Applications of Fractal Analytical Techniques in the Estimation of Operational Scale

NASA Technical Reports Server (NTRS)

Emerson, Charles W.; Quattrochi, Dale A.

2000-01-01

The observational scale and the resolution of remotely sensed imagery are essential considerations in the interpretation process. Many atmospheric, hydrologic, and other natural and human-influenced spatial phenomena are inherently scale dependent and are governed by different physical processes at different spatial domains. This spatial and operational heterogeneity constrains the ability to compare interpretations of phenomena and processes observed in higher spatial resolution imagery to similar interpretations obtained from lower resolution imagery. This is a particularly acute problem, since longterm global change investigations will require high spatial resolution Earth Observing System (EOS), Landsat 7, or commercial satellite data to be combined with lower resolution imagery from older sensors such as Landsat TM and MSS. Fractal analysis is a useful technique for identifying the effects of scale changes on remotely sensed imagery. The fractal dimension of an image is a non-integer value between two and three which indicates the degree of complexity in the texture and shapes depicted in the image. A true fractal surface exhibits self-similarity, a property of curves or surfaces where each part is indistinguishable from the whole, or where the form of the curve or surface is invariant with respect to scale. Theoretically, if the digital numbers of a remotely sensed image resemble an ideal fractal surface, then due to the self-similarity property, the fractal dimension of the image will not vary with scale and resolution, and the slope of the fractal dimension-resolution relationship would be zero. Most geographical phenomena, however, are not self-similar at all scales, but they can be modeled by a stochastic fractal in which the scaling properties of the image exhibit patterns that can be described by statistics such as area-perimeter ratios and autocovariances. Stochastic fractal sets relax the self-similarity assumption and measure many scales and resolutions to represent the varying form of a phenomenon as the pixel size is increased in a convolution process. We have observed that for images of homogeneous land covers, the fractal dimension varies linearly with changes in resolution or pixel size over the range of past, current, and planned space-borne sensors. This relationship differs significantly in images of agricultural, urban, and forest land covers, with urban areas retaining the same level of complexity, forested areas growing smoother, and agricultural areas growing more complex as small pixels are aggregated into larger, mixed pixels. Images of scenes having a mixture of land covers have fractal dimensions that exhibit a non-linear, complex relationship to pixel size. Measuring the fractal dimension of a difference image derived from two images of the same area obtained on different dates showed that the fractal dimension increased steadily, then exhibited a sharp decrease at increasing levels of pixel aggregation. This breakpoint of the fractal dimension/resolution plot is related to the spatial domain or operational scale of the phenomenon exhibiting the predominant visible difference between the two images (in this case, mountain snow cover). The degree to which an image departs from a theoretical ideal fractal surface provides clues as to how much information is altered or lost in the processes of rescaling and rectification. The measured fractal dimension of complex, composite land covers such as urban areas also provides a useful textural index that can assist image classification of complex scenes.

Performance assessment of methods for estimation of fractal dimension from scanning electron microscope images.

PubMed

Risović, Dubravko; Pavlović, Zivko

2013-01-01

Processing of gray scale images in order to determine the corresponding fractal dimension is very important due to widespread use of imaging technologies and application of fractal analysis in many areas of science, technology, and medicine. To this end, many methods for estimation of fractal dimension from gray scale images have been developed and routinely used. Unfortunately different methods (dimension estimators) often yield significantly different results in a manner that makes interpretation difficult. Here, we report results of comparative assessment of performance of several most frequently used algorithms/methods for estimation of fractal dimension. To that purpose, we have used scanning electron microscope images of aluminum oxide surfaces with different fractal dimensions. The performance of algorithms/methods was evaluated using the statistical Z-score approach. The differences between performances of six various methods are discussed and further compared with results obtained by electrochemical impedance spectroscopy on the same samples. The analysis of results shows that the performance of investigated algorithms varies considerably and that systematically erroneous fractal dimensions could be estimated using certain methods. The differential cube counting, triangulation, and box counting algorithms showed satisfactory performance in the whole investigated range of fractal dimensions. Difference statistic is proved to be less reliable generating 4% of unsatisfactory results. The performances of the Power spectrum, Partitioning and EIS were unsatisfactory in 29%, 38%, and 75% of estimations, respectively. The results of this study should be useful and provide guidelines to researchers using/attempting fractal analysis of images obtained by scanning microscopy or atomic force microscopy. © Wiley Periodicals, Inc.

Micro and MACRO Fractals Generated by Multi-Valued Dynamical Systems

NASA Astrophysics Data System (ADS)

Banakh, T.; Novosad, N.

2014-08-01

Given a multi-valued function Φ : X \\mumap X on a topological space X we study the properties of its fixed fractal \\malteseΦ, which is defined as the closure of the orbit Φω(*Φ) = ⋃n∈ωΦn(*Φ) of the set *Φ = {x ∈ X : x ∈ Φ(x)} of fixed points of Φ. A special attention is paid to the duality between micro-fractals and macro-fractals, which are fixed fractals \\maltese Φ and \\maltese {Φ -1} for a contracting compact-valued function Φ : X \\mumap X on a complete metric space X. With help of algorithms (described in this paper) we generate various images of macro-fractals which are dual to some well-known micro-fractals like the fractal cross, the Sierpiński triangle, Sierpiński carpet, the Koch curve, or the fractal snowflakes. The obtained images show that macro-fractals have a large-scale fractal structure, which becomes clearly visible after a suitable zooming.

A Lossless hybrid wavelet-fractal compression for welding radiographic images.

PubMed

Mekhalfa, Faiza; Avanaki, Mohammad R N; Berkani, Daoud

2016-01-01

In this work a lossless wavelet-fractal image coder is proposed. The process starts by compressing and decompressing the original image using wavelet transformation and fractal coding algorithm. The decompressed image is removed from the original one to obtain a residual image which is coded by using Huffman algorithm. Simulation results show that with the proposed scheme, we achieve an infinite peak signal to noise ratio (PSNR) with higher compression ratio compared to typical lossless method. Moreover, the use of wavelet transform speeds up the fractal compression algorithm by reducing the size of the domain pool. The compression results of several welding radiographic images using the proposed scheme are evaluated quantitatively and compared with the results of Huffman coding algorithm.

MORPH-II, a software package for the analysis of scanning-electron-micrograph images for the assessment of the fractal dimension of exposed stone surfaces

USGS Publications Warehouse

Mossotti, Victor G.; Eldeeb, A. Raouf

2000-01-01

Turcotte, 1997, and Barton and La Pointe, 1995, have identified many potential uses for the fractal dimension in physicochemical models of surface properties. The image-analysis program described in this report is an extension of the program set MORPH-I (Mossotti and others, 1998), which provided the fractal analysis of electron-microscope images of pore profiles (Mossotti and Eldeeb, 1992). MORPH-II, an integration of the modified kernel of the program MORPH-I with image calibration and editing facilities, was designed to measure the fractal dimension of the exposed surfaces of stone specimens as imaged in cross section in an electron microscope.

Fractals, malware, and data models

NASA Astrophysics Data System (ADS)

Jaenisch, Holger M.; Potter, Andrew N.; Williams, Deborah; Handley, James W.

2012-06-01

We examine the hypothesis that the decision boundary between malware and non-malware is fractal. We introduce a novel encoding method derived from text mining for converting disassembled programs first into opstrings and then filter these into a reduced opcode alphabet. These opcodes are enumerated and encoded into real floating point number format and used for characterizing frequency of occurrence and distribution properties of malware functions to compare with non-malware functions. We use the concept of invariant moments to characterize the highly non-Gaussian structure of the opcode distributions. We then derive Data Model based classifiers from identified features and interpolate and extrapolate the parameter sample space for the derived Data Models. This is done to examine the nature of the parameter space classification boundary between families of malware and the general non-malware category. Preliminary results strongly support the fractal boundary hypothesis, and a summary of our methods and results are presented here.

Analysis of the fractal dimension of volcano geomorphology through Synthetic Aperture Radar (SAR) amplitude images acquired in C and X band.

NASA Astrophysics Data System (ADS)

Pepe, S.; Di Martino, G.; Iodice, A.; Manzo, M.; Pepe, A.; Riccio, D.; Ruello, G.; Sansosti, E.; Tizzani, P.; Zinno, I.

2012-04-01

In the last two decades several aspects relevant to volcanic activity have been analyzed in terms of fractal parameters that effectively describe natural objects geometry. More specifically, these researches have been aimed at the identification of (1) the power laws that governed the magma fragmentation processes, (2) the energy of explosive eruptions, and (3) the distribution of the associated earthquakes. In this paper, the study of volcano morphology via satellite images is dealt with; in particular, we use the complete forward model developed by some of the authors (Di Martino et al., 2012) that links the stochastic characterization of amplitude Synthetic Aperture Radar (SAR) images to the fractal dimension of the imaged surfaces, modelled via fractional Brownian motion (fBm) processes. Based on the inversion of such a model, a SAR image post-processing has been implemented (Di Martino et al., 2010), that allows retrieving the fractal dimension of the observed surfaces, dictating the distribution of the roughness over different spatial scales. The fractal dimension of volcanic structures has been related to the specific nature of materials and to the effects of active geodynamic processes. Hence, the possibility to estimate the fractal dimension from a single amplitude-only SAR image is of fundamental importance for the characterization of volcano structures and, moreover, can be very helpful for monitoring and crisis management activities in case of eruptions and other similar natural hazards. The implemented SAR image processing performs the extraction of the point-by-point fractal dimension of the scene observed by the sensor, providing - as an output product - the map of the fractal dimension of the area of interest. In this work, such an analysis is performed on Cosmo-SkyMed, ERS-1/2 and ENVISAT images relevant to active stratovolcanoes in different geodynamic contexts, such as Mt. Somma-Vesuvio, Mt. Etna, Vulcano and Stromboli in Southern Italy, Shinmoe in Japan, Merapi in Indonesia. Preliminary results reveal that the fractal dimension of natural areas, being related only to the roughness of the observed surface, is very stable as the radar illumination geometry, the resolution and the wavelength change, thus holding a very unique property in SAR data inversion. Such a behavior is not verified in case of non-natural objects. As a matter of fact, when the fractal estimation is performed in the presence of either man-made objects or SAR image features depending on geometrical distortions due to the SAR system acquisition (i.e. layover, shadowing), fractal dimension (D) values outside the range of fractality of natural surfaces (2 < D < 3) are retrieved. These non-fractal characteristics show to be heavily dependent on sensor acquisition parameters (e.g. view angle, resolution). In this work, the behaviour of the maps generated starting from the C- and X- band SAR data, relevant to all the considered volcanoes, is analyzed: the distribution of the obtained fractal dimension values is investigated on different zones of the maps. In particular, it is verified that the fore-slope and back-slope areas of the image share a very similar fractal dimension distribution that is placed around the mean value of D=2.3. We conclude that, in this context, the fractal dimension could be considered as a signature of the identification of the volcano growth as a natural process. The COSMO-SkyMed data used in this study have been processed at IREA-CNR within the SAR4Volcanoes project under Italian Space Agency agreement n. I/034/11/0.

Fractal analysis as a potential tool for surface morphology of thin films

NASA Astrophysics Data System (ADS)

Soumya, S.; Swapna, M. S.; Raj, Vimal; Mahadevan Pillai, V. P.; Sankararaman, S.

2017-12-01

Fractal geometry developed by Mandelbrot has emerged as a potential tool for analyzing complex systems in the diversified fields of science, social science, and technology. Self-similar objects having the same details in different scales are referred to as fractals and are analyzed using the mathematics of non-Euclidean geometry. The present work is an attempt to correlate fractal dimension for surface characterization by Atomic Force Microscopy (AFM). Taking the AFM images of zinc sulphide (ZnS) thin films prepared by pulsed laser deposition (PLD) technique, under different annealing temperatures, the effect of annealing temperature and surface roughness on fractal dimension is studied. The annealing temperature and surface roughness show a strong correlation with fractal dimension. From the regression equation set, the surface roughness at a given annealing temperature can be calculated from the fractal dimension. The AFM images are processed using Photoshop and fractal dimension is calculated by box-counting method. The fractal dimension decreases from 1.986 to 1.633 while the surface roughness increases from 1.110 to 3.427, for a change of annealing temperature 30 ° C to 600 ° C. The images are also analyzed by power spectrum method to find the fractal dimension. The study reveals that the box-counting method gives better results compared to the power spectrum method.

Test-Retest Reliability of fMRI Brain Activity during Memory Encoding

PubMed Central

Brandt, David J.; Sommer, Jens; Krach, Sören; Bedenbender, Johannes; Kircher, Tilo; Paulus, Frieder M.; Jansen, Andreas

2013-01-01

The mechanisms underlying hemispheric specialization of memory are not completely understood. Functional magnetic resonance imaging (fMRI) can be used to develop and test models of hemispheric specialization. In particular for memory tasks however, the interpretation of fMRI results is often hampered by the low reliability of the data. In the present study we therefore analyzed the test-retest reliability of fMRI brain activation related to an implicit memory encoding task, with a particular focus on brain activity of the medial temporal lobe (MTL). Fifteen healthy subjects were scanned with fMRI on two sessions (average retest interval 35 days) using a commonly applied novelty encoding paradigm contrasting known and unknown stimuli. To assess brain lateralization, we used three different stimuli classes that differed in their verbalizability (words, scenes, fractals). Test-retest reliability of fMRI brain activation was assessed by an intraclass-correlation coefficient (ICC), describing the stability of inter-individual differences in the brain activation magnitude over time. We found as expected a left-lateralized brain activation network for the words paradigm, a bilateral network for the scenes paradigm, and predominantly right-hemispheric brain activation for the fractals paradigm. Although these networks were consistently activated in both sessions on the group level, across-subject reliabilities were only poor to fair (ICCs ≤ 0.45). Overall, the highest ICC values were obtained for the scenes paradigm, but only in strongly activated brain regions. In particular the reliability of brain activity of the MTL was poor for all paradigms. In conclusion, for novelty encoding paradigms the interpretation of fMRI results on a single subject level is hampered by its low reliability. More studies are needed to optimize the retest reliability of fMRI activation for memory tasks. PMID:24367338

An Evaluation of Fractal Surface Measurement Methods for Characterizing Landscape Complexity from Remote-Sensing Imagery

NASA Technical Reports Server (NTRS)

Lam, Nina Siu-Ngan; Qiu, Hong-Lie; Quattrochi, Dale A.; Emerson, Charles W.; Arnold, James E. (Technical Monitor)

2001-01-01

The rapid increase in digital data volumes from new and existing sensors necessitates the need for efficient analytical tools for extracting information. We developed an integrated software package called ICAMS (Image Characterization and Modeling System) to provide specialized spatial analytical functions for interpreting remote sensing data. This paper evaluates the three fractal dimension measurement methods: isarithm, variogram, and triangular prism, along with the spatial autocorrelation measurement methods Moran's I and Geary's C, that have been implemented in ICAMS. A modified triangular prism method was proposed and implemented. Results from analyzing 25 simulated surfaces having known fractal dimensions show that both the isarithm and triangular prism methods can accurately measure a range of fractal surfaces. The triangular prism method is most accurate at estimating the fractal dimension of higher spatial complexity, but it is sensitive to contrast stretching. The variogram method is a comparatively poor estimator for all of the surfaces, particularly those with higher fractal dimensions. Similar to the fractal techniques, the spatial autocorrelation techniques are found to be useful to measure complex images but not images with low dimensionality. These fractal measurement methods can be applied directly to unclassified images and could serve as a tool for change detection and data mining.

Detection and classification of Breast Cancer in Wavelet Sub-bands of Fractal Segmented Cancerous Zones.

PubMed

Shirazinodeh, Alireza; Noubari, Hossein Ahmadi; Rabbani, Hossein; Dehnavi, Alireza Mehri

2015-01-01

Recent studies on wavelet transform and fractal modeling applied on mammograms for the detection of cancerous tissues indicate that microcalcifications and masses can be utilized for the study of the morphology and diagnosis of cancerous cases. It is shown that the use of fractal modeling, as applied to a given image, can clearly discern cancerous zones from noncancerous areas. In this paper, for fractal modeling, the original image is first segmented into appropriate fractal boxes followed by identifying the fractal dimension of each windowed section using a computationally efficient two-dimensional box-counting algorithm. Furthermore, using appropriate wavelet sub-bands and image Reconstruction based on modified wavelet coefficients, it is shown that it is possible to arrive at enhanced features for detection of cancerous zones. In this paper, we have attempted to benefit from the advantages of both fractals and wavelets by introducing a new algorithm. By using a new algorithm named F1W2, the original image is first segmented into appropriate fractal boxes, and the fractal dimension of each windowed section is extracted. Following from that, by applying a maximum level threshold on fractal dimensions matrix, the best-segmented boxes are selected. In the next step, the segmented Cancerous zones which are candidates are then decomposed by utilizing standard orthogonal wavelet transform and db2 wavelet in three different resolution levels, and after nullifying wavelet coefficients of the image at the first scale and low frequency band of the third scale, the modified reconstructed image is successfully utilized for detection of breast cancer regions by applying an appropriate threshold. For detection of cancerous zones, our simulations indicate the accuracy of 90.9% for masses and 88.99% for microcalcifications detection results using the F1W2 method. For classification of detected mictocalcification into benign and malignant cases, eight features are identified and utilized in radial basis function neural network. Our simulation results indicate the accuracy of 92% classification using F1W2 method.

The analysis of the influence of fractal structure of stimuli on fractal dynamics in fixational eye movements and EEG signal

NASA Astrophysics Data System (ADS)

Namazi, Hamidreza; Kulish, Vladimir V.; Akrami, Amin

2016-05-01

One of the major challenges in vision research is to analyze the effect of visual stimuli on human vision. However, no relationship has been yet discovered between the structure of the visual stimulus, and the structure of fixational eye movements. This study reveals the plasticity of human fixational eye movements in relation to the ‘complex’ visual stimulus. We demonstrated that the fractal temporal structure of visual dynamics shifts towards the fractal dynamics of the visual stimulus (image). The results showed that images with higher complexity (higher fractality) cause fixational eye movements with lower fractality. Considering the brain, as the main part of nervous system that is engaged in eye movements, we analyzed the governed Electroencephalogram (EEG) signal during fixation. We have found out that there is a coupling between fractality of image, EEG and fixational eye movements. The capability observed in this research can be further investigated and applied for treatment of different vision disorders.

Fractal scaling of apparent soil moisture estimated from vertical planes of Vertisol pit images

NASA Astrophysics Data System (ADS)

Cumbrera, Ramiro; Tarquis, Ana M.; Gascó, Gabriel; Millán, Humberto

2012-07-01

SummaryImage analysis could be a useful tool for investigating the spatial patterns of apparent soil moisture at multiple resolutions. The objectives of the present work were (i) to define apparent soil moisture patterns from vertical planes of Vertisol pit images and (ii) to describe the scaling of apparent soil moisture distribution using fractal parameters. Twelve soil pits (0.70 m long × 0.60 m width × 0.30 m depth) were excavated on a bare Mazic Pellic Vertisol. Six of them were excavated in April/2011 and six pits were established in May/2011 after 3 days of a moderate rainfall event. Digital photographs were taken from each Vertisol pit using a Kodak™ digital camera. The mean image size was 1600 × 945 pixels with one physical pixel ≈373 μm of the photographed soil pit. Each soil image was analyzed using two fractal scaling exponents, box counting (capacity) dimension (DBC) and interface fractal dimension (Di), and three prefractal scaling coefficients, the total number of boxes intercepting the foreground pattern at a unit scale (A), fractal lacunarity at the unit scale (Λ1) and Shannon entropy at the unit scale (S1). All the scaling parameters identified significant differences between both sets of spatial patterns. Fractal lacunarity was the best discriminator between apparent soil moisture patterns. Soil image interpretation with fractal exponents and prefractal coefficients can be incorporated within a site-specific agriculture toolbox. While fractal exponents convey information on space filling characteristics of the pattern, prefractal coefficients represent the investigated soil property as seen through a higher resolution microscope. In spite of some computational and practical limitations, image analysis of apparent soil moisture patterns could be used in connection with traditional soil moisture sampling, which always renders punctual estimates.

A Double-Minded Fractal

ERIC Educational Resources Information Center

Simoson, Andrew J.

2009-01-01

This article presents a fun activity of generating a double-minded fractal image for a linear algebra class once the idea of rotation and scaling matrices are introduced. In particular the fractal flip-flops between two words, depending on the level at which the image is viewed. (Contains 5 figures.)

A Fractal Analysis of CT Liver Images for the Discrimination of Hepatic Lesions: A Comparative Study

DTIC Science & Technology

2001-10-25

liver images in order to estimate their fractal dimension and to differentiate normal liver parenchyma from hepatocellular carcinoma . Four fractal...methods; thus discriminating up to 93% of the normal parenchyma and up to 82% of the hepatocellular carcinoma , correctly.

A comparison of the fractal and JPEG algorithms

NASA Technical Reports Server (NTRS)

Cheung, K.-M.; Shahshahani, M.

1991-01-01

A proprietary fractal image compression algorithm and the Joint Photographic Experts Group (JPEG) industry standard algorithm for image compression are compared. In every case, the JPEG algorithm was superior to the fractal method at a given compression ratio according to a root mean square criterion and a peak signal to noise criterion.

