to reduce the average number of vectors in the approximation generator and still to obtain the minimal degradation, we combine a Ritz variational method for the actual minimization on a patch, and a complementary fractional variational principle. Thus, the proposed method becomes computationally feasible and applicable for practical purposes. We confirm our claims with experimental results, by comparing the proposed method with a couple of PDE-based methods, where we get significantly better denoising results specially on the oscillatory regions.

What Lies Beneath Can Be Imaged

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

Johnson, Tim

The Hanford Site was quickly established to help end World War II, making history for producing the plutonium used in the world’s first nuclear weapons. Throughout the Cold War years, Hanford employees produced plutonium for most of the more than 60,000 weapons in the U.S. nuclear arsenal stockpile. Today, the once highly active nuclear reactors are shut down. And the mission at Hanford turned full-circle as scientists, engineers and specialists work to clean up our nation’s most contaminated nuclear site. PNNL Computational Geophysicist Tim Johnson is helping decision-makers understand the complexity and breadth of the contamination in soils at Hanford.more » Tim and others are applying remote, high-resolution geophysical imaging to determine the extent of contamination in the soil below the surface and understand the processes controlling its movement. They also provide real-time imaging of remediation processes that are working to limit the movement of contaminants below the surface and toward water resources. Geophysical imaging simply means that PNNL scientists are combining the techniques of geology, physics, mathematics and chemistry with supercomputer modeling to create three-dimensional images of the waste and its movement. These real-time, remote images are essential in reducing the uncertainty associated with cleanup costs and remediation technologies.« less

Effective Moment Feature Vectors for Protein Domain Structures

PubMed Central

Shi, Jian-Yu; Yiu, Siu-Ming; Zhang, Yan-Ning; Chin, Francis Yuk-Lun

2013-01-01

Imaging processing techniques have been shown to be useful in studying protein domain structures. The idea is to represent the pairwise distances of any two residues of the structure in a 2D distance matrix (DM). Features and/or submatrices are extracted from this DM to represent a domain. Existing approaches, however, may involve a large number of features (100–400) or complicated mathematical operations. Finding fewer but more effective features is always desirable. In this paper, based on some key observations on DMs, we are able to decompose a DM image into four basic binary images, each representing the structural characteristics of a fundamental secondary structure element (SSE) or a motif in the domain. Using the concept of moments in image processing, we further derive 45 structural features based on the four binary images. Together with 4 features extracted from the basic images, we represent the structure of a domain using 49 features. We show that our feature vectors can represent domain structures effectively in terms of the following. (1) We show a higher accuracy for domain classification. (2) We show a clear and consistent distribution of domains using our proposed structural vector space. (3) We are able to cluster the domains according to our moment features and demonstrate a relationship between structural variation and functional diversity. PMID:24391828

A learning tool for optical and microwave satellite image processing and analysis

NASA Astrophysics Data System (ADS)

Dashondhi, Gaurav K.; Mohanty, Jyotirmoy; Eeti, Laxmi N.; Bhattacharya, Avik; De, Shaunak; Buddhiraju, Krishna M.

2016-04-01

This paper presents a self-learning tool, which contains a number of virtual experiments for processing and analysis of Optical/Infrared and Synthetic Aperture Radar (SAR) images. The tool is named Virtual Satellite Image Processing and Analysis Lab (v-SIPLAB) Experiments that are included in Learning Tool are related to: Optical/Infrared - Image and Edge enhancement, smoothing, PCT, vegetation indices, Mathematical Morphology, Accuracy Assessment, Supervised/Unsupervised classification etc.; Basic SAR - Parameter extraction and range spectrum estimation, Range compression, Doppler centroid estimation, Azimuth reference function generation and compression, Multilooking, image enhancement, texture analysis, edge and detection. etc.; SAR Interferometry - BaseLine Calculation, Extraction of single look SAR images, Registration, Resampling, and Interferogram generation; SAR Polarimetry - Conversion of AirSAR or Radarsat data to S2/C3/T3 matrix, Speckle Filtering, Power/Intensity image generation, Decomposition of S2/C3/T3, Classification of S2/C3/T3 using Wishart Classifier [3]. A professional quality polarimetric SAR software can be found at [8], a part of whose functionality can be found in our system. The learning tool also contains other modules, besides executable software experiments, such as aim, theory, procedure, interpretation, quizzes, link to additional reading material and user feedback. Students can have understanding of Optical and SAR remotely sensed images through discussion of basic principles and supported by structured procedure for running and interpreting the experiments. Quizzes for self-assessment and a provision for online feedback are also being provided to make this Learning tool self-contained. One can download results after performing experiments.

Automatic archaeological feature extraction from satellite VHR images

NASA Astrophysics Data System (ADS)

Jahjah, Munzer; Ulivieri, Carlo

2010-05-01

Archaeological applications need a methodological approach on a variable scale able to satisfy the intra-site (excavation) and the inter-site (survey, environmental research). The increased availability of high resolution and micro-scale data has substantially favoured archaeological applications and the consequent use of GIS platforms for reconstruction of archaeological landscapes based on remotely sensed data. Feature extraction of multispectral remotely sensing image is an important task before any further processing. High resolution remote sensing data, especially panchromatic, is an important input for the analysis of various types of image characteristics; it plays an important role in the visual systems for recognition and interpretation of given data. The methods proposed rely on an object-oriented approach based on a theory for the analysis of spatial structures called mathematical morphology. The term "morphology" stems from the fact that it aims at analysing object shapes and forms. It is mathematical in the sense that the analysis is based on the set theory, integral geometry, and lattice algebra. Mathematical morphology has proven to be a powerful image analysis technique; two-dimensional grey tone images are seen as three-dimensional sets by associating each image pixel with an elevation proportional to its intensity level. An object of known shape and size, called the structuring element, is then used to investigate the morphology of the input set. This is achieved by positioning the origin of the structuring element to every possible position of the space and testing, for each position, whether the structuring element either is included or has a nonempty intersection with the studied set. The shape and size of the structuring element must be selected according to the morphology of the searched image structures. Other two feature extraction techniques were used, eCognition and ENVI module SW, in order to compare the results. These techniques were applied to different archaeological sites in Turkmenistan (Nisa) and in Iraq (Babylon); a further change detection analysis was applied to the Babylon site using two HR images as a pre-post second gulf war. We had different results or outputs, taking into consideration the fact that the operative scale of sensed data determines the final result of the elaboration and the output of the information quality, because each of them was sensitive to specific shapes in each input image, we had mapped linear and nonlinear objects, updating archaeological cartography, automatic change detection analysis for the Babylon site. The discussion of these techniques has the objective to provide the archaeological team with new instruments for the orientation and the planning of a remote sensing application.

Multimedia Environments in Mathematics Teacher Education: Preparing Regular and Special Educators for Inclusive Classrooms

ERIC Educational Resources Information Center

De La Paz, Susan; Hernandez-Ramos, Pedro; Barron, Linda

2004-01-01

A multimedia CD-ROM program, Mathematics Teaching and Learning in Inclusive Classrooms, was produced to help preservice teachers learn mathematics teaching methods in the context of inclusive classrooms. The contents include text resources, video segments of experts and of classroom lessons, images of student work, an electronic notebook, and a…

Images of Mathematics in Popular Culture/Adults' Lives: A Study of Advertisements in the UK Press

ERIC Educational Resources Information Center

Evans, Jeff; Tsatsaroni, Anna; Staub, Natalie

2007-01-01

The success of policies to attract adults back to the learning of mathematics, at various levels, is often linked to questions of motivation. However, motivations depend on relevant beliefs, attitudes and emotions about mathematics--which themselves reflect, together with experiences with maths in school and in the home, wider cultural discourses…

Understanding of Prospective Mathematics Teachers of the Concept of Diagonal

ERIC Educational Resources Information Center

Ayvaz, Ülkü; Gündüz, Nazan; Bozkus, Figen

2017-01-01

This study aims to investigate the concept images of prospective mathematics teachers about the concept of diagonal. With this aim, case study method was used in the study. The participants of the study were consisted of 7 prospective teachers educating at the Department of Mathematics Education. Criterion sampling method was used to select the…

Research on registration algorithm for check seal verification

NASA Astrophysics Data System (ADS)

Wang, Shuang; Liu, Tiegen

2008-03-01

Nowadays seals play an important role in China. With the development of social economy, the traditional method of manual check seal identification can't meet the need s of banking transactions badly. This paper focus on pre-processing and registration algorithm for check seal verification using theory of image processing and pattern recognition. First of all, analyze the complex characteristics of check seals. To eliminate the difference of producing conditions and the disturbance caused by background and writing in check image, many methods are used in the pre-processing of check seal verification, such as color components transformation, linearity transform to gray-scale image, medium value filter, Otsu, close calculations and labeling algorithm of mathematical morphology. After the processes above, the good binary seal image can be obtained. On the basis of traditional registration algorithm, a double-level registration method including rough and precise registration method is proposed. The deflection angle of precise registration method can be precise to 0.1°. This paper introduces the concepts of difference inside and difference outside and use the percent of difference inside and difference outside to judge whether the seal is real or fake. The experimental results of a mass of check seals are satisfied. It shows that the methods and algorithmic presented have good robustness to noise sealing conditions and satisfactory tolerance of difference within class.

Cognitive Predictors of Achievement Growth in Mathematics: A Five Year Longitudinal Study

PubMed Central

Geary, David C.

2011-01-01

The study's goal was to identify the beginning of first grade quantitative competencies that predict mathematics achievement start point and growth through fifth grade. Measures of number, counting, and arithmetic competencies were administered in early first grade and used to predict mathematics achievement through fifth (n = 177), while controlling for intelligence, working memory, and processing speed. Multilevel models revealed intelligence, processing speed, and the central executive component of working memory predicted achievement or achievement growth in mathematics and, as a contrast domain, word reading. The phonological loop was uniquely predictive of word reading and the visuospatial sketch pad of mathematics. Early fluency in processing and manipulating numerical set size and Arabic numerals, accurate use of sophisticated counting procedures for solving addition problems, and accuracy in making placements on a mathematical number line were uniquely predictive of mathematics achievement. Use of memory-based processes to solve addition problems predicted mathematics and reading achievement but in different ways. The results identify the early quantitative competencies that uniquely contribute to mathematics learning. PMID:21942667

Simulating patient-specific heart shape and motion using SPECT perfusion images with the MCAT phantom

NASA Astrophysics Data System (ADS)

Faber, Tracy L.; Garcia, Ernest V.; Lalush, David S.; Segars, W. Paul; Tsui, Benjamin M.

2001-05-01

The spline-based Mathematical Cardiac Torso (MCAT) phantom is a realistic software simulation designed to simulate single photon emission computed tomographic (SPECT) data. It incorporates a heart model of known size and shape; thus, it is invaluable for measuring accuracy of acquisition, reconstruction, and post-processing routines. New functionality has been added by replacing the standard heart model with left ventricular (LV) epicaridal and endocardial surface points detected from actual patient SPECT perfusion studies. LV surfaces detected from standard post-processing quantitation programs are converted through interpolation in space and time into new B-spline models. Perfusion abnormalities are added to the model based on results of standard perfusion quantification. The new LV is translated and rotated to fit within existing atria and right ventricular models, which are scaled based on the size of the LV. Simulations were created for five different patients with myocardial infractions who had undergone SPECT perfusion imaging. Shape, size, and motion of the resulting activity map were compared visually to the original SPECT images. In all cases, size, shape and motion of simulated LVs matched well with the original images. Thus, realistic simulations with known physiologic and functional parameters can be created for evaluating efficacy of processing algorithms.

Mobile-based text recognition from water quality devices

NASA Astrophysics Data System (ADS)

Dhakal, Shanti; Rahnemoonfar, Maryam

2015-03-01

Measuring water quality of bays, estuaries, and gulfs is a complicated and time-consuming process. YSI Sonde is an instrument used to measure water quality parameters such as pH, temperature, salinity, and dissolved oxygen. This instrument is taken to water bodies in a boat trip and researchers note down different parameters displayed by the instrument's display monitor. In this project, a mobile application is developed for Android platform that allows a user to take a picture of the YSI Sonde monitor, extract text from the image and store it in a file on the phone. The image captured by the application is first processed to remove perspective distortion. Probabilistic Hough line transform is used to identify lines in the image and the corner of the image is then obtained by determining the intersection of the detected horizontal and vertical lines. The image is warped using the perspective transformation matrix, obtained from the corner points of the source image and the destination image, hence, removing the perspective distortion. Mathematical morphology operation, black-hat is used to correct the shading of the image. The image is binarized using Otsu's binarization technique and is then passed to the Optical Character Recognition (OCR) software for character recognition. The extracted information is stored in a file on the phone and can be retrieved later for analysis. The algorithm was tested on 60 different images of YSI Sonde with different perspective features and shading. Experimental results, in comparison to ground-truth results, demonstrate the effectiveness of the proposed method.

Medical revolution in Argentina.

PubMed

Ballarin, V L; Isoardi, R A

2010-01-01

The paper discusses the major Argentineans contributors, medical physicists and scientists, in medical imaging and the development of medical imaging in Argentina. The following are presented: history of medical imaging in Argentina: the pioneers; medical imaging and medical revolution; nuclear medicine imaging; ultrasound imaging; and mathematics, physics, and electronics in medical image research: a multidisciplinary endeavor.

A mathematical model of neuro-fuzzy approximation in image classification

NASA Astrophysics Data System (ADS)

Gopalan, Sasi; Pinto, Linu; Sheela, C.; Arun Kumar M., N.

2016-06-01

Image digitization and explosion of World Wide Web has made traditional search for image, an inefficient method for retrieval of required grassland image data from large database. For a given input query image Content-Based Image Retrieval (CBIR) system retrieves the similar images from a large database. Advances in technology has increased the use of grassland image data in diverse areas such has agriculture, art galleries, education, industry etc. In all the above mentioned diverse areas it is necessary to retrieve grassland image data efficiently from a large database to perform an assigned task and to make a suitable decision. A CBIR system based on grassland image properties and it uses the aid of a feed-forward back propagation neural network for an effective image retrieval is proposed in this paper. Fuzzy Memberships plays an important role in the input space of the proposed system which leads to a combined neural fuzzy approximation in image classification. The CBIR system with mathematical model in the proposed work gives more clarity about fuzzy-neuro approximation and the convergence of the image features in a grassland image.

Application of automatic threshold in dynamic target recognition with low contrast

NASA Astrophysics Data System (ADS)

Miao, Hua; Guo, Xiaoming; Chen, Yu

2014-11-01

Hybrid photoelectric joint transform correlator can realize automatic real-time recognition with high precision through the combination of optical devices and electronic devices. When recognizing targets with low contrast using photoelectric joint transform correlator, because of the difference of attitude, brightness and grayscale between target and template, only four to five frames of dynamic targets can be recognized without any processing. CCD camera is used to capture the dynamic target images and the capturing speed of CCD is 25 frames per second. Automatic threshold has many advantages like fast processing speed, effectively shielding noise interference, enhancing diffraction energy of useful information and better reserving outline of target and template, so this method plays a very important role in target recognition with optical correlation method. However, the automatic obtained threshold by program can not achieve the best recognition results for dynamic targets. The reason is that outline information is broken to some extent. Optimal threshold is obtained by manual intervention in most cases. Aiming at the characteristics of dynamic targets, the processing program of improved automatic threshold is finished by multiplying OTSU threshold of target and template by scale coefficient of the processed image, and combining with mathematical morphology. The optimal threshold can be achieved automatically by improved automatic threshold processing for dynamic low contrast target images. The recognition rate of dynamic targets is improved through decreased background noise effect and increased correlation information. A series of dynamic tank images with the speed about 70 km/h are adapted as target images. The 1st frame of this series of tanks can correlate only with the 3rd frame without any processing. Through OTSU threshold, the 80th frame can be recognized. By automatic threshold processing of the joint images, this number can be increased to 89 frames. Experimental results show that the improved automatic threshold processing has special application value for the recognition of dynamic target with low contrast.

Tunable wavefront coded imaging system based on detachable phase mask: Mathematical analysis, optimization and underlying applications

NASA Astrophysics Data System (ADS)

Zhao, Hui; Wei, Jingxuan

2014-09-01

The key to the concept of tunable wavefront coding lies in detachable phase masks. Ojeda-Castaneda et al. (Progress in Electronics Research Symposium Proceedings, Cambridge, USA, July 5-8, 2010) described a typical design in which two components with cosinusoidal phase variation operate together to make defocus sensitivity tunable. The present study proposes an improved design and makes three contributions: (1) A mathematical derivation based on the stationary phase method explains why the detachable phase mask of Ojeda-Castaneda et al. tunes the defocus sensitivity. (2) The mathematical derivations show that the effective bandwidth wavefront coded imaging system is also tunable by making each component of the detachable phase mask move asymmetrically. An improved Fisher information-based optimization procedure was also designed to ascertain the optimal mask parameters corresponding to specific bandwidth. (3) Possible applications of the tunable bandwidth are demonstrated by simulated imaging.

Fundamental remote science research program. Part 2: Status report of the mathematical pattern recognition and image analysis project

NASA Technical Reports Server (NTRS)

Heydorn, R. P.

1984-01-01

The Mathematical Pattern Recognition and Image Analysis (MPRIA) Project is concerned with basic research problems related to the study of he Earth from remotely sensed measurements of its surface characteristics. The program goal is to better understand how to analyze the digital image that represents the spatial, spectral, and temporal arrangement of these measurements for purposing of making selected inferences about the Earth. This report summarizes the progress that has been made toward this program goal by each of the principal investigators in the MPRIA Program.

How to build a course in mathematical-biological modeling: content and processes for knowledge and skill.

PubMed

Hoskinson, Anne-Marie

2010-01-01

Biological problems in the twenty-first century are complex and require mathematical insight, often resulting in mathematical models of biological systems. Building mathematical-biological models requires cooperation among biologists and mathematicians, and mastery of building models. A new course in mathematical modeling presented the opportunity to build both content and process learning of mathematical models, the modeling process, and the cooperative process. There was little guidance from the literature on how to build such a course. Here, I describe the iterative process of developing such a course, beginning with objectives and choosing content and process competencies to fulfill the objectives. I include some inductive heuristics for instructors seeking guidance in planning and developing their own courses, and I illustrate with a description of one instructional model cycle. Students completing this class reported gains in learning of modeling content, the modeling process, and cooperative skills. Student content and process mastery increased, as assessed on several objective-driven metrics in many types of assessments.

Neonatal MRI is associated with future cognition and academic achievement in preterm children

PubMed Central

Spencer-Smith, Megan; Thompson, Deanne K.; Doyle, Lex W.; Inder, Terrie E.; Anderson, Peter J.; Klingberg, Torkel

2015-01-01

School-age children born preterm are particularly at risk for low mathematical achievement, associated with reduced working memory and number skills. Early identification of preterm children at risk for future impairments using brain markers might assist in referral for early intervention. This study aimed to examine the use of neonatal magnetic resonance imaging measures derived from automated methods (Jacobian maps from deformation-based morphometry; fractional anisotropy maps from diffusion tensor images) to predict skills important for mathematical achievement (working memory, early mathematical skills) at 5 and 7 years in a cohort of preterm children using both univariable (general linear model) and multivariable models (support vector regression). Participants were preterm children born <30 weeks’ gestational age and healthy control children born ≥37 weeks’ gestational age at the Royal Women’s Hospital in Melbourne, Australia between July 2001 and December 2003 and recruited into a prospective longitudinal cohort study. At term-equivalent age ( ±2 weeks) 224 preterm and 46 control infants were recruited for magnetic resonance imaging. Working memory and early mathematics skills were assessed at 5 years (n = 195 preterm; n = 40 controls) and 7 years (n = 197 preterm; n = 43 controls). In the preterm group, results identified localized regions around the insula and putamen in the neonatal Jacobian map that were positively associated with early mathematics at 5 and 7 years (both P < 0.05), even after covarying for important perinatal clinical factors using general linear model but not support vector regression. The neonatal Jacobian map showed the same trend for association with working memory at 7 years (models ranging from P = 0.07 to P = 0.05). Neonatal fractional anisotropy was positively associated with working memory and early mathematics at 5 years (both P < 0.001) even after covarying for clinical factors using support vector regression but not general linear model. These significant relationships were not observed in the control group. In summary, we identified, in the preterm brain, regions around the insula and putamen using neonatal deformation-based morphometry, and brain microstructural organization using neonatal diffusion tensor imaging, associated with skills important for childhood mathematical achievement. Results contribute to the growing evidence for the clinical utility of neonatal magnetic resonance imaging for early identification of preterm infants at risk for childhood cognitive and academic impairment. PMID:26329284

Lights All Askew: Systematics in Galaxy Images from Megaparsecs to Microns

NASA Astrophysics Data System (ADS)

Bradshaw, Andrew Kenneth

The stars and galaxies are not where they seem. In the process of imaging and measurement, the light from distant objects is distorted, blurred, and skewed by several physical effects on scales from megaparsecs to microns. Charge-coupled devices (CCDs) provide sensitive detection of this light, but introduce their own problems in the form of systematic biases. Images of these stars and galaxies are formed in CCDs when incoming light generates photoelectrons which are then collected in a pixel's potential well and measured as signal. However, these signal electrons can be diverted from purely parallel paths toward the pixel wells by transverse fields sourced by structural elements of the CCD, accidental imperfections in fabrication, or dynamic electric fields induced by other collected charges. These charge transport anomalies lead to measurable systematic errors in the images which bias cosmological inferences based on them. The physics of imaging therefore deserves thorough investigation, which is performed in the laboratory using a unique optical beam simulator and in computer simulations of charge transport. On top of detector systematics, there are often biases in the mathematical analysis of pixelized images; in particular, the location, shape, and orientation of stars and galaxies. Using elliptical Gaussians as a toy model for galaxies, it is demonstrated how small biases in the computed image moments lead to observable orientation patterns in modern survey data. Also presented are examples of the reduction of data and fitting of optical aberrations of images in the lab and on the sky which are modeled by physically or mathematically-motivated methods. Finally, end-to-end analysis of the weak gravitational lensing signal is presented using deep sky data as well as in N-body simulations. It is demonstrated how measured weak lens shear can be transformed by signal matched filters which aid in the detection of mass overdensities and separate signal from noise. A commonly-used decomposition of shear into two components, E- and B-modes, is thoroughly tested and both modes are shown to be useful in the detection of large scale structure. We find several astrophysical sources of B-mode and explain their apparent origin. The methods presented therefore offer an optimal way to filter weak gravitational shear into maps of large scale structure through the process of cosmic mass cartography.