Multispectral image fusion based on fractal features

NASA Astrophysics Data System (ADS)

Tian, Jie; Chen, Jie; Zhang, Chunhua

2004-01-01

Imagery sensors have been one indispensable part of the detection and recognition systems. They are widely used to the field of surveillance, navigation, control and guide, et. However, different imagery sensors depend on diverse imaging mechanisms, and work within diverse range of spectrum. They also perform diverse functions and have diverse circumstance requires. So it is unpractical to accomplish the task of detection or recognition with a single imagery sensor under the conditions of different circumstances, different backgrounds and different targets. Fortunately, the multi-sensor image fusion technique emerged as important route to solve this problem. So image fusion has been one of the main technical routines used to detect and recognize objects from images. While, loss of information is unavoidable during fusion process, so it is always a very important content of image fusion how to preserve the useful information to the utmost. That is to say, it should be taken into account before designing the fusion schemes how to avoid the loss of useful information or how to preserve the features helpful to the detection. In consideration of these issues and the fact that most detection problems are actually to distinguish man-made objects from natural background, a fractal-based multi-spectral fusion algorithm has been proposed in this paper aiming at the recognition of battlefield targets in the complicated backgrounds. According to this algorithm, source images are firstly orthogonally decomposed according to wavelet transform theories, and then fractal-based detection is held to each decomposed image. At this step, natural background and man-made targets are distinguished by use of fractal models that can well imitate natural objects. Special fusion operators are employed during the fusion of area that contains man-made targets so that useful information could be preserved and features of targets could be extruded. The final fused image is reconstructed from the composition of source pyramid images. So this fusion scheme is a multi-resolution analysis. The wavelet decomposition of image can be actually considered as special pyramid decomposition. According to wavelet decomposition theories, the approximation of image (formula available in paper) at resolution 2j+1 equal to its orthogonal projection in space , that is, where Ajf is the low-frequency approximation of image f(x, y) at resolution 2j and , , represent the vertical, horizontal and diagonal wavelet coefficients respectively at resolution 2j. These coefficients describe the high-frequency information of image at direction of vertical, horizontal and diagonal respectively. Ajf, , and are independent and can be considered as images. In this paper J is set to be 1, so the source image is decomposed to produce the son-images Af, D1f, D2f and D3f. To solve the problem of detecting artifacts, the concepts of vertical fractal dimension FD1, horizontal fractal dimension FD2 and diagonal fractal dimension FD3 are proposed in this paper. The vertical fractal dimension FD1 corresponds to the vertical wavelet coefficients image after the wavelet decomposition of source image, the horizontal fractal dimension FD2 corresponds to the horizontal wavelet coefficients and the diagonal fractal dimension FD3 the diagonal one. These definitions enrich the illustration of source images. Therefore they are helpful to classify the targets. Then the detection of artifacts in the decomposed images is a problem of pattern recognition in 4-D space. The combination of FD0, FD1, FD2 and FD3 make a vector of (FD0, FD1, FD2, FD3), which can be considered as a united feature vector of the studied image. All the parts of the images are classified in the 4-D pattern space created by the vector of (FD0, FD1, FD2, FD3) so that the area that contains man-made objects could be detected. This detection can be considered as a coarse recognition, and then the significant areas in each son-images are signed so that they can be dealt with special rules. There has been various fusion rules developed with each one aiming at a special problem. These rules have different performance, so it is very important to select an appropriate rule during the design of an image fusion system. Recent research denotes that the rule should be adjustable so that it is always suitable to extrude the features of targets and to preserve the pixels of useful information. In this paper, owing to the consideration that fractal dimension is one of the main features to distinguish man-made targets from natural objects, the fusion rule was defined that if the studied region of image contains man-made target, the pixels of the source image whose fractal dimension is minimal are saved to be the pixels of the fused image, otherwise, a weighted average operator is adopted to avoid loss of information. The main idea of this rule is to store the pixels with low fractal dimensions, so it can be named Minimal Fractal dimensions (MFD) fusion rule. This fractal-based algorithm is compared with a common weighted average fusion algorithm. An objective assessment is taken to the two fusion results. The criteria of Entropy, Cross-Entropy, Peak Signal-to-Noise Ratio (PSNR) and Standard Gray Scale Difference are defined in this paper. Reversely to the idea of constructing an ideal image as the assessing reference, the source images are selected to be the reference in this paper. It can be deemed that this assessment is to calculate how much the image quality has been enhanced and the quantity of information has been increased when the fused image is compared with the source images. The experimental results imply that the fractal-based multi-spectral fusion algorithm can effectively preserve the information of man-made objects with a high contrast. It is proved that this algorithm could well preserve features of military targets because that battlefield targets are most man-made objects and in common their images differ from fractal models obviously. Furthermore, the fractal features are not sensitive to the imaging conditions and the movement of targets, so this fractal-based algorithm may be very practical.

Fractal analysis of bone structure with applications to osteoporosis and microgravity effects

NASA Astrophysics Data System (ADS)

Acharya, Raj S.; LeBlanc, Adrian; Shackelford, Linda; Swarnakar, Vivek; Krishnamurthy, Ram; Hausman, E.; Lin, Chin-Shoou

1995-05-01

We characterize the trabecular structure with the aid of fractal dimension. We use alternating sequential filters (ASF) to generate a nonlinear pyramid for fractal dimension computations. We do not make any assumptions of the statistical distributions of the underlying fractal bone structure. The only assumption of our scheme is the rudimentary definition of self-similarity. This allows us the freedom of not being constrained by statistical estimation schemes. With mathematical simulations, we have shown that the ASF methods outperform other existing methods for fractal dimension estimation. We have shown that the fractal dimension remains the same when computed with both the x-ray images and the MRI images of the patella. We have shown that the fractal dimension of osteoporotic subjects is lower than that of the normal subjects. In animal models, we have shown that the fractal dimension of osteoporotic rats was lower than that of the normal rats. In a 17 week bedrest study, we have shown that the subject's prebedrest fractal dimension is higher than that of the postbedrest fractal dimension.

Fractal analysis of bone structure with applications to osteoporosis and microgravity effects

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

Acharya, R.S.; Swarnarkar, V.; Krishnamurthy, R.

1995-12-31

The authors characterize the trabecular structure with the aid of fractal dimension. The authors use Alternating Sequential filters to generate a nonlinear pyramid for fractal dimension computations. The authors do not make any assumptions of the statistical distributions of the underlying fractal bone structure. The only assumption of the scheme is the rudimentary definition of self similarity. This allows them the freedom of not being constrained by statistical estimation schemes. With mathematical simulations, the authors have shown that the ASF methods outperform other existing methods for fractal dimension estimation. They have shown that the fractal dimension remains the same whenmore » computed with both the X-Ray images and the MRI images of the patella. They have shown that the fractal dimension of osteoporotic subjects is lower than that of the normal subjects. In animal models, the authors have shown that the fractal dimension of osteoporotic rats was lower than that of the normal rats. In a 17 week bedrest study, they have shown that the subject`s prebedrest fractal dimension is higher than that of the postbedrest fractal dimension.« less

Image characterization by fractal descriptors in variational mode decomposition domain: Application to brain magnetic resonance

NASA Astrophysics Data System (ADS)

Lahmiri, Salim

2016-08-01

The main purpose of this work is to explore the usefulness of fractal descriptors estimated in multi-resolution domains to characterize biomedical digital image texture. In this regard, three multi-resolution techniques are considered: the well-known discrete wavelet transform (DWT) and the empirical mode decomposition (EMD), and; the newly introduced; variational mode decomposition mode (VMD). The original image is decomposed by the DWT, EMD, and VMD into different scales. Then, Fourier spectrum based fractal descriptors is estimated at specific scales and directions to characterize the image. The support vector machine (SVM) was used to perform supervised classification. The empirical study was applied to the problem of distinguishing between normal and abnormal brain magnetic resonance images (MRI) affected with Alzheimer disease (AD). Our results demonstrate that fractal descriptors estimated in VMD domain outperform those estimated in DWT and EMD domains; and also those directly estimated from the original image.

Analysis of fractal dimensions of rat bones from film and digital images

NASA Technical Reports Server (NTRS)

Pornprasertsuk, S.; Ludlow, J. B.; Webber, R. L.; Tyndall, D. A.; Yamauchi, M.

2001-01-01

OBJECTIVES: (1) To compare the effect of two different intra-oral image receptors on estimates of fractal dimension; and (2) to determine the variations in fractal dimensions between the femur, tibia and humerus of the rat and between their proximal, middle and distal regions. METHODS: The left femur, tibia and humerus from 24 4-6-month-old Sprague-Dawley rats were radiographed using intra-oral film and a charge-coupled device (CCD). Films were digitized at a pixel density comparable to the CCD using a flat-bed scanner. Square regions of interest were selected from proximal, middle, and distal regions of each bone. Fractal dimensions were estimated from the slope of regression lines fitted to plots of log power against log spatial frequency. RESULTS: The fractal dimensions estimates from digitized films were significantly greater than those produced from the CCD (P=0.0008). Estimated fractal dimensions of three types of bone were not significantly different (P=0.0544); however, the three regions of bones were significantly different (P=0.0239). The fractal dimensions estimated from radiographs of the proximal and distal regions of the bones were lower than comparable estimates obtained from the middle region. CONCLUSIONS: Different types of image receptors significantly affect estimates of fractal dimension. There was no difference in the fractal dimensions of the different bones but the three regions differed significantly.

Multi-year encoding of daily rainfall and streamflow via the fractal-multifractal method

NASA Astrophysics Data System (ADS)

Puente, C. E.; Maskey, M.; Sivakumar, B.

2017-12-01

A deterministic geometric approach, the fractal-multifractal (FM) method, which has been proven to be faithful in encoding daily geophysical sets over a year, is used to describe records over multiple years at a time. Looking for FM parameter trends over longer periods, the present study shows FM descriptions of daily rainfall and streamflow gathered over five consecutive years optimizing deviations on accumulated sets. The results for 100 and 60 sets of five years for rainfall streamflow, respectively, near Sacramento, California illustrate that: (a) encoding of both types of data sets may be accomplished with relatively small errors; and (b) predicting the geometry of both variables appears to be possible, even five years ahead, training neural networks on the respective FM parameters. It is emphasized that the FM approach not only captures the accumulated sets over successive pentades but also preserves other statistical attributes including the overall "texture" of the records.

Crack image segmentation based on improved DBC method

NASA Astrophysics Data System (ADS)

Cao, Ting; Yang, Nan; Wang, Fengping; Gao, Ting; Wang, Weixing

2017-11-01

With the development of computer vision technology, crack detection based on digital image segmentation method arouses global attentions among researchers and transportation ministries. Since the crack always exhibits the random shape and complex texture, it is still a challenge to accomplish reliable crack detection results. Therefore, a novel crack image segmentation method based on fractal DBC (differential box counting) is introduced in this paper. The proposed method can estimate every pixel fractal feature based on neighborhood information which can consider the contribution from all possible direction in the related block. The block moves just one pixel every time so that it could cover all the pixels in the crack image. Unlike the classic DBC method which only describes fractal feature for the related region, this novel method can effectively achieve crack image segmentation according to the fractal feature of every pixel. The experiment proves the proposed method can achieve satisfactory results in crack detection.

Singular spectrum decomposition of Bouligand-Minkowski fractal descriptors: an application to the classification of texture Images

NASA Astrophysics Data System (ADS)

Florindo, João. Batista

2018-04-01

This work proposes the use of Singular Spectrum Analysis (SSA) for the classification of texture images, more specifically, to enhance the performance of the Bouligand-Minkowski fractal descriptors in this task. Fractal descriptors are known to be a powerful approach to model and particularly identify complex patterns in natural images. Nevertheless, the multiscale analysis involved in those descriptors makes them highly correlated. Although other attempts to address this point was proposed in the literature, none of them investigated the relation between the fractal correlation and the well-established analysis employed in time series. And SSA is one of the most powerful techniques for this purpose. The proposed method was employed for the classification of benchmark texture images and the results were compared with other state-of-the-art classifiers, confirming the potential of this analysis in image classification.

Time Series Analysis OF SAR Image Fractal Maps: The Somma-Vesuvio Volcanic Complex Case Study

NASA Astrophysics Data System (ADS)

Pepe, Antonio; De Luca, Claudio; Di Martino, Gerardo; Iodice, Antonio; Manzo, Mariarosaria; Pepe, Susi; Riccio, Daniele; Ruello, Giuseppe; Sansosti, Eugenio; Zinno, Ivana

2016-04-01

The fractal dimension is a significant geophysical parameter describing natural surfaces representing the distribution of the roughness over different spatial scale; in case of volcanic structures, it has been related to the specific nature of materials and to the effects of active geodynamic processes. In this work, we present the analysis of the temporal behavior of the fractal dimension estimates generated from multi-pass SAR images relevant to the Somma-Vesuvio volcanic complex (South Italy). To this aim, we consider a Cosmo-SkyMed data-set of 42 stripmap images acquired from ascending orbits between October 2009 and December 2012. Starting from these images, we generate a three-dimensional stack composed by the corresponding fractal maps (ordered according to the acquisition dates), after a proper co-registration. The time-series of the pixel-by-pixel estimated fractal dimension values show that, over invariant natural areas, the fractal dimension values do not reveal significant changes; on the contrary, over urban areas, it correctly assumes values outside the natural surfaces fractality range and show strong fluctuations. As a final result of our analysis, we generate a fractal map that includes only the areas where the fractal dimension is considered reliable and stable (i.e., whose standard deviation computed over the time series is reasonably small). The so-obtained fractal dimension map is then used to identify areas that are homogeneous from a fractal viewpoint. Indeed, the analysis of this map reveals the presence of two distinctive landscape units corresponding to the Mt. Vesuvio and Gran Cono. The comparison with the (simplified) geological map clearly shows the presence in these two areas of volcanic products of different age. The presented fractal dimension map analysis demonstrates the ability to get a figure about the evolution degree of the monitored volcanic edifice and can be profitably extended in the future to other volcanic systems with very distinctive characteristics, with the aim to perform land classification, such as the identification of areas characterized by similar soil use, slopes and exposures.

Characterization of Atrophic Changes in the Cerebral Cortex Using Fractal Dimensional Analysis

PubMed Central

George, Anuh T.; Jeon, Tina; Hynan, Linda S.; Youn, Teddy S.; Kennedy, David N.; Dickerson, Bradford

2010-01-01

The purpose of this project is to apply a modified fractal analysis technique to high-resolution T1 weighted magnetic resonance images in order to quantify the alterations in the shape of the cerebral cortex that occur in patients with Alzheimer’s disease. Images were selected from the Alzheimer’s Disease Neuroimaging Initiative database (Control N=15, Mild-Moderate AD N=15). The images were segmented using a semi-automated analysis program. Four coronal and three axial profiles of the cerebral cortical ribbon were created. The fractal dimensions (Df) of the cortical ribbons were then computed using a box-counting algorithm. The mean Df of the cortical ribbons from AD patients were lower than age-matched controls on six of seven profiles. The fractal measure has regional variability which reflects local differences in brain structure. Fractal dimension is complementary to volumetric measures and may assist in identifying disease state or disease progression. PMID:20740072

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.

Edge detection of optical subaperture image based on improved differential box-counting method

NASA Astrophysics Data System (ADS)

Li, Yi; Hui, Mei; Liu, Ming; Dong, Liquan; Kong, Lingqin; Zhao, Yuejin

2018-01-01

Optical synthetic aperture imaging technology is an effective approach to improve imaging resolution. Compared with monolithic mirror system, the image of optical synthetic aperture system is often more complex at the edge, and as a result of the existence of gap between segments, which makes stitching becomes a difficult problem. So it is necessary to extract the edge of subaperture image for achieving effective stitching. Fractal dimension as a measure feature can describe image surface texture characteristics, which provides a new approach for edge detection. In our research, an improved differential box-counting method is used to calculate fractal dimension of image, then the obtained fractal dimension is mapped to grayscale image to detect edges. Compared with original differential box-counting method, this method has two improvements as follows: by modifying the box-counting mechanism, a box with a fixed height is replaced by a box with adaptive height, which solves the problem of over-counting the number of boxes covering image intensity surface; an image reconstruction method based on super-resolution convolutional neural network is used to enlarge small size image, which can solve the problem that fractal dimension can't be calculated accurately under the small size image, and this method may well maintain scale invariability of fractal dimension. The experimental results show that the proposed algorithm can effectively eliminate noise and has a lower false detection rate compared with the traditional edge detection algorithms. In addition, this algorithm can maintain the integrity and continuity of image edge in the case of retaining important edge information.

[Modeling continuous scaling of NDVI based on fractal theory].

PubMed

Luan, Hai-Jun; Tian, Qing-Jiu; Yu, Tao; Hu, Xin-Li; Huang, Yan; Du, Ling-Tong; Zhao, Li-Min; Wei, Xi; Han, Jie; Zhang, Zhou-Wei; Li, Shao-Peng

2013-07-01

Scale effect was one of the very important scientific problems of remote sensing. The scale effect of quantitative remote sensing can be used to study retrievals' relationship between different-resolution images, and its research became an effective way to confront the challenges, such as validation of quantitative remote sensing products et al. Traditional up-scaling methods cannot describe scale changing features of retrievals on entire series of scales; meanwhile, they are faced with serious parameters correction issues because of imaging parameters' variation of different sensors, such as geometrical correction, spectral correction, etc. Utilizing single sensor image, fractal methodology was utilized to solve these problems. Taking NDVI (computed by land surface radiance) as example and based on Enhanced Thematic Mapper Plus (ETM+) image, a scheme was proposed to model continuous scaling of retrievals. Then the experimental results indicated that: (a) For NDVI, scale effect existed, and it could be described by fractal model of continuous scaling; (2) The fractal method was suitable for validation of NDVI. All of these proved that fractal was an effective methodology of studying scaling of quantitative remote sensing.

Fractal and Gray Level Cooccurrence Matrix Computational Analysis of Primary Osteosarcoma Magnetic Resonance Images Predicts the Chemotherapy Response.

PubMed

Djuričić, Goran J; Radulovic, Marko; Sopta, Jelena P; Nikitović, Marina; Milošević, Nebojša T

2017-01-01

The prediction of induction chemotherapy response at the time of diagnosis may improve outcomes in osteosarcoma by allowing for personalized tailoring of therapy. The aim of this study was thus to investigate the predictive potential of the so far unexploited computational analysis of osteosarcoma magnetic resonance (MR) images. Fractal and gray level cooccurrence matrix (GLCM) algorithms were employed in retrospective analysis of MR images of primary osteosarcoma localized in distal femur prior to the OsteoSa induction chemotherapy. The predicted and actual chemotherapy response outcomes were then compared by means of receiver operating characteristic (ROC) analysis and accuracy calculation. Dbin, Λ, and SCN were the standard fractal and GLCM features which significantly associated with the chemotherapy outcome, but only in one of the analyzed planes. Our newly developed normalized fractal dimension, called the space-filling ratio (SFR) exerted an independent and much better predictive value with the prediction significance accomplished in two of the three imaging planes, with accuracy of 82% and area under the ROC curve of 0.20 (95% confidence interval 0-0.41). In conclusion, SFR as the newly designed fractal coefficient provided superior predictive performance in comparison to standard image analysis features, presumably by compensating for the tumor size variation in MR images.

Fractal morphology, imaging and mass spectrometry of single aerosol particles in flight (CXIDB ID 16)

DOE Data Explorer

Loh, N. Duane

2012-06-20

This deposition includes the aerosol diffraction images used for phasing, fractal morphology, and time-of-flight mass spectrometry. Files in this deposition are ordered in subdirectories that reflect the specifics.

A Comparison of Local Variance, Fractal Dimension, and Moran's I as Aids to Multispectral Image Classification

NASA Technical Reports Server (NTRS)

Emerson, Charles W.; Sig-NganLam, Nina; Quattrochi, Dale A.

2004-01-01

The accuracy of traditional multispectral maximum-likelihood image classification is limited by the skewed statistical distributions of reflectances from the complex heterogenous mixture of land cover types in urban areas. This work examines the utility of local variance, fractal dimension and Moran's I index of spatial autocorrelation in segmenting multispectral satellite imagery. Tools available in the Image Characterization and Modeling System (ICAMS) were used to analyze Landsat 7 imagery of Atlanta, Georgia. Although segmentation of panchromatic images is possible using indicators of spatial complexity, different land covers often yield similar values of these indices. Better results are obtained when a surface of local fractal dimension or spatial autocorrelation is combined as an additional layer in a supervised maximum-likelihood multispectral classification. The addition of fractal dimension measures is particularly effective at resolving land cover classes within urbanized areas, as compared to per-pixel spectral classification techniques.

Multitemporal and Multiscaled Fractal Analysis of Landsat Satellite Data Using the Image Characterization and Modeling System (ICAMS)

NASA Technical Reports Server (NTRS)

Quattrochi, Dale A.; Emerson, Charles W.; Lam, Nina Siu-Ngan; Laymon, Charles A.

1997-01-01

The Image Characterization And Modeling System (ICAMS) is a public domain software package that is designed to provide scientists with innovative spatial analytical tools to visualize, measure, and characterize landscape patterns so that environmental conditions or processes can be assessed and monitored more effectively. In this study ICAMS has been used to evaluate how changes in fractal dimension, as a landscape characterization index, and resolution, are related to differences in Landsat images collected at different dates for the same area. Landsat Thematic Mapper (TM) data obtained in May and August 1993 over a portion of the Great Basin Desert in eastern Nevada were used for analysis. These data represent contrasting periods of peak "green-up" and "dry-down" for the study area. The TM data sets were converted into Normalized Difference Vegetation Index (NDVI) images to expedite analysis of differences in fractal dimension between the two dates. These NDVI images were also resampled to resolutions of 60, 120, 240, 480, and 960 meters from the original 30 meter pixel size, to permit an assessment of how fractal dimension varies with spatial resolution. Tests of fractal dimension for two dates at various pixel resolutions show that the D values in the August image become increasingly more complex as pixel size increases to 480 meters. The D values in the May image show an even more complex relationship to pixel size than that expressed in the August image. Fractal dimension for a difference image computed for the May and August dates increase with pixel size up to a resolution of 120 meters, and then decline with increasing pixel size. This means that the greatest complexity in the difference images occur around a resolution of 120 meters, which is analogous to the operational domain of changes in vegetation and snow cover that constitute differences between the two dates.

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

PubMed

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

2018-08-01

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

a New Method for Calculating Fractal Dimensions of Porous Media Based on Pore Size Distribution

NASA Astrophysics Data System (ADS)

Xia, Yuxuan; Cai, Jianchao; Wei, Wei; Hu, Xiangyun; Wang, Xin; Ge, Xinmin

Fractal theory has been widely used in petrophysical properties of porous rocks over several decades and determination of fractal dimensions is always the focus of researches and applications by means of fractal-based methods. In this work, a new method for calculating pore space fractal dimension and tortuosity fractal dimension of porous media is derived based on fractal capillary model assumption. The presented work establishes relationship between fractal dimensions and pore size distribution, which can be directly used to calculate the fractal dimensions. The published pore size distribution data for eight sandstone samples are used to calculate the fractal dimensions and simultaneously compared with prediction results from analytical expression. In addition, the proposed fractal dimension method is also tested through Micro-CT images of three sandstone cores, and are compared with fractal dimensions by box-counting algorithm. The test results also prove a self-similar fractal range in sandstone when excluding smaller pores.

[Fractal research of neurite growth in immunofluorescent images].

PubMed

Tang, Min; Wang, Huinan

2008-12-01

Fractal dimension has been widely used in medical images processing and analysis. The neurite growth of cultured dorsal root ganglion (DRG) was detected by fluorescent immunocytochemistry treated with nerve regeneration factor (0.1, 0.5, 2.0 mg/L). A novel method based on triangular prism surface area (TPSA) was introduced and adopted to calculate the fractal dimension of the two-dimensional immunofluorescent images. Experimental results demonstrate that this method is easy to understand and convenient to operate, and the quantititve results are concordant with the observational findings under microscope. This method can be guidelines for analyzing and deciding experimental results.

Implicit Weight Bias in Children Age 9 to 11 Years.

PubMed

Skinner, Asheley Cockrell; Payne, Keith; Perrin, Andrew J; Panter, Abigail T; Howard, Janna B; Bardone-Cone, Anna; Bulik, Cynthia M; Steiner, Michael J; Perrin, Eliana M

2017-07-01

Assess implicit weight bias in children 9 to 11 years old. Implicit weight bias was measured in children ages 9 to 11 ( N = 114) by using the Affect Misattribution Procedure. Participants were shown a test image of a child for 350 milliseconds followed by a meaningless fractal (200 milliseconds), and then they were asked to rate the fractal image as "good" or "bad." We used 9 image pairs matched on age, race, sex, and activity but differing by weight of the child. Implicit bias was the difference between positive ratings for fractals preceded by an image of a healthy-weight child and positive ratings for fractals preceded by an image of an overweight child. On average, 64% of abstract fractals shown after pictures of healthy-weight children were rated as "good," compared with 59% of those shown after pictures of overweight children, reflecting an overall implicit bias rate of 5.4% against overweight children ( P < .001). Healthy-weight participants showed greater implicit bias than over- and underweight participants (7.9%, 1.4%, and 0.3% respectively; P = .049). Implicit bias toward overweight individuals is evident in children aged 9 to 11 years with a magnitude of implicit bias (5.4%) similar to that in studies of implicit racial bias among adults. Copyright © 2017 by the American Academy of Pediatrics.

Plant Identification Based on Leaf Midrib Cross-Section Images Using Fractal Descriptors.

PubMed

da Silva, Núbia Rosa; Florindo, João Batista; Gómez, María Cecilia; Rossatto, Davi Rodrigo; Kolb, Rosana Marta; Bruno, Odemir Martinez

2015-01-01

The correct identification of plants is a common necessity not only to researchers but also to the lay public. Recently, computational methods have been employed to facilitate this task, however, there are few studies front of the wide diversity of plants occurring in the world. This study proposes to analyse images obtained from cross-sections of leaf midrib using fractal descriptors. These descriptors are obtained from the fractal dimension of the object computed at a range of scales. In this way, they provide rich information regarding the spatial distribution of the analysed structure and, as a consequence, they measure the multiscale morphology of the object of interest. In Biology, such morphology is of great importance because it is related to evolutionary aspects and is successfully employed to characterize and discriminate among different biological structures. Here, the fractal descriptors are used to identify the species of plants based on the image of their leaves. A large number of samples are examined, being 606 leaf samples of 50 species from Brazilian flora. The results are compared to other imaging methods in the literature and demonstrate that fractal descriptors are precise and reliable in the taxonomic process of plant species identification.

Texture segmentation of non-cooperative spacecrafts images based on wavelet and fractal dimension

NASA Astrophysics Data System (ADS)

Wu, Kanzhi; Yue, Xiaokui

2011-06-01

With the increase of on-orbit manipulations and space conflictions, missions such as tracking and capturing the target spacecrafts are aroused. Unlike cooperative spacecrafts, fixing beacons or any other marks on the targets is impossible. Due to the unknown shape and geometry features of non-cooperative spacecraft, in order to localize the target and obtain the latitude, we need to segment the target image and recognize the target from the background. The data and errors during the following procedures such as feature extraction and matching can also be reduced. Multi-resolution analysis of wavelet theory reflects human beings' recognition towards images from low resolution to high resolution. In addition, spacecraft is the only man-made object in the image compared to the natural background and the differences will be certainly observed between the fractal dimensions of target and background. Combined wavelet transform and fractal dimension, in this paper, we proposed a new segmentation algorithm for the images which contains complicated background such as the universe and planet surfaces. At first, Daubechies wavelet basis is applied to decompose the image in both x axis and y axis, thus obtain four sub-images. Then, calculate the fractal dimensions in four sub-images using different methods; after analyzed the results of fractal dimensions in sub-images, we choose Differential Box Counting in low resolution image as the principle to segment the texture which has the greatest divergences between different sub-images. This paper also presents the results of experiments by using the algorithm above. It is demonstrated that an accurate texture segmentation result can be obtained using the proposed technique.

GENERATING FRACTAL PATTERNS BY USING p-CIRCLE INVERSION

NASA Astrophysics Data System (ADS)

Ramírez, José L.; Rubiano, Gustavo N.; Zlobec, Borut Jurčič

2015-10-01

In this paper, we introduce the p-circle inversion which generalizes the classical inversion with respect to a circle (p = 2) and the taxicab inversion (p = 1). We study some basic properties and we also show the inversive images of some basic curves. We apply this new transformation to well-known fractals such as Sierpinski triangle, Koch curve, dragon curve, Fibonacci fractal, among others. Then we obtain new fractal patterns. Moreover, we generalize the method called circle inversion fractal be means of the p-circle inversion.

Fractal Image Filters for Specialized Image Recognition Tasks

DTIC Science & Technology

2010-02-11

butter sets of fractal geometers, such as Sierpinski triangles, twin- dragons , Koch curves, Cantor sets, fractal ferns, and so on. The geometries and...K is a centrally symmetric convex body in R m, then the function ‖x‖K defines a norm on R m. Moreover, the set K is the unit ball with respect to the...positive numbers r and R such that K contains a ball of radius r and is contained in a ball of radius R, the following proposition is clear

Exsanguinated blood volume estimation using fractal analysis of digital images.

PubMed

Sant, Sonia P; Fairgrieve, Scott I

2012-05-01

The estimation of bloodstain volume using fractal analysis of digital images of passive blood stains is presented. Binary digital photos of bloodstains of known volumes (ranging from 1 to 7 mL), dispersed in a defined area, were subjected to image analysis using FracLac V. 2.0 for ImageJ. The box-counting method was used to generate a fractal dimension for each trial. A positive correlation between the generated fractal number and the volume of blood was found (R(2) = 0.99). Regression equations were produced to estimate the volume of blood in blind trials. An error rate ranging from 78% for 1 mL to 7% for 6 mL demonstrated that as the volume increases so does the accuracy of the volume estimation. This method used in the preliminary study proved that bloodstain patterns may be deconstructed into mathematical parameters, thus removing the subjective element inherent in other methods of volume estimation. © 2012 American Academy of Forensic Sciences.

Mathematical models used in segmentation and fractal methods of 2-D ultrasound images

NASA Astrophysics Data System (ADS)

Moldovanu, Simona; Moraru, Luminita; Bibicu, Dorin

2012-11-01

Mathematical models are widely used in biomedical computing. The extracted data from images using the mathematical techniques are the "pillar" achieving scientific progress in experimental, clinical, biomedical, and behavioural researches. This article deals with the representation of 2-D images and highlights the mathematical support for the segmentation operation and fractal analysis in ultrasound images. A large number of mathematical techniques are suitable to be applied during the image processing stage. The addressed topics cover the edge-based segmentation, more precisely the gradient-based edge detection and active contour model, and the region-based segmentation namely Otsu method. Another interesting mathematical approach consists of analyzing the images using the Box Counting Method (BCM) to compute the fractal dimension. The results of the paper provide explicit samples performed by various combination of methods.

Buried mine detection using fractal geometry analysis to the LWIR successive line scan data image

NASA Astrophysics Data System (ADS)

Araki, Kan

2012-06-01

We have engaged in research on buried mine/IED detection by remote sensing method using LWIR camera. A IR image of a ground, containing buried objects can be assumed as a superimposed pattern including thermal scattering which may depend on the ground surface roughness, vegetation canopy, and effect of the sun light, and radiation due to various heat interaction caused by differences in specific heat, size, and buried depth of the objects and local temperature of their surrounding environment. In this cumbersome environment, we introduce fractal geometry for analyzing from an IR image. Clutter patterns due to these complex elements have oftentimes low ordered fractal dimension of Hausdorff Dimension. On the other hand, the target patterns have its tendency of obtaining higher ordered fractal dimension in terms of Information Dimension. Random Shuffle Surrogate method or Fourier Transform Surrogate method is used to evaluate fractional statistics by applying shuffle of time sequence data or phase of spectrum. Fractal interpolation to each line scan was also applied to improve the signal processing performance in order to evade zero division and enhance information of data. Some results of target extraction by using relationship between low and high ordered fractal dimension are to be presented.

Multifractal modeling, segmentation, prediction, and statistical validation of posterior fossa tumors

NASA Astrophysics Data System (ADS)

Islam, Atiq; Iftekharuddin, Khan M.; Ogg, Robert J.; Laningham, Fred H.; Sivakumar, Bhuvaneswari

2008-03-01

In this paper, we characterize the tumor texture in pediatric brain magnetic resonance images (MRIs) and exploit these features for automatic segmentation of posterior fossa (PF) tumors. We focus on PF tumor because of the prevalence of such tumor in pediatric patients. Due to varying appearance in MRI, we propose to model the tumor texture with a multi-fractal process, such as a multi-fractional Brownian motion (mBm). In mBm, the time-varying Holder exponent provides flexibility in modeling irregular tumor texture. We develop a detailed mathematical framework for mBm in two-dimension and propose a novel algorithm to estimate the multi-fractal structure of tissue texture in brain MRI based on wavelet coefficients. This wavelet based multi-fractal feature along with MR image intensity and a regular fractal feature obtained using our existing piecewise-triangular-prism-surface-area (PTPSA) method, are fused in segmenting PF tumor and non-tumor regions in brain T1, T2, and FLAIR MR images respectively. We also demonstrate a non-patient-specific automated tumor prediction scheme based on these image features. We experimentally show the tumor discriminating power of our novel multi-fractal texture along with intensity and fractal features in automated tumor segmentation and statistical prediction. To evaluate the performance of our tumor prediction scheme, we obtain ROCs and demonstrate how sharply the curves reach the specificity of 1.0 sacrificing minimal sensitivity. Experimental results show the effectiveness of our proposed techniques in automatic detection of PF tumors in pediatric MRIs.

Pond fractals in a tidal flat.

PubMed

Cael, B B; Lambert, Bennett; Bisson, Kelsey

2015-11-01

Studies over the past decade have reported power-law distributions for the areas of terrestrial lakes and Arctic melt ponds, as well as fractal relationships between their areas and coastlines. Here we report similar fractal structure of ponds in a tidal flat, thereby extending the spatial and temporal scales on which such phenomena have been observed in geophysical systems. Images taken during low tide of a tidal flat in Damariscotta, Maine, reveal a well-resolved power-law distribution of pond sizes over three orders of magnitude with a consistent fractal area-perimeter relationship. The data are consistent with the predictions of percolation theory for unscreened perimeters and scale-free cluster size distributions and are robust to alterations of the image processing procedure. The small spatial and temporal scales of these data suggest this easily observable system may serve as a useful model for investigating the evolution of pond geometries, while emphasizing the generality of fractal behavior in geophysical surfaces.

Pond fractals in a tidal flat

NASA Astrophysics Data System (ADS)

Cael, B. B.; Lambert, Bennett; Bisson, Kelsey

2015-11-01

Studies over the past decade have reported power-law distributions for the areas of terrestrial lakes and Arctic melt ponds, as well as fractal relationships between their areas and coastlines. Here we report similar fractal structure of ponds in a tidal flat, thereby extending the spatial and temporal scales on which such phenomena have been observed in geophysical systems. Images taken during low tide of a tidal flat in Damariscotta, Maine, reveal a well-resolved power-law distribution of pond sizes over three orders of magnitude with a consistent fractal area-perimeter relationship. The data are consistent with the predictions of percolation theory for unscreened perimeters and scale-free cluster size distributions and are robust to alterations of the image processing procedure. The small spatial and temporal scales of these data suggest this easily observable system may serve as a useful model for investigating the evolution of pond geometries, while emphasizing the generality of fractal behavior in geophysical surfaces.

Fractal analysis of mandibular trabecular bone: optimal tile sizes for the tile counting method.

PubMed

Huh, Kyung-Hoe; Baik, Jee-Seon; Yi, Won-Jin; Heo, Min-Suk; Lee, Sam-Sun; Choi, Soon-Chul; Lee, Sun-Bok; Lee, Seung-Pyo

2011-06-01

This study was performed to determine the optimal tile size for the fractal dimension of the mandibular trabecular bone using a tile counting method. Digital intraoral radiographic images were obtained at the mandibular angle, molar, premolar, and incisor regions of 29 human dry mandibles. After preprocessing, the parameters representing morphometric characteristics of the trabecular bone were calculated. The fractal dimensions of the processed images were analyzed in various tile sizes by the tile counting method. The optimal range of tile size was 0.132 mm to 0.396 mm for the fractal dimension using the tile counting method. The sizes were closely related to the morphometric parameters. The fractal dimension of mandibular trabecular bone, as calculated with the tile counting method, can be best characterized with a range of tile sizes from 0.132 to 0.396 mm.

Fractal analysis of mandibular trabecular bone: optimal tile sizes for the tile counting method

PubMed Central

Huh, Kyung-Hoe; Baik, Jee-Seon; Heo, Min-Suk; Lee, Sam-Sun; Choi, Soon-Chul; Lee, Sun-Bok; Lee, Seung-Pyo

2011-01-01

Purpose This study was performed to determine the optimal tile size for the fractal dimension of the mandibular trabecular bone using a tile counting method. Materials and Methods Digital intraoral radiographic images were obtained at the mandibular angle, molar, premolar, and incisor regions of 29 human dry mandibles. After preprocessing, the parameters representing morphometric characteristics of the trabecular bone were calculated. The fractal dimensions of the processed images were analyzed in various tile sizes by the tile counting method. Results The optimal range of tile size was 0.132 mm to 0.396 mm for the fractal dimension using the tile counting method. The sizes were closely related to the morphometric parameters. Conclusion The fractal dimension of mandibular trabecular bone, as calculated with the tile counting method, can be best characterized with a range of tile sizes from 0.132 to 0.396 mm. PMID:21977478

FAST TRACK COMMUNICATION: Weyl law for fat fractals

NASA Astrophysics Data System (ADS)

Spina, María E.; García-Mata, Ignacio; Saraceno, Marcos

2010-10-01

It has been conjectured that for a class of piecewise linear maps the closure of the set of images of the discontinuity has the structure of a fat fractal, that is, a fractal with positive measure. An example of such maps is the sawtooth map in the elliptic regime. In this work we analyze this problem quantum mechanically in the semiclassical regime. We find that the fraction of states localized on the unstable set satisfies a modified fractal Weyl law, where the exponent is given by the exterior dimension of the fat fractal.

Holographic Characterization of Colloidal Fractal Aggregates

NASA Astrophysics Data System (ADS)

Wang, Chen; Cheong, Fook Chiong; Ruffner, David B.; Zhong, Xiao; Ward, Michael D.; Grier, David G.

In-line holographic microscopy images of micrometer-scale fractal aggregates can be interpreted with the Lorenz-Mie theory of light scattering and an effective-sphere model to obtain each aggregate's size and the population-averaged fractal dimension. We demonstrate this technique experimentally using model fractal clusters of polystyrene nanoparticles and fractal protein aggregates composed of bovine serum albumin and bovine pancreas insulin. This technique can characterize several thousand aggregates in ten minutes and naturally distinguishes aggregates from contaminants such as silicone oil droplets. Work supported by the SBIR program of the NSF.

Fractals, Fuzzy Sets And Image Representation

NASA Astrophysics Data System (ADS)

Dodds, D. R.

1988-10-01

This paper addresses some uses of fractals, fuzzy sets and image representation as it pertains to robotic grip planning and autonomous vehicle navigation AVN. The robot/vehicle is assumed to be equipped with multimodal sensors including ultrashort pulse imaging laser rangefinder. With a temporal resolution of 50 femtoseconds a time of flight laser rangefinder can resolve distances within approximately half an inch or 1.25 centimeters. (Fujimoto88)

Fractal Dimensions of Umbral and Penumbral Regions of Sunspots

NASA Astrophysics Data System (ADS)

Rajkumar, B.; Haque, S.; Hrudey, W.

2017-11-01

The images of sunspots in 16 active regions taken at the University College of the Cayman Islands (UCCI) Observatory on Grand Cayman during June-November 2015 were used to determine their fractal dimensions using the perimeter-area method for the umbral and the penumbral region. Scale-free fractal dimensions of 2.09 ±0.42 and 1.72 ±0.4 were found, respectively. This value was higher than the value determined by Chumak and Chumak ( Astron. Astrophys. Trans. 10, 329, 1996), who used a similar method, but only for the penumbral region of their sample set. The umbral and penumbral fractal dimensions for the specific sunspots are positively correlated with r = 0.58. Furthermore, a similar time-series analysis was performed on eight images of AR 12403, from 21 August 2015 to 28 August 2015 taken from the Debrecen Photoheliographic Data (DPD). The correlation is r = 0.623 between the umbral and penumbral fractal dimensions in the time series, indicating that the complexity in morphology indicated by the fractal dimension between the umbra and penumbra followed each other in time as well.

Experimental criteria for the determination of fractal parameters of premixed turbulent flames

NASA Astrophysics Data System (ADS)

Shepherd, I. G.; Cheng, Robert K.; Talbot, L.

1992-10-01

The influence of spatial resolution, digitization noise, the number of records used for averaging, and the method of analysis on the determination of the fractal parameters of a high Damköhler number, methane/air, premixed, turbulent stagnation-point flame are investigated in this paper. The flow exit velocity was 5 m/s and the turbulent Reynolds number was 70 based on a integral scale of 3 mm and a turbulent intensity of 7%. The light source was a copper vapor laser which delivered 20 nsecs, 5 mJ pulses at 4 kHz and the tomographic cross-sections of the flame were recorded by a high speed movie camera. The spatial resolution of the images is 155 × 121 μm/pixel with a field of view of 50 × 65 mm. The stepping caliper technique for obtaining the fractal parameters is found to give the clearest indication of the cutoffs and the effects of noise. It is necessary to ensemble average the results from more than 25 statistically independent images to reduce sufficiently the scatter in the fractal parameters. The effects of reduced spatial resolution on fractal plots are estimated by artificial degradation of the resolution of the digitized flame boundaries. The effect of pixel resolution, an apparent increase in flame length below the inner scale rolloff, appears in the fractal plots when the measurent scale is less than approximately twice the pixel resolution. Although a clearer determination of fractal parameters is obtained by local averaging of the flame boundaries which removes digitization noise, at low spatial resolution this technique can reduce the fractal dimension. The degree of fractal isotropy of the flame surface can have a significant effect on the estimation of the flame surface area and hence burning rate from two-dimensional images. To estimate this isotropy a determination of the outer cutoff is required and three-dimensional measurements are probably also necessary.

Fractality of pulsatile flow in speckle images

NASA Astrophysics Data System (ADS)

Nemati, M.; Kenjeres, S.; Urbach, H. P.; Bhattacharya, N.

2016-05-01

The scattering of coherent light from a system with underlying flow can be used to yield essential information about dynamics of the process. In the case of pulsatile flow, there is a rapid change in the properties of the speckle images. This can be studied using the standard laser speckle contrast and also the fractality of images. In this paper, we report the results of experiments performed to study pulsatile flow with speckle images, under different experimental configurations to verify the robustness of the techniques for applications. In order to study flow under various levels of complexity, the measurements were done for three in-vitro phantoms and two in-vivo situations. The pumping mechanisms were varied ranging from mechanical pumps to the human heart for the in vivo case. The speckle images were analyzed using the techniques of fractal dimension and speckle contrast analysis. The results of these techniques for the various experimental scenarios were compared. The fractal dimension is a more sensitive measure to capture the complexity of the signal though it was observed that it is also extremely sensitive to the properties of the scattering medium and cannot recover the signal for thicker diffusers in comparison to speckle contrast.