Nature and origins of mathematics difficulties in very preterm children: a different etiology than developmental dyscalculia.

PubMed

Simms, Victoria; Gilmore, Camilla; Cragg, Lucy; Clayton, Sarah; Marlow, Neil; Johnson, Samantha

2015-02-01

Children born very preterm (<32 wk) are at high risk for mathematics learning difficulties that are out of proportion to other academic and cognitive deficits. However, the etiology of mathematics difficulties in very preterm children is unknown. We sought to identify the nature and origins of preterm children's mathematics difficulties. One hundred and fifteen very preterm children aged 8-10 y were assessed in school with a control group of 77 term-born classmates. Achievement in mathematics, working memory, visuospatial processing, inhibition, and processing speed were assessed using standardized tests. Numerical representations and specific mathematics skills were assessed using experimental tests. Very preterm children had significantly poorer mathematics achievement, working memory, and visuospatial skills than term-born controls. Although preterm children had poorer performance in specific mathematics skills, there was no evidence of imprecise numerical representations. Difficulties in mathematics were associated with deficits in visuospatial processing and working memory. Mathematics difficulties in very preterm children are associated with deficits in working memory and visuospatial processing not numerical representations. Thus, very preterm children's mathematics difficulties are different in nature from those of children with developmental dyscalculia. Interventions targeting general cognitive problems, rather than numerical representations, may improve very preterm children's mathematics achievement.

Phobos Viewed from Mars

NASA Image and Video Library

2005-09-11

Taking advantage of extra solar energy collected during the day, NASA's Mars Exploration Rover Spirit settled in for an evening of stargazing, photographing the two moons of Mars as they crossed the night sky. The first two images in this sequence show gradual enhancements in the surface detail of Mars' largest moon, Phobos, made possible through a combination technique known as "stacking." In "stacking," scientists use a mathematical process known as Laplacian sharpening to reinforce features that appear consistently in repetitive images and minimize features that show up only intermittently. In this view of Phobos, the large crater named Stickney is just out of sight on the moon's upper right limb. Spirit acquired the first two images with the panoramic camera on the night of sol 585 (Aug. 26,2005). The far right image of Phobos, for comparison, was taken by the High Resolution Stereo Camera on Mars Express, a European Space Agency orbiter. The third image in this sequence was derived from the far right image by making it blurrier for comparison with the panoramic camera images to the left http://photojournal.jpl.nasa.gov/catalog/PIA06335

"Attrition Processes Out of Mathematics for Undergraduate Students." Attrition from Mathematics as a Social Process. Final Report.

ERIC Educational Resources Information Center

Maines, David R.; And Others

Investigated were those long-term processes which contribute to high rates of attrition for women out of mathematics. It is based on the contention that university students drop out of mathematics as a consequence of prior socialization, educational career contingencies, and goal commitment and career aspirations, with the mix of these factors…

A Case Study on Pre-Service Secondary School Mathematics Teachers' Cognitive-Metacognitive Behaviours in Mathematical Modelling Process

ERIC Educational Resources Information Center

Sagirli, Meryem Özturan

2016-01-01

The aim of the present study is to investigate pre-service secondary mathematics teachers' cognitive-metacognitive behaviours during the mathematical problem-solving process considering class level. The study, in which the case study methodology was employed, was carried out with eight pre-service mathematics teachers, enrolled at a university in…

Integrating Algebra and Proof in High School Mathematics: An Exploratory Study

ERIC Educational Resources Information Center

Martinez, Mara V.; Brizuela, Barbara M.; Superfine, Alison Castro

2011-01-01

Frequently, in the US students' work with proofs is largely concentrated to the domain of high school geometry, thus providing students with a distorted image of what proof entails, which is at odds with the central role that proof plays in mathematics. Despite the centrality of proof in mathematics, there is a lack of studies addressing how to…

Enhancing Interpretation of Natural Phenomena through a Mathematical Apparatus: A Proposal of an Interactive Unit in Optics

ERIC Educational Resources Information Center

Sokolowski, Andrzej

2012-01-01

This paper integrates technology, in the form of a physics simulation; science concepts, via image formation by lenses; and a mathematics apparatus, in the form of rational functions. All constituents merge into an instructional unit that can be embedded into a high school or undergraduate mathematics or physics course. The cognitive purpose of…

Mathematics anxiety affects counting but not subitizing during visual enumeration.

PubMed

Maloney, Erin A; Risko, Evan F; Ansari, Daniel; Fugelsang, Jonathan

2010-02-01

Individuals with mathematics anxiety have been found to differ from their non-anxious peers on measures of higher-level mathematical processes, but not simple arithmetic. The current paper examines differences between mathematics anxious and non-mathematics anxious individuals in more basic numerical processing using a visual enumeration task. This task allows for the assessment of two systems of basic number processing: subitizing and counting. Mathematics anxious individuals, relative to non-mathematics anxious individuals, showed a deficit in the counting but not in the subitizing range. Furthermore, working memory was found to mediate this group difference. These findings demonstrate that the problems associated with mathematics anxiety exist at a level more basic than would be predicted from the extant literature. Copyright 2009 Elsevier B.V. All rights reserved.

Proceedings of the Second Annual Symposium on Mathematical Pattern Recognition and Image Analysis Program

NASA Technical Reports Server (NTRS)

Guseman, L. F., Jr. (Principal Investigator)

1984-01-01

Several papers addressing image analysis and pattern recognition techniques for satellite imagery are presented. Texture classification, image rectification and registration, spatial parameter estimation, and surface fitting are discussed.

Cognition in Children's Mathematical Processing: Bringing Psychology to the Classroom

ERIC Educational Resources Information Center

Witt, Marcus

2010-01-01

Introduction: The cognitive processes that underpin successful mathematical processing in children have been well researched by experimental psychologists, but are not widely understood among teachers of primary mathematics. This is a shame, as an understanding of these cognitive processes could be highly useful to practitioners. This paper…

Hough transform for human action recognition

NASA Astrophysics Data System (ADS)

Siemon, Mia S. N.

2016-09-01

Nowadays, the demand of computer analysis, especially regarding team sports, continues drastically growing. More and more decisions are made by electronic devices for the live to become `easier' to a certain context. There already exist application areas in sports, during which critical situations are being handled by means of digital software. This paper aims at the evaluation and introduction to the necessary foundation which would make it possible to develop a concept similar to that of `hawk-eye', a decision-making program to evaluate the impact of a ball with respect to a target line and to apply it to the sport of volleyball. The pattern recognition process is in this case performed by means of the mathematical model of Hough transform which is able of identifying relevant lines and circles in the image in order to later on use them for the necessary evaluation of the image and the decision-making process.

Meteorological Instruction Software

NASA Technical Reports Server (NTRS)

1990-01-01

At Florida State University and the Naval Postgraduate School, meteorology students have the opportunity to apply theoretical studies to current weather phenomena, even prepare forecasts and see how their predictions stand up utilizing GEMPAK. GEMPAK can display data quickly in both conventional and non-traditional ways, allowing students to view multiple perspectives of the complex three-dimensional atmospheric structure. With GEMPAK, mathematical equations come alive as students do homework and laboratory assignments on the weather events happening around them. Since GEMPAK provides data on a 'today' basis, each homework assignment is new. At the Naval Postgraduate School, students are now using electronically-managed environmental data in the classroom. The School's Departments of Meteorology and Oceanography have developed the Interactive Digital Environment Analysis (IDEA) Laboratory. GEMPAK is the IDEA Lab's general purpose display package; the IDEA image processing package is a modified version of NASA's Device Management System. Bringing the graphic and image processing packages together is NASA's product, the Transportable Application Executive (TAE).

Rotation-robust math symbol recognition and retrieval using outer contours and image subsampling

NASA Astrophysics Data System (ADS)

Zhu, Siyu; Hu, Lei; Zanibbi, Richard

2013-01-01

This paper presents an unified recognition and retrieval system for isolated offline printed mathematical symbols for the first time. The system is based on nearest neighbor scheme and uses modified Turning Function and Grid Features to calculate the distance between two symbols based on Sum of Squared Difference. An unwrap process and an alignment process are applied to modify Turning Function to deal with the horizontal and vertical shift caused by the changing of staring point and rotation. This modified Turning Function make our system robust against rotation of the symbol image. The system obtains top-1 recognition rate of 96.90% and 47.27% Area Under Curve (AUC) of precision/recall plot on the InftyCDB-3 dataset. Experiment result shows that the system with modified Turning Function performs significantly better than the system with original Turning Function on the rotated InftyCDB-3 dataset.

Explicating mathematical thinking in differential equations using a computer algebra system

NASA Astrophysics Data System (ADS)

Zeynivandnezhad, Fereshteh; Bates, Rachel

2018-07-01

The importance of developing students' mathematical thinking is frequently highlighted in literature regarding the teaching and learning of mathematics. Despite this importance, most curricula and instructional activities for undergraduate mathematics fail to bring the learner beyond the mathematics. The purpose of this study was to enhance students' mathematical thinking by implementing a computer algebra system and active learning pedagogical approaches. students' mathematical thinking processes were analyzed while completing specific differential equations tasks based on posed prompts and questions and Instrumental Genesis. Data were collected from 37 engineering students in a public Malaysian university. This study used the descriptive and interpretive qualitative research design to investigate the students' perspectives of emerging mathematical understanding and approaches to learning mathematics in an undergraduate differential equations course. Results of this study concluded that students used a variety of mathematical thinking processes in a non-sequential manner. Additionally, the outcomes provide justification for continued use of technologies such as computer algebra systems in undergraduate mathematics courses and the need for further studies to uncover the various processes students utilize to complete specific mathematical tasks.

Kinematic reconstruction in cardiovascular imaging.

PubMed

Bastarrika, G; Huebra Rodríguez, I J González de la; Calvo-Imirizaldu, M; Suárez Vega, V M; Alonso-Burgos, A

2018-05-17

Advances in clinical applications of computed tomography have been accompanied by improvements in advanced post-processing tools. In addition to multiplanar reconstructions, curved planar reconstructions, maximum intensity projections, and volumetric reconstructions, very recently kinematic reconstruction has been developed. This new technique, based on mathematical models that simulate the propagation of light beams through a volume of data, makes it possible to obtain very realistic three dimensional images. This article illustrates examples of kinematic reconstructions and compares them with classical volumetric reconstructions in patients with cardiovascular disease in a way that makes it easy to establish the differences between the two types of reconstruction. Kinematic reconstruction is a new method for representing three dimensional images that facilitates the explanation and comprehension of the findings. Copyright © 2018 SERAM. Publicado por Elsevier España, S.L.U. All rights reserved.

Novel imaging analysis system to measure the spatial dimension of engineered tissue construct.

PubMed

Choi, Kyoung-Hwan; Yoo, Byung-Su; Park, So Ra; Choi, Byung Hyune; Min, Byoung-Hyun

2010-02-01

The measurement of the spatial dimensions of tissue-engineered constructs is very important for their clinical applications. In this study, a novel method to measure the volume of tissue-engineered constructs was developed using iterative mathematical computations. The method measures and analyzes three-dimensional (3D) parameters of a construct to estimate its actual volume using a sequence of software-based mathematical algorithms. The mathematical algorithm is composed of two stages: the shape extraction and the determination of volume. The shape extraction utilized 3D images of a construct: length, width, and thickness, captured by a high-quality camera with charge coupled device. The surface of the 3D images was then divided into fine sections. The area of each section was measured and combined to obtain the total surface area. The 3D volume of the target construct was then mathematically obtained using its total surface area and thickness. The accuracy of the measurement method was verified by comparing the results with those obtained from the hydrostatic weighing method (Korea Research Institute of Standards and Science [KRISS], Korea). The mean difference in volume between two methods was 0.0313 +/- 0.0003% (n = 5, P = 0.523) with no significant statistical difference. In conclusion, our image-based spatial measurement system is a reliable and easy method to obtain an accurate 3D volume of a tissue-engineered construct.

The effects of geometric uncertainties on computational modelling of knee biomechanics

PubMed Central

Fisher, John; Wilcox, Ruth

2017-01-01

The geometry of the articular components of the knee is an important factor in predicting joint mechanics in computational models. There are a number of uncertainties in the definition of the geometry of cartilage and meniscus, and evaluating the effects of these uncertainties is fundamental to understanding the level of reliability of the models. In this study, the sensitivity of knee mechanics to geometric uncertainties was investigated by comparing polynomial-based and image-based knee models and varying the size of meniscus. The results suggested that the geometric uncertainties in cartilage and meniscus resulting from the resolution of MRI and the accuracy of segmentation caused considerable effects on the predicted knee mechanics. Moreover, even if the mathematical geometric descriptors can be very close to the imaged-based articular surfaces, the detailed contact pressure distribution produced by the mathematical geometric descriptors was not the same as that of the image-based model. However, the trends predicted by the models based on mathematical geometric descriptors were similar to those of the imaged-based models. PMID:28879008

International Neural Network Society Annual Meeting (1994) Held in San Diego, California on 5-9 June 1994. Volume 1

DTIC Science & Technology

1994-06-09

Ethics and the Soul 1-221 P. Werbos A Net Program for Natural Language Comprehension 1-863 J. Weiss Applications Oral ANN Design of Image Processing...Controlling Nonlinear Dynamic Systems Using Neuro-Fuzzy Networks 1-787 E. Teixera, G. Laforga, H. Azevedo Neural Fuzzy Logics as a Tool for Design Ecological ...Discrete Neural Network 11-466 Z. Cheng-fu Representation of Number A Theory of Mathematical Modeling 11-479 J. Cristofano An Ecological Approach to

Travelogue--a newcomer encounters statistics and the computer.

PubMed

Bruce, Peter

2011-11-01

Computer-intensive methods have revolutionized statistics, giving rise to new areas of analysis and expertise in predictive analytics, image processing, pattern recognition, machine learning, genomic analysis, and more. Interest naturally centers on the new capabilities the computer allows the analyst to bring to the table. This article, instead, focuses on the account of how computer-based resampling methods, with their relative simplicity and transparency, enticed one individual, untutored in statistics or mathematics, on a long journey into learning statistics, then teaching it, then starting an education institution.

Oki-Doku: Number Puzzles

ERIC Educational Resources Information Center

Gomez, Cristina; Novak, Dani

2014-01-01

The Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) emphasize the Standards for Mathematical Practice (SMP) that describe processes and proficiencies included in the NCTM Process Standards (NCTM 2000) and in the Strands for Mathematical Proficiency (NRC 2001). The development of these mathematical practices should happen in…

Quantitative imaging with Fucci and mathematics to uncover temporal dynamics of cell cycle progression.

PubMed

Saitou, Takashi; Imamura, Takeshi

2016-01-01

Cell cycle progression is strictly coordinated to ensure proper tissue growth, development, and regeneration of multicellular organisms. Spatiotemporal visualization of cell cycle phases directly helps us to obtain a deeper understanding of controlled, multicellular, cell cycle progression. The fluorescent ubiquitination-based cell cycle indicator (Fucci) system allows us to monitor, in living cells, the G1 and the S/G2/M phases of the cell cycle in red and green fluorescent colors, respectively. Since the discovery of Fucci technology, it has found numerous applications in the characterization of the timing of cell cycle phase transitions under diverse conditions and various biological processes. However, due to the complexity of cell cycle dynamics, understanding of specific patterns of cell cycle progression is still far from complete. In order to tackle this issue, quantitative approaches combined with mathematical modeling seem to be essential. Here, we review several studies that attempted to integrate Fucci technology and mathematical models to obtain quantitative information regarding cell cycle regulatory patterns. Focusing on the technological development of utilizing mathematics to retrieve meaningful information from the Fucci producing data, we discuss how the combined methods advance a quantitative understanding of cell cycle regulation. © 2015 Japanese Society of Developmental Biologists.

Algorithm for repairing the damaged images of grain structures obtained from the cellular automata and measurement of grain size

NASA Astrophysics Data System (ADS)

Ramírez-López, A.; Romero-Romo, M. A.; Muñoz-Negron, D.; López-Ramírez, S.; Escarela-Pérez, R.; Duran-Valencia, C.

2012-10-01

Computational models are developed to create grain structures using mathematical algorithms based on the chaos theory such as cellular automaton, geometrical models, fractals, and stochastic methods. Because of the chaotic nature of grain structures, some of the most popular routines are based on the Monte Carlo method, statistical distributions, and random walk methods, which can be easily programmed and included in nested loops. Nevertheless, grain structures are not well defined as the results of computational errors and numerical inconsistencies on mathematical methods. Due to the finite definition of numbers or the numerical restrictions during the simulation of solidification, damaged images appear on the screen. These images must be repaired to obtain a good measurement of grain geometrical properties. Some mathematical algorithms were developed to repair, measure, and characterize grain structures obtained from cellular automata in the present work. An appropriate measurement of grain size and the corrected identification of interfaces and length are very important topics in materials science because they are the representation and validation of mathematical models with real samples. As a result, the developed algorithms are tested and proved to be appropriate and efficient to eliminate the errors and characterize the grain structures.

Neural activity during natural viewing of Sesame Street statistically predicts test scores in early childhood.

PubMed

Cantlon, Jessica F; Li, Rosa

2013-01-01

It is not currently possible to measure the real-world thought process that a child has while observing an actual school lesson. However, if it could be done, children's neural processes would presumably be predictive of what they know. Such neural measures would shed new light on children's real-world thought. Toward that goal, this study examines neural processes that are evoked naturalistically, during educational television viewing. Children and adults all watched the same Sesame Street video during functional magnetic resonance imaging (fMRI). Whole-brain intersubject correlations between the neural timeseries from each child and a group of adults were used to derive maps of "neural maturity" for children. Neural maturity in the intraparietal sulcus (IPS), a region with a known role in basic numerical cognition, predicted children's formal mathematics abilities. In contrast, neural maturity in Broca's area correlated with children's verbal abilities, consistent with prior language research. Our data show that children's neural responses while watching complex real-world stimuli predict their cognitive abilities in a content-specific manner. This more ecologically natural paradigm, combined with the novel measure of "neural maturity," provides a new method for studying real-world mathematics development in the brain.

Method of transmission of dynamic multibit digital images from micro-unmanned aerial vehicles

NASA Astrophysics Data System (ADS)

Petrov, E. P.; Kharina, N. L.

2018-01-01

In connection with successful usage of nanotechnologies in remote sensing great attention is paid to the systems in micro-unmanned aerial vehicles (MUAVs) capable to provide high spatial resolution of dynamic multibit digital images (MDI). Limited energy resources on board the MUAV do not allow transferring a large amount of video information in the shortest possible time. It keeps back the broad development of MUAV. The search for methods to shorten the transmission time of dynamic MDIs from MUAV over the radio channel leads to the methods of MDI compression without computational operations onboard the MUAV. The known compression codecs of video information can not be applied because of the limited energy resources. In this paper we propose a method for reducing the transmission time of dynamic MDIs without computational operations and distortions onboard the MUAV. To develop the method a mathematical apparatus of the theory of conditional Markov processes with discrete arguments was used. On its basis a mathematical model for the transformation of the MDI represented by binary images (BI) in the MDI, consisting of groups of neighboring BIs (GBI) transmitted by multiphase (MP) signals, is constructed. The algorithm for multidimensional nonlinear filtering of MP signals is synthesized, realizing the statistical redundancy of the MDI to compensate for the noise stability losses caused by the use of MP signals.

Particle tracking velocimetry in three-dimensional flows

NASA Astrophysics Data System (ADS)

Maas, H. G.; Gruen, A.; Papantoniou, D.

1993-07-01

Particle Tracking Velocimetry (PTV) is a well-known technique for the determination of velocity vectors within an observation volume. However, for a long time it has rarely been applied because of the intensive effort necessary to measure coordinates of a large number of flow marker particles in many images. With today's imaging hardware in combination with the methods of digital image processing and digital photogrammetry, however, new possibilities have arisen for the design of completely automatic PTV systems. A powerful 3 D PTV has been developed in a cooperation of the Institute of Geodesy and Photogrammetry with the Institute of Hydromechanics and Water Resources Management at the Swiss Federal Institute of Technology. In this paper hardware components for 3 D PTV systems wil be discussed, and a strict mathematical model of photogrammetric 3 D coordinate determination, taking into account the different refractive indices in the optical path, will be presented. The system described is capable of determining coordinate sets of some 1000 particles in a flow field at a time resolution of 25 datasets per second and almost arbitrary sequence length completely automatically after an initialization by an operator. The strict mathematical modelling of the measurement geometry, together with a thorough calibration of the system provide for a coordinate accuracy of typically 0.06 mm in X, Y and 0.18 mm in Z (depth coordinate) in a volume of 200 × 160 × 50 mm3.