Fractal analysis of seafloor textures for target detection in synthetic aperture sonar imagery

NASA Astrophysics Data System (ADS)

Nabelek, T.; Keller, J.; Galusha, A.; Zare, A.

2018-04-01

Fractal analysis of an image is a mathematical approach to generate surface related features from an image or image tile that can be applied to image segmentation and to object recognition. In undersea target countermeasures, the targets of interest can appear as anomalies in a variety of contexts, visually different textures on the seafloor. In this paper, we evaluate the use of fractal dimension as a primary feature and related characteristics as secondary features to be extracted from synthetic aperture sonar (SAS) imagery for the purpose of target detection. We develop three separate methods for computing fractal dimension. Tiles with targets are compared to others from the same background textures without targets. The different fractal dimension feature methods are tested with respect to how well they can be used to detect targets vs. false alarms within the same contexts. These features are evaluated for utility using a set of image tiles extracted from a SAS data set generated by the U.S. Navy in conjunction with the Office of Naval Research. We find that all three methods perform well in the classification task, with a fractional Brownian motion model performing the best among the individual methods. We also find that the secondary features are just as useful, if not more so, in classifying false alarms vs. targets. The best classification accuracy overall, in our experimentation, is found when the features from all three methods are combined into a single feature vector.

[Recent progress of research and applications of fractal and its theories in medicine].

PubMed

Cai, Congbo; Wang, Ping

2014-10-01

Fractal, a mathematics concept, is used to describe an image of self-similarity and scale invariance. Some organisms have been discovered with the fractal characteristics, such as cerebral cortex surface, retinal vessel structure, cardiovascular network, and trabecular bone, etc. It has been preliminarily confirmed that the three-dimensional structure of cells cultured in vitro could be significantly enhanced by bionic fractal surface. Moreover, fractal theory in clinical research will help early diagnosis and treatment of diseases, reducing the patient's pain and suffering. The development process of diseases in the human body can be expressed by the fractal theories parameter. It is of considerable significance to retrospectively review the preparation and application of fractal surface and its diagnostic value in medicine. This paper gives an application of fractal and its theories in the medical science, based on the research achievements in our laboratory.

MORPH-I (Ver 1.0) a software package for the analysis of scanning electron micrograph (binary formatted) images for the assessment of the fractal dimension of enclosed pore surfaces

USGS Publications Warehouse

Mossotti, Victor G.; Eldeeb, A. Raouf; Oscarson, Robert

1998-01-01

MORPH-I is a set of C-language computer programs for the IBM PC and compatible minicomputers. The programs in MORPH-I are used for the fractal analysis of scanning electron microscope and electron microprobe images of pore profiles exposed in cross-section. The program isolates and traces the cross-sectional profiles of exposed pores and computes the Richardson fractal dimension for each pore. Other programs in the set provide for image calibration, display, and statistical analysis of the computed dimensions for highly complex porous materials. Requirements: IBM PC or compatible; minimum 640 K RAM; mathcoprocessor; SVGA graphics board providing mode 103 display.

The Calculation of Fractal Dimension in the Presence of Non-Fractal Clutter

NASA Technical Reports Server (NTRS)

Herren, Kenneth A.; Gregory, Don A.

1999-01-01

The area of information processing has grown dramatically over the last 50 years. In the areas of image processing and information storage the technology requirements have far outpaced the ability of the community to meet demands. The need for faster recognition algorithms and more efficient storage of large quantities of data has forced the user to accept less than lossless retrieval of that data for analysis. In addition to clutter that is not the object of interest in the data set, often the throughput requirements forces the user to accept "noisy" data and to tolerate the clutter inherent in that data. It has been shown that some of this clutter, both the intentional clutter (clouds, trees, etc) as well as the noise introduced on the data by processing requirements can be modeled as fractal or fractal-like. Traditional methods using Fourier deconvolution on these sources of noise in frequency space leads to loss of signal and can, in many cases, completely eliminate the target of interest. The parameters that characterize fractal-like noise (predominately the fractal dimension) have been investigated and a technique to reduce or eliminate noise from real scenes has been developed. Examples of clutter reduced images are presented.

Self-Similarity of Plasmon Edge Modes on Koch Fractal Antennas.

PubMed

Bellido, Edson P; Bernasconi, Gabriel D; Rossouw, David; Butet, Jérémy; Martin, Olivier J F; Botton, Gianluigi A

2017-11-28

We investigate the plasmonic behavior of Koch snowflake fractal geometries and their possible application as broadband optical antennas. Lithographically defined planar silver Koch fractal antennas were fabricated and characterized with high spatial and spectral resolution using electron energy loss spectroscopy. The experimental data are supported by numerical calculations carried out with a surface integral equation method. Multiple surface plasmon edge modes supported by the fractal structures have been imaged and analyzed. Furthermore, by isolating and reproducing self-similar features in long silver strip antennas, the edge modes present in the Koch snowflake fractals are identified. We demonstrate that the fractal response can be obtained by the sum of basic self-similar segments called characteristic edge units. Interestingly, the plasmon edge modes follow a fractal-scaling rule that depends on these self-similar segments formed in the structure after a fractal iteration. As the size of a fractal structure is reduced, coupling of the modes in the characteristic edge units becomes relevant, and the symmetry of the fractal affects the formation of hybrid modes. This analysis can be utilized not only to understand the edge modes in other planar structures but also in the design and fabrication of fractal structures for nanophotonic applications.

Fractal analysis of the susceptibility weighted imaging patterns in malignant brain tumors during antiangiogenic treatment: technical report on four cases serially imaged by 7 T magnetic resonance during a period of four weeks.

PubMed

Di Ieva, Antonio; Matula, Christian; Grizzi, Fabio; Grabner, Günther; Trattnig, Siegfried; Tschabitscher, Manfred

2012-01-01

The need for new and objective indexes for the neuroradiologic follow-up of brain tumors and for monitoring the effects of antiangiogenic strategies in vivo led us to perform a technical study on four patients who received computerized analysis of tumor-associated vasculature with ultra-high-field (7 T) magnetic resonance imaging (MRI). The image analysis involved the application of susceptibility weighted imaging (SWI) to evaluate vascular structures. Four patients affected by recurrent malignant brain tumors were enrolled in the present study. After the first 7-T SWI MRI procedure, the patients underwent antiangiogenic treatment with bevacizumab. The imaging was repeated every 2 weeks for a period of 4 weeks. The SWI patterns visualized in the three MRI temporal sequences were analyzed by means of a computer-aided fractal-based method to objectively quantify their geometric complexity. In two clinically deteriorating patients we found an increase of the geometric complexity of the space-filling properties of the SWI patterns over time despite the antiangiogenic treatment. In one patient, who showed improvement with the therapy, the fractal dimension of the intratumoral structure decreased, whereas in the fourth patient, no differences were found. The qualitative changes of the intratumoral SWI patterns during a period of 4 weeks were quantified with the fractal dimension. Because SWI patterns are also related to the presence of vascular structures, the quantification of their space-filling properties with fractal dimension seemed to be a valid tool for the in vivo neuroradiologic follow-up of brain tumors. Copyright © 2012 Elsevier Inc. All rights reserved.

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.

Consideration of the method of image diagnosis with respect to frontal lobe atrophy

NASA Astrophysics Data System (ADS)

Sato, K.; Sugawara, K.; Narita, Y.; Namura, I.

1996-12-01

Proposes a segmentation method for a quantitative image diagnosis as a means of realizing an objective diagnosis of the frontal lobe atrophy. From the data obtained on the grade of membership, the fractal dimensions of the cerebral tissue [cerebral spinal fluid (CSF), gray matter, and white matter] and the contours are estimated. The mutual relationship between the degree of atrophy and the fractal dimension has been analyzed based on the estimated fractal dimensions. Using a sample of 42 male and female cases, ranging In age from 50's to 70's, it has been concluded that the frontal lobe atrophy can be quantified by regarding it as an expansion of CSF region on the magnetic resonance imaging (MRI) of the brain. Furthermore, when the process of frontal lobe atrophy is separated into early and advanced stages, the volumetric change of CSF and white matter in frontal lobe displays meaningful differences between the two stages, demonstrating that the fractal dimension of CSF rises with the progress of atrophy. Moreover, an interpolation method for three-dimensional (3-D) shape reconstruction of the region of diagnostic interest is proposed and 3-D shape visualization, with respect to the degree and form of atrophy, is performed on the basis of the estimated fractal dimension of the segmented cerebral tissue.

SU-D-BRA-04: Fractal Dimension Analysis of Edge-Detected Rectal Cancer CTs for Outcome Prediction

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

Zhong, H; Wang, J; Hu, W

2015-06-15

Purpose: To extract the fractal dimension features from edge-detected rectal cancer CTs, and to examine the predictability of fractal dimensions to outcomes of primary rectal cancer patients. Methods: Ninety-seven rectal cancer patients treated with neo-adjuvant chemoradiation were enrolled in this study. CT images were obtained before chemoradiotherapy. The primary lesions of the rectal cancer were delineated by experienced radiation oncologists. These images were extracted and filtered by six different Laplacian of Gaussian (LoG) filters with different filter values (0.5–3.0: from fine to coarse) to achieve primary lesions in different anatomical scales. Edges of the original images were found at zero-crossingsmore » of the filtered images. Three different fractal dimensions (box-counting dimension, Minkowski dimension, mass dimension) were calculated upon the image slice with the largest cross-section of the primary lesion. The significance of these fractal dimensions in survival, recurrence and metastasis were examined by Student’s t-test. Results: For a follow-up time of two years, 18 of 97 patients had experienced recurrence, 24 had metastasis, and 18 were dead. Minkowski dimensions under large filter values (2.0, 2.5, 3.0) were significantly larger (p=0.014, 0.006, 0.015) in patients with recurrence than those without. For metastasis, only box-counting dimensions under a single filter value (2.5) showed differences (p=0.016) between patients with and without. For overall survival, box-counting dimensions (filter values = 0.5, 1.0, 1.5), Minkowski dimensions (filter values = 0.5, 1.5, 2.0, 2,5) and mass dimensions (filter values = 1.5, 2.0) were all significant (p<0.05). Conclusion: It is feasible to extract shape information by edge detection and fractal dimensions analysis in neo-adjuvant rectal cancer patients. This information can be used to prognosis prediction.« less

Fractal characteristic in the wearing of cutting tool

NASA Astrophysics Data System (ADS)

Mei, Anhua; Wang, Jinghui

1995-11-01

This paper studies the cutting tool wear with fractal geometry. The wearing image of the flank has been collected by machine vision which consists of CCD camera and personal computer. After being processed by means of preserving smoothing, binary making and edge extracting, the clear boundary enclosing the worn area has been obtained. The fractal dimension of the worn surface is calculated by the methods called `Slit Island' and `Profile'. The experiments and calciating give the conclusion that the worn surface is enclosed by a irregular boundary curve with some fractal dimension and characteristics of self-similarity. Furthermore, the relation between the cutting velocity and the fractal dimension of the worn region has been submitted. This paper presents a series of methods for processing and analyzing the fractal information in the blank wear, which can be applied to research the projective relation between the fractal structure and the wear state, and establish the fractal model of the cutting tool wear.

Contour fractal analysis of grains

NASA Astrophysics Data System (ADS)

Guida, Giulia; Casini, Francesca; Viggiani, Giulia MB

2017-06-01

Fractal analysis has been shown to be useful in image processing to characterise the shape and the grey-scale complexity in different applications spanning from electronic to medical engineering (e.g. [1]). Fractal analysis consists of several methods to assign a dimension and other fractal characteristics to a dataset describing geometric objects. Limited studies have been conducted on the application of fractal analysis to the classification of the shape characteristics of soil grains. The main objective of the work described in this paper is to obtain, from the results of systematic fractal analysis of artificial simple shapes, the characterization of the particle morphology at different scales. The long term objective of the research is to link the microscopic features of granular media with the mechanical behaviour observed in the laboratory and in situ.

Investigating the complexity of precipitation sets within California via the fractal-multifractal method

NASA Astrophysics Data System (ADS)

Puente, Carlos E.; Maskey, Mahesh L.; Sivakumar, Bellie

2017-04-01

A deterministic geometric approach, the fractal-multifractal (FM) method, is adapted in order to encode highly intermittent daily rainfall records observed over a year. Using such a notion, this research investigates the complexity of rainfall in various stations within the State of California. Specifically, records gathered at (from South to North) Cherry Valley, Merced, Sacramento and Shasta Dam, containing 59, 116, 115 and 72 years, all ending at water year 2015, were encoded and analyzed in detail. The analysis reveals that: (a) the FM approach yields faithful encodings of all records, by years, with mean square and maximum errors in accumulated rain that are less than a mere 2% and 10%, respectively; (b) the evolution of the corresponding "best" FM parameters, allowing visualization of the inter-annual rainfall dynamics from a reduced vantage point, exhibit implicit variability that precludes discriminating between sites and extrapolating to the future; (c) the evolution of the FM parameters, restricted to specific regions within space, allows finding sensible future simulations; and (d) the rain signals at all sites may be termed "equally complex," as usage of k-means clustering and conventional phase space analysis of FM parameters yields comparable results for all sites.

Factors Affecting the Changes of Ice Crystal Form in Ice Cream

NASA Astrophysics Data System (ADS)

Wang, Xin; Watanabe, Manabu; Suzuki, Toru

In this study, the shape of ice crystals in ice cream was quantitatively evaluated by introducing fractal analysis. A small droplet of commercial ice cream mix was quickly cooled to about -30°C on the cold stage of microscope. Subsequently, it was heated to -5°C or -10°C and then held for various holding time. Based on the captured images at each holding time, the cross-sectional area and the length of circumference for each ice crystal were measured to calculate fractal dimension using image analysis software. The results showed that the ice crystals were categorized into two groups, e.g. simple-shape and complicated-shape, according to their fractal dimensions. The fractal dimension of ice crystals became lower with increasing holding time and holding temperature. It was also indicated that the growing rate of complicated-shape ice crystals was relatively higher because of aggregation.

Functional slit lamp biomicroscopy for imaging bulbar conjunctival microvasculature in contact lens wearers

PubMed Central

Jiang, Hong; Zhong, Jianguang; DeBuc, Delia Cabrera; Tao, Aizhu; Xu, Zhe; Lam, Byron L.; Liu, Che; Wang, Jianhua

2014-01-01

Purpose To develop, test and validate functional slit lamp biomicroscopy (FSLB) for generating non-invasive bulbar conjunctival microvascular perfusion maps (nMPMs) and assessing morphometry and hemodyanmics. Methods FSLB was adapted from a traditional slit-lamp microscope by attaching a digital camera to image the bulbar conjunctiva to create nMPMs and measure venular blood flow hemodyanmics. High definition images with a large field of view were obtained on the temporal bulbar conjunctiva for creating nMPMs. A high imaging rate of 60 frame per second and a ~210× high magnification were achieved using the camera inherited high speed setting and movie crop function, for imaging hemodyanmics. Custom software was developed to segment bulbar conjunctival nMPMs for further fractal analysis and quantitatively measure blood vessel diameter, blood flow velocity and flow rate. Six human subjects were imaged before and after 6 hours of wearing contact lenses. Monofractal and multifractal analyses were performed to quantify fractality of the nMPMs. Results The mean bulbar conjunctival vessel diameter was 18.8 ± 2.7 μm at baseline and increased to 19.6 ± 2.4 μm after 6 hours of lens wear (P = 0.020). The blood flow velocity was increased from 0.60 ± 0.12 mm/s to 0.88 ± 0.21 mm/s (P = 0.001). The blood flow rate was also increased from 129.8 ± 59.9 pl/s to 207.2 ± 81.3 pl/s (P = 0.001). Bulbar conjunctival nMPMs showed the intricate details of the bulbar conjunctival microvascular network. At baseline, fractal dimension was 1.63 ± 0.05 and 1.71 ± 0.03 analyzed by monofractal and multifractal analysis, respectively. Significant increases in fractal dimensions were found after 6 hours of lens wear (P < 0.05). Conclusions Microvascular network’s fractality, morphometry and hemodyanmics of the human bulbar conjunctiva can be measured easily and reliably using FSLB. The alternations of the fractal dimensions, morphometry and hemodyanmics during contact lens wear may indicate ocular microvascular responses to contact lens wear. PMID:24444784

Investigating the effect of suspensions nanostructure on the thermophysical properties of nanofluids

NASA Astrophysics Data System (ADS)

Tesfai, Waka; Singh, Pawan K.; Masharqa, Salim J. S.; Souier, Tewfik; Chiesa, Matteo; Shatilla, Youssef

2012-12-01

The effect of fractal dimensions and Feret diameter of aggregated nanoparticle on predicting the thermophysical properties of nanofluids is demonstrated. The fractal dimensions and Feret diameter distributions of particle agglomerates are quantified from scanning electron and probe microscope imaging of yttria nanofluids. The results are compared with the fractal dimensions calculated by fitting the rheological properties of yttria nanofluids against the modified Krieger-Dougherty model. Nanofluids of less than 1 vol. % particle loading are found to have fractal dimensions of below 1.8, which is typical for diffusion controlled cluster formation. By contrast, an increase in the particle loading increases the fractal dimension to 2.0-2.2. The fractal dimensions obtained from both methods are employed to predict the thermal conductivity of the nanofluids using the modified Maxwell-Garnet (M-G) model. The prediction from rheology is found inadequate and might lead up to 8% error in thermal conductivity for an improper choice of aspect ratio. Nevertheless, the prediction of the modified M-G model from the imaging is found to agree well with the experimentally observed effective thermal conductivity of the nanofluids. In addition, this study opens a new window on the study of aggregate kinetics, which is critical in tuning the properties of multiphase systems.

The fractal dimension of cell membrane correlates with its capacitance: A new fractal single-shell model

PubMed Central

Wang, Xujing; Becker, Frederick F.; Gascoyne, Peter R. C.

2010-01-01

The scale-invariant property of the cytoplasmic membrane of biological cells is examined by applying the Minkowski–Bouligand method to digitized scanning electron microscopy images of the cell surface. The membrane is found to exhibit fractal behavior, and the derived fractal dimension gives a good description of its morphological complexity. Furthermore, we found that this fractal dimension correlates well with the specific membrane dielectric capacitance derived from the electrorotation measurements. Based on these findings, we propose a new fractal single-shell model to describe the dielectrics of mammalian cells, and compare it with the conventional single-shell model (SSM). We found that while both models fit with experimental data well, the new model is able to eliminate the discrepancy between the measured dielectric property of cells and that predicted by the SSM. PMID:21198103

Fractal-based wideband invisibility cloak

NASA Astrophysics Data System (ADS)

Cohen, Nathan; Okoro, Obinna; Earle, Dan; Salkind, Phil; Unger, Barry; Yen, Sean; McHugh, Daniel; Polterzycki, Stefan; Shelman-Cohen, A. J.

2015-03-01

A wideband invisibility cloak (IC) at microwave frequencies is described. Using fractal resonators in closely spaced (sub wavelength) arrays as a minimal number of cylindrical layers (rings), the IC demonstrates that it is physically possible to attain a `see through' cloaking device with: (a) wideband coverage; (b) simple and attainable fabrication; (c) high fidelity emulation of the free path; (d) minimal side scattering; (d) a near absence of shadowing in the scattering. Although not a practical device, this fractal-enabled technology demonstrator opens up new opportunities for diverted-image (DI) technology and use of fractals in wideband optical, infrared, and microwave applications.

Fractal analysis of MRI data for the characterization of patients with schizophrenia and bipolar disorder.

PubMed

Squarcina, Letizia; De Luca, Alberto; Bellani, Marcella; Brambilla, Paolo; Turkheimer, Federico E; Bertoldo, Alessandra

2015-02-21

Fractal geometry can be used to analyze shape and patterns in brain images. With this study we use fractals to analyze T1 data of patients affected by schizophrenia or bipolar disorder, with the aim of distinguishing between healthy and pathological brains using the complexity of brain structure, in particular of grey matter, as a marker of disease. 39 healthy volunteers, 25 subjects affected by schizophrenia and 11 patients affected by bipolar disorder underwent an MRI session. We evaluated fractal dimension of the brain cortex and its substructures, calculated with an algorithm based on the box-count algorithm. We modified this algorithm, with the aim of avoiding the segmentation processing step and using all the information stored in the image grey levels. Moreover, to increase sensitivity to local structural changes, we computed a value of fractal dimension for each slice of the brain or of the particular structure. To have reference values in comparing healthy subjects with patients, we built a template by averaging fractal dimension values of the healthy volunteers data. Standard deviation was evaluated and used to create a confidence interval. We also performed a slice by slice t-test to assess the difference at slice level between the three groups. Consistent average fractal dimension values were found across all the structures in healthy controls, while in the pathological groups we found consistent differences, indicating a change in brain and structures complexity induced by these disorders.

Fractal analysis of MRI data for the characterization of patients with schizophrenia and bipolar disorder

NASA Astrophysics Data System (ADS)

Squarcina, Letizia; De Luca, Alberto; Bellani, Marcella; Brambilla, Paolo; Turkheimer, Federico E.; Bertoldo, Alessandra

2015-02-01

Fractal geometry can be used to analyze shape and patterns in brain images. With this study we use fractals to analyze T1 data of patients affected by schizophrenia or bipolar disorder, with the aim of distinguishing between healthy and pathological brains using the complexity of brain structure, in particular of grey matter, as a marker of disease. 39 healthy volunteers, 25 subjects affected by schizophrenia and 11 patients affected by bipolar disorder underwent an MRI session. We evaluated fractal dimension of the brain cortex and its substructures, calculated with an algorithm based on the box-count algorithm. We modified this algorithm, with the aim of avoiding the segmentation processing step and using all the information stored in the image grey levels. Moreover, to increase sensitivity to local structural changes, we computed a value of fractal dimension for each slice of the brain or of the particular structure. To have reference values in comparing healthy subjects with patients, we built a template by averaging fractal dimension values of the healthy volunteers data. Standard deviation was evaluated and used to create a confidence interval. We also performed a slice by slice t-test to assess the difference at slice level between the three groups. Consistent average fractal dimension values were found across all the structures in healthy controls, while in the pathological groups we found consistent differences, indicating a change in brain and structures complexity induced by these disorders.

The fractal heart — embracing mathematics in the cardiology clinic

PubMed Central

Captur, Gabriella; Karperien, Audrey L.; Hughes, Alun D.; Francis, Darrel P.; Moon, James C.

2017-01-01

For clinicians grappling with quantifying the complex spatial and temporal patterns of cardiac structure and function (such as myocardial trabeculae, coronary microvascular anatomy, tissue perfusion, myocyte histology, electrical conduction, heart rate, and blood-pressure variability), fractal analysis is a powerful, but still underused, mathematical tool. In this Perspectives article, we explain some fundamental principles of fractal geometry and place it in a familiar medical setting. We summarize studies in the cardiovascular sciences in which fractal methods have successfully been used to investigate disease mechanisms, and suggest potential future clinical roles in cardiac imaging and time series measurements. We believe that clinical researchers can deploy innovative fractal solutions to common cardiac problems that might ultimately translate into advancements for patient care. PMID:27708281

The fractal-multifractal method and temporal resolution: Application to precipitation and streamflow

NASA Astrophysics Data System (ADS)

Maskey, M.; Puente, C. E.; Sivakumar, B.

2017-12-01

In the past, we have established that the deterministic fractal-multifractal (FM) method is a promising geometric tool to analyze hydro-climatic variables, such as precipitation, river flow, and temperature. In this study, we address the issue of temporal resolution to advance the suitability and usefulness of the FM approach in hydro-climate. Specifically, we elucidate the evolution of FM geometric parameters as computed at different time scales ranging from a day to a month (30-day) in increments of a day. For this purpose, both rainfall and river discharge records at Sacramento, California gathered over a year are encoded at different time scales. The analysis reveals that: (a) the FM approach yields faithful encodings of both kinds of data sets at the resolutions considered with reasonably small errors; and (b) the "best" FM parameters ultimately converge when the resolution is increased, thus allowing visualizing both hydrologic attributes. By addressing the scalability of the geometric patterns, these results further advance the suitability of the FM approach.

Beyond maximum entropy: Fractal Pixon-based image reconstruction

NASA Technical Reports Server (NTRS)

Puetter, Richard C.; Pina, R. K.

1994-01-01

We have developed a new Bayesian image reconstruction method that has been shown to be superior to the best implementations of other competing methods, including Goodness-of-Fit methods such as Least-Squares fitting and Lucy-Richardson reconstruction, as well as Maximum Entropy (ME) methods such as those embodied in the MEMSYS algorithms. Our new method is based on the concept of the pixon, the fundamental, indivisible unit of picture information. Use of the pixon concept provides an improved image model, resulting in an image prior which is superior to that of standard ME. Our past work has shown how uniform information content pixons can be used to develop a 'Super-ME' method in which entropy is maximized exactly. Recently, however, we have developed a superior pixon basis for the image, the Fractal Pixon Basis (FPB). Unlike the Uniform Pixon Basis (UPB) of our 'Super-ME' method, the FPB basis is selected by employing fractal dimensional concepts to assess the inherent structure in the image. The Fractal Pixon Basis results in the best image reconstructions to date, superior to both UPB and the best ME reconstructions. In this paper, we review the theory of the UPB and FPB pixon and apply our methodology to the reconstruction of far-infrared imaging of the galaxy M51. The results of our reconstruction are compared to published reconstructions of the same data using the Lucy-Richardson algorithm, the Maximum Correlation Method developed at IPAC, and the MEMSYS ME algorithms. The results show that our reconstructed image has a spatial resolution a factor of two better than best previous methods (and a factor of 20 finer than the width of the point response function), and detects sources two orders of magnitude fainter than other methods.

Fractal dimension of trabecular bone projection texture is related to three-dimensional microarchitecture.

PubMed

Pothuaud, L; Benhamou, C L; Porion, P; Lespessailles, E; Harba, R; Levitz, P

2000-04-01

The purpose of this work was to understand how fractal dimension of two-dimensional (2D) trabecular bone projection images could be related to three-dimensional (3D) trabecular bone properties such as porosity or connectivity. Two alteration processes were applied to trabecular bone images obtained by magnetic resonance imaging: a trabeculae dilation process and a trabeculae removal process. The trabeculae dilation process was applied from the 3D skeleton graph to the 3D initial structure with constant connectivity. The trabeculae removal process was applied from the initial structure to an altered structure having 99% of porosity, in which both porosity and connectivity were modified during this second process. Gray-level projection images of each of the altered structures were simply obtained by summation of voxels, and fractal dimension (Df) was calculated. Porosity (phi) and connectivity per unit volume (Cv) were calculated from the 3D structure. Significant relationships were found between Df, phi, and Cv. Df values increased when porosity increased (dilation and removal processes) and when connectivity decreased (only removal process). These variations were in accordance with all previous clinical studies, suggesting that fractal evaluation of trabecular bone projection has real meaning in terms of porosity and connectivity of the 3D architecture. Furthermore, there was a statistically significant linear dependence between Df and Cv when phi remained constant. Porosity is directly related to bone mineral density and fractal dimension can be easily evaluated in clinical routine. These two parameters could be associated to evaluate the connectivity of the structure.

Fractal dimension and the navigational information provided by natural scenes.

PubMed

Shamsyeh Zahedi, Moosarreza; Zeil, Jochen

2018-01-01

Recent work on virtual reality navigation in humans has suggested that navigational success is inversely correlated with the fractal dimension (FD) of artificial scenes. Here we investigate the generality of this claim by analysing the relationship between the fractal dimension of natural insect navigation environments and a quantitative measure of the navigational information content of natural scenes. We show that the fractal dimension of natural scenes is in general inversely proportional to the information they provide to navigating agents on heading direction as measured by the rotational image difference function (rotIDF). The rotIDF determines the precision and accuracy with which the orientation of a reference image can be recovered or maintained and the range over which a gradient descent in image differences will find the minimum of the rotIDF, that is the reference orientation. However, scenes with similar fractal dimension can differ significantly in the depth of the rotIDF, because FD does not discriminate between the orientations of edges, while the rotIDF is mainly affected by edge orientation parallel to the axis of rotation. We present a new equation for the rotIDF relating navigational information to quantifiable image properties such as contrast to show (1) that for any given scene the maximum value of the rotIDF (its depth) is proportional to pixel variance and (2) that FD is inversely proportional to pixel variance. This contrast dependence, together with scene differences in orientation statistics, explains why there is no strict relationship between FD and navigational information. Our experimental data and their numerical analysis corroborate these results.

Surface Fractal Analysis for Estimating the Fracture Energy Absorption of Nanoparticle Reinforced Composites

PubMed Central

Pramanik, Brahmananda; Tadepalli, Tezeswi; Mantena, P. Raju

2012-01-01

In this study, the fractal dimensions of failure surfaces of vinyl ester based nanocomposites are estimated using two classical methods, Vertical Section Method (VSM) and Slit Island Method (SIM), based on the processing of 3D digital microscopic images. Self-affine fractal geometry has been observed in the experimentally obtained failure surfaces of graphite platelet reinforced nanocomposites subjected to quasi-static uniaxial tensile and low velocity punch-shear loading. Fracture energy and fracture toughness are estimated analytically from the surface fractal dimensionality. Sensitivity studies show an exponential dependency of fracture energy and fracture toughness on the fractal dimensionality. Contribution of fracture energy to the total energy absorption of these nanoparticle reinforced composites is demonstrated. For the graphite platelet reinforced nanocomposites investigated, surface fractal analysis has depicted the probable ductile or brittle fracture propagation mechanism, depending upon the rate of loading. PMID:28817017

Focusing behavior of the fractal vector optical fields designed by fractal lattice growth model.

PubMed

Gao, Xu-Zhen; Pan, Yue; Zhao, Meng-Dan; Zhang, Guan-Lin; Zhang, Yu; Tu, Chenghou; Li, Yongnan; Wang, Hui-Tian

2018-01-22

We introduce a general fractal lattice growth model, significantly expanding the application scope of the fractal in the realm of optics. This model can be applied to construct various kinds of fractal "lattices" and then to achieve the design of a great diversity of fractal vector optical fields (F-VOFs) combinating with various "bases". We also experimentally generate the F-VOFs and explore their universal focusing behaviors. Multiple focal spots can be flexibly enginnered, and the optical tweezers experiment validates the simulated tight focusing fields, which means that this model allows the diversity of the focal patterns to flexibly trap and manipulate micrometer-sized particles. Furthermore, the recovery performance of the F-VOFs is also studied when the input fields and spatial frequency spectrum are obstructed, and the results confirm the robustness of the F-VOFs in both focusing and imaging processes, which is very useful in information transmission.

A brief discussion about image quality and SEM methods for quantitative fractography of polymer composites.

PubMed

Hein, L R O; Campos, K A; Caltabiano, P C R O; Kostov, K G

2013-01-01

The methodology for fracture analysis of polymeric composites with scanning electron microscopes (SEM) is still under discussion. Many authors prefer to use sputter coating with a conductive material instead of applying low-voltage (LV) or variable-pressure (VP) methods, which preserves the original surfaces. The present work examines the effects of sputter coating with 25 nm of gold on the topography of carbon-epoxy composites fracture surfaces, using an atomic force microscope. Also, the influence of SEM imaging parameters on fractal measurements is evaluated for the VP-SEM and LV-SEM methods. It was observed that topographic measurements were not significantly affected by the gold coating at tested scale. Moreover, changes on SEM setup leads to nonlinear outcome on texture parameters, such as fractal dimension and entropy values. For VP-SEM or LV-SEM, fractal dimension and entropy values did not present any evident relation with image quality parameters, but the resolution must be optimized with imaging setup, accompanied by charge neutralization. © Wiley Periodicals, Inc.

A Complex Story: Universal Preference vs. Individual Differences Shaping Aesthetic Response to Fractals Patterns.

PubMed

Street, Nichola; Forsythe, Alexandra M; Reilly, Ronan; Taylor, Richard; Helmy, Mai S

2016-01-01

Fractal patterns offer one way to represent the rough complexity of the natural world. Whilst they dominate many of our visual experiences in nature, little large-scale perceptual research has been done to explore how we respond aesthetically to these patterns. Previous research (Taylor et al., 2011) suggests that the fractal patterns with mid-range fractal dimensions (FDs) have universal aesthetic appeal. Perceptual and aesthetic responses to visual complexity have been more varied with findings suggesting both linear (Forsythe et al., 2011) and curvilinear (Berlyne, 1970) relationships. Individual differences have been found to account for many of the differences we see in aesthetic responses but some, such as culture, have received little attention within the fractal and complexity research fields. This two-study article aims to test preference responses to FD and visual complexity, using a large cohort (N = 443) of participants from around the world to allow universality claims to be tested. It explores the extent to which age, culture and gender can predict our preferences for fractally complex patterns. Following exploratory analysis that found strong correlations between FD and visual complexity, a series of linear mixed-effect models were implemented to explore if each of the individual variables could predict preference. The first tested a linear complexity model (likelihood of selecting the more complex image from the pair of images) and the second a mid-range FD model (likelihood of selecting an image within mid-range). Results show that individual differences can reliably predict preferences for complexity across culture, gender and age. However, in fitting with current findings the mid-range models show greater consistency in preference not mediated by gender, age or culture. This article supports the established theory that the mid-range fractal patterns appear to be a universal construct underlying preference but also highlights the fragility of universal claims by demonstrating individual differences in preference for the interrelated concept of visual complexity. This highlights a current stalemate in the field of empirical aesthetics.

Hyper-Fractal Analysis: A visual tool for estimating the fractal dimension of 4D objects

NASA Astrophysics Data System (ADS)

Grossu, I. V.; Grossu, I.; Felea, D.; Besliu, C.; Jipa, Al.; Esanu, T.; Bordeianu, C. C.; Stan, E.

2013-04-01

This work presents a new version of a Visual Basic 6.0 application for estimating the fractal dimension of images and 3D objects (Grossu et al. (2010) [1]). The program was extended for working with four-dimensional objects stored in comma separated values files. This might be of interest in biomedicine, for analyzing the evolution in time of three-dimensional images. New version program summaryProgram title: Hyper-Fractal Analysis (Fractal Analysis v03) Catalogue identifier: AEEG_v3_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEEG_v3_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC license, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 745761 No. of bytes in distributed program, including test data, etc.: 12544491 Distribution format: tar.gz Programming language: MS Visual Basic 6.0 Computer: PC Operating system: MS Windows 98 or later RAM: 100M Classification: 14 Catalogue identifier of previous version: AEEG_v2_0 Journal reference of previous version: Comput. Phys. Comm. 181 (2010) 831-832 Does the new version supersede the previous version? Yes Nature of problem: Estimating the fractal dimension of 4D images. Solution method: Optimized implementation of the 4D box-counting algorithm. Reasons for new version: Inspired by existing applications of 3D fractals in biomedicine [3], we extended the optimized version of the box-counting algorithm [1, 2] to the four-dimensional case. This might be of interest in analyzing the evolution in time of 3D images. The box-counting algorithm was extended in order to support 4D objects, stored in comma separated values files. A new form was added for generating 2D, 3D, and 4D test data. The application was tested on 4D objects with known dimension, e.g. the Sierpinski hypertetrahedron gasket, Df=ln(5)/ln(2) (Fig. 1). The algorithm could be extended, with minimum effort, to higher number of dimensions. Easy integration with other applications by using the very simple comma separated values file format for storing multi-dimensional images. Implementation of χ2 test as a criterion for deciding whether an object is fractal or not. User friendly graphical interface. Hyper-Fractal Analysis-Test on the Sierpinski hypertetrahedron 4D gasket (Df=ln(5)/ln(2)≅2.32). Running time: In a first approximation, the algorithm is linear [2]. References: [1] V. Grossu, D. Felea, C. Besliu, Al. Jipa, C.C. Bordeianu, E. Stan, T. Esanu, Computer Physics Communications, 181 (2010) 831-832. [2] I.V. Grossu, C. Besliu, M.V. Rusu, Al. Jipa, C. C. Bordeianu, D. Felea, Computer Physics Communications, 180 (2009) 1999-2001. [3] J. Ruiz de Miras, J. Navas, P. Villoslada, F.J. Esteban, Computer Methods and Programs in Biomedicine, 104 Issue 3 (2011) 452-460.

Zone specific fractal dimension of retinal images as predictor of stroke incidence.

PubMed

Aliahmad, Behzad; Kumar, Dinesh Kant; Hao, Hao; Unnikrishnan, Premith; Che Azemin, Mohd Zulfaezal; Kawasaki, Ryo; Mitchell, Paul

2014-01-01

Fractal dimensions (FDs) are frequently used for summarizing the complexity of retinal vascular. However, previous techniques on this topic were not zone specific. A new methodology to measure FD of a specific zone in retinal images has been developed and tested as a marker for stroke prediction. Higuchi's fractal dimension was measured in circumferential direction (FDC) with respect to optic disk (OD), in three concentric regions between OD boundary and 1.5 OD diameter from its margin. The significance of its association with future episode of stroke event was tested using the Blue Mountain Eye Study (BMES) database and compared against spectrum fractal dimension (SFD) and box-counting (BC) dimension. Kruskal-Wallis analysis revealed FDC as a better predictor of stroke (H = 5.80, P = 0.016, α = 0.05) compared with SFD (H = 0.51, P = 0.475, α = 0.05) and BC (H = 0.41, P = 0.520, α = 0.05) with overall lower median value for the cases compared to the control group. This work has shown that there is a significant association between zone specific FDC of eye fundus images with future episode of stroke while this difference is not significant when other FD methods are employed.

Fractal analysis of Xylella fastidiosa biofilm formation

NASA Astrophysics Data System (ADS)

Moreau, A. L. D.; Lorite, G. S.; Rodrigues, C. M.; Souza, A. A.; Cotta, M. A.

2009-07-01

We have investigated the growth process of Xylella fastidiosa biofilms inoculated on a glass. The size and the distance between biofilms were analyzed by optical images; a fractal analysis was carried out using scaling concepts and atomic force microscopy images. We observed that different biofilms show similar fractal characteristics, although morphological variations can be identified for different biofilm stages. Two types of structural patterns are suggested from the observed fractal dimensions Df. In the initial and final stages of biofilm formation, Df is 2.73±0.06 and 2.68±0.06, respectively, while in the maturation stage, Df=2.57±0.08. These values suggest that the biofilm growth can be understood as an Eden model in the former case, while diffusion-limited aggregation (DLA) seems to dominate the maturation stage. Changes in the correlation length parallel to the surface were also observed; these results were correlated with the biofilm matrix formation, which can hinder nutrient diffusion and thus create conditions to drive DLA growth.

Using Fractal And Morphological Criteria For Automatic Classification Of Lung Diseases

NASA Astrophysics Data System (ADS)

Vehel, Jacques Levy

1989-11-01

Medical Images are difficult to analyze by means of classical image processing tools because they are very complex and irregular. Such shapes are obtained for instance in Nuclear Medecine with the spatial distribution of activity for organs such as lungs, liver, and heart. We have tried to apply two different theories to these signals: - Fractal Geometry deals with the analysis of complex irregular shapes which cannot well be described by the classical Euclidean geometry. - Integral Geometry treats sets globally and allows to introduce robust measures. We have computed three parameters on three kinds of Lung's SPECT images: normal, pulmonary embolism and chronic desease: - The commonly used fractal dimension (FD), that gives a measurement of the irregularity of the 3D shape. - The generalized lacunarity dimension (GLD), defined as the variance of the ratio of the local activity by the mean activity, which is only sensitive to the distribution and the size of gaps in the surface. - The Favard length that gives an approximation of the surface of a 3-D shape. The results show that each slice of the lung, considered as a 3D surface, is fractal and that the fractal dimension is the same for each slice and for the three kind of lungs; as for the lacunarity and Favard length, they are clearly different for normal lungs, pulmonary embolisms and chronic diseases. These results indicate that automatic classification of Lung's SPECT can be achieved, and that a quantitative measurement of the evolution of the disease could be made.

Heterogeneity of Glucose Metabolism in Esophageal Cancer Measured by Fractal Analysis of Fluorodeoxyglucose Positron Emission Tomography Image: Correlation between Metabolic Heterogeneity and Survival.

PubMed

Tochigi, Toru; Shuto, Kiyohiko; Kono, Tsuguaki; Ohira, Gaku; Tohma, Takayuki; Gunji, Hisashi; Hayano, Koichi; Narushima, Kazuo; Fujishiro, Takeshi; Hanaoka, Toshiharu; Akutsu, Yasunori; Okazumi, Shinichi; Matsubara, Hisahiro

2017-01-01

Intratumoral heterogeneity is a well-recognized characteristic feature of cancer. The purpose of this study is to assess the heterogeneity of the intratumoral glucose metabolism using fractal analysis, and evaluate its prognostic value in patients with esophageal squamous cell carcinoma (ESCC). 18F-fluorodeoxyglucose positron emission tomography (FDG-PET) studies of 79 patients who received curative surgery were evaluated. FDG-PET images were analyzed using fractal analysis software, where differential box-counting method was employed to calculate the fractal dimension (FD) of the tumor lesion. Maximum standardized uptake value (SUVmax) and FD were compared with overall survival (OS). The median SUVmax and FD of ESCCs in this cohort were 13.8 and 1.95, respectively. In univariate analysis performed using Cox's proportional hazard model, T stage and FD showed significant associations with OS (p = 0.04, p < 0.0001, respectively), while SUVmax did not (p = 0.1). In Kaplan-Meier analysis, the low FD tumor (<1.95) showed a significant association with favorable OS (p < 0.0001). In wthe multivariate analysis among TNM staging, serum tumor markers, FD, and SUVmax, the FD was identified as the only independent prognostic factor for OS (p = 0.0006; hazards ratio 0.251, 95% CI 0.104-0.562). Metabolic heterogeneity measured by fractal analysis can be a novel imaging biomarker for survival in patients with ESCC. © 2016 S. Karger AG, Basel.

Depth of focus enhancement of a modified imaging quasi-fractal zone plate.

PubMed

Zhang, Qinqin; Wang, Jingang; Wang, Mingwei; Bu, Jing; Zhu, Siwei; Gao, Bruce Z; Yuan, Xiaocong

2012-10-01

We propose a new parameter w for optimization of foci distribution of conventional fractal zone plates (FZPs) with a greater depth of focus (DOF) in imaging. Numerical simulations of DOF distribution on axis directions indicate that the values of DOF can be extended by a factor of 1.5 or more by a modified quasi-FZP. In experiments, we employ a simple object-lens-image-plane arrangement to pick up images at various positions within the DOF of a conventional FZP and a quasi-FZP, respectively. Experimental results show that the parameter w improves foci distribution of FZPs in good agreement with theoretical predictions.