Adding structure to the transition process to advanced mathematical activity

NASA Astrophysics Data System (ADS)

Engelbrecht, Johann

2010-03-01

The transition process to advanced mathematical thinking is experienced as traumatic by many students. Experiences that students had of school mathematics differ greatly to what is expected from them at university. Success in school mathematics meant application of different methods to get an answer. Students are not familiar with logical deductive reasoning, required in advanced mathematics. It is necessary to assist students in this transition process, in moving from general to mathematical thinking. In this article some structure is suggested for this transition period. This essay is an argumentative exposition supported by personal experience and international literature. This makes this study theoretical rather than empirical.

Image-analysis library

NASA Technical Reports Server (NTRS)

1980-01-01

MATHPAC image-analysis library is collection of general-purpose mathematical and statistical routines and special-purpose data-analysis and pattern-recognition routines for image analysis. MATHPAC library consists of Linear Algebra, Optimization, Statistical-Summary, Densities and Distribution, Regression, and Statistical-Test packages.

Automatic protein structure solution from weak X-ray data

NASA Astrophysics Data System (ADS)

Skubák, Pavol; Pannu, Navraj S.

2013-11-01

Determining new protein structures from X-ray diffraction data at low resolution or with a weak anomalous signal is a difficult and often an impossible task. Here we propose a multivariate algorithm that simultaneously combines the structure determination steps. In tests on over 140 real data sets from the protein data bank, we show that this combined approach can automatically build models where current algorithms fail, including an anisotropically diffracting 3.88 Å RNA polymerase II data set. The method seamlessly automates the process, is ideal for non-specialists and provides a mathematical framework for successfully combining various sources of information in image processing.

Synchrotron-based X-ray computed tomography during compression loading of cellular materials

DOE PAGES

Cordes, Nikolaus L.; Henderson, Kevin; Stannard, Tyler; ...

2015-04-29

Three-dimensional X-ray computed tomography (CT) of in situ dynamic processes provides internal snapshot images as a function of time. Tomograms are mathematically reconstructed from a series of radiographs taken in rapid succession as the specimen is rotated in small angular increments. In addition to spatial resolution, temporal resolution is important. Thus temporal resolution indicates how close together in time two distinct tomograms can be acquired. Tomograms taken in rapid succession allow detailed analyses of internal processes that cannot be obtained by other means. This article describes the state-of-the-art for such measurements acquired using synchrotron radiation as the X-ray source.

A biomimetic algorithm for the improved detection of microarray features

NASA Astrophysics Data System (ADS)

Nicolau, Dan V., Jr.; Nicolau, Dan V.; Maini, Philip K.

2007-02-01

One the major difficulties of microarray technology relate to the processing of large and - importantly - error-loaded images of the dots on the chip surface. Whatever the source of these errors, those obtained in the first stage of data acquisition - segmentation - are passed down to the subsequent processes, with deleterious results. As it has been demonstrated recently that biological systems have evolved algorithms that are mathematically efficient, this contribution attempts to test an algorithm that mimics a bacterial-"patented" algorithm for the search of available space and nutrients to find, "zero-in" and eventually delimitate the features existent on the microarray surface.

Proceedings of the Conference of the International Group for the Psychology of Mathematics Education (PME) (15th, Assisi, Italy, June 29-July 4, 1991), Volume 1.

ERIC Educational Resources Information Center

Furinghetti, Fulvia, Ed.

This document, the first of three volumes, reports on the 15th annual conference of the International Group for the Psychology of Mathematics Education (PME) held in Italy 1991. Plenary addresses and speakers are: "Social Interaction and Mathematical Knowledge" (B. M. Bartolini); "Meaning: Image Schemata and Protocols" (W.…

Computational oncology.

PubMed

Lefor, Alan T

2011-08-01

Oncology research has traditionally been conducted using techniques from the biological sciences. The new field of computational oncology has forged a new relationship between the physical sciences and oncology to further advance research. By applying physics and mathematics to oncologic problems, new insights will emerge into the pathogenesis and treatment of malignancies. One major area of investigation in computational oncology centers around the acquisition and analysis of data, using improved computing hardware and software. Large databases of cellular pathways are being analyzed to understand the interrelationship among complex biological processes. Computer-aided detection is being applied to the analysis of routine imaging data including mammography and chest imaging to improve the accuracy and detection rate for population screening. The second major area of investigation uses computers to construct sophisticated mathematical models of individual cancer cells as well as larger systems using partial differential equations. These models are further refined with clinically available information to more accurately reflect living systems. One of the major obstacles in the partnership between physical scientists and the oncology community is communications. Standard ways to convey information must be developed. Future progress in computational oncology will depend on close collaboration between clinicians and investigators to further the understanding of cancer using these new approaches.

Mathematical Foundation for Plane Covering Using Hexagons

NASA Technical Reports Server (NTRS)

Johnson, Gordon G.

1999-01-01

This work is to indicate the development and mathematical underpinnings of the algorithms previously developed for covering the plane and the addressing of the elements of the covering. The algorithms are of interest in that they provides a simple systematic way of increasing or decreasing resolution, in the sense that if we have the covering in place and there is an image superimposed upon the covering, then we may view the image in a rough form or in a very detailed form with minimal effort. Such ability allows for quick searches of crude forms to determine a class in which to make a detailed search. In addition, the addressing algorithms provide an efficient way to process large data sets that have related subsets. The algorithms produced were based in part upon the work of D. Lucas "A Multiplication in N Space" which suggested a set of three vectors, any two of which would serve as a bases for the plane and also that the hexagon is the natural geometric object to be used in a covering with a suggested bases. The second portion is a refinement of the eyeball vision system, the globular viewer.

Interactivity of Visual Mathematical Representations: Factors Affecting Learning and Cognitive Processes

ERIC Educational Resources Information Center

Sedig, Kamran; Liang, Hai-Ning

2006-01-01

Computer-based mathematical cognitive tools (MCTs) are a category of external aids intended to support and enhance learning and cognitive processes of learners. MCTs often contain interactive visual mathematical representations (VMRs), where VMRs are graphical representations that encode properties and relationships of mathematical concepts. In…

Development of Multi-perspective Diagnostics and Analysis Algorithms with Applications to Subsonic and Supersonic Combustors

NASA Astrophysics Data System (ADS)

Wickersham, Andrew Joseph

There are two critical research needs for the study of hydrocarbon combustion in high speed flows: 1) combustion diagnostics with adequate temporal and spatial resolution, and 2) mathematical techniques that can extract key information from large datasets. The goal of this work is to address these needs, respectively, by the use of high speed and multi-perspective chemiluminescence and advanced mathematical algorithms. To obtain the measurements, this work explored the application of high speed chemiluminescence diagnostics and the use of fiber-based endoscopes (FBEs) for non-intrusive and multi-perspective chemiluminescence imaging up to 20 kHz. Non-intrusive and full-field imaging measurements provide a wealth of information for model validation and design optimization of propulsion systems. However, it is challenging to obtain such measurements due to various implementation difficulties such as optical access, thermal management, and equipment cost. This work therefore explores the application of FBEs for non-intrusive imaging to supersonic propulsion systems. The FBEs used in this work are demonstrated to overcome many of the aforementioned difficulties and provided datasets from multiple angular positions up to 20 kHz in a supersonic combustor. The combustor operated on ethylene fuel at Mach 2 with an inlet stagnation temperature and pressure of approximately 640 degrees Fahrenheit and 70 psia, respectively. The imaging measurements were obtained from eight perspectives simultaneously, providing full-field datasets under such flow conditions for the first time, allowing the possibility of inferring multi-dimensional measurements. Due to the high speed and multi-perspective nature, such new diagnostic capability generates a large volume of data and calls for analysis algorithms that can process the data and extract key physics effectively. To extract the key combustion dynamics from the measurements, three mathematical methods were investigated in this work: Fourier analysis, proper orthogonal decomposition (POD), and wavelet analysis (WA). These algorithms were first demonstrated and tested on imaging measurements obtained from one perspective in a sub-sonic combustor (up to Mach 0.2). The results show that these algorithms are effective in extracting the key physics from large datasets, including the characteristic frequencies of flow-flame interactions especially during transient processes such as lean blow off and ignition. After these relatively simple tests and demonstrations, these algorithms were applied to process the measurements obtained from multi-perspective in the supersonic combustor. compared to past analyses (which have been limited to data obtained from one perspective only), the availability of data at multiple perspective provide further insights into the flame and flow structures in high speed flows. In summary, this work shows that high speed chemiluminescence is a simple yet powerful combustion diagnostic. Especially when combined with FBEs and the analyses algorithms described in this work, such diagnostics provide full-field imaging at high repetition rate in challenging flows. Based on such measurements, a wealth of information can be obtained from proper analysis algorithms, including characteristic frequency, dominating flame modes, and even multi-dimensional flame and flow structures.

Epithelial invasion outcompetes hypha development during Candida albicans infection as revealed by an image-based systems biology approach.

PubMed

Mech, Franziska; Wilson, Duncan; Lehnert, Teresa; Hube, Bernhard; Thilo Figge, Marc

2014-02-01

Candida albicans is the most common opportunistic fungal pathogen of the human mucosal flora, frequently causing infections. The fungus is responsible for invasive infections in immunocompromised patients that can lead to sepsis. The yeast to hypha transition and invasion of host-tissue represent major determinants in the switch from benign colonizer to invasive pathogen. A comprehensive understanding of the infection process requires analyses at the quantitative level. Utilizing fluorescence microscopy with differential staining, we obtained images of C. albicans undergoing epithelial invasion during a time course of 6 h. An image-based systems biology approach, combining image analysis and mathematical modeling, was applied to quantify the kinetics of hyphae development, hyphal elongation, and epithelial invasion. The automated image analysis facilitates high-throughput screening and provided quantities that allow for the time-resolved characterization of the morphological and invasive state of fungal cells. The interpretation of these data was supported by two mathematical models, a kinetic growth model and a kinetic transition model, that were developed using differential equations. The kinetic growth model describes the increase in hyphal length and revealed that hyphae undergo mass invasion of epithelial cells following primary hypha formation. We also provide evidence that epithelial cells stimulate the production of secondary hyphae by C. albicans. Based on the kinetic transition model, the route of invasion was quantified in the state space of non-invasive and invasive fungal cells depending on their number of hyphae. This analysis revealed that the initiation of hyphae formation represents an ultimate commitment to invasive growth and suggests that in vivo, the yeast to hypha transition must be under exquisitely tight negative regulation to avoid the transition from commensal to pathogen invading the epithelium. © 2013 International Society for Advancement of Cytometry.

A mathematical model for the virus medical imaging technique

NASA Astrophysics Data System (ADS)

Fioranelli, Massimo; Sepehri, Alireza

In this paper, we introduce a mathematical model for the virus medical imaging (VMI). In this method, first, by proposing a mathematical model, we show that there are two types of viruses that each of them produce one type of signal. Some of these signals can be received by males and others by females. Then, we will show that in the VMI technique, viruses can communicate with cells, interior to human’s body via two ways. (1) Viruses can form a wire that passes the skin and reaches to a special cell. (2) Viruses can communicate with viruses interior to body in the wireless form and send some signals for controlling evolutions of cells interior to human’s body.

Sparse radar imaging using 2D compressed sensing

NASA Astrophysics Data System (ADS)

Hou, Qingkai; Liu, Yang; Chen, Zengping; Su, Shaoying

2014-10-01

Radar imaging is an ill-posed linear inverse problem and compressed sensing (CS) has been proved to have tremendous potential in this field. This paper surveys the theory of radar imaging and a conclusion is drawn that the processing of ISAR imaging can be denoted mathematically as a problem of 2D sparse decomposition. Based on CS, we propose a novel measuring strategy for ISAR imaging radar and utilize random sub-sampling in both range and azimuth dimensions, which will reduce the amount of sampling data tremendously. In order to handle 2D reconstructing problem, the ordinary solution is converting the 2D problem into 1D by Kronecker product, which will increase the size of dictionary and computational cost sharply. In this paper, we introduce the 2D-SL0 algorithm into the reconstruction of imaging. It is proved that 2D-SL0 can achieve equivalent result as other 1D reconstructing methods, but the computational complexity and memory usage is reduced significantly. Moreover, we will state the results of simulating experiments and prove the effectiveness and feasibility of our method.

The research of statistical properties of colorimetric features of screens with a three-component color formation principle

NASA Astrophysics Data System (ADS)

Zharinov, I. O.; Zharinov, O. O.

2017-12-01

The problem of the research is concerned with quantitative analysis of influence of technological variation of the screen color profile parameters on chromaticity coordinates of the displayed image. Some mathematical expressions which approximate the two-dimensional distribution of chromaticity coordinates of an image, which is displayed on the screen with a three-component color formation principle were proposed. Proposed mathematical expressions show the way to development of correction techniques to improve reproducibility of the colorimetric features of displays.

Concept Study of Multi Sensor Detection Imaging and Explosive Confirmation of Mines

DTIC Science & Technology

1998-03-20

surface feature removal can be achieved in LMR images. Small Business Technology Transfer (STTR) Solicitation Topic 97T006 Mufi -Sensor Detection...divided by the applied voltage. This is mathematically given by: 00 Y-I-G+jB = 1o+2E’. COS m4; m1l 1-1 = j120 72(+a) where G = the input conductance...of detector operation that are incorporated into a mathematical algorithm to convert detector impedance characteristics into recognizable indicators

Model-Based Building Detection from Low-Cost Optical Sensors Onboard Unmanned Aerial Vehicles

NASA Astrophysics Data System (ADS)

Karantzalos, K.; Koutsourakis, P.; Kalisperakis, I.; Grammatikopoulos, L.

2015-08-01

The automated and cost-effective building detection in ultra high spatial resolution is of major importance for various engineering and smart city applications. To this end, in this paper, a model-based building detection technique has been developed able to extract and reconstruct buildings from UAV aerial imagery and low-cost imaging sensors. In particular, the developed approach through advanced structure from motion, bundle adjustment and dense image matching computes a DSM and a true orthomosaic from the numerous GoPro images which are characterised by important geometric distortions and fish-eye effect. An unsupervised multi-region, graphcut segmentation and a rule-based classification is responsible for delivering the initial multi-class classification map. The DTM is then calculated based on inpaininting and mathematical morphology process. A data fusion process between the detected building from the DSM/DTM and the classification map feeds a grammar-based building reconstruction and scene building are extracted and reconstructed. Preliminary experimental results appear quite promising with the quantitative evaluation indicating detection rates at object level of 88% regarding the correctness and above 75% regarding the detection completeness.

Graph-based unsupervised segmentation algorithm for cultured neuronal networks' structure characterization and modeling.

PubMed

de Santos-Sierra, Daniel; Sendiña-Nadal, Irene; Leyva, Inmaculada; Almendral, Juan A; Ayali, Amir; Anava, Sarit; Sánchez-Ávila, Carmen; Boccaletti, Stefano

2015-06-01

Large scale phase-contrast images taken at high resolution through the life of a cultured neuronal network are analyzed by a graph-based unsupervised segmentation algorithm with a very low computational cost, scaling linearly with the image size. The processing automatically retrieves the whole network structure, an object whose mathematical representation is a matrix in which nodes are identified neurons or neurons' clusters, and links are the reconstructed connections between them. The algorithm is also able to extract any other relevant morphological information characterizing neurons and neurites. More importantly, and at variance with other segmentation methods that require fluorescence imaging from immunocytochemistry techniques, our non invasive measures entitle us to perform a longitudinal analysis during the maturation of a single culture. Such an analysis furnishes the way of individuating the main physical processes underlying the self-organization of the neurons' ensemble into a complex network, and drives the formulation of a phenomenological model yet able to describe qualitatively the overall scenario observed during the culture growth. © 2014 International Society for Advancement of Cytometry.

Image preprocessing for improving computational efficiency in implementation of restoration and superresolution algorithms.

PubMed

Sundareshan, Malur K; Bhattacharjee, Supratik; Inampudi, Radhika; Pang, Ho-Yuen

2002-12-10

Computational complexity is a major impediment to the real-time implementation of image restoration and superresolution algorithms in many applications. Although powerful restoration algorithms have been developed within the past few years utilizing sophisticated mathematical machinery (based on statistical optimization and convex set theory), these algorithms are typically iterative in nature and require a sufficient number of iterations to be executed to achieve the desired resolution improvement that may be needed to meaningfully perform postprocessing image exploitation tasks in practice. Additionally, recent technological breakthroughs have facilitated novel sensor designs (focal plane arrays, for instance) that make it possible to capture megapixel imagery data at video frame rates. A major challenge in the processing of these large-format images is to complete the execution of the image processing steps within the frame capture times and to keep up with the output rate of the sensor so that all data captured by the sensor can be efficiently utilized. Consequently, development of novel methods that facilitate real-time implementation of image restoration and superresolution algorithms is of significant practical interest and is the primary focus of this study. The key to designing computationally efficient processing schemes lies in strategically introducing appropriate preprocessing steps together with the superresolution iterations to tailor optimized overall processing sequences for imagery data of specific formats. For substantiating this assertion, three distinct methods for tailoring a preprocessing filter and integrating it with the superresolution processing steps are outlined. These methods consist of a region-of-interest extraction scheme, a background-detail separation procedure, and a scene-derived information extraction step for implementing a set-theoretic restoration of the image that is less demanding in computation compared with the superresolution iterations. A quantitative evaluation of the performance of these algorithms for restoring and superresolving various imagery data captured by diffraction-limited sensing operations are also presented.

An imaging informatics-based ePR (electronic patient record) system for providing decision support in evaluating dose optimization in stroke rehabilitation

NASA Astrophysics Data System (ADS)

Liu, Brent J.; Winstein, Carolee; Wang, Ximing; Konersman, Matt; Martinez, Clarisa; Schweighofer, Nicolas

2012-02-01

Stroke is one of the major causes of death and disability in America. After stroke, about 65% of survivors still suffer from severe paresis, while rehabilitation treatment strategy after stroke plays an essential role in recovery. Currently, there is a clinical trial (NIH award #HD065438) to determine the optimal dose of rehabilitation for persistent recovery of arm and hand paresis. For DOSE (Dose Optimization Stroke Evaluation), laboratory-based measurements, such as the Wolf Motor Function test, behavioral questionnaires (e.g. Motor Activity Log-MAL), and MR, DTI, and Transcranial Magnetic Stimulation (TMS) imaging studies are planned. Current data collection processes are tedious and reside in various standalone systems including hardcopy forms. In order to improve the efficiency of this clinical trial and facilitate decision support, a web-based imaging informatics system has been implemented together with utilizing mobile devices (eg, iPAD, tablet PC's, laptops) for collecting input data and integrating all multi-media data into a single system. The system aims to provide clinical imaging informatics management and a platform to develop tools to predict the treatment effect based on the imaging studies and the treatment dosage with mathematical models. Since there is a large amount of information to be recorded within the DOSE project, the system provides clinical data entry through mobile device applications thus allowing users to collect data at the point of patient interaction without typing into a desktop computer, which is inconvenient. Imaging analysis tools will also be developed for structural MRI, DTI, and TMS imaging studies that will be integrated within the system and correlated with the clinical and behavioral data. This system provides a research platform for future development of mathematical models to evaluate the differences between prediction and reality and thus improve and refine the models rapidly and efficiently.

Use of image registration and fusion algorithms and techniques in radiotherapy: Report of the AAPM Radiation Therapy Committee Task Group No. 132.

PubMed

Brock, Kristy K; Mutic, Sasa; McNutt, Todd R; Li, Hua; Kessler, Marc L

2017-07-01

Image registration and fusion algorithms exist in almost every software system that creates or uses images in radiotherapy. Most treatment planning systems support some form of image registration and fusion to allow the use of multimodality and time-series image data and even anatomical atlases to assist in target volume and normal tissue delineation. Treatment delivery systems perform registration and fusion between the planning images and the in-room images acquired during the treatment to assist patient positioning. Advanced applications are beginning to support daily dose assessment and enable adaptive radiotherapy using image registration and fusion to propagate contours and accumulate dose between image data taken over the course of therapy to provide up-to-date estimates of anatomical changes and delivered dose. This information aids in the detection of anatomical and functional changes that might elicit changes in the treatment plan or prescription. As the output of the image registration process is always used as the input of another process for planning or delivery, it is important to understand and communicate the uncertainty associated with the software in general and the result of a specific registration. Unfortunately, there is no standard mathematical formalism to perform this for real-world situations where noise, distortion, and complex anatomical variations can occur. Validation of the software systems performance is also complicated by the lack of documentation available from commercial systems leading to use of these systems in undesirable 'black-box' fashion. In view of this situation and the central role that image registration and fusion play in treatment planning and delivery, the Therapy Physics Committee of the American Association of Physicists in Medicine commissioned Task Group 132 to review current approaches and solutions for image registration (both rigid and deformable) in radiotherapy and to provide recommendations for quality assurance and quality control of these clinical processes. © 2017 American Association of Physicists in Medicine.

Conclusiveness of natural languages and recognition of images

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

Wojcik, Z.M.