Depth of focus enhancement of a modified imaging quasi-fractal zone plate

PubMed Central

Zhang, Qinqin; Wang, Jingang; Wang, Mingwei; Bu, Jing; Zhu, Siwei; Gao, Bruce Z.; Yuan, Xiaocong

2013-01-01

We propose a new parameter w for optimization of foci distribution of conventional fractal zone plates (FZPs) with a greater depth of focus (DOF) in imaging. Numerical simulations of DOF distribution on axis directions indicate that the values of DOF can be extended by a factor of 1.5 or more by a modified quasi-FZP. In experiments, we employ a simple object–lens–image-plane arrangement to pick up images at various positions within the DOF of a conventional FZP and a quasi-FZP, respectively. Experimental results show that the parameter w improves foci distribution of FZPs in good agreement with theoretical predictions. PMID:24285908

Classification of diabetic retinopathy using fractal dimension analysis of eye fundus image

NASA Astrophysics Data System (ADS)

Safitri, Diah Wahyu; Juniati, Dwi

2017-08-01

Diabetes Mellitus (DM) is a metabolic disorder when pancreas produce inadequate insulin or a condition when body resist insulin action, so the blood glucose level is high. One of the most common complications of diabetes mellitus is diabetic retinopathy which can lead to a vision problem. Diabetic retinopathy can be recognized by an abnormality in eye fundus. Those abnormalities are characterized by microaneurysms, hemorrhage, hard exudate, cotton wool spots, and venous's changes. The diabetic retinopathy is classified depends on the conditions of abnormality in eye fundus, that is grade 1 if there is a microaneurysm only in the eye fundus; grade 2, if there are a microaneurysm and a hemorrhage in eye fundus; and grade 3: if there are microaneurysm, hemorrhage, and neovascularization in the eye fundus. This study proposed a method and a process of eye fundus image to classify of diabetic retinopathy using fractal analysis and K-Nearest Neighbor (KNN). The first phase was image segmentation process using green channel, CLAHE, morphological opening, matched filter, masking, and morphological opening binary image. After segmentation process, its fractal dimension was calculated using box-counting method and the values of fractal dimension were analyzed to make a classification of diabetic retinopathy. Tests carried out by used k-fold cross validation method with k=5. In each test used 10 different grade K of KNN. The accuracy of the result of this method is 89,17% with K=3 or K=4, it was the best results than others K value. Based on this results, it can be concluded that the classification of diabetic retinopathy using fractal analysis and KNN had a good performance.

Fractal analysis of scatter imaging signatures to distinguish breast pathologies

NASA Astrophysics Data System (ADS)

Eguizabal, Alma; Laughney, Ashley M.; Krishnaswamy, Venkataramanan; Wells, Wendy A.; Paulsen, Keith D.; Pogue, Brian W.; López-Higuera, José M.; Conde, Olga M.

2013-02-01

Fractal analysis combined with a label-free scattering technique is proposed for describing the pathological architecture of tumors. Clinicians and pathologists are conventionally trained to classify abnormal features such as structural irregularities or high indices of mitosis. The potential of fractal analysis lies in the fact of being a morphometric measure of the irregular structures providing a measure of the object's complexity and self-similarity. As cancer is characterized by disorder and irregularity in tissues, this measure could be related to tumor growth. Fractal analysis has been probed in the understanding of the tumor vasculature network. This work addresses the feasibility of applying fractal analysis to the scattering power map (as a physical modeling) and principal components (as a statistical modeling) provided by a localized reflectance spectroscopic system. Disorder, irregularity and cell size variation in tissue samples is translated into the scattering power and principal components magnitude and its fractal dimension is correlated with the pathologist assessment of the samples. The fractal dimension is computed applying the box-counting technique. Results show that fractal analysis of ex-vivo fresh tissue samples exhibits separated ranges of fractal dimension that could help classifier combining the fractal results with other morphological features. This contrast trend would help in the discrimination of tissues in the intraoperative context and may serve as a useful adjunct to surgeons.

Applications of fractals in ecology.

PubMed

Sugihara, G; M May, R

1990-03-01

Fractal models describe the geometry of a wide variety of natural objects such as coastlines, island chains, coral reefs, satellite ocean-color images and patches of vegetation. Cast in the form of modified diffusion models, they can mimic natural and artificial landscapes having different types of complexity of shape. This article provides a brief introduction to fractals and reports on how they can be used by ecologists to answer a variety of basic questions, about scale, measurement and hierarchy in, ecological systems. Copyright © 1990. Published by Elsevier Ltd.

[Lithology feature extraction of CASI hyperspectral data based on fractal signal algorithm].

PubMed

Tang, Chao; Chen, Jian-Ping; Cui, Jing; Wen, Bo-Tao

2014-05-01

Hyperspectral data is characterized by combination of image and spectrum and large data volume dimension reduction is the main research direction. Band selection and feature extraction is the primary method used for this objective. In the present article, the authors tested methods applied for the lithology feature extraction from hyperspectral data. Based on the self-similarity of hyperspectral data, the authors explored the application of fractal algorithm to lithology feature extraction from CASI hyperspectral data. The "carpet method" was corrected and then applied to calculate the fractal value of every pixel in the hyperspectral data. The results show that fractal information highlights the exposed bedrock lithology better than the original hyperspectral data The fractal signal and characterized scale are influenced by the spectral curve shape, the initial scale selection and iteration step. At present, research on the fractal signal of spectral curve is rare, implying the necessity of further quantitative analysis and investigation of its physical implications.

The Plasma Membrane is Compartmentalized by a Self-Similar Cortical Actin Fractal

NASA Astrophysics Data System (ADS)

Sadegh, Sanaz; Higgin, Jenny; Mannion, Patrick; Tamkun, Michael; Krapf, Diego

A broad range of membrane proteins display anomalous diffusion on the cell surface. Different methods provide evidence for obstructed subdiffusion and diffusion on a fractal space, but the underlying structure inducing anomalous diffusion has never been visualized due to experimental challenges. We addressed this problem by imaging the cortical actin at high resolution while simultaneously tracking individual membrane proteins in live mammalian cells. Our data show that actin introduces barriers leading to compartmentalization of the plasma membrane and that membrane proteins are transiently confined within actin fences. Furthermore, superresolution imaging shows that the cortical actin is organized into a self-similar fractal. These results present a hierarchical nanoscale picture of the plasma membrane and demonstrate direct interactions between the actin cortex and the cell surface.

Predicting beauty: fractal dimension and visual complexity in art.

PubMed

Forsythe, A; Nadal, M; Sheehy, N; Cela-Conde, C J; Sawey, M

2011-02-01

Visual complexity has been known to be a significant predictor of preference for artistic works for some time. The first study reported here examines the extent to which perceived visual complexity in art can be successfully predicted using automated measures of complexity. Contrary to previous findings the most successful predictor of visual complexity was Gif compression. The second study examined the extent to which fractal dimension could account for judgments of perceived beauty. The fractal dimension measure accounts for more of the variance in judgments of perceived beauty in visual art than measures of visual complexity alone, particularly for abstract and natural images. Results also suggest that when colour is removed from an artistic image observers are unable to make meaningful judgments as to its beauty. ©2010 The British Psychological Society.

Jupiter Fractal Art

NASA Image and Video Library

2017-08-10

See Jupiter's Great Red Spot as you've never seen it before in this new Jovian work of art. Artist Mik Petter created this unique, digital artwork using data from the JunoCam imager on NASA's Juno spacecraft. The art form, known as fractals, uses mathematical formulas to create art with an infinite variety of form, detail, color and light. The tumultuous atmospheric zones in and around the Great Red Spot are highlighted by the author's use of colorful fractals. Vibrant colors of various tints and hues, combined with the almost organic-seeming shapes, make this image seem to be a colorized and crowded petri dish of microorganisms, or a close-up view of microscopic and wildly-painted seashells. The original JunoCam image was taken on July 10, 2017 at 7:10 p.m. PDT (10:10 p.m. EDT), as the Juno spacecraft performed its seventh close flyby of Jupiter. The spacecraft captured the image from about 8,648 miles (13,917 kilometers) above the tops of the clouds of the planet at a latitude of -32.6 degrees. https://photojournal.jpl.nasa.gov/catalog/PIA21777

Characterization of microgravity effects on bone structure and strength using fractal analysis

NASA Technical Reports Server (NTRS)

Acharya, Raj S.; Shackelford, Linda

1995-01-01

The effect of micro-gravity on the musculoskeletal system has been well studied. Significant changes in bone and muscle have been shown after long term space flight. Similar changes have been demonstrated due to bed rest. Bone demineralization is particularly profound in weight bearing bones. Much of the current techniques to monitor bone condition use bone mass measurements. However, bone mass measurements are not reliable to distinguish Osteoporotic and Normal subjects. It has been shown that the overlap between normals and osteoporosis is found for all of the bone mass measurement technologies: single and dual photon absorptiometry, quantitative computed tomography and direct measurement of bone area/volume on biopsy as well as radiogrammetry. A similar discordance is noted in the fact that it has not been regularly possible to find the expected correlation between severity of osteoporosis and degree of bone loss. Structural parameters such as trabecular connectivity have been proposed as features for assessing bone conditions. In this report, we use fractal analysis to characterize bone structure. We show that the fractal dimension computed with MRI images and X-Ray images of the patella are the same. Preliminary experimental results show that the fractal dimension computed from MRI images of vertebrae of human subjects before bedrest is higher than during bedrest.

Visual tool for estimating the fractal dimension of images

NASA Astrophysics Data System (ADS)

Grossu, I. V.; Besliu, C.; Rusu, M. V.; Jipa, Al.; Bordeianu, C. C.; Felea, D.

2009-10-01

This work presents a new Visual Basic 6.0 application for estimating the fractal dimension of images, based on an optimized version of the box-counting algorithm. Following the attempt to separate the real information from "noise", we considered also the family of all band-pass filters with the same band-width (specified as parameter). The fractal dimension can be thus represented as a function of the pixel color code. The program was used for the study of paintings cracks, as an additional tool which can help the critic to decide if an artistic work is original or not. Program summaryProgram title: Fractal Analysis v01 Catalogue identifier: AEEG_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEEG_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 29 690 No. of bytes in distributed program, including test data, etc.: 4 967 319 Distribution format: tar.gz Programming language: MS Visual Basic 6.0 Computer: PC Operating system: MS Windows 98 or later RAM: 30M Classification: 14 Nature of problem: Estimating the fractal dimension of images. Solution method: Optimized implementation of the box-counting algorithm. Use of a band-pass filter for separating the real information from "noise". User friendly graphical interface. Restrictions: Although various file-types can be used, the application was mainly conceived for the 8-bit grayscale, windows bitmap file format. Running time: In a first approximation, the algorithm is linear.

Temporal and spatial variation of morphological descriptors for atmospheric aerosols collected in Mexico City

NASA Astrophysics Data System (ADS)

China, S.; Mazzoleni, C.; Dubey, M. K.; Chakrabarty, R. K.; Moosmuller, H.; Onasch, T. B.; Herndon, S. C.

2010-12-01

We present an analysis of morphological characteristics of atmospheric aerosol collected during the MILAGRO (Megacity Initiative: Local and Global Research Observations) field campaign that took place in Mexico City in March 2006. The sampler was installed on the Aerodyne mobile laboratory. The aerosol samples were collected on nuclepore clear polycarbonate filters mounted in Costar pop-top membrane holders. More than one hundred filters were collected at different ground sites with different atmospheric and geographical characteristics (urban, sub-urban, mountain-top, industrial, etc.) over a month period. Selected subsets of these filters were analyzed for aerosol morphology using a scanning electron microscope and image analysis techniques. In this study we investigate spatial and temporal variations of aerosol shape descriptors, morphological parameters, and fractal dimension. We also compare the morphological results with other aerosol measurements such as aerosol optical properties(scattering and absorption) and size distribution data. Atmospheric aerosols have different morphological characteristics depending on many parameters such as emission sources, atmospheric formation pathways, aging processes, and aerosol mixing state. The aerosol morphology influences aerosol chemical and mechanical interactions with the environment, physical properties, and radiative effects. In this study, ambient aerosol particles have been classified in different shape groups as spherical, irregularly shaped, and fractal-like aggregates. Different morphological parameters such as aspect ratio, roundness, feret diameter, etc. have been estimated for irregular shaped and spherical particles and for different kinds of soot particles including fresh soot, collapsed and coated soot. Fractal geometry and image processing have been used to obtain morphological characteristics of different soot particles. The number of monomers constituting each aggregate and their diameters were measured and used to estimate an ensemble three-dimensional (3-d) fractal dimension. One-dimensional (1-d) and two-dimensional (2-d) fractal geometries have been measured using a power-law scaling relationship between 1-d and 2-d properties of projected images. Temporal variations in fractal dimension of soot-like aggregates have been observed at the mountaintop site and spatial variation of fractal dimension and other morphological descriptors of different shaped particles have been investigated for the different ground sites.

A Complex Story: Universal Preference vs. Individual Differences Shaping Aesthetic Response to Fractals Patterns

PubMed Central

Street, Nichola; Forsythe, Alexandra M.; Reilly, Ronan; Taylor, Richard; Helmy, Mai S.

2016-01-01

Fractal patterns offer one way to represent the rough complexity of the natural world. Whilst they dominate many of our visual experiences in nature, little large-scale perceptual research has been done to explore how we respond aesthetically to these patterns. Previous research (Taylor et al., 2011) suggests that the fractal patterns with mid-range fractal dimensions (FDs) have universal aesthetic appeal. Perceptual and aesthetic responses to visual complexity have been more varied with findings suggesting both linear (Forsythe et al., 2011) and curvilinear (Berlyne, 1970) relationships. Individual differences have been found to account for many of the differences we see in aesthetic responses but some, such as culture, have received little attention within the fractal and complexity research fields. This two-study article aims to test preference responses to FD and visual complexity, using a large cohort (N = 443) of participants from around the world to allow universality claims to be tested. It explores the extent to which age, culture and gender can predict our preferences for fractally complex patterns. Following exploratory analysis that found strong correlations between FD and visual complexity, a series of linear mixed-effect models were implemented to explore if each of the individual variables could predict preference. The first tested a linear complexity model (likelihood of selecting the more complex image from the pair of images) and the second a mid-range FD model (likelihood of selecting an image within mid-range). Results show that individual differences can reliably predict preferences for complexity across culture, gender and age. However, in fitting with current findings the mid-range models show greater consistency in preference not mediated by gender, age or culture. This article supports the established theory that the mid-range fractal patterns appear to be a universal construct underlying preference but also highlights the fragility of universal claims by demonstrating individual differences in preference for the interrelated concept of visual complexity. This highlights a current stalemate in the field of empirical aesthetics. PMID:27252634

Turbulence Enhancement by Fractal Square Grids: Effects of the Number of Fractal Scales

NASA Astrophysics Data System (ADS)

Omilion, Alexis; Ibrahim, Mounir; Zhang, Wei

2017-11-01

Fractal square grids offer a unique solution for passive flow control as they can produce wakes with a distinct turbulence intensity peak and a prolonged turbulence decay region at the expense of only minimal pressure drop. While previous studies have solidified this characteristic of fractal square grids, how the number of scales (or fractal iterations N) affect turbulence production and decay of the induced wake is still not well understood. The focus of this research is to determine the relationship between the fractal iteration N and the turbulence produced in the wake flow using well-controlled water-tunnel experiments. Particle Image Velocimetry (PIV) is used to measure the instantaneous velocity fields downstream of four different fractal grids with increasing number of scales (N = 1, 2, 3, and 4) and a conventional single-scale grid. By comparing the turbulent scales and statistics of the wake, we are able to determine how each iteration affects the peak turbulence intensity and the production/decay of turbulence from the grid. In light of the ability of these fractal grids to increase turbulence intensity with low pressure drop, this work can potentially benefit a wide variety of applications where energy efficient mixing or convective heat transfer is a key process.

Fractal characterization and wettability of ion treated silicon surfaces

NASA Astrophysics Data System (ADS)

Yadav, R. P.; Kumar, Tanuj; Baranwal, V.; Vandana, Kumar, Manvendra; Priya, P. K.; Pandey, S. N.; Mittal, A. K.

2017-02-01

Fractal characterization of surface morphology can be useful as a tool for tailoring the wetting properties of solid surfaces. In this work, rippled surfaces of Si (100) are grown using 200 keV Ar+ ion beam irradiation at different ion doses. Relationship between fractal and wetting properties of these surfaces are explored. The height-height correlation function extracted from atomic force microscopic images, demonstrates an increase in roughness exponent with an increase in ion doses. A steep variation in contact angle values is found for low fractal dimensions. Roughness exponent and fractal dimensions are found correlated with the static water contact angle measurement. It is observed that after a crossover of the roughness exponent, the surface morphology has a rippled structure. Larger values of interface width indicate the larger ripples on the surface. The contact angle of water drops on such surfaces is observed to be lowest. Autocorrelation function is used for the measurement of ripple wavelength.

A new set of wavelet- and fractals-based features for Gleason grading of prostate cancer histopathology images

NASA Astrophysics Data System (ADS)

Mosquera Lopez, Clara; Agaian, Sos

2013-02-01

Prostate cancer detection and staging is an important step towards patient treatment selection. Advancements in digital pathology allow the application of new quantitative image analysis algorithms for computer-assisted diagnosis (CAD) on digitized histopathology images. In this paper, we introduce a new set of features to automatically grade pathological images using the well-known Gleason grading system. The goal of this study is to classify biopsy images belonging to Gleason patterns 3, 4, and 5 by using a combination of wavelet and fractal features. For image classification we use pairwise coupling Support Vector Machine (SVM) classifiers. The accuracy of the system, which is close to 97%, is estimated through three different cross-validation schemes. The proposed system offers the potential for automating classification of histological images and supporting prostate cancer diagnosis.

Fractal Dimensionality of Pore and Grain Volume of a Siliciclastic Marine Sand

NASA Astrophysics Data System (ADS)

Reed, A. H.; Pandey, R. B.; Lavoie, D. L.

Three-dimensional (3D) spatial distributions of pore and grain volumes were determined from high-resolution computer tomography (CT) images of resin-impregnated marine sands. Using a linear gradient extrapolation method, cubic three-dimensional samples were constructed from two-dimensional CT images. Image porosity (0.37) was found to be consistent with the estimate of porosity by water weight loss technique (0.36). Scaling of the pore volume (Vp) with the linear size (L), V~LD provides the fractal dimensionalities of the pore volume (D=2.74+/-0.02) and grain volume (D=2.90+/-0.02) typical for sedimentary materials.

Fractal evaluation of drug amorphicity from optical and scanning electron microscope images

NASA Astrophysics Data System (ADS)

Gavriloaia, Bogdan-Mihai G.; Vizireanu, Radu C.; Neamtu, Catalin I.; Gavriloaia, Gheorghe V.

2013-09-01

Amorphous materials are metastable, more reactive than the crystalline ones, and have to be evaluated before pharmaceutical compound formulation. Amorphicity is interpreted as a spatial chaos, and patterns of molecular aggregates of dexamethasone, D, were investigated in this paper by using fractal dimension, FD. Images having three magnifications of D were taken from an optical microscope, OM, and with eight magnifications, from a scanning electron microscope, SEM, were analyzed. The average FD for pattern irregularities of OM images was 1.538, and about 1.692 for SEM images. The FDs of the two kinds of images are less sensitive of threshold level. 3D images were shown to illustrate dependence of FD of threshold and magnification level. As a result, optical image of single scale is enough to characterize the drug amorphicity. As a result, the OM image at a single scale is enough to characterize the amorphicity of D.

Higuchi Dimension of Digital Images

PubMed Central

Ahammer, Helmut

2011-01-01

There exist several methods for calculating the fractal dimension of objects represented as 2D digital images. For example, Box counting, Minkowski dilation or Fourier analysis can be employed. However, there appear to be some limitations. It is not possible to calculate only the fractal dimension of an irregular region of interest in an image or to perform the calculations in a particular direction along a line on an arbitrary angle through the image. The calculations must be made for the whole image. In this paper, a new method to overcome these limitations is proposed. 2D images are appropriately prepared in order to apply 1D signal analyses, originally developed to investigate nonlinear time series. The Higuchi dimension of these 1D signals is calculated using Higuchi's algorithm, and it is shown that both regions of interests and directional dependencies can be evaluated independently of the whole picture. A thorough validation of the proposed technique and a comparison of the new method to the Fourier dimension, a common two dimensional method for digital images, are given. The main result is that Higuchi's algorithm allows a direction dependent as well as direction independent analysis. Actual values for the fractal dimensions are reliable and an effective treatment of regions of interests is possible. Moreover, the proposed method is not restricted to Higuchi's algorithm, as any 1D method of analysis, can be applied. PMID:21931854

Mathematical morphology for automated analysis of remotely sensed objects in radar images

NASA Technical Reports Server (NTRS)

Daida, Jason M.; Vesecky, John F.

1991-01-01

A symbiosis of pyramidal segmentation and morphological transmission is described. The pyramidal segmentation portion of the symbiosis has resulted in low (2.6 percent) misclassification error rate for a one-look simulation. Other simulations indicate lower error rates (1.8 percent for a four-look image). The morphological transformation portion has resulted in meaningful partitions with a minimal loss of fractal boundary information. An unpublished version of Thicken, suitable for watersheds transformations of fractal objects, is also presented. It is demonstrated that the proposed symbiosis works with SAR (synthetic aperture radar) images: in this case, a four-look Seasat image of sea ice. It is concluded that the symbiotic forms of both segmentation and morphological transformation seem well suited for unsupervised geophysical analysis.

Alpha-spectrometry and fractal analysis of surface micro-images for characterisation of porous materials used in manufacture of targets for laser plasma experiments

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

Aushev, A A; Barinov, S P; Vasin, M G

2015-06-30

We present the results of employing the alpha-spectrometry method to determine the characteristics of porous materials used in targets for laser plasma experiments. It is shown that the energy spectrum of alpha-particles, after their passage through porous samples, allows one to determine the distribution of their path length in the foam skeleton. We describe the procedure of deriving such a distribution, excluding both the distribution broadening due to statistical nature of the alpha-particle interaction with an atomic structure (straggling) and hardware effects. The fractal analysis of micro-images is applied to the same porous surface samples that have been studied bymore » alpha-spectrometry. The fractal dimension and size distribution of the number of the foam skeleton grains are obtained. Using the data obtained, a distribution of the total foam skeleton thickness along a chosen direction is constructed. It roughly coincides with the path length distribution of alpha-particles within a range of larger path lengths. It is concluded that the combined use of the alpha-spectrometry method and fractal analysis of images will make it possible to determine the size distribution of foam skeleton grains (or pores). The results can be used as initial data in theoretical studies on propagation of the laser and X-ray radiation in specific porous samples. (laser plasma)« less

Assessment of changes in crystallization properties of pressurized milk fat.

PubMed

Staniewski, Bogusław; Smoczyński, Michał; Staniewska, Katarzyna; Baranowska, Maria; Kiełczewska, Katarzyna; Zulewska, Justyna

2015-04-01

The aim of the study was to demonstrate the use of fractal image analysis as a possible tool to monitor the effect of pressurization on the crystallization pattern of anhydrous milk fat. This approach can be useful when developing new products based on milk fat. The samples were subjected to different hydrostatic pressure (100, 200, 300, and 400 MPa) and temperature (10 and 40 °C) treatments. The crystallization microphotographs were taken with a scanning electron microscope. The image analysis of scanning electron microscope photographs was done to determine a fractal dimension. Milk-fat pressurization under the applied parameters resulted in slight, but statistically significant, changes in the course of crystallization curves, related to the triacylglycerol fraction crystallizing in the lowest temperature (I exothermic effect). These changes were dependent on the value of pressure but not dependent on the temperatures applied during the process of pressurization (at either 10 or 40 °C). In turn, significant differences were observed in crystallization images of milk-fat samples subjected to this process compared with the control sample. The results of additional fractal analysis additionally demonstrated the highest degree of irregularity of the surface of the crystalline form for the nonpressurized sample and the samples pressurized at 200 and 300 MPa at 10 °C. The lowest value of fractal dimension-indicative of the least irregularity-was achieved for the fat samples pressurized at 400 MPa, 10 °C and at 100 MPa, 40 °C. The possibilities of wider application of the fractal analysis for the evaluation of effects of parameters of various technological processes on crystallization properties of milk fat require further extensive investigations. Copyright © 2015 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.

Trabecular Bone Mechanical Properties and Fractal Dimension

NASA Technical Reports Server (NTRS)

Hogan, Harry A.

1996-01-01

Countermeasures for reducing bone loss and muscle atrophy due to extended exposure to the microgravity environment of space are continuing to be developed and improved. An important component of this effort is finite element modeling of the lower extremity and spinal column. These models will permit analysis and evaluation specific to each individual and thereby provide more efficient and effective exercise protocols. Inflight countermeasures and post-flight rehabilitation can then be customized and targeted on a case-by-case basis. Recent Summer Faculty Fellowship participants have focused upon finite element mesh generation, muscle force estimation, and fractal calculations of trabecular bone microstructure. Methods have been developed for generating the three-dimensional geometry of the femur from serial section magnetic resonance images (MRI). The use of MRI as an imaging modality avoids excessive exposure to radiation associated with X-ray based methods. These images can also detect trabecular bone microstructure and architecture. The goal of the current research is to determine the degree to which the fractal dimension of trabecular architecture can be used to predict the mechanical properties of trabecular bone tissue. The elastic modulus and the ultimate strength (or strain) can then be estimated from non-invasive, non-radiating imaging and incorporated into the finite element models to more accurately represent the bone tissue of each individual of interest. Trabecular bone specimens from the proximal tibia are being studied in this first phase of the work. Detailed protocols and procedures have been developed for carrying test specimens through all of the steps of a multi-faceted test program. The test program begins with MRI and X-ray imaging of the whole bones before excising a smaller workpiece from the proximal tibia region. High resolution MRI scans are then made and the piece further cut into slabs (roughly 1 cm thick). The slabs are X-rayed again and also scanned using dual-energy X-ray absorptiometry (DEXA). Cube specimens are then cut from the slabs and tested mechanically in compression. Correlations between mechanical properties and fractal dimension will then be examined to assess and quantify the predictive capability of the fractal calculations.

Fractal Geometry Enables Classification of Different Lung Morphologies in a Model of Experimental Asthma

NASA Astrophysics Data System (ADS)

Obert, Martin; Hagner, Stefanie; Krombach, Gabriele A.; Inan, Selcuk; Renz, Harald

2015-06-01

Animal models represent the basis of our current understanding of the pathophysiology of asthma and are of central importance in the preclinical development of drug therapies. The characterization of irregular lung shapes is a major issue in radiological imaging of mice in these models. The aim of this study was to find out whether differences in lung morphology can be described by fractal geometry. Healthy and asthmatic mouse groups, before and after an acute asthma attack induced by methacholine, were studied. In vivo flat-panel-based high-resolution Computed Tomography (CT) was used for mice's thorax imaging. The digital image data of the mice's lungs were segmented from the surrounding tissue. After that, the lungs were divided by image gray-level thresholds into two additional subsets. One subset contained basically the air transporting bronchial system. The other subset corresponds mainly to the blood vessel system. We estimated the fractal dimension of all sets of the different mouse groups using the mass radius relation (mrr). We found that the air transporting subset of the bronchial lung tissue enables a complete and significant differentiation between all four mouse groups (mean D of control mice before methacholine treatment: 2.64 ± 0.06; after treatment: 2.76 ± 0.03; asthma mice before methacholine treatment: 2.37 ± 0.16; after treatment: 2.71 ± 0.03; p < 0.05). We conclude that the concept of fractal geometry allows a well-defined, quantitative numerical and objective differentiation of lung shapes — applicable most likely also in human asthma diagnostics.

Investigation of changes in fractal dimension from layered retinal structures of healthy and diabetic eyes with optical coherence tomography

NASA Astrophysics Data System (ADS)

Gao, Wei; Zakharov, Valery P.; Myakinin, Oleg O.; Bratchenko, Ivan A.; Artemyev, Dmitry N.; Kornilin, Dmitry V.

2015-07-01

Optical coherence tomography (OCT) is usually employed for the measurement of retinal thickness characterizing the structural changes of tissue. However, fractal dimension (FD) could also character the structural changes of tissue. Therefore, fractal dimension changes may provide further information regarding cellular layers and early damage in ocular diseases. We investigated the possibility of OCT in detecting changes in fractal dimension from layered retinal structures. OCT images were obtained from diabetic patients without retinopathy (DM, n = 38 eyes) or mild diabetic retinopathy (MDR, n = 43 eyes) and normal healthy subjects (Controls, n = 74 eyes). Fractal dimension was calculated using the differentiate box counting methodology. We evaluated the usefulness of quantifying fractal dimension of layered structures in the detection of retinal damage. Generalized estimating equations considering within-subject intereye relations were used to test for differences between the groups. A modified p value of <0.001 was considered statistically significant. Receiver operating characteristic (ROC) curves were constructed to describe the ability of fractal dimension to discriminate between the eyes of DM, MDR and healthy eyes. Significant decreases of fractal dimension were observed in all layers in the MDR eyes compared with controls except in the inner nuclear layer (INL). Significant decreases of fractal dimension were also observed in all layers in the MDR eyes compared with DM eyes. The highest area under receiver operating characteristic curve (AUROC) values estimated for fractal dimension were observed for the outer plexiform layer (OPL) and outer segment photoreceptors (OS) when comparing MDR eyes with controls. The highest AUROC value estimated for fractal dimension were also observed for the retinal nerve fiber layer (RNFL) and OS when comparing MDR eyes with DM eyes. Our results suggest that fractal dimension of the intraretinal layers may provide useful information to differentiate pathological from healthy eyes. Further research is warranted to determine how this approach may be used to improve diagnosis of early retinal neurodegeneration.

Assessment of disintegrant efficacy with fractal dimensions from real-time MRI.

PubMed

Quodbach, Julian; Moussavi, Amir; Tammer, Roland; Frahm, Jens; Kleinebudde, Peter

2014-11-20

An efficient disintegrant is capable of breaking up a tablet in the smallest possible particles in the shortest time. Until now, comparative data on the efficacy of different disintegrants is based on dissolution studies or the disintegration time. Extending these approaches, this study introduces a method, which defines the evolution of fractal dimensions of tablets as surrogate parameter for the available surface area. Fractal dimensions are a measure for the tortuosity of a line, in this case the upper surface of a disintegrating tablet. High-resolution real-time MRI was used to record videos of disintegrating tablets. The acquired video images were processed to depict the upper surface of the tablets and a box-counting algorithm was used to estimate the fractal dimensions. The influence of six different disintegrants, of different relative tablet density, and increasing disintegrant concentration was investigated to evaluate the performance of the novel method. Changing relative densities hardly affect the progression of fractal dimensions, whereas an increase in disintegrant concentration causes increasing fractal dimensions during disintegration, which are also reached quicker. Different disintegrants display only minor differences in the maximal fractal dimension, yet the kinetic in which the maximum is reached allows a differentiation and classification of disintegrants. Copyright © 2014 Elsevier B.V. All rights reserved.

Seeing shapes in seemingly random spatial patterns: Fractal analysis of Rorschach inkblots

PubMed Central

Taylor, R. P.; Martin, T. P.; Montgomery, R. D.; Smith, J. H.; Micolich, A. P.; Boydston, C.; Scannell, B. C.; Fairbanks, M. S.; Spehar, B.

2017-01-01

Rorschach inkblots have had a striking impact on the worlds of art and science because of the remarkable variety of associations with recognizable and namable objects they induce. Originally adopted as a projective psychological tool to probe mental health, psychologists and artists have more recently interpreted the variety of induced images simply as a signature of the observers’ creativity. Here we analyze the relationship between the spatial scaling parameters of the inkblot patterns and the number of induced associations, and suggest that the perceived images are induced by the fractal characteristics of the blot edges. We discuss how this relationship explains the frequent observation of images in natural scenery. PMID:28196082

Retinal vasculature classification using novel multifractal features

NASA Astrophysics Data System (ADS)

Ding, Y.; Ward, W. O. C.; Duan, Jinming; Auer, D. P.; Gowland, Penny; Bai, L.

2015-11-01

Retinal blood vessels have been implicated in a large number of diseases including diabetic retinopathy and cardiovascular diseases, which cause damages to retinal blood vessels. The availability of retinal vessel imaging provides an excellent opportunity for monitoring and diagnosis of retinal diseases, and automatic analysis of retinal vessels will help with the processes. However, state of the art vascular analysis methods such as counting the number of branches or measuring the curvature and diameter of individual vessels are unsuitable for the microvasculature. There has been published research using fractal analysis to calculate fractal dimensions of retinal blood vessels, but so far there has been no systematic research extracting discriminant features from retinal vessels for classifications. This paper introduces new methods for feature extraction from multifractal spectra of retinal vessels for classification. Two publicly available retinal vascular image databases are used for the experiments, and the proposed methods have produced accuracies of 85.5% and 77% for classification of healthy and diabetic retinal vasculatures. Experiments show that classification with multiple fractal features produces better rates compared with methods using a single fractal dimension value. In addition to this, experiments also show that classification accuracy can be affected by the accuracy of vessel segmentation algorithms.

Microtopographic Inspection and Fractal Analysis of Skin Neoplasia

NASA Astrophysics Data System (ADS)

Costa, Manuel F. M.; Hipolito, Alberto Valencia; Gutierrez, Gustavo Fidel; Chanona, Jorge; Gallegos, Eva Ramón

2008-04-01

Early detection of skin cancer is fundamental to a successful treatment. Changes in the shape, including the relief, of skin lesions are an indicator of a possible malignity. Optical microtopographic inspection of skin lesions can be used to identify diagnostic patterns of benign and malign skin' lesions. Statistical parameters like the mean roughness (Ra) may allow the discrimination between different types of lesions and degree of malignity. Fractal analysis of bi-dimensional and 3D images of skin lesions can validate or complement that assessment by calculation of its fractal dimensions (FD). On the study herein reported the microtopographic inspection of the skin lesions were performed using the optical triangulation based microtopographer developed at the Physics Department of the University of Minho, MICROTOP.03.MFC. The patients that participated in this research work were men and women older than 15 years with the clinical and histopathology diagnoses of: melanoma, basocellular carcinoma, epidermoide carcinoma, actinic keratosis, keratoacantosis and benign nevus. Latex impressions of the lesions were taken and microtopographically analyzed. Characteristic information for each type of studied lesion was obtained. For melanoma it was observed that on the average these tumors present an increased roughness of around 67 percent compared to the roughness of the healthy skin. This feature allows the distinction from other tumors as basocellular carcinoma (were the roughness increase was in the average of 49 percent) and benign lesions as the epidermoide cyst (37 percent) or the seborrhea keratosis (4 percent). Tumor size and roughness are directly proportional to the grade of malignality. The characterization of the fractal geometry of 2D (histological slides) and 3D images of skin lesions was performed by obtaining its FD evaluated by means of the Box counting method. Results obtained showed that the average fractal dimension of histological slide images (FDh) corresponding to some neoplasia is higher (1.334+/-0.072) than those for healthy skin (1.091+/-0.082). A significant difference between the fractal dimensions of neoplasia and healhty skin (>0.001) was registered. The FD of microtopography maps (FDm) can also distinguish between healthy and malignant tissue in general (2.277+/-0.070 to 2.309+/-0.040), but not discriminate the different types of skin neoplasias. The combination of the rugometric evaluation and fractal geometry characterization provides valuable information about the malignity of skin lesions and type of lesion.

Analysis and classification of commercial ham slice images using directional fractal dimension features.

PubMed

Mendoza, Fernando; Valous, Nektarios A; Allen, Paul; Kenny, Tony A; Ward, Paddy; Sun, Da-Wen

2009-02-01

This paper presents a novel and non-destructive approach to the appearance characterization and classification of commercial pork, turkey and chicken ham slices. Ham slice images were modelled using directional fractal (DF(0°;45°;90°;135°)) dimensions and a minimum distance classifier was adopted to perform the classification task. Also, the role of different colour spaces and the resolution level of the images on DF analysis were investigated. This approach was applied to 480 wafer thin ham slices from four types of hams (120 slices per type): i.e., pork (cooked and smoked), turkey (smoked) and chicken (roasted). DF features were extracted from digitalized intensity images in greyscale, and R, G, B, L(∗), a(∗), b(∗), H, S, and V colour components for three image resolution levels (100%, 50%, and 25%). Simulation results show that in spite of the complexity and high variability in colour and texture appearance, the modelling of ham slice images with DF dimensions allows the capture of differentiating textural features between the four commercial ham types. Independent DF features entail better discrimination than that using the average of four directions. However, DF dimensions reveal a high sensitivity to colour channel, orientation and image resolution for the fractal analysis. The classification accuracy using six DF dimension features (a(90°)(∗),a(135°)(∗),H(0°),H(45°),S(0°),H(90°)) was 93.9% for training data and 82.2% for testing data.

Wavelet-based 3D reconstruction of microcalcification clusters from two mammographic views: new evidence that fractal tumors are malignant and Euclidean tumors are benign.

PubMed

Batchelder, Kendra A; Tanenbaum, Aaron B; Albert, Seth; Guimond, Lyne; Kestener, Pierre; Arneodo, Alain; Khalil, Andre

2014-01-01

The 2D Wavelet-Transform Modulus Maxima (WTMM) method was used to detect microcalcifications (MC) in human breast tissue seen in mammograms and to characterize the fractal geometry of benign and malignant MC clusters. This was done in the context of a preliminary analysis of a small dataset, via a novel way to partition the wavelet-transform space-scale skeleton. For the first time, the estimated 3D fractal structure of a breast lesion was inferred by pairing the information from two separate 2D projected mammographic views of the same breast, i.e. the cranial-caudal (CC) and mediolateral-oblique (MLO) views. As a novelty, we define the "CC-MLO fractal dimension plot", where a "fractal zone" and "Euclidean zones" (non-fractal) are defined. 118 images (59 cases, 25 malignant and 34 benign) obtained from a digital databank of mammograms with known radiologist diagnostics were analyzed to determine which cases would be plotted in the fractal zone and which cases would fall in the Euclidean zones. 92% of malignant breast lesions studied (23 out of 25 cases) were in the fractal zone while 88% of the benign lesions were in the Euclidean zones (30 out of 34 cases). Furthermore, a Bayesian statistical analysis shows that, with 95% credibility, the probability that fractal breast lesions are malignant is between 74% and 98%. Alternatively, with 95% credibility, the probability that Euclidean breast lesions are benign is between 76% and 96%. These results support the notion that the fractal structure of malignant tumors is more likely to be associated with an invasive behavior into the surrounding tissue compared to the less invasive, Euclidean structure of benign tumors. Finally, based on indirect 3D reconstructions from the 2D views, we conjecture that all breast tumors considered in this study, benign and malignant, fractal or Euclidean, restrict their growth to 2-dimensional manifolds within the breast tissue.

Feature extraction algorithm for space targets based on fractal theory

NASA Astrophysics Data System (ADS)

Tian, Balin; Yuan, Jianping; Yue, Xiaokui; Ning, Xin

2007-11-01

In order to offer a potential for extending the life of satellites and reducing the launch and operating costs, satellite servicing including conducting repairs, upgrading and refueling spacecraft on-orbit become much more frequently. Future space operations can be more economically and reliably executed using machine vision systems, which can meet real time and tracking reliability requirements for image tracking of space surveillance system. Machine vision was applied to the research of relative pose for spacecrafts, the feature extraction algorithm was the basis of relative pose. In this paper fractal geometry based edge extraction algorithm which can be used in determining and tracking the relative pose of an observed satellite during proximity operations in machine vision system was presented. The method gets the gray-level image distributed by fractal dimension used the Differential Box-Counting (DBC) approach of the fractal theory to restrain the noise. After this, we detect the consecutive edge using Mathematical Morphology. The validity of the proposed method is examined by processing and analyzing images of space targets. The edge extraction method not only extracts the outline of the target, but also keeps the inner details. Meanwhile, edge extraction is only processed in moving area to reduce computation greatly. Simulation results compared edge detection using the method which presented by us with other detection methods. The results indicate that the presented algorithm is a valid method to solve the problems of relative pose for spacecrafts.

Fractal analysis of the ischemic transition region in chronic ischemic heart disease using magnetic resonance imaging.

PubMed

Michallek, Florian; Dewey, Marc

2017-04-01

To introduce a novel hypothesis and method to characterise pathomechanisms underlying myocardial ischemia in chronic ischemic heart disease by local fractal analysis (FA) of the ischemic myocardial transition region in perfusion imaging. Vascular mechanisms to compensate ischemia are regulated at various vascular scales with their superimposed perfusion pattern being hypothetically self-similar. Dedicated FA software ("FraktalWandler") has been developed. Fractal dimensions during first-pass (FD first-pass ) and recirculation (FD recirculation ) are hypothesised to indicate the predominating pathomechanism and ischemic severity, respectively. Twenty-six patients with evidence of myocardial ischemia in 108 ischemic myocardial segments on magnetic resonance imaging (MRI) were analysed. The 40th and 60th percentiles of FD first-pass were used for pathomechanical classification, assigning lesions with FD first-pass  ≤ 2.335 to predominating coronary microvascular dysfunction (CMD) and ≥2.387 to predominating coronary artery disease (CAD). Optimal classification point in ROC analysis was FD first-pass  = 2.358. FD recirculation correlated moderately with per cent diameter stenosis in invasive coronary angiography in lesions classified CAD (r = 0.472, p = 0.001) but not CMD (r = 0.082, p = 0.600). The ischemic transition region may provide information on pathomechanical composition and severity of myocardial ischemia. FA of this region is feasible and may improve diagnosis compared to traditional noninvasive myocardial perfusion analysis. • A novel hypothesis and method is introduced to pathophysiologically characterise myocardial ischemia. • The ischemic transition region appears a meaningful diagnostic target in perfusion imaging. • Fractal analysis may characterise pathomechanical composition and severity of myocardial ischemia.

Polymer Self-Assembly into Unique Fractal Nanostructures in Solution by a One-Shot Synthetic Procedure.

PubMed

Shin, Suyong; Gu, Ming-Long; Yu, Chin-Yang; Jeon, Jongseol; Lee, Eunji; Choi, Tae-Lim

2018-01-10

A fractal nanostructure having a high surface area is potentially useful in sensors, catalysts, functional coatings, and biomedical and electronic applications. Preparation of fractal nanostructures on solid substrates has been reported using various inorganic or organic compounds. However, achieving such a process using polymers in solution has been extremely challenging. Here, we report a simple one-shot preparation of polymer fractal nanostructures in solution via an unprecedented assembly mechanism controlled by polymerization and self-assembly kinetics. This was possible only because one monomer was significantly more reactive than the other, thereby easily forming a diblock copolymer microstructure. Then, the second insoluble block containing poly(p-phenylenevinylene) (PPV) without any side chains spontaneously underwent self-assembly during polymerization by an in situ nanoparticlization of conjugated polymers (INCP) method. The formation of fractal structures in solution was confirmed by various imaging techniques such as atomic force microscopy, transmission electron microscopy (TEM), and cryogenic TEM. The diffusion-limited aggregation theory was adopted to explain the branching patterns of the fractal nanostructures according to the changes in polymerization conditions such as the monomer concentration and the presence of additives. Finally, after detailed kinetic analyses, we proposed a plausible mechanism for the formation of unique fractal nanostructures, where the gradual formation and continuous growth of micelles in a chain-growth-like manner were accounted for.