1983-01-01

The conclusiveness is investigated using recognition processes and one-one correspondence between expressions of a natural language and graphs representing events. The graphs, as conceived in psycholinguistics, are obtained as a result of perception processes. It is possible to generate and process the graphs automatically, using computers and then to convert the resulting graphs into expressions of a natural language. Correctness and conclusiveness of the graphs and sentences are investigated using the fundamental condition for events representation processes. Some consequences of the conclusiveness are discussed, e.g. undecidability of arithmetic, human brain assymetry, correctness of statistical calculations and operations research. It ismore » suggested that the group theory should be imposed on mathematical models of any real system. Proof of the fundamental condition is also presented. 14 references.« less

Content-based cell pathology image retrieval by combining different features

NASA Astrophysics Data System (ADS)

Zhou, Guangquan; Jiang, Lu; Luo, Limin; Bao, Xudong; Shu, Huazhong

2004-04-01

Content Based Color Cell Pathology Image Retrieval is one of the newest computer image processing applications in medicine. Recently, some algorithms have been developed to achieve this goal. Because of the particularity of cell pathology images, the result of the image retrieval based on single characteristic is not satisfactory. A new method for pathology image retrieval by combining color, texture and morphologic features to search cell images is proposed. Firstly, nucleus regions of leukocytes in images are automatically segmented by K-mean clustering method. Then single leukocyte region is detected by utilizing thresholding algorithm segmentation and mathematics morphology. The features that include color, texture and morphologic features are extracted from single leukocyte to represent main attribute in the search query. The features are then normalized because the numerical value range and physical meaning of extracted features are different. Finally, the relevance feedback system is introduced. So that the system can automatically adjust the weights of different features and improve the results of retrieval system according to the feedback information. Retrieval results using the proposed method fit closely with human perception and are better than those obtained with the methods based on single feature.

Remote Sensing of Landscapes with Spectral Images

NASA Astrophysics Data System (ADS)

Adams, John B.; Gillespie, Alan R.

2006-05-01

Remote Sensing of Landscapes with Spectral Images describes how to process and interpret spectral images using physical models to bridge the gap between the engineering and theoretical sides of remote-sensing and the world that we encounter when we venture outdoors. The emphasis is on the practical use of images rather than on theory and mathematical derivations. Examples are drawn from a variety of landscapes and interpretations are tested against the reality seen on the ground. The reader is led through analysis of real images (using figures and explanations); the examples are chosen to illustrate important aspects of the analytic framework. This textbook will form a valuable reference for graduate students and professionals in a variety of disciplines including ecology, forestry, geology, geography, urban planning, archeology and civil engineering. It is supplemented by a web-site hosting digital color versions of figures in the book as well as ancillary images (www.cambridge.org/9780521662214). Presents a coherent view of practical remote sensing, leading from imaging and field work to the generation of useful thematic maps Explains how to apply physical models to help interpret spectral images Supplemented by a website hosting digital colour versions of figures in the book, as well as additional colour figures

Computational photography with plenoptic camera and light field capture: tutorial.

PubMed

Lam, Edmund Y

2015-11-01

Photography is a cornerstone of imaging. Ever since cameras became consumer products more than a century ago, we have witnessed great technological progress in optics and recording mediums, with digital sensors replacing photographic films in most instances. The latest revolution is computational photography, which seeks to make image reconstruction computation an integral part of the image formation process; in this way, there can be new capabilities or better performance in the overall imaging system. A leading effort in this area is called the plenoptic camera, which aims at capturing the light field of an object; proper reconstruction algorithms can then adjust the focus after the image capture. In this tutorial paper, we first illustrate the concept of plenoptic function and light field from the perspective of geometric optics. This is followed by a discussion on early attempts and recent advances in the construction of the plenoptic camera. We will then describe the imaging model and computational algorithms that can reconstruct images at different focus points, using mathematical tools from ray optics and Fourier optics. Last, but not least, we will consider the trade-off in spatial resolution and highlight some research work to increase the spatial resolution of the resulting images.

Quantification of differences between nailfold capillaroscopy images with a scleroderma pattern and normal pattern using measures of geometric and algorithmic complexity.

PubMed

Urwin, Samuel George; Griffiths, Bridget; Allen, John

2017-02-01

This study aimed to quantify and investigate differences in the geometric and algorithmic complexity of the microvasculature in nailfold capillaroscopy (NFC) images displaying a scleroderma pattern and those displaying a 'normal' pattern. 11 NFC images were qualitatively classified by a capillary specialist as indicative of 'clear microangiopathy' (CM), i.e. a scleroderma pattern, and 11 as 'not clear microangiopathy' (NCM), i.e. a 'normal' pattern. Pre-processing was performed, and fractal dimension (FD) and Kolmogorov complexity (KC) were calculated following image binarisation. FD and KC were compared between groups, and a k-means cluster analysis (n  =  2) on all images was performed, without prior knowledge of the group assigned to them (i.e. CM or NCM), using FD and KC as inputs. CM images had significantly reduced FD and KC compared to NCM images, and the cluster analysis displayed promising results that the quantitative classification of images into CM and NCM groups is possible using the mathematical measures of FD and KC. The analysis techniques used show promise for quantitative microvascular investigation in patients with systemic sclerosis.

Effect of image quality on calcification detection in digital mammography

PubMed Central

Warren, Lucy M.; Mackenzie, Alistair; Cooke, Julie; Given-Wilson, Rosalind M.; Wallis, Matthew G.; Chakraborty, Dev P.; Dance, David R.; Bosmans, Hilde; Young, Kenneth C.

2012-01-01

Purpose: This study aims to investigate if microcalcification detection varies significantly when mammographic images are acquired using different image qualities, including: different detectors, dose levels, and different image processing algorithms. An additional aim was to determine how the standard European method of measuring image quality using threshold gold thickness measured with a CDMAM phantom and the associated limits in current EU guidelines relate to calcification detection. Methods: One hundred and sixty two normal breast images were acquired on an amorphous selenium direct digital (DR) system. Microcalcification clusters extracted from magnified images of slices of mastectomies were electronically inserted into half of the images. The calcification clusters had a subtle appearance. All images were adjusted using a validated mathematical method to simulate the appearance of images from a computed radiography (CR) imaging system at the same dose, from both systems at half this dose, and from the DR system at quarter this dose. The original 162 images were processed with both Hologic and Agfa (Musica-2) image processing. All other image qualities were processed with Agfa (Musica-2) image processing only. Seven experienced observers marked and rated any identified suspicious regions. Free response operating characteristic (FROC) and ROC analyses were performed on the data. The lesion sensitivity at a nonlesion localization fraction (NLF) of 0.1 was also calculated. Images of the CDMAM mammographic test phantom were acquired using the automatic setting on the DR system. These images were modified to the additional image qualities used in the observer study. The images were analyzed using automated software. In order to assess the relationship between threshold gold thickness and calcification detection a power law was fitted to the data. Results: There was a significant reduction in calcification detection using CR compared with DR: the alternative FROC (AFROC) area decreased from 0.84 to 0.63 and the ROC area decreased from 0.91 to 0.79 (p < 0.0001). This corresponded to a 30% drop in lesion sensitivity at a NLF equal to 0.1. Detection was also sensitive to the dose used. There was no significant difference in detection between the two image processing algorithms used (p > 0.05). It was additionally found that lower threshold gold thickness from CDMAM analysis implied better cluster detection. The measured threshold gold thickness passed the acceptable limit set in the EU standards for all image qualities except half dose CR. However, calcification detection varied significantly between image qualities. This suggests that the current EU guidelines may need revising. Conclusions: Microcalcification detection was found to be sensitive to detector and dose used. Standard measurements of image quality were a good predictor of microcalcification cluster detection. PMID:22755704

Effect of image quality on calcification detection in digital mammography.

PubMed

Warren, Lucy M; Mackenzie, Alistair; Cooke, Julie; Given-Wilson, Rosalind M; Wallis, Matthew G; Chakraborty, Dev P; Dance, David R; Bosmans, Hilde; Young, Kenneth C

2012-06-01

This study aims to investigate if microcalcification detection varies significantly when mammographic images are acquired using different image qualities, including: different detectors, dose levels, and different image processing algorithms. An additional aim was to determine how the standard European method of measuring image quality using threshold gold thickness measured with a CDMAM phantom and the associated limits in current EU guidelines relate to calcification detection. One hundred and sixty two normal breast images were acquired on an amorphous selenium direct digital (DR) system. Microcalcification clusters extracted from magnified images of slices of mastectomies were electronically inserted into half of the images. The calcification clusters had a subtle appearance. All images were adjusted using a validated mathematical method to simulate the appearance of images from a computed radiography (CR) imaging system at the same dose, from both systems at half this dose, and from the DR system at quarter this dose. The original 162 images were processed with both Hologic and Agfa (Musica-2) image processing. All other image qualities were processed with Agfa (Musica-2) image processing only. Seven experienced observers marked and rated any identified suspicious regions. Free response operating characteristic (FROC) and ROC analyses were performed on the data. The lesion sensitivity at a nonlesion localization fraction (NLF) of 0.1 was also calculated. Images of the CDMAM mammographic test phantom were acquired using the automatic setting on the DR system. These images were modified to the additional image qualities used in the observer study. The images were analyzed using automated software. In order to assess the relationship between threshold gold thickness and calcification detection a power law was fitted to the data. There was a significant reduction in calcification detection using CR compared with DR: the alternative FROC (AFROC) area decreased from 0.84 to 0.63 and the ROC area decreased from 0.91 to 0.79 (p < 0.0001). This corresponded to a 30% drop in lesion sensitivity at a NLF equal to 0.1. Detection was also sensitive to the dose used. There was no significant difference in detection between the two image processing algorithms used (p > 0.05). It was additionally found that lower threshold gold thickness from CDMAM analysis implied better cluster detection. The measured threshold gold thickness passed the acceptable limit set in the EU standards for all image qualities except half dose CR. However, calcification detection varied significantly between image qualities. This suggests that the current EU guidelines may need revising. Microcalcification detection was found to be sensitive to detector and dose used. Standard measurements of image quality were a good predictor of microcalcification cluster detection. © 2012 American Association of Physicists in Medicine.

On the importance of mathematical methods for analysis of MALDI-imaging mass spectrometry data.

PubMed

Trede, Dennis; Kobarg, Jan Hendrik; Oetjen, Janina; Thiele, Herbert; Maass, Peter; Alexandrov, Theodore

2012-03-21

In the last decade, matrix-assisted laser desorption/ionization (MALDI) imaging mass spectrometry (IMS), also called as MALDI-imaging, has proven its potential in proteomics and was successfully applied to various types of biomedical problems, in particular to histopathological label-free analysis of tissue sections. In histopathology, MALDI-imaging is used as a general analytic tool revealing the functional proteomic structure of tissue sections, and as a discovery tool for detecting new biomarkers discriminating a region annotated by an experienced histologist, in particular, for cancer studies. A typical MALDI-imaging data set contains 10⁸ to 10⁹ intensity values occupying more than 1 GB. Analysis and interpretation of such huge amount of data is a mathematically, statistically and computationally challenging problem. In this paper we overview some computational methods for analysis of MALDI-imaging data sets. We discuss the importance of data preprocessing, which typically includes normalization, baseline removal and peak picking, and hightlight the importance of image denoising when visualizing IMS data.

On the Importance of Mathematical Methods for Analysis of MALDI-Imaging Mass Spectrometry Data.

PubMed

Trede, Dennis; Kobarg, Jan Hendrik; Oetjen, Janina; Thiele, Herbert; Maass, Peter; Alexandrov, Theodore

2012-03-01

In the last decade, matrix-assisted laser desorption/ionization (MALDI) imaging mass spectrometry (IMS), also called as MALDI-imaging, has proven its potential in proteomics and was successfully applied to various types of biomedical problems, in particular to histopathological label-free analysis of tissue sections. In histopathology, MALDI-imaging is used as a general analytic tool revealing the functional proteomic structure of tissue sections, and as a discovery tool for detecting new biomarkers discriminating a region annotated by an experienced histologist, in particular, for cancer studies. A typical MALDI-imaging data set contains 108 to 109 intensity values occupying more than 1 GB. Analysis and interpretation of such huge amount of data is a mathematically, statistically and computationally challenging problem. In this paper we overview some computational methods for analysis of MALDI-imaging data sets. We discuss the importance of data preprocessing, which typically includes normalization, baseline removal and peak picking, and hightlight the importance of image denoising when visualizing IMS data.

Virtual Visualisation Laboratory for Science and Mathematics Content (Vlab-SMC) with Special Reference to Teaching and Learning of Chemistry

NASA Astrophysics Data System (ADS)

Badioze Zaman, Halimah; Bakar, Norashiken; Ahmad, Azlina; Sulaiman, Riza; Arshad, Haslina; Mohd. Yatim, Nor Faezah

Research on the teaching of science and mathematics in schools and universities have shown that available teaching models are not effective in instilling the understanding of scientific and mathematics concepts, and the right scientific and mathematics skills required for learners to become good future scientists (mathematicians included). The extensive development of new technologies has a marked influence on education, by facilitating the design of new learning and teaching materials, that can improve the attitude of learners towards Science and Mathematics and the plausibility of advanced interactive, personalised learning process. The usefulness of the computer in Science and Mathematics education; as an interactive communication medium that permits access to all types of information (texts, images, different types of data such as sound, graphics and perhaps haptics like smell and touch); as an instrument for problem solving through simulations of scientific and mathematics phenomenon and experiments; as well as measuring and monitoring scientific laboratory experiments. This paper will highlight on the design and development of the virtual Visualisation Laboratory for Science & Mathematics Content (VLab-SMC) based on the Cognitivist- Constructivist-Contextual development life cycle model as well as the Instructional Design (ID) model, in order to achieve its objectives in teaching and learning. However, this paper with only highlight one of the virtual labs within VLab-SMC that is, the Virtual Lab for teaching Chemistry (VLab- Chem). The development life cycle involves the educational media to be used, measurement of content, and the authoring and programming involved; whilst the ID model involves the application of the cognitivist, constructivist and contextual theories in the modeling of the modules of VLab-SMC generally and Vlab-Chem specifically, using concepts such as 'learning by doing', contextual learning, experimental simulations 3D and real-time animations to create a virtual laboratory based on a real laboratory. Initial preliminary study shows positive indicators of VLab-Chem for the teaching and learning of Chemistry on the topic of 'Salts and Acids'.

Asteroid (21) Lutetia: Semi-Automatic Impact Craters Detection and Classification

NASA Astrophysics Data System (ADS)

Jenerowicz, M.; Banaszkiewicz, M.

2018-05-01

The need to develop an automated method, independent of lighting and surface conditions, for the identification and measurement of impact craters, as well as the creation of a reliable and efficient tool, has become a justification of our studies. This paper presents a methodology for the detection of impact craters based on their spectral and spatial features. The analysis aims at evaluation of the algorithm capabilities to determinate the spatial parameters of impact craters presented in a time series. In this way, time-consuming visual interpretation of images would be reduced to the special cases. The developed algorithm is tested on a set of OSIRIS high resolution images of asteroid Lutetia surface which is characterized by varied landforms and the abundance of craters created by collisions with smaller bodies of the solar system.The proposed methodology consists of three main steps: characterisation of objects of interest on limited set of data, semi-automatic extraction of impact craters performed for total set of data by applying the Mathematical Morphology image processing (Serra, 1988, Soille, 2003), and finally, creating libraries of spatial and spectral parameters for extracted impact craters, i.e. the coordinates of the crater center, semi-major and semi-minor axis, shadow length and cross-section. The overall accuracy of the proposed method is 98 %, the Kappa coefficient is 0.84, the correlation coefficient is ∼ 0.80, the omission error 24.11 %, the commission error 3.45 %. The obtained results show that methods based on Mathematical Morphology operators are effective also with a limited number of data and low-contrast images.

A mathematical model approach toward combining information from multiple image projections of the same patient

NASA Astrophysics Data System (ADS)

Chawla, Amarpreet S.; Samei, Ehsan; Abbey, Craig

2007-03-01

In this study, we used a mathematical observer model to combine information obtained from multiple angular projections of the same breast to determine the overall detection performance of a multi-projection breast imaging system in detectability of a simulated mass. 82 subjects participated in the study and 25 angular projections of each breast were acquired. Projections from a simulated 3 mm 3-D lesion were added to the projection images. The lesion was assumed to be embedded in the compressed breast at a distance of 3 cm from the detector. Hotelling observer with Laguerre-Gauss channels (LG CHO) was applied to each image. Detectability was analyzed in terms of ROC curves and the area under ROC curves (AUC). The critical question studied is how to best integrate the individual decision variables across multiple (correlated) views. Towards that end, three different methods were investigated. Specifically, 1) ROCs from different projections were simply averaged; 2) the test statistics from different projections were averaged; and 3) a Bayesian decision fusion rule was used. Finally, AUC of the combined ROC was used as a parameter to optimize the acquisition parameters to maximize the performance of the system. It was found that the Bayesian decision fusion technique performs better than the other two techniques and likely offers the best approximation of the diagnostic process. Furthermore, if the total dose level is held constant at 1/25th of dual-view mammographic screening dose, the highest detectability performance is observed when considering only two projections spread along an angular span of 11.4°.

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

Arimura, Hidetaka, E-mail: arimurah@med.kyushu-u.ac.jp; Kamezawa, Hidemi; Jin, Ze

Good relationships between computational image analysis and radiological physics have been constructed for increasing the accuracy of medical diagnostic imaging and radiation therapy in radiological physics. Computational image analysis has been established based on applied mathematics, physics, and engineering. This review paper will introduce how computational image analysis is useful in radiation therapy with respect to radiological physics.

Adding Structure to the Transition Process to Advanced Mathematical Activity

ERIC Educational Resources Information Center

Engelbrecht, Johann

2010-01-01

The transition process to advanced mathematical thinking is experienced as traumatic by many students. Experiences that students had of school mathematics differ greatly to what is expected from them at university. Success in school mathematics meant application of different methods to get an answer. Students are not familiar with logical…

Striking a Balance: Students' Tendencies to Oversimplify or Overcomplicate in Mathematical Modeling

ERIC Educational Resources Information Center

Gould, Heather; Wasserman, Nicholas H.

2014-01-01

With the adoption of the "Common Core State Standards for Mathematics" (CCSSM), the process of mathematical modeling has been given increased attention in mathematics education. This article reports on a study intended to inform the implementation of modeling in classroom contexts by examining students' interactions with the process of…

Promoting Students' Self-Directed Learning Ability through Teaching Mathematics for Social Justice

ERIC Educational Resources Information Center

Voss, Richard; Rickards, Tony

2016-01-01

Mathematics is a subject which is often taught using abstract methods and processes. These methods by their very nature may for students alienate the relationship between Mathematics and real life situations. Further, these abstract methods and processes may disenfranchise students from becoming self-directed learners of Mathematics. A solution to…

The Process of Student Cognition in Constructing Mathematical Conjecture

ERIC Educational Resources Information Center

Astawa, I. Wayan Puja; Budayasa, I. Ketut; Juniati, Dwi

2018-01-01

This research aims to describe the process of student cognition in constructing mathematical conjecture. Many researchers have studied this process but without giving a detailed explanation of how students understand the information to construct a mathematical conjecture. The researchers focus their analysis on how to construct and prove the…

Self and Peer Assessment of Mathematical Processes

ERIC Educational Resources Information Center

Onion, Alice; Javaheri, Elnaz

2011-01-01

This article explores using Bowland assessment tasks and Nuffield Applying Mathematical Processes (AMP) activities as part of a scheme of work. The Bowland tasks and Nuffield AMP activities are designed to develop students' mathematical thinking; they are focused on key processes. Unfamiliar demands are made on the students and they are challenged…

In Vivo Bioluminescence Tomography for Monitoring Breast Tumor Growth and Metastatic Spreading: Comparative Study and Mathematical Modeling

PubMed Central

Mollard, Séverine; Fanciullino, Raphaelle; Giacometti, Sarah; Serdjebi, Cindy; Benzekry, Sebastien; Ciccolini, Joseph

2016-01-01

This study aimed at evaluating the reliability and precision of Diffuse Luminescent Imaging Tomography (DLIT) for monitoring primary tumor and metastatic spreading in breast cancer mice, and to develop a biomathematical model to describe the collected data. Using orthotopic mammary fat pad model of breast cancer (MDAMB231-Luc) in mice, we monitored tumor and metastatic spreading by three-dimensional (3D) bioluminescence and cross-validated it with standard bioluminescence imaging, caliper measurement and necropsy examination. DLIT imaging proved to be reproducible and reliable throughout time. It was possible to discriminate secondary lesions from the main breast cancer, without removing the primary tumor. Preferential metastatic sites were lungs, peritoneum and lymph nodes. Necropsy examinations confirmed DLIT measurements. Marked differences in growth profiles were observed, with an overestimation of the exponential phase when using a caliper as compared with bioluminescence. Our mathematical model taking into account the balance between living and necrotic cells proved to be able to reproduce the experimental data obtained with a caliper or DLIT imaging, because it could discriminate proliferative living cells from a more composite mass consisting of tumor cells, necrotic cell, or inflammatory tissues. DLIT imaging combined with mathematical modeling could be a powerful and informative tool in experimental oncology. PMID:27812027

Biometric identification

NASA Astrophysics Data System (ADS)

Syryamkim, V. I.; Kuznetsov, D. N.; Kuznetsova, A. S.

2018-05-01

Image recognition is an information process implemented by some information converter (intelligent information channel, recognition system) having input and output. The input of the system is fed with information about the characteristics of the objects being presented. The output of the system displays information about which classes (generalized images) the recognized objects are assigned to. When creating and operating an automated system for pattern recognition, a number of problems are solved, while for different authors the formulations of these tasks, and the set itself, do not coincide, since it depends to a certain extent on the specific mathematical model on which this or that recognition system is based. This is the task of formalizing the domain, forming a training sample, learning the recognition system, reducing the dimensionality of space.

Spatiotemporal Characterization of a Fibrin Clot Using Quantitative Phase Imaging

PubMed Central

Gannavarpu, Rajshekhar; Bhaduri, Basanta; Tangella, Krishnarao; Popescu, Gabriel

2014-01-01

Studying the dynamics of fibrin clot formation and its morphology is an important problem in biology and has significant impact for several scientific and clinical applications. We present a label-free technique based on quantitative phase imaging to address this problem. Using quantitative phase information, we characterized fibrin polymerization in real-time and present a mathematical model describing the transition from liquid to gel state. By exploiting the inherent optical sectioning capability of our instrument, we measured the three-dimensional structure of the fibrin clot. From this data, we evaluated the fractal nature of the fibrin network and extracted the fractal dimension. Our non-invasive and speckle-free approach analyzes the clotting process without the need for external contrast agents. PMID:25386701

Modern morphometry: new perspectives in physical anthropology.

PubMed

Mantini, Simone; Ripani, Maurizio

2009-06-01

In the past one hundred years physical anthropology has recourse to more and more efficient methods, which provide several new information regarding, human evolution and biology. Apart from the molecular approach, the introduction of new computed assisted techniques gave rise to a new concept of morphometry. Computed tomography and 3D-imaging, allowed providing anatomical description of the external and inner structures exceeding the problems encountered with the traditional morphometric methods. Furthermore, the support of geometric morphometrics, allowed creating geometric models to investigate morphological variation in terms of evolution, ontogeny and variability. The integration of these new tools gave rise to the virtual anthropology and to a new image of the anthropologist in which anatomical, biological, mathematical statistical and data processing information are fused in a multidisciplinary approach.

TLM-Tracker: software for cell segmentation, tracking and lineage analysis in time-lapse microscopy movies.

PubMed

Klein, Johannes; Leupold, Stefan; Biegler, Ilona; Biedendieck, Rebekka; Münch, Richard; Jahn, Dieter

2012-09-01

Time-lapse imaging in combination with fluorescence microscopy techniques enable the investigation of gene regulatory circuits and uncovered phenomena like culture heterogeneity. In this context, computational image processing for the analysis of single cell behaviour plays an increasing role in systems biology and mathematical modelling approaches. Consequently, we developed a software package with graphical user interface for the analysis of single bacterial cell behaviour. A new software called TLM-Tracker allows for the flexible and user-friendly interpretation for the segmentation, tracking and lineage analysis of microbial cells in time-lapse movies. The software package, including manual, tutorial video and examples, is available as Matlab code or executable binaries at http://www.tlmtracker.tu-bs.de.

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

Warren, Lucy M.; Mackenzie, Alistair; Cooke, Julie

Purpose: This study aims to investigate if microcalcification detection varies significantly when mammographic images are acquired using different image qualities, including: different detectors, dose levels, and different image processing algorithms. An additional aim was to determine how the standard European method of measuring image quality using threshold gold thickness measured with a CDMAM phantom and the associated limits in current EU guidelines relate to calcification detection. Methods: One hundred and sixty two normal breast images were acquired on an amorphous selenium direct digital (DR) system. Microcalcification clusters extracted from magnified images of slices of mastectomies were electronically inserted into halfmore » of the images. The calcification clusters had a subtle appearance. All images were adjusted using a validated mathematical method to simulate the appearance of images from a computed radiography (CR) imaging system at the same dose, from both systems at half this dose, and from the DR system at quarter this dose. The original 162 images were processed with both Hologic and Agfa (Musica-2) image processing. All other image qualities were processed with Agfa (Musica-2) image processing only. Seven experienced observers marked and rated any identified suspicious regions. Free response operating characteristic (FROC) and ROC analyses were performed on the data. The lesion sensitivity at a nonlesion localization fraction (NLF) of 0.1 was also calculated. Images of the CDMAM mammographic test phantom were acquired using the automatic setting on the DR system. These images were modified to the additional image qualities used in the observer study. The images were analyzed using automated software. In order to assess the relationship between threshold gold thickness and calcification detection a power law was fitted to the data. Results: There was a significant reduction in calcification detection using CR compared with DR: the alternative FROC (AFROC) area decreased from 0.84 to 0.63 and the ROC area decreased from 0.91 to 0.79 (p < 0.0001). This corresponded to a 30% drop in lesion sensitivity at a NLF equal to 0.1. Detection was also sensitive to the dose used. There was no significant difference in detection between the two image processing algorithms used (p > 0.05). It was additionally found that lower threshold gold thickness from CDMAM analysis implied better cluster detection. The measured threshold gold thickness passed the acceptable limit set in the EU standards for all image qualities except half dose CR. However, calcification detection varied significantly between image qualities. This suggests that the current EU guidelines may need revising. Conclusions: Microcalcification detection was found to be sensitive to detector and dose used. Standard measurements of image quality were a good predictor of microcalcification cluster detection.« less

Mathematical Abstraction: Constructing Concept of Parallel Coordinates

NASA Astrophysics Data System (ADS)

Nurhasanah, F.; Kusumah, Y. S.; Sabandar, J.; Suryadi, D.

2017-09-01

Mathematical abstraction is an important process in teaching and learning mathematics so pre-service mathematics teachers need to understand and experience this process. One of the theoretical-methodological frameworks for studying this process is Abstraction in Context (AiC). Based on this framework, abstraction process comprises of observable epistemic actions, Recognition, Building-With, Construction, and Consolidation called as RBC + C model. This study investigates and analyzes how pre-service mathematics teachers constructed and consolidated concept of Parallel Coordinates in a group discussion. It uses AiC framework for analyzing mathematical abstraction of a group of pre-service teachers consisted of four students in learning Parallel Coordinates concepts. The data were collected through video recording, students’ worksheet, test, and field notes. The result shows that the students’ prior knowledge related to concept of the Cartesian coordinate has significant role in the process of constructing Parallel Coordinates concept as a new knowledge. The consolidation process is influenced by the social interaction between group members. The abstraction process taken place in this group were dominated by empirical abstraction that emphasizes on the aspect of identifying characteristic of manipulated or imagined object during the process of recognizing and building-with.

SU-E-T-04: 3D Dose Based Patient Compensator QA Procedure for Proton Radiotherapy

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

Zou, W; Reyhan, M; Zhang, M

2015-06-15

Purpose: In proton double-scattering radiotherapy, compensators are the essential patient specific devices to contour the distal dose distribution to the tumor target. Traditional compensator QA is limited to checking the drilled surface profiles against the plan. In our work, a compensator QA process was established that assess the entire compensator including its internal structure for patient 3D dose verification. Methods: The fabricated patient compensators were CT scanned. Through mathematical image processing and geometric transformations, the CT images of the proton compensator were combined with the patient simulation CT images into a new series of CT images, in which the imagedmore » compensator is placed at the planned location along the corresponding beam line. The new CT images were input into the Eclipse treatment planning system. The original plan was calculated to the combined CT image series without the plan compensator. The newly computed patient 3D dose from the combined patientcompensator images was verified against the original plan dose. Test plans include the compensators with defects intentionally created inside the fabricated compensators. Results: The calculated 3D dose with the combined compensator and patient CT images reflects the impact of the fabricated compensator to the patient. For the test cases in which no defects were created, the dose distributions were in agreement between our method and the corresponding original plans. For the compensator with the defects, the purposely changed material and a purposely created internal defect were successfully detected while not possible with just the traditional compensator profiles detection methods. Conclusion: We present here a 3D dose verification process to qualify the fabricated proton double-scattering compensator. Such compensator detection process assesses the patient 3D impact of the fabricated compensator surface profile as well as the compensator internal material and structure changes. This research receives funding support from CURA Medical Technologies.« less

Your Students' Images of Mathematicians and Mathematics.

ERIC Educational Resources Information Center

Picker, Susan H.; Berry, John S.

2001-01-01

Discusses the subliminal images that students might have of mathematicians. Presents the disparity between boys and girls in envisioning mathematicians of their own sex. Explores implications for pedagogy. (KHR)

MO-PIS-Exhibit Hall-01: Tools for TG-142 Linac Imaging QA I

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

Clements, M; Wiesmeyer, M

2014-06-15

Partners in Solutions is an exciting new program in which AAPM partners with our vendors to present practical “hands-on” information about the equipment and software systems that we use in our clinics. The therapy topic this year is solutions for TG-142 recommendations for linear accelerator imaging QA. Note that the sessions are being held in a special purpose room built on the Exhibit Hall Floor, to encourage further interaction with the vendors. Automated Imaging QA for TG-142 with RIT Presentation Time: 2:45 – 3:15 PM This presentation will discuss software tools for automated imaging QA and phantom analysis for TG-142.more » All modalities used in radiation oncology will be discussed, including CBCT, planar kV imaging, planar MV imaging, and imaging and treatment coordinate coincidence. Vendor supplied phantoms as well as a variety of third-party phantoms will be shown, along with appropriate analyses, proper phantom setup procedures and scanning settings, and a discussion of image quality metrics. Tools for process automation will be discussed which include: RIT Cognition (machine learning for phantom image identification), RIT Cerberus (automated file system monitoring and searching), and RunQueueC (batch processing of multiple images). In addition to phantom analysis, tools for statistical tracking, trending, and reporting will be discussed. This discussion will include an introduction to statistical process control, a valuable tool in analyzing data and determining appropriate tolerances. An Introduction to TG-142 Imaging QA Using Standard Imaging Products Presentation Time: 3:15 – 3:45 PM Medical Physicists want to understand the logic behind TG-142 Imaging QA. What is often missing is a firm understanding of the connections between the EPID and OBI phantom imaging, the software “algorithms” that calculate the QA metrics, the establishment of baselines, and the analysis and interpretation of the results. The goal of our brief presentation will be to establish and solidify these connections. Our talk will be motivated by the Standard Imaging, Inc. phantom and software solutions. We will present and explain each of the image quality metrics in TG-142 in terms of the theory, mathematics, and algorithms used to implement them in the Standard Imaging PIPSpro software. In the process, we will identify the regions of phantom images that are analyzed by each algorithm. We then will discuss the process of the creation of baselines and typical ranges of acceptable values for each imaging quality metric.« less

[Study on the 3D mathematical mode of the muscle groups applied to human mandible by a linear programming method].

PubMed

Wang, Dongmei; Yu, Liniu; Zhou, Xianlian; Wang, Chengtao

2004-02-01

Four types of 3D mathematical mode of the muscle groups applied to the human mandible have been developed. One is based on electromyography (EMG) and the others are based on linear programming with different objective function. Each model contains 26 muscle forces and two joint forces, allowing simulation of static bite forces and concomitant joint reaction forces for various bite point locations and mandibular positions. In this paper, the method of image processing to measure the position and direction of muscle forces according to 3D CAD model was built with CT data. Matlab optimization toolbox is applied to solve the three modes based on linear programming. Results show that the model with an objective function requiring a minimum sum of the tensions in the muscles is reasonable and agrees very well with the normal physiology activity.

Relationships between autofocus methods for SAR and self-survey techniques for SONAR. [Synthetic Aperture Radar (SAR)

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

Wahl, D.E.; Jakowatz, C.V. Jr.; Ghiglia, D.C.

1991-01-01

Autofocus methods in SAR and self-survey techniques in SONAR have a common mathematical basis in that they both involve estimation and correction of phase errors introduced by sensor position uncertainties. Time delay estimation and correlation methods have been shown to be effective in solving the self-survey problem for towed SONAR arrays. Since it can be shown that platform motion errors introduce similar time-delay estimation problems in SAR imaging, the question arises as to whether such techniques could be effectively employed for autofocus of SAR imagery. With a simple mathematical model for motion errors in SAR, we will show why suchmore » correlation/time-delay techniques are not nearly as effective as established SAR autofocus algorithms such as phase gradient autofocus or sub-aperture based methods. This analysis forms an important bridge between signal processing methodologies for SAR and SONAR. 5 refs., 4 figs.« less

Biomechanical and mathematical analysis of human movement in medical rehabilitation science using time-series data from two video cameras and force-plate sensor

NASA Astrophysics Data System (ADS)

Tsuruoka, Masako; Shibasaki, Ryosuke; Box, Elgene O.; Murai, Shunji; Mori, Eiji; Wada, Takao; Kurita, Masahiro; Iritani, Makoto; Kuroki, Yoshikatsu

1994-08-01

In medical rehabilitation science, quantitative understanding of patient movement in 3-D space is very important. The patient with any joint disorder will experience its influence on other body parts in daily movement. The alignment of joints in movement is able to improve under medical therapy process. In this study, the newly developed system is composed of two non- metri CCD video cameras and a force plate sensor, which are controlled simultaneously by a personal computer. By this system time-series digital data from 3-D image photogrammetry, each foot pressure and its center position, is able to provide efficient information for biomechanical and mathematical analysis of human movement. Each specific and common points are indicated in any patient movement. This study suggests more various, quantitative understanding in medical rehabilitation science.

A Local Learning Rule for Independent Component Analysis

PubMed Central

Isomura, Takuya; Toyoizumi, Taro

2016-01-01

Humans can separately recognize independent sources when they sense their superposition. This decomposition is mathematically formulated as independent component analysis (ICA). While a few biologically plausible learning rules, so-called local learning rules, have been proposed to achieve ICA, their performance varies depending on the parameters characterizing the mixed signals. Here, we propose a new learning rule that is both easy to implement and reliable. Both mathematical and numerical analyses confirm that the proposed rule outperforms other local learning rules over a wide range of parameters. Notably, unlike other rules, the proposed rule can separate independent sources without any preprocessing, even if the number of sources is unknown. The successful performance of the proposed rule is then demonstrated using natural images and movies. We discuss the implications of this finding for our understanding of neuronal information processing and its promising applications to neuromorphic engineering. PMID:27323661

Interpretation of HCMM images: A regional study

NASA Technical Reports Server (NTRS)

1982-01-01

Potential users of HCMM data, especially those with only a cursory background in thermal remote sensing are familiarized with the kinds of information contained in the images that can be extracted with some reliability solely from inspection of such standard products as those generated at NASA/GSFC and now achieved in the National Space Science Data Center. Visual analysis of photoimagery is prone to various misimpressions and outright errors brought on by unawareness of the influence of physical factors as well as by sometimes misleading tonal patterns introduced during photoprocessing. The quantitative approach, which relies on computer processing of digital HCMM data, field measurements, and integration of rigorous mathematical models, can usually be used to identify, compensate for, or correct the contributions from at least some of the natural factors and those associated with photoprocessing. Color composite, day-IR, night-IR and visible images of California and Nevada are examined.

TASI: A software tool for spatial-temporal quantification of tumor spheroid dynamics.

PubMed

Hou, Yue; Konen, Jessica; Brat, Daniel J; Marcus, Adam I; Cooper, Lee A D

2018-05-08

Spheroid cultures derived from explanted cancer specimens are an increasingly utilized resource for studying complex biological processes like tumor cell invasion and metastasis, representing an important bridge between the simplicity and practicality of 2-dimensional monolayer cultures and the complexity and realism of in vivo animal models. Temporal imaging of spheroids can capture the dynamics of cell behaviors and microenvironments, and when combined with quantitative image analysis methods, enables deep interrogation of biological mechanisms. This paper presents a comprehensive open-source software framework for Temporal Analysis of Spheroid Imaging (TASI) that allows investigators to objectively characterize spheroid growth and invasion dynamics. TASI performs spatiotemporal segmentation of spheroid cultures, extraction of features describing spheroid morpho-phenotypes, mathematical modeling of spheroid dynamics, and statistical comparisons of experimental conditions. We demonstrate the utility of this tool in an analysis of non-small cell lung cancer spheroids that exhibit variability in metastatic and proliferative behaviors.

Analysis of rocket flight stability based on optical image measurement

NASA Astrophysics Data System (ADS)

Cui, Shuhua; Liu, Junhu; Shen, Si; Wang, Min; Liu, Jun

2018-02-01

Based on the abundant optical image measurement data from the optical measurement information, this paper puts forward the method of evaluating the rocket flight stability performance by using the measurement data of the characteristics of the carrier rocket in imaging. On the basis of the method of measuring the characteristics of the carrier rocket, the attitude parameters of the rocket body in the coordinate system are calculated by using the measurements data of multiple high-speed television sets, and then the parameters are transferred to the rocket body attack angle and it is assessed whether the rocket has a good flight stability flying with a small attack angle. The measurement method and the mathematical algorithm steps through the data processing test, where you can intuitively observe the rocket flight stability state, and also can visually identify the guidance system or failure analysis.

Systematic approach to study of thinly and thickly sectioned melanoma tissues with scanning acoustic microscopy

NASA Astrophysics Data System (ADS)

Miyasaka, C.; Tittmann, B. R.; Tutwiler, R.; Tian, Y.; Maeva, E.; Shum, D.

2010-03-01

The present study is to investigate the feasibility of applying in-vivo acoustic microscopy to the analysis of cancerous tissue. The study was implemented with mechanical scanning reflection acoustic microscope (SAM) by the following procedures. First, we ultrasonically visualized thick sections of normal and tumor tissues to determine the lowest transducer frequency required for cellular imaging. We used skin for normal tissue and the tumor was a malignant melanoma. Thin sections of the tissue were also studied with the optical and high-frequency-ultrasonic imaging for pathological evaluation. Secondly, we ultrasonically visualized subsurface cellular details of thin tissue specimens with different modes (i.e., pulse and tone-burst wave modes) to obtain the highest quality ultrasonic images. The objective is to select the best mode for the future design of a future SAM for in-vivo examination. Thirdly, we developed a mathematical modeling technique based on an angular spectrum approach for improving image processing and comparing numerical to experimental results.

Knowledge Representation Of CT Scans Of The Head

NASA Astrophysics Data System (ADS)

Ackerman, Laurens V.; Burke, M. W.; Rada, Roy

1984-06-01

We have been investigating diagnostic knowledge models which assist in the automatic classification of medical images by combining information extracted from each image with knowledge specific to that class of images. In a more general sense we are trying to integrate verbal and pictorial descriptions of disease via representations of knowledge, study automatic hypothesis generation as related to clinical medicine, evolve new mathematical image measures while integrating them into the total diagnostic process, and investigate ways to augment the knowledge of the physician. Specifically, we have constructed an artificial intelligence knowledge model using the technique of a production system blending pictorial and verbal knowledge about the respective CT scan and patient history. It is an attempt to tie together different sources of knowledge representation, picture feature extraction and hypothesis generation. Our knowledge reasoning and representation system (KRRS) works with data at the conscious reasoning level of the practicing physician while at the visual perceptional level we are building another production system, the picture parameter extractor (PPE). This paper describes KRRS and its relationship to PPE.

Intravital Microscopy Imaging Approaches for Image-Guided Drug Delivery Systems

PubMed Central

Kirui, Dickson K.; Ferrari, Mauro

2016-01-01

Rapid technical advances in the field of non-linear microscopy have made intravital microscopy a vital pre-clinical tool for research and development of imaging-guided drug delivery systems. The ability to dynamically monitor the fate of macromolecules in live animals provides invaluable information regarding properties of drug carriers (size, charge, and surface coating), physiological, and pathological processes that exist between point-of-injection and the projected of site of delivery, all of which influence delivery and effectiveness of drug delivery systems. In this Review, we highlight how integrating intravital microscopy imaging with experimental designs (in vitro analyses and mathematical modeling) can provide unique information critical in the design of novel disease-relevant drug delivery platforms with improved diagnostic and therapeutic indexes. The Review will provide the reader an overview of the various applications for which intravital microscopy has been used to monitor the delivery of diagnostic and therapeutic agents and discuss some of their potential clinical applications. PMID:25901526

Reconstruction of electrical impedance tomography (EIT) images based on the expectation maximum (EM) method.

PubMed

Wang, Qi; Wang, Huaxiang; Cui, Ziqiang; Yang, Chengyi

2012-11-01

Electrical impedance tomography (EIT) calculates the internal conductivity distribution within a body using electrical contact measurements. The image reconstruction for EIT is an inverse problem, which is both non-linear and ill-posed. The traditional regularization method cannot avoid introducing negative values in the solution. The negativity of the solution produces artifacts in reconstructed images in presence of noise. A statistical method, namely, the expectation maximization (EM) method, is used to solve the inverse problem for EIT in this paper. The mathematical model of EIT is transformed to the non-negatively constrained likelihood minimization problem. The solution is obtained by the gradient projection-reduced Newton (GPRN) iteration method. This paper also discusses the strategies of choosing parameters. Simulation and experimental results indicate that the reconstructed images with higher quality can be obtained by the EM method, compared with the traditional Tikhonov and conjugate gradient (CG) methods, even with non-negative processing. Copyright © 2012 ISA. Published by Elsevier Ltd. All rights reserved.

Image analysis of the blood cells for cytomorphodiagnostics and control of the effectiveness treatment

NASA Astrophysics Data System (ADS)

Zhukotsky, Alexander V.; Kogan, Emmanuil M.; Kopylov, Victor F.; Marchenko, Oleg V.; Lomakin, O. A.

1994-07-01

A new method for morphodensitometric analysis of blood cells was applied for medically screening some ecological influence and infection pathologies. A complex algorithm of computational image processing was created for supra molecular restructurings of interphase chromatin of lymphocytes research. It includes specific methods of staining and unifies different quantitative analysis methods. Our experience with the use of a television image analyzer in cytological and immunological studies made it possible to carry out some research in morphometric analysis of chromatin structure in interphase lymphocyte nuclei in genetic and virus pathologies. In our study to characterize lymphocytes as an image-forming system by a rigorous mathematical description we used an approach involving contaminant evaluation of the topography of chromatin network intact and victims' lymphocytes. It is also possible to digitize data, which revealed significant distinctions between control and experiment. The method allows us to observe the minute structural changes in chromatin, especially eu- and hetero-chromatin that were previously studied by genetics only in chromosomes.

Measuring single-cell gene expression dynamics in bacteria using fluorescence time-lapse microscopy

PubMed Central

Young, Jonathan W; Locke, James C W; Altinok, Alphan; Rosenfeld, Nitzan; Bacarian, Tigran; Swain, Peter S; Mjolsness, Eric; Elowitz, Michael B

2014-01-01

Quantitative single-cell time-lapse microscopy is a powerful method for analyzing gene circuit dynamics and heterogeneous cell behavior. We describe the application of this method to imaging bacteria by using an automated microscopy system. This protocol has been used to analyze sporulation and competence differentiation in Bacillus subtilis, and to quantify gene regulation and its fluctuations in individual Escherichia coli cells. The protocol involves seeding and growing bacteria on small agarose pads and imaging the resulting microcolonies. Images are then reviewed and analyzed using our laboratory's custom MATLAB analysis code, which segments and tracks cells in a frame-to-frame method. This process yields quantitative expression data on cell lineages, which can illustrate dynamic expression profiles and facilitate mathematical models of gene circuits. With fast-growing bacteria, such as E. coli or B. subtilis, image acquisition can be completed in 1 d, with an additional 1–2 d for progressing through the analysis procedure. PMID:22179594

Defective Number Module or Impaired Access? Numerical Magnitude Processing in First Graders with Mathematical Difficulties

ERIC Educational Resources Information Center

De Smedt, Bert; Gilmore, Camilla K.

2011-01-01

This study examined numerical magnitude processing in first graders with severe and mild forms of mathematical difficulties, children with mathematics learning disabilities (MLD) and children with low achievement (LA) in mathematics, respectively. In total, 20 children with MLD, 21 children with LA, and 41 regular achievers completed a numerical…

A Framework for Proofs and Refutations in School Mathematics: Increasing Content by Deductive Guessing

ERIC Educational Resources Information Center

Komatsu, Kotaro

2016-01-01

The process of proofs and refutations described by Lakatos is essential in school mathematics to provide students with an opportunity to experience how mathematical knowledge develops dynamically within the discipline of mathematics. In this paper, a framework for describing student processes of proofs and refutations is constructed using a set of…

An Interdisciplinary Approach to Designing Online Learning: Fostering Pre-Service Mathematics Teachers' Capabilities in Mathematical Modelling

ERIC Educational Resources Information Center

Geiger, Vince; Mulligan, Joanne; Date-Huxtable, Liz; Ahlip, Rehez; Jones, D. Heath; May, E. Julian; Rylands, Leanne; Wright, Ian

2018-01-01

In this article we describe and evaluate processes utilized to develop an online learning module on mathematical modelling for pre-service teachers. The module development process involved a range of professionals working within the STEM disciplines including mathematics and science educators, mathematicians, scientists, in-service and pre-service…

[Study of Image Quality Comparison Based on the MTF Method Between Different Medical Rigid Endoscopes in an In Vitro Model].

PubMed

Wang, Yunlong; Ji, Jun; Jiang, Changsong; Huang, Zengyue

2015-04-01

This study was aimed to use the method of modulation transfer function (MTF) to compare image quality among three different Olympus medical rigid cystoscopes in an in vitro model. During the experimental processes, we firstly used three different types of cystoscopes (i. e. OLYMPUS cystourethroscopy with FOV of 12 degrees, OLYMPUS Germany A22003A and OLYMPUS A2013A) to collect raster images at different brightness with industrial camera and computer from the resolution target which is with different spatial frequency, and then we processed the collected images using MALAB software with the optical transfer function MTF to obtain the values of MTF at different brightness and different spatial frequency. We then did data mathematical statistics and compared imaging quality. The statistical data showed that all three MTF values were smaller than 1. MTF values with the spatial frequency gradually increasing would decrease approaching 0 at the same brightness. When the brightness enhanced in the same process at the same spatial frequency, MTF values showed a slowly increasing trend. The three endoscopes' MTF values were completely different. In some cases the MTF values had a large difference, and the maximum difference could reach 0.7. Conclusion can be derived from analysis of experimental data that three Olympus medical rigid cystoscopes have completely different imaging quality abilities. The No. 3 endoscope OLYMPUS A2013A has low resolution but high contrast. The No. 1 endoscope OLYMPUS cystourethroscopy with FOV of 12 degrees, on the contrary, had high resolution and lower contrast. The No. 2 endoscope OLYMPUS Germany A22003A had high contrast and high resolution, and its image quality was the best.

Investigating the Representational Fluency of Pre-Service Mathematics Teachers in a Modelling Process

ERIC Educational Resources Information Center

Delice, Ali; Kertil, Mahmut

2015-01-01

This article reports the results of a study that investigated pre-service mathematics teachers' modelling processes in terms of representational fluency in a modelling activity related to a cassette player. A qualitative approach was used in the data collection process. Students' individual and group written responses to the mathematical modelling…

MIST: An Open Source Environmental Modelling Programming Language Incorporating Easy to Use Data Parallelism.

NASA Astrophysics Data System (ADS)

Bellerby, Tim

2014-05-01

Model Integration System (MIST) is open-source environmental modelling programming language that directly incorporates data parallelism. The language is designed to enable straightforward programming structures, such as nested loops and conditional statements to be directly translated into sequences of whole-array (or more generally whole data-structure) operations. MIST thus enables the programmer to use well-understood constructs, directly relating to the mathematical structure of the model, without having to explicitly vectorize code or worry about details of parallelization. A range of common modelling operations are supported by dedicated language structures operating on cell neighbourhoods rather than individual cells (e.g.: the 3x3 local neighbourhood needed to implement an averaging image filter can be simply accessed from within a simple loop traversing all image pixels). This facility hides details of inter-process communication behind more mathematically relevant descriptions of model dynamics. The MIST automatic vectorization/parallelization process serves both to distribute work among available nodes and separately to control storage requirements for intermediate expressions - enabling operations on very large domains for which memory availability may be an issue. MIST is designed to facilitate efficient interpreter based implementations. A prototype open source interpreter is available, coded in standard FORTRAN 95, with tools to rapidly integrate existing FORTRAN 77 or 95 code libraries. The language is formally specified and thus not limited to FORTRAN implementation or to an interpreter-based approach. A MIST to FORTRAN compiler is under development and volunteers are sought to create an ANSI-C implementation. Parallel processing is currently implemented using OpenMP. However, parallelization code is fully modularised and could be replaced with implementations using other libraries. GPU implementation is potentially possible.

The Physics and Mathematics of MRI

NASA Astrophysics Data System (ADS)

Ansorge, Richard; Graves, Martin

2016-10-01

Magnetic Resonance Imaging is a very important clinical imaging tool. It combines different fields of physics and engineering in a uniquely complex way. MRI is also surprisingly versatile, `pulse sequences' can be designed to yield many different types of contrast. This versatility is unique to MRI. This short book gives both an in depth account of the methods used for the operation and construction of modern MRI systems and also the principles of sequence design and many examples of applications. An important additional feature of this book is the detailed discussion of the mathematical principles used in building optimal MRI systems and for sequence design. The mathematical discussion is very suitable for undergraduates attending medical physics courses. It is also more complete than usually found in alternative books for physical scientists or more clinically orientated works.

Hyperspectral feature mapping classification based on mathematical morphology

NASA Astrophysics Data System (ADS)

Liu, Chang; Li, Junwei; Wang, Guangping; Wu, Jingli

2016-03-01

This paper proposed a hyperspectral feature mapping classification algorithm based on mathematical morphology. Without the priori information such as spectral library etc., the spectral and spatial information can be used to realize the hyperspectral feature mapping classification. The mathematical morphological erosion and dilation operations are performed respectively to extract endmembers. The spectral feature mapping algorithm is used to carry on hyperspectral image classification. The hyperspectral image collected by AVIRIS is applied to evaluate the proposed algorithm. The proposed algorithm is compared with minimum Euclidean distance mapping algorithm, minimum Mahalanobis distance mapping algorithm, SAM algorithm and binary encoding mapping algorithm. From the results of the experiments, it is illuminated that the proposed algorithm's performance is better than that of the other algorithms under the same condition and has higher classification accuracy.

Age-dependent Fourier model of the shape of the isolated ex vivo human crystalline lens.

PubMed

Urs, Raksha; Ho, Arthur; Manns, Fabrice; Parel, Jean-Marie

2010-06-01

To develop an age-dependent mathematical model of the zero-order shape of the isolated ex vivo human crystalline lens, using one mathematical function, that can be subsequently used to facilitate the development of other models for specific purposes such as optical modeling and analytical and numerical modeling of the lens. Profiles of whole isolated human lenses (n=30) aged 20-69, were measured from shadow-photogrammetric images. The profiles were fit to a 10th-order Fourier series consisting of cosine functions in polar-co-ordinate system that included terms for tilt and decentration. The profiles were corrected using these terms and processed in two ways. In the first, each lens was fit to a 10th-order Fourier series to obtain thickness and diameter, while in the second, all lenses were simultaneously fit to a Fourier series equation that explicitly include linear terms for age to develop an age-dependent mathematical model for the whole lens shape. Thickness and diameter obtained from Fourier series fits exhibited high correlation with manual measurements made from shadow-photogrammetric images. The root-mean-squared-error of the age-dependent fit was 205 microm. The age-dependent equations provide a reliable lens model for ages 20-60 years. The contour of the whole human crystalline lens can be modeled with a Fourier series. Shape obtained from the age-dependent model described in this paper can be used to facilitate the development of other models for specific purposes such as optical modeling and analytical and numerical modeling of the lens. Copyright (c) 2010 Elsevier Ltd. All rights reserved.

Handwritten mathematical symbols dataset.

PubMed

Chajri, Yassine; Bouikhalene, Belaid

2016-06-01

Due to the technological advances in recent years, paper scientific documents are used less and less. Thus, the trend in the scientific community to use digital documents has increased considerably. Among these documents, there are scientific documents and more specifically mathematics documents. In this context, we present our own dataset of handwritten mathematical symbols composed of 10,379 images. This dataset gathers Arabic characters, Latin characters, Arabic numerals, Latin numerals, arithmetic operators, set-symbols, comparison symbols, delimiters, etc.

Development and Performance Evaluation of Image-Based Robotic Waxing System for Detailing Automobiles

PubMed Central

Hsu, Bing-Cheng

2018-01-01

Waxing is an important aspect of automobile detailing, aimed at protecting the finish of the car and preventing rust. At present, this delicate work is conducted manually due to the need for iterative adjustments to achieve acceptable quality. This paper presents a robotic waxing system in which surface images are used to evaluate the quality of the finish. An RGB-D camera is used to build a point cloud that details the sheet metal components to enable path planning for a robot manipulator. The robot is equipped with a multi-axis force sensor to measure and control the forces involved in the application and buffing of wax. Images of sheet metal components that were waxed by experienced car detailers were analyzed using image processing algorithms. A Gaussian distribution function and its parameterized values were obtained from the images for use as a performance criterion in evaluating the quality of surfaces prepared by the robotic waxing system. Waxing force and dwell time were optimized using a mathematical model based on the image-based criterion used to measure waxing performance. Experimental results demonstrate the feasibility of the proposed robotic waxing system and image-based performance evaluation scheme. PMID:29757940

Advances in Spectral-Spatial Classification of Hyperspectral Images

NASA Technical Reports Server (NTRS)

Fauvel, Mathieu; Tarabalka, Yuliya; Benediktsson, Jon Atli; Chanussot, Jocelyn; Tilton, James C.

2012-01-01

Recent advances in spectral-spatial classification of hyperspectral images are presented in this paper. Several techniques are investigated for combining both spatial and spectral information. Spatial information is extracted at the object (set of pixels) level rather than at the conventional pixel level. Mathematical morphology is first used to derive the morphological profile of the image, which includes characteristics about the size, orientation and contrast of the spatial structures present in the image. Then the morphological neighborhood is defined and used to derive additional features for classification. Classification is performed with support vector machines using the available spectral information and the extracted spatial information. Spatial post-processing is next investigated to build more homogeneous and spatially consistent thematic maps. To that end, three presegmentation techniques are applied to define regions that are used to regularize the preliminary pixel-wise thematic map. Finally, a multiple classifier system is defined to produce relevant markers that are exploited to segment the hyperspectral image with the minimum spanning forest algorithm. Experimental results conducted on three real hyperspectral images with different spatial and spectral resolutions and corresponding to various contexts are presented. They highlight the importance of spectral-spatial strategies for the accurate classification of hyperspectral images and validate the proposed methods.

Development and Performance Evaluation of Image-Based Robotic Waxing System for Detailing Automobiles.

PubMed

Lin, Chi-Ying; Hsu, Bing-Cheng

2018-05-14

Waxing is an important aspect of automobile detailing, aimed at protecting the finish of the car and preventing rust. At present, this delicate work is conducted manually due to the need for iterative adjustments to achieve acceptable quality. This paper presents a robotic waxing system in which surface images are used to evaluate the quality of the finish. An RGB-D camera is used to build a point cloud that details the sheet metal components to enable path planning for a robot manipulator. The robot is equipped with a multi-axis force sensor to measure and control the forces involved in the application and buffing of wax. Images of sheet metal components that were waxed by experienced car detailers were analyzed using image processing algorithms. A Gaussian distribution function and its parameterized values were obtained from the images for use as a performance criterion in evaluating the quality of surfaces prepared by the robotic waxing system. Waxing force and dwell time were optimized using a mathematical model based on the image-based criterion used to measure waxing performance. Experimental results demonstrate the feasibility of the proposed robotic waxing system and image-based performance evaluation scheme.

Knowledge Driven Image Mining with Mixture Density Mercer Kernels

NASA Technical Reports Server (NTRS)

Srivastava, Ashok N.; Oza, Nikunj

2004-01-01

This paper presents a new methodology for automatic knowledge driven image mining based on the theory of Mercer Kernels; which are highly nonlinear symmetric positive definite mappings from the original image space to a very high, possibly infinite dimensional feature space. In that high dimensional feature space, linear clustering, prediction, and classification algorithms can be applied and the results can be mapped back down to the original image space. Thus, highly nonlinear structure in the image can be recovered through the use of well-known linear mathematics in the feature space. This process has a number of advantages over traditional methods in that it allows for nonlinear interactions to be modelled with only a marginal increase in computational costs. In this paper, we present the theory of Mercer Kernels, describe its use in image mining, discuss a new method to generate Mercer Kernels directly from data, and compare the results with existing algorithms on data from the MODIS (Moderate Resolution Spectral Radiometer) instrument taken over the Arctic region. We also discuss the potential application of these methods on the Intelligent Archive, a NASA initiative for developing a tagged image data warehouse for the Earth Sciences.

Knowledge Driven Image Mining with Mixture Density Mercer Kernals

NASA Technical Reports Server (NTRS)

Srivastava, Ashok N.; Oza, Nikunj

2004-01-01

This paper presents a new methodology for automatic knowledge driven image mining based on the theory of Mercer Kernels, which are highly nonlinear symmetric positive definite mappings from the original image space to a very high, possibly infinite dimensional feature space. In that high dimensional feature space, linear clustering, prediction, and classification algorithms can be applied and the results can be mapped back down to the original image space. Thus, highly nonlinear structure in the image can be recovered through the use of well-known linear mathematics in the feature space. This process has a number of advantages over traditional methods in that it allows for nonlinear interactions to be modelled with only a marginal increase in computational costs. In this paper we present the theory of Mercer Kernels; describe its use in image mining, discuss a new method to generate Mercer Kernels directly from data, and compare the results with existing algorithms on data from the MODIS (Moderate Resolution Spectral Radiometer) instrument taken over the Arctic region. We also discuss the potential application of these methods on the Intelligent Archive, a NASA initiative for developing a tagged image data warehouse for the Earth Sciences.

Understanding bone responses in B-mode ultrasound images and automatic bone surface extraction using a Bayesian probabilistic framework

NASA Astrophysics Data System (ADS)

Jain, Ameet K.; Taylor, Russell H.

2004-04-01

The registration of preoperative CT to intra-operative reality systems is a crucial step in Computer Assisted Orthopedic Surgery (CAOS). The intra-operative sensors include 3D digitizers, fiducials, X-rays and Ultrasound (US). Although US has many advantages over others, tracked US for Orthopedic Surgery has been researched by only a few authors. An important factor limiting the accuracy of tracked US to CT registration (1-3mm) has been the difficulty in determining the exact location of the bone surfaces in the US images (the response could range from 2-4mm). Thus it is crucial to localize the bone surface accurately from these images. Moreover conventional US imaging systems are known to have certain inherent inaccuracies, mainly due to the fact that the imaging model is assumed planar. This creates the need to develop a bone segmentation framework that can couple information from various post-processed spatially separated US images (of the bone) to enhance the localization of the bone surface. In this paper we discuss the various reasons that cause inherent uncertainties in the bone surface localization (in B-mode US images) and suggest methods to account for these. We also develop a method for automatic bone surface detection. To do so, we account objectively for the high-level understanding of the various bone surface features visible in typical US images. A combination of these features would finally decide the surface position. We use a Bayesian probabilistic framework, which strikes a fair balance between high level understanding from features in an image and the low level number crunching of standard image processing techniques. It also provides us with a mathematical approach that facilitates combining multiple images to augment the bone surface estimate.

An analysis of primary school students’ representational ability in mathematics based on gender perspective

NASA Astrophysics Data System (ADS)

Kowiyah; Mulyawati, I.

2018-01-01

Mathematic representation is one of the basic mathematic skills that allows students to communicate their mathematic ideas through visual realities such as pictures, tables, mathematic expressions and mathematic equities. The present research aims at: 1) analysing students’ mathematic representation ability in solving mathematic problems and 2) examining the difference of students’ mathematic ability based on their gender. A total of sixty primary school students participated in this study comprising of thirty males and thirty females. Data required in this study were collected through mathematic representation tests, interviews and test evaluation rubric. Findings of this study showed that students’ mathematic representation of visual realities (image and tables) was reported higher at 62.3% than at in the form of description (or statement) at 8.6%. From gender perspective, male students performed better than the females at action planning stage. The percentage of males was reported at 68% (the highest), 33% (medium) and 21.3% (the lowest) while the females were at 36% (the highest), 37.7% (medium) and 32.6% (the lowest).

Mathematics Education Graduate Students' Understanding of Trigonometric Ratios

ERIC Educational Resources Information Center

Yigit Koyunkaya, Melike

2016-01-01

This study describes mathematics education graduate students' understanding of relationships between sine and cosine of two base angles in a right triangle. To explore students' understanding of these relationships, an elaboration of Skemp's views of instrumental and relational understanding using Tall and Vinner's concept image and concept…

Students' Images of Mathematics

ERIC Educational Resources Information Center

Martin, Lee; Gourley-Delaney, Pamela

2014-01-01

Students' judgments about "what counts" as mathematics in and out of school have important consequences for problem solving and transfer, yet our understanding of the source and nature of these judgments remains incomplete. Thirty-five sixth grade students participated in a study focused on what activities students judge as…

Multiparametric fat-water separation method for fast chemical-shift imaging guidance of thermal therapies.

PubMed

Lin, Jonathan S; Hwang, Ken-Pin; Jackson, Edward F; Hazle, John D; Stafford, R Jason; Taylor, Brian A

2013-10-01

A k-means-based classification algorithm is investigated to assess suitability for rapidly separating and classifying fat/water spectral peaks from a fast chemical shift imaging technique for magnetic resonance temperature imaging. Algorithm testing is performed in simulated mathematical phantoms and agar gel phantoms containing mixed fat/water regions. Proton resonance frequencies (PRFs), apparent spin-spin relaxation (T2*) times, and T1-weighted (T1-W) amplitude values were calculated for each voxel using a single-peak autoregressive moving average (ARMA) signal model. These parameters were then used as criteria for k-means sorting, with the results used to determine PRF ranges of each chemical species cluster for further classification. To detect the presence of secondary chemical species, spectral parameters were recalculated when needed using a two-peak ARMA signal model during the subsequent classification steps. Mathematical phantom simulations involved the modulation of signal-to-noise ratios (SNR), maximum PRF shift (MPS) values, analysis window sizes, and frequency expansion factor sizes in order to characterize the algorithm performance across a variety of conditions. In agar, images were collected on a 1.5T clinical MR scanner using acquisition parameters close to simulation, and algorithm performance was assessed by comparing classification results to manually segmented maps of the fat/water regions. Performance was characterized quantitatively using the Dice Similarity Coefficient (DSC), sensitivity, and specificity. The simulated mathematical phantom experiments demonstrated good fat/water separation depending on conditions, specifically high SNR, moderate MPS value, small analysis window size, and low but nonzero frequency expansion factor size. Physical phantom results demonstrated good identification for both water (0.997 ± 0.001, 0.999 ± 0.001, and 0.986 ± 0.001 for DSC, sensitivity, and specificity, respectively) and fat (0.763 ± 0.006, 0.980 ± 0.004, and 0.941 ± 0.002 for DSC, sensitivity, and specificity, respectively). Temperature uncertainties, based on PRF uncertainties from a 5 × 5-voxel ROI, were 0.342 and 0.351°C for pure and mixed fat/water regions, respectively. Algorithm speed was tested using 25 × 25-voxel and whole image ROIs containing both fat and water, resulting in average processing times per acquisition of 2.00 ± 0.07 s and 146 ± 1 s, respectively, using uncompiled MATLAB scripts running on a shared CPU server with eight Intel Xeon(TM) E5640 quad-core processors (2.66 GHz, 12 MB cache) and 12 GB RAM. Results from both the mathematical and physical phantom suggest the k-means-based classification algorithm could be useful for rapid, dynamic imaging in an ROI for thermal interventions. Successful separation of fat/water information would aid in reducing errors from the nontemperature sensitive fat PRF, as well as potentially facilitate using fat as an internal reference for PRF shift thermometry when appropriate. Additionally, the T1-W or R2* signals may be used for monitoring temperature in surrounding adipose tissue.

X-ray Computed Tomography.

ERIC Educational Resources Information Center

Michael, Greg

2001-01-01

Describes computed tomography (CT), a medical imaging technique that produces images of transaxial planes through the human body. A CT image is reconstructed mathematically from a large number of one-dimensional projections of a plane. The technique is used in radiological examinations and radiotherapy treatment planning. (Author/MM)

Effects of Mathematics Anxiety and Mathematical Metacognition on Word Problem Solving in Children with and without Mathematical Learning Difficulties.

PubMed

Lai, Yinghui; Zhu, Xiaoshuang; Chen, Yinghe; Li, Yanjun

2015-01-01

Mathematics is one of the most objective, logical, and practical academic disciplines. Yet, in addition to cognitive skills, mathematical problem solving also involves affective factors. In the current study, we first investigated effects of mathematics anxiety (MA) and mathematical metacognition on word problem solving (WPS). We tested 224 children (116 boys, M = 10.15 years old, SD = 0.56) with the Mathematics Anxiety Scale for Children, the Chinese Revised-edition Questionnaire of Pupil's Metacognitive Ability in Mathematics, and WPS tasks. The results indicated that mathematical metacognition mediated the effect of MA on WPS after controlling for IQ. Second, we divided the children into four mathematics achievement groups including high achieving (HA), typical achieving (TA), low achieving (LA), and mathematical learning difficulty (MLD). Because mathematical metacognition and MA predicted mathematics achievement, we compared group differences in metacognition and MA with IQ partialled out. The results showed that children with MLD scored lower in self-image and higher in learning mathematics anxiety (LMA) than the TA and HA children, but not in mathematical evaluation anxiety (MEA). MLD children's LMA was also higher than that of their LA counterparts. These results provide insight into factors that may mediate poor WPS performance which emerges under pressure in mathematics. These results also suggest that the anxiety during learning mathematics should be taken into account in mathematical learning difficulty interventions.

Effects of Mathematics Anxiety and Mathematical Metacognition on Word Problem Solving in Children with and without Mathematical Learning Difficulties

PubMed Central

Lai, Yinghui; Zhu, Xiaoshuang; Chen, Yinghe; Li, Yanjun

2015-01-01

Mathematics is one of the most objective, logical, and practical academic disciplines. Yet, in addition to cognitive skills, mathematical problem solving also involves affective factors. In the current study, we first investigated effects of mathematics anxiety (MA) and mathematical metacognition on word problem solving (WPS). We tested 224 children (116 boys, M = 10.15 years old, SD = 0.56) with the Mathematics Anxiety Scale for Children, the Chinese Revised-edition Questionnaire of Pupil’s Metacognitive Ability in Mathematics, and WPS tasks. The results indicated that mathematical metacognition mediated the effect of MA on WPS after controlling for IQ. Second, we divided the children into four mathematics achievement groups including high achieving (HA), typical achieving (TA), low achieving (LA), and mathematical learning difficulty (MLD). Because mathematical metacognition and MA predicted mathematics achievement, we compared group differences in metacognition and MA with IQ partialled out. The results showed that children with MLD scored lower in self-image and higher in learning mathematics anxiety (LMA) than the TA and HA children, but not in mathematical evaluation anxiety (MEA). MLD children’s LMA was also higher than that of their LA counterparts. These results provide insight into factors that may mediate poor WPS performance which emerges under pressure in mathematics. These results also suggest that the anxiety during learning mathematics should be taken into account in mathematical learning difficulty interventions. PMID:26090806

Conceptualization of Approaches and Thought Processes Emerging in Validating of Model in Mathematical Modeling in Technology Aided Environment

ERIC Educational Resources Information Center

Hidiroglu, Çaglar Naci; Bukova Güzel, Esra

2013-01-01

The aim of the present study is to conceptualize the approaches displayed for validation of model and thought processes provided in mathematical modeling process performed in technology-aided learning environment. The participants of this grounded theory study were nineteen secondary school mathematics student teachers. The data gathered from the…

Analysis of Mathematics Teachers' Self-Efficacy Levels Concerning the Teaching Process

ERIC Educational Resources Information Center

Ünsal, Serkan; Korkmaz, Fahrettin; Perçin, Safiye

2016-01-01

The purpose of this study is to identify mathematics teachers' opinions on the teaching process self-efficacy levels; and to examine mathematics teachers' teaching process self-efficacy beliefs with regards to specific variables. The study was conducted in Turkey during the second term of the 2015-2016 academic year. The study sample consisted of…

Optoelectronic image processing for cervical cancer screening

NASA Astrophysics Data System (ADS)

Narayanswamy, Ramkumar; Sharpe, John P.; Johnson, Kristina M.

1994-05-01

Automation of the Pap-smear cervical screening method is highly desirable as it relieves tedium for the human operators, reduces cost and should increase accuracy and provide repeatability. We present here the design for a high-throughput optoelectronic system which forms the first stage of a two stage system to automate pap-smear screening. We use a mathematical morphological technique called the hit-or-miss transform to identify the suspicious areas on a pap-smear slide. This algorithm is implemented using a VanderLugt architecture and a time-sequential ANDing smart pixel array.

Multimedia Analysis plus Visual Analytics = Multimedia Analytics

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

Chinchor, Nancy; Thomas, James J.; Wong, Pak C.

2010-10-01

Multimedia analysis has focused on images, video, and to some extent audio and has made progress in single channels excluding text. Visual analytics has focused on the user interaction with data during the analytic process plus the fundamental mathematics and has continued to treat text as did its precursor, information visualization. The general problem we address in this tutorial is the combining of multimedia analysis and visual analytics to deal with multimedia information gathered from different sources, with different goals or objectives, and containing all media types and combinations in common usage.

Mathematical Modelling in the Junior Secondary Years: An Approach Incorporating Mathematical Technology

ERIC Educational Resources Information Center

Lowe, James; Carter, Merilyn; Cooper, Tom

2018-01-01

Mathematical models are conceptual processes that use mathematics to describe, explain, and/or predict the behaviour of complex systems. This article is written for teachers of mathematics in the junior secondary years (including out-of-field teachers of mathematics) who may be unfamiliar with mathematical modelling, to explain the steps involved…

Complex optimization for big computational and experimental neutron datasets

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

Bao, Feng; Oak Ridge National Lab.; Archibald, Richard

Here, we present a framework to use high performance computing to determine accurate solutions to the inverse optimization problem of big experimental data against computational models. We demonstrate how image processing, mathematical regularization, and hierarchical modeling can be used to solve complex optimization problems on big data. We also demonstrate how both model and data information can be used to further increase solution accuracy of optimization by providing confidence regions for the processing and regularization algorithms. Finally, we use the framework in conjunction with the software package SIMPHONIES to analyze results from neutron scattering experiments on silicon single crystals, andmore » refine first principles calculations to better describe the experimental data.« less

Complex optimization for big computational and experimental neutron datasets

DOE PAGES

Bao, Feng; Oak Ridge National Lab.; Archibald, Richard; ...

2016-11-07

Here, we present a framework to use high performance computing to determine accurate solutions to the inverse optimization problem of big experimental data against computational models. We demonstrate how image processing, mathematical regularization, and hierarchical modeling can be used to solve complex optimization problems on big data. We also demonstrate how both model and data information can be used to further increase solution accuracy of optimization by providing confidence regions for the processing and regularization algorithms. Finally, we use the framework in conjunction with the software package SIMPHONIES to analyze results from neutron scattering experiments on silicon single crystals, andmore » refine first principles calculations to better describe the experimental data.« less

Assessing the blood pressure waveform of the carotid artery using an ultrasound image processing method

PubMed Central

Fatouraee, Nasser; Saberi, Hazhir

2017-01-01

Purpose The aim of this study was to introduce and implement a noninvasive method to derive the carotid artery pressure waveform directly by processing diagnostic sonograms of the carotid artery. Methods Ultrasound image sequences of 20 healthy male subjects (age, 36±9 years) were recorded during three cardiac cycles. The internal diameter and blood velocity waveforms were extracted from consecutive sonograms over the cardiac cycles by using custom analysis programs written in MATLAB. Finally, the application of a mathematical equation resulted in time changes of the arterial pressure. The resulting pressures were calibrated using the mean and the diastolic pressure of the radial artery. Results A good correlation was found between the mean carotid blood pressure obtained from the ultrasound image processing and the mean radial blood pressure obtained using a standard digital sphygmomanometer (R=0.91). The mean absolute difference between the carotid calibrated pulse pressures and those measured clinically was -1.333±6.548 mm Hg. Conclusion The results of this study suggest that consecutive sonograms of the carotid artery can be used for estimating a blood pressure waveform. We believe that our results promote a noninvasive technique for clinical applications that overcomes the reproducibility problems of common carotid artery tonometry with technical and anatomical causes. PMID:27776401

Advances in Measurement of Skin Friction in Airflow

NASA Technical Reports Server (NTRS)

Brown, James L.; Naughton, Jonathan W.

2006-01-01

The surface interferometric skin-friction (SISF) measurement system is an instrument for determining the distribution of surface shear stress (skin friction) on a wind-tunnel model. The SISF system utilizes the established oil-film interference method, along with advanced image-data-processing techniques and mathematical models that express the relationship between interferograms and skin friction, to determine the distribution of skin friction over an observed region of the surface of a model during a single wind-tunnel test. In the oil-film interference method, a wind-tunnel model is coated with a thin film of oil of known viscosity and is illuminated with quasi-monochromatic, collimated light, typically from a mercury lamp. The light reflected from the outer surface of the oil film interferes with the light reflected from the oil-covered surface of the model. In the present version of the oil-film interference method, a camera captures an image of the illuminated model and the image in the camera is modulated by the interference pattern. The interference pattern depends on the oil-thickness distribution on the observed surface, and this distribution can be extracted through analysis of the image acquired by the camera. The oil-film technique is augmented by a tracer technique for observing the streamline pattern. To make the streamlines visible, small dots of fluorescentchalk/oil mixture are placed on the model just before a test. During the test, the chalk particles are embedded in the oil flow and produce chalk streaks that mark the streamlines. The instantaneous rate of thinning of the oil film at a given position on the surface of the model can be expressed as a function of the instantaneous thickness, the skin-friction distribution on the surface, and the streamline pattern on the surface; the functional relationship is expressed by a mathematical model that is nonlinear in the oil-film thickness and is known simply as the thin-oil-film equation. From the image data acquired as described, the time-dependent oil-thickness distribution and streamline pattern are extracted and by inversion of the thin-oil-film equation it is then possible to determine the skin-friction distribution. In addition to a quasi-monochromatic light source, the SISF system includes a beam splitter and two video cameras equipped with filters for observing the same area on a model in different wavelength ranges, plus a frame grabber and a computer for digitizing the video images and processing the image data. One video camera acquires the interference pattern in a narrow wavelength range of the quasi-monochromatic source. The other video camera acquires the streamline image of fluorescence from the chalk in a nearby but wider wavelength range. The interference- pattern and fluorescence images are digitized, and the resulting data are processed by an algorithm that inverts the thin-oil-film equation to find the skin-friction distribution.

The pattern of trabecular bone microarchitecture in the distal femur of typically developing children and its effect on processing of magnetic resonance images.

PubMed

Modlesky, Christopher M; Whitney, Daniel G; Carter, Patrick T; Allerton, Brianne M; Kirby, Joshua T; Miller, Freeman

2014-03-01

Magnetic resonance imaging (MRI) is used to assess trabecular bone microarchitecture in humans; however, image processing can be labor intensive and time consuming. One aim of this study was to determine the pattern of trabecular bone microarchitecture in the distal femur of typically developing children. A second aim was to determine the proportion and location of magnetic resonance images that need to be processed to yield representative estimates of trabecular bone microarchitecture. Twenty-six high resolution magnetic resonance images were collected immediately above the growth plate in the distal femur of 6-12year-old typically developing children (n=40). Measures of trabecular bone microarchitecture [i.e., apparent trabecular bone volume to total volume (appBV/TV), trabecular number (appTb.N), trabecular thickness (appTb.Th) and trabecular separation (appTb.Sp)] in the lateral aspect of the distal femur were determined using the twenty most central images (20IM). The average values for appBV/TV, appTb.N, appTb.Th and appTb.Sp from 20IM were compared to the average values from 10 images (10IM), 5 images (5IM) and 3 images (3IM) equally dispersed throughout the total image set and one image (1IM) from the center of the total image set using linear regression analysis. The resulting mathematical models were cross-validated using the leave-one-out technique. Distance from the growth plate was strongly and inversely related to appBV/TV (r(2)=0.68, p<0.001) and appTb.N (r(2)=0.92, p<0.001) and was strongly and positively related to appTb.Sp (r(2)=0.86, p<0.001). The relationship between distance from the growth plate and appTb.Th was not linear (r(2)=0.06, p=0.28), but instead it was quadratic and statistically significant (r(2)=0.54, p<0.001). Trabecular bone microarchitecture estimates from 10IM, 5IM, 3IM and 1IM were not different from estimates from 20IM (p>0.05). However, there was a progressive decrease in the strength of the relationships as a smaller proportion of images were used to predict estimates from 20IM (r(2)=0.98 to 0.99 using 10IM, 0.94 to 0.96 using 5IM, 0.87 to 0.90 using 3IM and 0.66 to 0.72 using 1IM; all p<0.001). Using the resulting mathematical models and the leave-one-out cross-validation analysis, measures of trabecular bone microarchitecture estimated from the 10IM and 5IM partial image sets agreed extremely well with estimates from 20IM. The findings indicate that partial magnetic resonance image sets can be used to provide reasonable estimates of trabecular bone microarchitecture status in the distal femur of typically developing children. However, because the relative amount of trabecular bone in the distal femur decreases with distance from the growth plate due to a decrease in trabecular number, careful positioning of the region of interest and sampling from throughout the region of interest is necessary. Copyright © 2013 Elsevier Inc. All rights reserved.

Mathematical problems in the application of multilinear models to facial emotion processing experiments

NASA Astrophysics Data System (ADS)

Andersen, Anders H.; Rayens, William S.; Li, Ren-Cang; Blonder, Lee X.

2000-10-01

In this paper we describe the enormous potential that multilinear models hold for the analysis of data from neuroimaging experiments that rely on functional magnetic resonance imaging (MRI) or other imaging modalities. A case is made for why one might fully expect that the successful introduction of these models to the neuroscience community could define the next generation of structure-seeking paradigms in the area. In spite of the potential for immediate application, there is much to do from the perspective of statistical science. That is, although multilinear models have already been particularly successful in chemistry and psychology, relatively little is known about their statistical properties. To that end, our research group at the University of Kentucky has made significant progress. In particular, we are in the process of developing formal influence measures for multilinear methods as well as associated classification models and effective implementations. We believe that these problems will be among the most important and useful to the scientific community. Details are presented herein and an application is given in the context of facial emotion processing experiments.

Rough-Fuzzy Clustering and Unsupervised Feature Selection for Wavelet Based MR Image Segmentation

PubMed Central

Maji, Pradipta; Roy, Shaswati

2015-01-01

Image segmentation is an indispensable process in the visualization of human tissues, particularly during clinical analysis of brain magnetic resonance (MR) images. For many human experts, manual segmentation is a difficult and time consuming task, which makes an automated brain MR image segmentation method desirable. In this regard, this paper presents a new segmentation method for brain MR images, integrating judiciously the merits of rough-fuzzy computing and multiresolution image analysis technique. The proposed method assumes that the major brain tissues, namely, gray matter, white matter, and cerebrospinal fluid from the MR images are considered to have different textural properties. The dyadic wavelet analysis is used to extract the scale-space feature vector for each pixel, while the rough-fuzzy clustering is used to address the uncertainty problem of brain MR image segmentation. An unsupervised feature selection method is introduced, based on maximum relevance-maximum significance criterion, to select relevant and significant textural features for segmentation problem, while the mathematical morphology based skull stripping preprocessing step is proposed to remove the non-cerebral tissues like skull. The performance of the proposed method, along with a comparison with related approaches, is demonstrated on a set of synthetic and real brain MR images using standard validity indices. PMID:25848961

Spatial Mapping of Translational Diffusion Coefficients Using Diffusion Tensor Imaging: A Mathematical Description

PubMed Central

SHETTY, ANIL N.; CHIANG, SHARON; MALETIC-SAVATIC, MIRJANA; KASPRIAN, GREGOR; VANNUCCI, MARINA; LEE, WESLEY

2016-01-01

In this article, we discuss the theoretical background for diffusion weighted imaging and diffusion tensor imaging. Molecular diffusion is a random process involving thermal Brownian motion. In biological tissues, the underlying microstructures restrict the diffusion of water molecules, making diffusion directionally dependent. Water diffusion in tissue is mathematically characterized by the diffusion tensor, the elements of which contain information about the magnitude and direction of diffusion and is a function of the coordinate system. Thus, it is possible to generate contrast in tissue based primarily on diffusion effects. Expressing diffusion in terms of the measured diffusion coefficient (eigenvalue) in any one direction can lead to errors. Nowhere is this more evident than in white matter, due to the preferential orientation of myelin fibers. The directional dependency is removed by diagonalization of the diffusion tensor, which then yields a set of three eigenvalues and eigenvectors, representing the magnitude and direction of the three orthogonal axes of the diffusion ellipsoid, respectively. For example, the eigenvalue corresponding to the eigenvector along the long axis of the fiber corresponds qualitatively to diffusion with least restriction. Determination of the principal values of the diffusion tensor and various anisotropic indices provides structural information. We review the use of diffusion measurements using the modified Stejskal–Tanner diffusion equation. The anisotropy is analyzed by decomposing the diffusion tensor based on symmetrical properties describing the geometry of diffusion tensor. We further describe diffusion tensor properties in visualizing fiber tract organization of the human brain. PMID:27441031

Profile of mathematics anxiety of 7th graders

NASA Astrophysics Data System (ADS)

Udil, Patrisius Afrisno; Kusmayadi, Tri Atmojo; Riyadi

2017-08-01

Mathematics anxiety is one of the important factors affect students mathematics achievement. This present research investigates profile of students' mathematics anxiety. This research focuses on analysis and description of students' mathematics anxiety level generally and its dominant domain and aspect. Qualitative research with case study strategy was used in this research. Subject in this research involved 15 students of 7th grade chosen with purposive sampling. Data in this research were students' mathematics anxiety scale result, interview record, and observation result during both mathematics learning activity and test. They were asked to complete mathematics anxiety scale before interviewed and observed. The results show that generally students' mathematics anxiety was identified in the moderate level. In addition, students' mathematics anxiety during mathematics test was identified in the high level, but it was in the moderate level during mathematics learning process. Based on the anxiety domain, students have a high mathematics anxiety on cognitive domain, while it was in the moderate level for psychological and physiological domains. On the other hand, it was identified in low level for psychological domain during mathematics learning process. Therefore, it can be concluded that students have serious and high anxiety regarding mathematics on the cognitive domain and mathematics test aspect.

Hands-On Fractals and the Unexpected in Mathematics

ERIC Educational Resources Information Center

Gluchoff, Alan

2006-01-01

This article describes a hands-on project in which unusual fractal images are produced using only a photocopy machine and office supplies. The resulting images are an example of the contraction mapping principle.

Construction of the mathematical concept of pseudo thinking students

NASA Astrophysics Data System (ADS)

Anggraini, D.; Kusmayadi, T. A.; Pramudya, I.

2018-05-01

Thinking process is a process that begins with the acceptance of information, information processing and information calling in memory with structural changes that include concepts or knowledges. The concept or knowledge is individually constructed by each individual. While, students construct a mathematical concept, students may experience pseudo thinking. Pseudo thinking is a thinking process that results in an answer to a problem or construction to a concept “that is not true”. Pseudo thinking can be classified into two forms there are true pseudo and false pseudo. The construction of mathematical concepts in students of pseudo thinking should be immediately known because the error will have an impact on the next construction of mathematical concepts and to correct the errors it requires knowledge of the source of the error. Therefore, in this article will be discussed thinking process in constructing of mathematical concepts in students who experience pseudo thinking.

Biological object recognition in μ-radiography images

NASA Astrophysics Data System (ADS)

Prochazka, A.; Dammer, J.; Weyda, F.; Sopko, V.; Benes, J.; Zeman, J.; Jandejsek, I.

2015-03-01

This study presents an applicability of real-time microradiography to biological objects, namely to horse chestnut leafminer, Cameraria ohridella (Insecta: Lepidoptera, Gracillariidae) and following image processing focusing on image segmentation and object recognition. The microradiography of insects (such as horse chestnut leafminer) provides a non-invasive imaging that leaves the organisms alive. The imaging requires a high spatial resolution (micrometer scale) radiographic system. Our radiographic system consists of a micro-focus X-ray tube and two types of detectors. The first is a charge integrating detector (Hamamatsu flat panel), the second is a pixel semiconductor detector (Medipix2 detector). The latter allows detection of single quantum photon of ionizing radiation. We obtained numerous horse chestnuts leafminer pupae in several microradiography images easy recognizable in automatic mode using the image processing methods. We implemented an algorithm that is able to count a number of dead and alive pupae in images. The algorithm was based on two methods: 1) noise reduction using mathematical morphology filters, 2) Canny edge detection. The accuracy of the algorithm is higher for the Medipix2 (average recall for detection of alive pupae =0.99, average recall for detection of dead pupae =0.83), than for the flat panel (average recall for detection of alive pupae =0.99, average recall for detection of dead pupae =0.77). Therefore, we conclude that Medipix2 has lower noise and better displays contours (edges) of biological objects. Our method allows automatic selection and calculation of dead and alive chestnut leafminer pupae. It leads to faster monitoring of the population of one of the world's important insect pest.

Mathematical Relationships between Neuron Morphology and Neurite Growth Dynamics in Drosophila melanogaster Larva Class IV Sensory Neurons

NASA Astrophysics Data System (ADS)

Ganguly, Sujoy; Liang, Xin; Grace, Michael; Lee, Daniel; Howard, Jonathon

The morphology of neurons is diverse and reflects the diversity of neuronal functions, yet the principles that govern neuronal morphogenesis are unclear. In an effort to better understand neuronal morphogenesis we will be focusing on the development of the dendrites of class IV sensory neuron in Drosophila melanogaster. In particular we attempt to determine how the the total length, and the number of branches of dendrites are mathematically related to the dynamics of neurite growth and branching. By imaging class IV neurons during early embryogenesis we are able to measure the change in neurite length l (t) as a function of time v (t) = dl / dt . We found that the distribution of v (t) is well characterized by a hyperbolic secant distribution, and that the addition of new branches per unit time is well described by a Poisson process. Combining these measurements with the assumption that branching occurs with equal probability anywhere along the dendrite we were able to construct a mathematical model that provides reasonable agreement with the observed number of branches, and total length of the dendrites of the class IV sensory neuron.

Students, Computers and Mathematics the Golden Trilogy in the Teaching-Learning Process

ERIC Educational Resources Information Center

García-Santillán, Arturo; Escalera-Chávez, Milka Elena; López-Morales, José Satsumi; Córdova Rangel, Arturo

2014-01-01

In this paper we examine the relationships between students' attitudes towards mathematics and technology, therefore, we take a Galbraith and Hines' scale (1998, 2000) about mathematics confidence, computer confidence, computer and mathematics interaction, mathematics motivation, computer motivation, and mathematics engagement. 164 questionnaires…

Sleeping Beauty Redefined: African American Girls in Transition.

ERIC Educational Resources Information Center

Kusimo, Patricia S.

This paper examines the interests, perceptions, and participation of 16 African American girls in a program designed to improve girls' persistence in science, mathematics, and technology (SMT). The girls are among 33 African American and 73 total original participants in "Rural and Urban Images: Voices of Girls in Science, Mathematics, and…

Re-Mythologizing Mathematics through Attention to Classroom Positioning

ERIC Educational Resources Information Center

Wagner, David; Herbel-Eisenmann, Beth

2009-01-01

With our conceptualization of Harre and van Langenhove's (1999) positioning theory, we draw attention to immanent experience and read transcendent discursive practices through the moment of interaction. We use a series of spatial images as metaphors to analyze the way positioning is conceptualized in current mathematics education literature and…

Pedagogical Content Knowledge in Mathematical Modelling Instruction

ERIC Educational Resources Information Center

Tan, Liang Soon; Ang, Keng Cheng

2012-01-01

This paper posits that teachers' pedagogical content knowledge in mathematical modelling instruction can be demonstrated in the crafting of action plans and expected teaching and learning moves via their lesson images (Schoenfeld, 1998). It can also be developed when teachers shape appropriate teaching moves in response to students' learning…

Does Early Mathematics Intervention Change the Processes Underlying Children’s Learning?

PubMed Central

Watts, Tyler W.; Clements, Douglas H.; Sarama, Julie; Wolfe, Christopher B.; Spitler, Mary Elaine; Bailey, Drew H.

2017-01-01

Early educational intervention effects typically fade in the years following treatment, and few studies have investigated why achievement impacts diminish over time. The current study tested the effects of a preschool mathematics intervention on two aspects of children’s mathematical development. We tested for separate effects of the intervention on “state” (occasion-specific) and “trait” (relatively stable) variability in mathematics achievement. Results indicated that, although the treatment had a large impact on state mathematics, the treatment had no effect on trait mathematics, or the aspect of mathematics achievement that influences stable individual differences in mathematics achievement over time. Results did suggest, however, that the intervention could affect the underlying processes in children’s mathematical development by inducing more transfer of knowledge immediately following the intervention for students in the treated group. PMID:29399243

Wavelength feature mapping as a proxy to mineral chemistry for investigating geologic systems: An example from the Rodalquilar epithermal system

NASA Astrophysics Data System (ADS)

van der Meer, Freek; Kopačková, Veronika; Koucká, Lucie; van der Werff, Harald M. A.; van Ruitenbeek, Frank J. A.; Bakker, Wim H.

2018-02-01

The final product of a geologic remote sensing data analysis using multi spectral and hyperspectral images is a mineral (abundance) map. Multispectral data, such as ASTER, Landsat, SPOT, Sentinel-2, typically allow to determine qualitative estimates of what minerals are in a pixel, while hyperspectral data allow to quantify this. As input to most image classification or spectral processing approach, endmembers are required. An alternative approach to classification is to derive absorption feature characteristics such as the wavelength position of the deepest absorption, depth of the absorption and symmetry of the absorption feature from hyperspectral data. Two approaches are presented, tested and compared in this paper: the 'Wavelength Mapper' and the 'QuanTools'. Although these algorithms use a different mathematical solution to derive absorption feature wavelength and depth, and use different image post-processing, the results are consistent, comparable and reproducible. The wavelength images can be directly linked to mineral type and abundance, but more importantly also to mineral chemical composition and subtle changes thereof. This in turn allows to interpret hyperspectral data in terms of mineral chemistry changes which is a proxy to pressure-temperature of formation of minerals. We show the case of the Rodalquilar epithermal system of the southern Spanish Gabo de Gata volcanic area using HyMAP airborne hyperspectral images.

Modelling and shadowgraph imaging of cocrystal dissolution and assessment of in vitro antimicrobial activity for sulfadimidine/4-aminosalicylic acid cocrystals.

PubMed

Serrano, Dolores R; Persoons, Tim; D'Arcy, Deirdre M; Galiana, Carolina; Dea-Ayuela, Maria Auxiliadora; Healy, Anne Marie

2016-06-30

The aim of this work was to evaluate the influence of crystal habit on the dissolution and in vitro antibacterial and anitiprotozoal activity of sulfadimidine:4-aminosalicylic acid cocrystals. Cocrystals were produced via milling or solvent mediated processes. In vitro dissolution was carried out in the flow-through apparatus, with shadowgraph imaging and mechanistic mathematical models used to observe and simulate particle dissolution. In vitro activity was tested using agar diffusion assays. Cocrystallisation via milling produced small polyhedral crystals with antimicrobial activity significantly higher than sulfadimidine alone, consistent with a fast dissolution rate which was matched only by cocrystals which were milled following solvent evaporation. Cocrystallisation by solvent evaporation (ethanol, acetone) or spray drying produced flattened, plate-like or quasi-spherical cocrystals, respectively, with more hydrophobic surfaces and greater tendency to form aggregates in aqueous media, limiting both the dissolution rate and in vitro activity. Deviation from predicted dissolution profiles was attributable to aggregation behaviour, supported by observations from shadowgraph imaging. Aggregation behaviour during dissolution of cocrystals with different habits affected the dissolution rate, consistent with in vitro activity. Combining mechanistic models with shadowgraph imaging is a valuable approach for dissolution process analysis. Copyright © 2016 Elsevier B.V. All rights reserved.

Handwritten mathematical symbols dataset

PubMed Central

Chajri, Yassine; Bouikhalene, Belaid

2016-01-01

Due to the technological advances in recent years, paper scientific documents are used less and less. Thus, the trend in the scientific community to use digital documents has increased considerably. Among these documents, there are scientific documents and more specifically mathematics documents. In this context, we present our own dataset of handwritten mathematical symbols composed of 10,379 images. This dataset gathers Arabic characters, Latin characters, Arabic numerals, Latin numerals, arithmetic operators, set-symbols, comparison symbols, delimiters, etc. PMID:27006975

Image analysis library software development

NASA Technical Reports Server (NTRS)

Guseman, L. F., Jr.; Bryant, J.

1977-01-01

The Image Analysis Library consists of a collection of general purpose mathematical/statistical routines and special purpose data analysis/pattern recognition routines basic to the development of image analysis techniques for support of current and future Earth Resources Programs. Work was done to provide a collection of computer routines and associated documentation which form a part of the Image Analysis Library.

Orientations toward Mathematical Processes of Prospective Secondary Mathematics Teachers as Related to Work with Tasks

ERIC Educational Resources Information Center

Cannon, Tenille

2016-01-01

Mathematics can be conceptualized in different ways. Policy documents such as the National Council of Teachers of Mathematics (NCTM) (2000) and the Common Core State Standards Initiative (CCSSI) (2010), classify mathematics in terms of mathematical content (e.g., quadratic functions, Pythagorean theorem) and mathematical activity in the form of…

Professional Development Processes That Promote Teacher Change: The Case of a Video-Based Program Focused on Leveraging Students' Mathematical Errors

ERIC Educational Resources Information Center

Santagata, Rossella; Bray, Wendy

2016-01-01

This study examined processes at the core of teacher professional development (PD) experiences that might positively impact teacher learning and more specifically teacher change. Four processes were considered in the context of a PD program focused on student mathematical errors: analysis of students' mathematical misconceptions as a lever for…

Individual Differences in Working Memory, Nonverbal IQ, and Mathematics Achievement and Brain Mechanisms Associated with Symbolic and Nonsymbolic Number Processing

ERIC Educational Resources Information Center

Gullick, Margaret M.; Sprute, Lisa A.; Temple, Elise

2011-01-01

Individual differences in mathematics performance may stem from domain-general factors like working memory and intelligence. Parietal and frontal brain areas have been implicated in number processing, but the influence of such cognitive factors on brain activity during mathematics processing is not known. The relationship between brain mechanisms…

Mathematical modeling of heat treatment processes conserving biological activity of plant bioresources

NASA Astrophysics Data System (ADS)

Rodionova, N. S.; Popov, E. S.; Pozhidaeva, E. A.; Pynzar, S. S.; Ryaskina, L. O.

2018-05-01

The aim of this study is to develop a mathematical model of the heat exchange process of LT-processing to estimate the dynamics of temperature field changes and optimize the regime parameters, due to the non-stationarity process, the physicochemical and thermophysical properties of food systems. The application of LT-processing, based on the use of low-temperature modes in thermal culinary processing of raw materials with preliminary vacuum packaging in a polymer heat- resistant film is a promising trend in the development of technics and technology in the catering field. LT-processing application of food raw materials guarantees the preservation of biologically active substances in food environments, which are characterized by a certain thermolability, as well as extend the shelf life and high consumer characteristics of food systems that are capillary-porous bodies. When performing the mathematical modeling of the LT-processing process, the packet of symbolic mathematics “Maple” was used, as well as the mathematical packet flexPDE that uses the finite element method for modeling objects with distributed parameters. The processing of experimental results was evaluated with the help of the developed software in the programming language Python 3.4. To calculate and optimize the parameters of the LT processing process of polycomponent food systems, the differential equation of non-stationary thermal conductivity was used, the solution of which makes it possible to identify the temperature change at any point of the solid at different moments. The present study specifies data on the thermophysical characteristics of the polycomponent food system based on plant raw materials, with the help of which the physico-mathematical model of the LT- processing process has been developed. The obtained mathematical model allows defining of the dynamics of the temperature field in different sections of the LT-processed polycomponent food systems on the basis of calculating the evolution profiles of temperature fields, which enable one to analyze the efficiency of the regime parameters of heat treatment.

Automation process for morphometric analysis of volumetric CT data from pulmonary vasculature in rats.

PubMed

Shingrani, Rahul; Krenz, Gary; Molthen, Robert

2010-01-01

With advances in medical imaging scanners, it has become commonplace to generate large multidimensional datasets. These datasets require tools for a rapid, thorough analysis. To address this need, we have developed an automated algorithm for morphometric analysis incorporating A Visualization Workshop computational and image processing libraries for three-dimensional segmentation, vascular tree generation and structural hierarchical ordering with a two-stage numeric optimization procedure for estimating vessel diameters. We combine this new technique with our mathematical models of pulmonary vascular morphology to quantify structural and functional attributes of lung arterial trees. Our physiological studies require repeated measurements of vascular structure to determine differences in vessel biomechanical properties between animal models of pulmonary disease. Automation provides many advantages including significantly improved speed and minimized operator interaction and biasing. The results are validated by comparison with previously published rat pulmonary arterial micro-CT data analysis techniques, in which vessels were manually mapped and measured using intense operator intervention. Published by Elsevier Ireland Ltd.

Some error bounds for K-iterated Gaussian recursive filters

NASA Astrophysics Data System (ADS)

Cuomo, Salvatore; Galletti, Ardelio; Giunta, Giulio; Marcellino, Livia

2016-10-01

Recursive filters (RFs) have achieved a central role in several research fields over the last few years. For example, they are used in image processing, in data assimilation and in electrocardiogram denoising. More in particular, among RFs, the Gaussian RFs are an efficient computational tool for approximating Gaussian-based convolutions and are suitable for digital image processing and applications of the scale-space theory. As is a common knowledge, the Gaussian RFs, applied to signals with support in a finite domain, generate distortions and artifacts, mostly localized at the boundaries. Heuristic and theoretical improvements have been proposed in literature to deal with this issue (namely boundary conditions). They include the case in which a Gaussian RF is applied more than once, i.e. the so called K-iterated Gaussian RFs. In this paper, starting from a summary of the comprehensive mathematical background, we consider the case of the K-iterated first-order Gaussian RF and provide the study of its numerical stability and some component-wise theoretical error bounds.

High-content screening for the discovery of pharmacological compounds: advantages, challenges and potential benefits of recent technological developments.

PubMed

Soleilhac, Emmanuelle; Nadon, Robert; Lafanechere, Laurence

2010-02-01

Screening compounds with cell-based assays and microscopy image-based analysis is an approach currently favored for drug discovery. Because of its high information yield, the strategy is called high-content screening (HCS). This review covers the application of HCS in drug discovery and also in basic research of potential new pathways that can be targeted for treatment of pathophysiological diseases. HCS faces several challenges, however, including the extraction of pertinent information from the massive amount of data generated from images. Several proposed approaches to HCS data acquisition and analysis are reviewed. Different solutions from the fields of mathematics, bioinformatics and biotechnology are presented. Potential applications and limits of these recent technical developments are also discussed. HCS is a multidisciplinary and multistep approach for understanding the effects of compounds on biological processes at the cellular level. Reliable results depend on the quality of the overall process and require strong interdisciplinary collaborations.

Emotions and Heuristics: The State of Perplexity in Mathematics

ERIC Educational Resources Information Center

Gómez-Chacón, Inés M.

2017-01-01

Using data provided by an empirical exploratory study with mathematics undergraduates, this paper discusses some key variables in the interaction between affective and cognitive dimensions in the perplexity state in problem solving. These variables are as follows: heuristics, mathematical processes, appraisal processes [pleasantness, attentional…

Direct Geolocation of TerraSAR-X Spotlight Mode Image and Error Correction

NASA Astrophysics Data System (ADS)

Zhou, Xiao; Zeng, Qiming; Jiao, Jian; Zhang, Jingfa; Gong, Lixia

2013-01-01

The GERMAN TerraSAR-X mission was launched in June 2007, operating a versatile new-generation SAR sensor in X-band. Its Spotlight mode providing SAR images at very high resolution of about 1m. The product’s specified 3-D geolocation accuracy is tightened to 1m according to the official technical report. However, this accuracy is able to be achieved relies on not only robust mathematical basis of SAR geolocation, but also well knowledge of error sources and their correction. The research focuses on geolocation of TerraSAR-X spotlight image. Mathematical model and resolving algorithms have been analyzed. Several error sources have been researched and corrected especially. The effectiveness and accuracy of the research was verified by the experiment results.

Macula segmentation and fovea localization employing image processing and heuristic based clustering for automated retinal screening.

PubMed

R, GeethaRamani; Balasubramanian, Lakshmi

2018-07-01

Macula segmentation and fovea localization is one of the primary tasks in retinal analysis as they are responsible for detailed vision. Existing approaches required segmentation of retinal structures viz. optic disc and blood vessels for this purpose. This work avoids knowledge of other retinal structures and attempts data mining techniques to segment macula. Unsupervised clustering algorithm is exploited for this purpose. Selection of initial cluster centres has a great impact on performance of clustering algorithms. A heuristic based clustering in which initial centres are selected based on measures defining statistical distribution of data is incorporated in the proposed methodology. The initial phase of proposed framework includes image cropping, green channel extraction, contrast enhancement and application of mathematical closing. Then, the pre-processed image is subjected to heuristic based clustering yielding a binary map. The binary image is post-processed to eliminate unwanted components. Finally, the component which possessed the minimum intensity is finalized as macula and its centre constitutes the fovea. The proposed approach outperforms existing works by reporting that 100%,of HRF, 100% of DRIVE, 96.92% of DIARETDB0, 97.75% of DIARETDB1, 98.81% of HEI-MED, 90% of STARE and 99.33% of MESSIDOR images satisfy the 1R criterion, a standard adopted for evaluating performance of macula and fovea identification. The proposed system thus helps the ophthalmologists in identifying the macula thereby facilitating to identify if any abnormality is present within the macula region. Copyright © 2018 Elsevier B.V. All rights reserved.

Spatio-temporal cerebral blood flow perfusion patterns in cortical spreading depression

NASA Astrophysics Data System (ADS)

Verisokin, Andrey Yu.; Verveyko, Darya V.; Postnov, Dmitry E.

2017-04-01

Cortical spreading depression (CSD) is an example of one of the most common abnormalities in biophysical brain functioning. Despite the fact that there are many mathematical models describing the cortical spreading depression (CSD), most of them do not take into consideration the role of redistribution of cerebral blood flow (CBF), that results in the formation of spatio-temporal patterns. The paper presents a mathematical model, which successfully explains the CBD role in the CSD process. Numerical study of this model has revealed the formation of stationary dissipative structures, visually analogous to Turing structures. However, the mechanism of their formation is not diffusion. We show these structures occur due to another type of spatial coupling, that is related to tissue perfusion rate. The proposed model predicts that at similar state of neurons the distribution of blood flow and oxygenation may by different. Currently, this effect is not taken into account when the Blood oxygen-level dependent (BOLD) contrast imaging used in functional magnetic resonance imaging (fMRI). Thus, the diagnosis on the BOLD signal can be ambiguous. We believe that our results can be used in the future for a more correct interpretation of the data obtained with fMRI, NIRS and other similar methods for research of the brain activity.

A theoretical Gaussian framework for anomalous change detection in hyperspectral images

NASA Astrophysics Data System (ADS)

Acito, Nicola; Diani, Marco; Corsini, Giovanni

2017-10-01

Exploitation of temporal series of hyperspectral images is a relatively new discipline that has a wide variety of possible applications in fields like remote sensing, area surveillance, defense and security, search and rescue and so on. In this work, we discuss how images taken at two different times can be processed to detect changes caused by insertion, deletion or displacement of small objects in the monitored scene. This problem is known in the literature as anomalous change detection (ACD) and it can be viewed as the extension, to the multitemporal case, of the well-known anomaly detection problem in a single image. In fact, in both cases, the hyperspectral images are processed blindly in an unsupervised manner and without a-priori knowledge about the target spectrum. We introduce the ACD problem using an approach based on the statistical decision theory and we derive a common framework including different ACD approaches. Particularly, we clearly define the observation space, the data statistical distribution conditioned to the two competing hypotheses and the procedure followed to come with the solution. The proposed overview places emphasis on techniques based on the multivariate Gaussian model that allows a formal presentation of the ACD problem and the rigorous derivation of the possible solutions in a way that is both mathematically more tractable and easier to interpret. We also discuss practical problems related to the application of the detectors in the real world and present affordable solutions. Namely, we describe the ACD processing chain including the strategies that are commonly adopted to compensate pervasive radiometric changes, caused by the different illumination/atmospheric conditions, and to mitigate the residual geometric image co-registration errors. Results obtained on real freely available data are discussed in order to test and compare the methods within the proposed general framework.