Fractal cometary dust - a window into the early Solar system

NASA Astrophysics Data System (ADS)

Mannel, T.; Bentley, M. S.; Schmied, R.; Jeszenszky, H.; Levasseur-Regourd, A. C.; Romstedt, J.; Torkar, K.

2016-11-01

The properties of dust in the protoplanetary disc are key to understanding the formation of planets in our Solar system. Many models of dust growth predict the development of fractal structures which evolve into non-fractal, porous dust pebbles representing the main component for planetesimal accretion. In order to understand comets and their origins, the Rosetta orbiter followed comet 67P/Churyumov-Gerasimenko for over two years and carried a dedicated instrument suite for dust analysis. One of these instruments, the MIDAS (Micro-Imaging Dust Analysis System) atomic force microscope, recorded the 3D topography of micro- to nanometre-sized dust. All particles analysed to date have been found to be hierarchical agglomerates. Most show compact packing; however, one is extremely porous. This paper contains a structural description of a compact aggregate and the outstanding porous one. Both particles are tens of micrometres in size and show rather narrow subunit size distributions with noticeably similar mean values of 1.48^{+0.13}_{-0.59} μm for the porous particle and 1.36^{+0.15}_{-0.59} μm for the compact. The porous particle allows a fractal analysis, where a density-density correlation function yields a fractal dimension of Df = 1.70 ± 0.1. GIADA, another dust analysis instrument on board Rosetta, confirms the existence of a dust population with a similar fractal dimension. The fractal particles are interpreted as pristine agglomerates built in the protoplanetary disc and preserved in the comet. The similar subunits of both fractal and compact dust indicate a common origin which is, given the properties of the fractal, dominated by slow agglomeration of equally sized aggregates known as cluster-cluster agglomeration.

Taxonomy of Individual Variations in Aesthetic Responses to Fractal Patterns

PubMed Central

Spehar, Branka; Walker, Nicholas; Taylor, Richard P.

2016-01-01

In two experiments, we investigate group and individual preferences in a range of different types of patterns with varying fractal-like scaling characteristics. In Experiment 1, we used 1/f filtered grayscale images as well as their thresholded (black and white) and edges only counterparts. Separate groups of observers viewed different types of images varying in slope of their amplitude spectra. Although with each image type, the groups exhibited the “universal” pattern of preference for intermediate amplitude spectrum slopes, we identified 4 distinct sub-groups in each case. Sub-group 1 exhibited a typical peak preference for intermediate amplitude spectrum slopes (“intermediate”; approx. 50%); sub-group 2 exhibited a linear increase in preference with increasing amplitude spectrum slope (“smooth”; approx. 20%), while sub-group 3 exhibited a linear decrease in preference as a function of the amplitude spectrum slope (“sharp”; approx. 20%). Sub-group 4 revealed no significant preference (“other”; approx. 10%). In Experiment 2, we extended the range of different image types and investigated preferences within the same observers. We replicate the results of our first experiment and show that individual participants exhibit stable patterns of preference across a wide range of image types. In both experiments, Q-mode factor analysis identified two principal factors that were able to explain more than 80% of interindividual variations in preference across all types of images, suggesting a highly similar dimensional structure of interindividual variations in preference for fractal-like scaling characteristics. PMID:27458365

Fractal design concepts for stretchable electronics.

PubMed

Fan, Jonathan A; Yeo, Woon-Hong; Su, Yewang; Hattori, Yoshiaki; Lee, Woosik; Jung, Sung-Young; Zhang, Yihui; Liu, Zhuangjian; Cheng, Huanyu; Falgout, Leo; Bajema, Mike; Coleman, Todd; Gregoire, Dan; Larsen, Ryan J; Huang, Yonggang; Rogers, John A

2014-01-01

Stretchable electronics provide a foundation for applications that exceed the scope of conventional wafer and circuit board technologies due to their unique capacity to integrate with soft materials and curvilinear surfaces. The range of possibilities is predicated on the development of device architectures that simultaneously offer advanced electronic function and compliant mechanics. Here we report that thin films of hard electronic materials patterned in deterministic fractal motifs and bonded to elastomers enable unusual mechanics with important implications in stretchable device design. In particular, we demonstrate the utility of Peano, Greek cross, Vicsek and other fractal constructs to yield space-filling structures of electronic materials, including monocrystalline silicon, for electrophysiological sensors, precision monitors and actuators, and radio frequency antennas. These devices support conformal mounting on the skin and have unique properties such as invisibility under magnetic resonance imaging. The results suggest that fractal-based layouts represent important strategies for hard-soft materials integration.

Fractal design concepts for stretchable electronics

NASA Astrophysics Data System (ADS)

Fan, Jonathan A.; Yeo, Woon-Hong; Su, Yewang; Hattori, Yoshiaki; Lee, Woosik; Jung, Sung-Young; Zhang, Yihui; Liu, Zhuangjian; Cheng, Huanyu; Falgout, Leo; Bajema, Mike; Coleman, Todd; Gregoire, Dan; Larsen, Ryan J.; Huang, Yonggang; Rogers, John A.

2014-02-01

Stretchable electronics provide a foundation for applications that exceed the scope of conventional wafer and circuit board technologies due to their unique capacity to integrate with soft materials and curvilinear surfaces. The range of possibilities is predicated on the development of device architectures that simultaneously offer advanced electronic function and compliant mechanics. Here we report that thin films of hard electronic materials patterned in deterministic fractal motifs and bonded to elastomers enable unusual mechanics with important implications in stretchable device design. In particular, we demonstrate the utility of Peano, Greek cross, Vicsek and other fractal constructs to yield space-filling structures of electronic materials, including monocrystalline silicon, for electrophysiological sensors, precision monitors and actuators, and radio frequency antennas. These devices support conformal mounting on the skin and have unique properties such as invisibility under magnetic resonance imaging. The results suggest that fractal-based layouts represent important strategies for hard-soft materials integration.

Fractal analysis of radiologists' visual scanning pattern in screening mammography

NASA Astrophysics Data System (ADS)

Alamudun, Folami T.; Yoon, Hong-Jun; Hudson, Kathy; Morin-Ducote, Garnetta; Tourassi, Georgia

2015-03-01

Several researchers have investigated radiologists' visual scanning patterns with respect to features such as total time examining a case, time to initially hit true lesions, number of hits, etc. The purpose of this study was to examine the complexity of the radiologists' visual scanning pattern when viewing 4-view mammographic cases, as they typically do in clinical practice. Gaze data were collected from 10 readers (3 breast imaging experts and 7 radiology residents) while reviewing 100 screening mammograms (24 normal, 26 benign, 50 malignant). The radiologists' scanpaths across the 4 mammographic views were mapped to a single 2-D image plane. Then, fractal analysis was applied on the composite 4- view scanpaths. For each case, the complexity of each radiologist's scanpath was measured using fractal dimension estimated with the box counting method. The association between the fractal dimension of the radiologists' visual scanpath, case pathology, case density, and radiologist experience was evaluated using fixed effects ANOVA. ANOVA showed that the complexity of the radiologists' visual search pattern in screening mammography is dependent on case specific attributes (breast parenchyma density and case pathology) as well as on reader attributes, namely experience level. Visual scanning patterns are significantly different for benign and malignant cases than for normal cases. There is also substantial inter-observer variability which cannot be explained only by experience level.

Correlating brain blood oxygenation level dependent (BOLD) fractal dimension mapping with magnetic resonance spectroscopy (MRS) in Alzheimer's disease.

PubMed

Warsi, Mohammed A; Molloy, William; Noseworthy, Michael D

2012-10-01

To correlate temporal fractal structure of resting state blood oxygen level dependent (rsBOLD) functional magnetic resonance imaging (fMRI) with in vivo proton magnetic resonance spectroscopy ((1)H-MRS), in Alzheimer's disease (AD) and healthy age-matched normal controls (NC). High temporal resolution (4 Hz) rsBOLD signal and single voxel (left putamen) magnetic resonance spectroscopy data was acquired in 33 AD patients and 13 NC. The rsBOLD data was analyzed using two types of fractal dimension (FD) analysis based on relative dispersion and frequency power spectrum. Comparisons in FD were performed between AD and NC, and FD measures were correlated with (1)H-MRS findings. Temporal fractal analysis of rsBOLD, was able to differentiate AD from NC subjects (P = 0.03). Low FD correlated with markers of AD severity including decreased concentrations of N-acetyl aspartate (R = 0.44, P = 0.015) and increased myoinositol (mI) (R = -0.45, P = 0.012). Based on these results we suggest fractal analysis of rsBOLD could provide an early marker of AD.

Synthetic Minority Oversampling Technique and Fractal Dimension for Identifying Multiple Sclerosis

NASA Astrophysics Data System (ADS)

Zhang, Yu-Dong; Zhang, Yin; Phillips, Preetha; Dong, Zhengchao; Wang, Shuihua

Multiple sclerosis (MS) is a severe brain disease. Early detection can provide timely treatment. Fractal dimension can provide statistical index of pattern changes with scale at a given brain image. In this study, our team used susceptibility weighted imaging technique to obtain 676 MS slices and 880 healthy slices. We used synthetic minority oversampling technique to process the unbalanced dataset. Then, we used Canny edge detector to extract distinguishing edges. The Minkowski-Bouligand dimension was a fractal dimension estimation method and used to extract features from edges. Single hidden layer neural network was used as the classifier. Finally, we proposed a three-segment representation biogeography-based optimization to train the classifier. Our method achieved a sensitivity of 97.78±1.29%, a specificity of 97.82±1.60% and an accuracy of 97.80±1.40%. The proposed method is superior to seven state-of-the-art methods in terms of sensitivity and accuracy.

Fractal analysis of phasic laser images of the myocardium for the purpose of diagnostics of acute coronary insufficiency

NASA Astrophysics Data System (ADS)

Wanchuliak, O. Y.; Bachinskyi, V. T.

2011-09-01

In this work on the base of Mueller-matrix description of optical anisotropy, the possibility of monitoring of time changes of myocardium tissue birefringence, has been considered. The optical model of polycrystalline networks of myocardium is suggested. The results of investigating the interrelation between the values correlation (correlation area, asymmetry coefficient and autocorrelation function excess) and fractal (dispersion of logarithmic dependencies of power spectra) parameters are presented. They characterize the distributions of Mueller matrix elements in the points of laser images of myocardium histological sections. The criteria of differentiation of death coming reasons are determined.

Numerical Approaches about the Morphological Description Parameters for the Manganese Deposits on the Magnesite Ore Surface

NASA Astrophysics Data System (ADS)

Bayirli, Mehmet; Ozbey, Tuba

2013-07-01

Black deposits usually found at the surface of magnesite ore or limestone as well as red deposits in quartz veins are named as natural manganese dendrites. According to their geometrical structures, they may take variable fractal shapes. The characteristic origins of these morphologies have rarely been studied by means of numerical analyses. Hence, digital images of magnesite ore are taken from its surface with a scanner. These images are then converted to binary images in the form of 8 bits, bitmap format. As a next step, the morphological description parameters of manganese dendrites are computed by the way of scaling methods such as occupied fractions, fractal dimensions, divergent ratios, and critical exponents of scaling. The fractal dimension and the scaling range are made dependent on the fraction of the particles. Morphological description parameters can be determined according to the geometrical evaluation of the natural manganese dendrites which are formed independently from the process. The formation of manganese dendrites may also explain the stochastic selected process in the nature. These results therefore may be useful to understand the deposits in quartz vein parameters in geophysics.

a New Improved Threshold Segmentation Method for Scanning Images of Reservoir Rocks Considering Pore Fractal Characteristics

NASA Astrophysics Data System (ADS)

Lin, Wei; Li, Xizhe; Yang, Zhengming; Lin, Lijun; Xiong, Shengchun; Wang, Zhiyuan; Wang, Xiangyang; Xiao, Qianhua

Based on the basic principle of the porosity method in image segmentation, considering the relationship between the porosity of the rocks and the fractal characteristics of the pore structures, a new improved image segmentation method was proposed, which uses the calculated porosity of the core images as a constraint to obtain the best threshold. The results of comparative analysis show that the porosity method can best segment images theoretically, but the actual segmentation effect is deviated from the real situation. Due to the existence of heterogeneity and isolated pores of cores, the porosity method that takes the experimental porosity of the whole core as the criterion cannot achieve the desired segmentation effect. On the contrary, the new improved method overcomes the shortcomings of the porosity method, and makes a more reasonable binary segmentation for the core grayscale images, which segments images based on the actual porosity of each image by calculated. Moreover, the image segmentation method based on the calculated porosity rather than the measured porosity also greatly saves manpower and material resources, especially for tight rocks.

Effect of Fractal Dimension on the Strain Behavior of Particulate Media

NASA Astrophysics Data System (ADS)

Altun, Selim; Sezer, Alper; Goktepe, A. Burak

2016-12-01

In this study, the influence of several fractal identifiers of granular materials on dynamic behavior of a flexible pavement structure as a particulate stratum is considered. Using experimental results and numerical methods as well, 15 different grain-shaped sands obtained from 5 different sources were analyzed as pavement base course materials. Image analyses were carried out by use of a stereomicroscope on 15 different samples to obtain quantitative particle shape information. Furthermore, triaxial compression tests were conducted to determine stress-strain and shear strength parameters of sands. Additionally, the dynamic response of the particulate media to standard traffic loads was computed using finite element modeling (FEM) technique. Using area-perimeter, line divider and box counting methods, over a hundred grains for each sand type were subjected to fractal analysis. Relationships among fractal dimension descriptors and dynamic strain levels were established for assessment of importance of shape descriptors of sands at various scales on the dynamic behavior. In this context, the advantage of fractal geometry concept to describe irregular and fractured shapes was used to characterize the sands used as base course materials. Results indicated that fractal identifiers can be preferred to analyze the effect of shape properties of sands on dynamic behavior of pavement base layers.

Fractal analysis of INSAR and correlation with graph-cut based image registration for coastline deformation analysis: post seismic hazard assessment of the 2011 Tohoku earthquake region

NASA Astrophysics Data System (ADS)

Dutta, P. K.; Mishra, O. P.

2012-04-01

Satellite imagery for 2011 earthquake off the Pacific coast of Tohoku has provided an opportunity to conduct image transformation analyses by employing multi-temporal images retrieval techniques. In this study, we used a new image segmentation algorithm to image coastline deformation by adopting graph cut energy minimization framework. Comprehensive analysis of available INSAR images using coastline deformation analysis helped extract disaster information of the affected region of the 2011 Tohoku tsunamigenic earthquake source zone. We attempted to correlate fractal analysis of seismic clustering behavior with image processing analogies and our observations suggest that increase in fractal dimension distribution is associated with clustering of events that may determine the level of devastation of the region. The implementation of graph cut based image registration technique helps us to detect the devastation across the coastline of Tohoku through change of intensity of pixels that carries out regional segmentation for the change in coastal boundary after the tsunami. The study applies transformation parameters on remotely sensed images by manually segmenting the image to recovering translation parameter from two images that differ by rotation. Based on the satellite image analysis through image segmentation, it is found that the area of 0.997 sq km for the Honshu region was a maximum damage zone localized in the coastal belt of NE Japan forearc region. The analysis helps infer using matlab that the proposed graph cut algorithm is robust and more accurate than other image registration methods. The analysis shows that the method can give a realistic estimate for recovered deformation fields in pixels corresponding to coastline change which may help formulate the strategy for assessment during post disaster need assessment scenario for the coastal belts associated with damages due to strong shaking and tsunamis in the world under disaster risk mitigation programs.

Monitoring the soil degradation by Metastatistical Analysis

NASA Astrophysics Data System (ADS)

Oleschko, K.; Gaona, C.; Tarquis, A.

2009-04-01

The effectiveness of fractal toolbox to capture the critical behavior of soil structural patterns during the chemical and physical degradation was documented by our numerous experiments (Oleschko et al., 2008 a; 2008 b). The spatio-temporal dynamics of these patterns was measured and mapped with high precision in terms of fractal descriptors. All tested fractal techniques were able to detect the statistically significant differences in structure between the perfect spongy and massive patterns of uncultivated and sodium-saline agricultural soils, respectively. For instance, the Hurst exponent, extracted from the Chernozeḿ micromorphological images and from the time series of its physical and mechanical properties measured in situ, detected the roughness decrease (and therefore the increase in H - from 0.17 to 0.30 for images) derived from the loss of original structure complexity. The combined use of different fractal descriptors brings statistical precision into the quantification of natural system degradation and provides a means for objective soil structure comparison (Oleschko et al., 2000). The ability of fractal parameters to capture critical behavior and phase transition was documented for different contrasting situations, including from Andosols deforestation and erosion, to Vertisols high fructuring and consolidation. The Hurst exponent is used to measure the type of persistence and degree of complexity of structure dynamics. We conclude that there is an urgent need to select and adopt a standardized toolbox for fractal analysis and complexity measures in Earth Sciences. We propose to use the second-order (meta-) statistics as subtle measures of complexity (Atmanspacher et al., 1997). The high degree of correlation was documented between the fractal and high-order statistical descriptors (four central moments of stochastic variable distribution) used to the system heterogeneity and variability analysis. We proposed to call this combined fractal/statistical toolbox Metastatistical Analysis and recommend it to the projects directed to soil degradation monitoring. References: 1. Oleschko, K., B.S. Figueroa, M.E. Miranda, M.A. Vuelvas and E.R. Solleiro, Soil & Till. Res. 55, 43 (2000). 2. Oleschko, K., Korvin, G., Figueroa S. B., Vuelvas, M.A., Balankin, A., Flores L., Carreño, D. Fractal radar scattering from soil. Physical Review E.67, 041403, 2003. 3. Zamora-Castro S., Oleschko, K. Flores, L., Ventura, E. Jr., Parrot, J.-F., 2008. Fractal mapping of pore and solids attributes. Vadose Zone Journal, v. 7, Issue2: 473-492. 4. Oleschko, K., Korvin, G., Muñoz, A., Velásquez, J., Miranda, M.E., Carreon, D., Flores, L., Martínez, M., Velásquez-Valle, M., Brambilla, F., Parrot, J.-F. Ronquillo, G., 2008. Fractal mapping of soil moisture content from remote sensed multi-scale data. Nonlinear Proceses in Geophysics Journal, 15: 711-725. 5. Atmanspacher, H., Räth, Ch., Wiedenmann, G., 1997. Statistics and meta-statistics in the concept of complexity. Physica A, 234: 819-829.

Fractal analysis of polyferric chloride-humic acid (PFC-HA) flocs in different topological spaces.

PubMed

Wang, Yili; Lu, Jia; Baiyu, Du; Shi, Baoyou; Wang, Dongsheng

2009-01-01

The fractal dimensions in different topological spaces of polyferric chloride-humic acid (PFC-HA) flocs, formed in flocculating different kinds of humic acids (HA) water at different initial pH (9.0, 7.0, 5.0) and PFC dosages, were calculated by effective density-maximum diameter, image analysis, and N2 absorption-desorption methods, respectively. The mass fractal dimensions (Df) of PFC-HA flocs were calculated by bi-logarithm relation of effective density with maximum diameter and Logan empirical equation. The Df value was more than 2.0 at initial pH of 7.0, which was 11% and 13% higher than those at pH 9.0 and 5.0, respectively, indicating the most compact flocs formed in flocculated HA water at initial pH of 7.0. The image analysis for those flocs indicates that after flocculating the HA water at initial pH greater than 7.0 with PFC flocculant, the fractal dimensions of D2 (logA vs. logdL) and D3 (logVsphere VS. logdL) of PFC-HA flocs decreased with the increase of PFC dosages, and PFC-HA flocs showed a gradually looser structure. At the optimum dosage of PFC, the D2 (logA vs. logdL) values of the flocs show 14%-43% difference with their corresponding Df, and they even had different tendency with the change of initial pH values. However, the D2 values of the flocs formed at three different initial pH in HA solution had a same tendency with the corresponding Dr. Based on fractal Frenkel-Halsey-Hill (FHH) adsorption and desorption equations, the pore surface fractal dimensions (Ds) for dried powders of PFC-HA flocs formed in HA water with initial pH 9.0 and 7.0 were all close to 2.9421, and the Ds values of flocs formed at initial pH 5.0 were less than 2.3746. It indicated that the pore surface fractal dimensions of PFC-HA flocs dried powder mainly show the irregularity from the mesopore-size distribution and marcopore-size distribution.

Connotations of pixel-based scale effect in remote sensing and the modified fractal-based analysis method

NASA Astrophysics Data System (ADS)

Feng, Guixiang; Ming, Dongping; Wang, Min; Yang, Jianyu

2017-06-01

Scale problems are a major source of concern in the field of remote sensing. Since the remote sensing is a complex technology system, there is a lack of enough cognition on the connotation of scale and scale effect in remote sensing. Thus, this paper first introduces the connotations of pixel-based scale and summarizes the general understanding of pixel-based scale effect. Pixel-based scale effect analysis is essentially important for choosing the appropriate remote sensing data and the proper processing parameters. Fractal dimension is a useful measurement to analysis pixel-based scale. However in traditional fractal dimension calculation, the impact of spatial resolution is not considered, which leads that the scale effect change with spatial resolution can't be clearly reflected. Therefore, this paper proposes to use spatial resolution as the modified scale parameter of two fractal methods to further analyze the pixel-based scale effect. To verify the results of two modified methods (MFBM (Modified Windowed Fractal Brownian Motion Based on the Surface Area) and MDBM (Modified Windowed Double Blanket Method)); the existing scale effect analysis method (information entropy method) is used to evaluate. And six sub-regions of building areas and farmland areas were cut out from QuickBird images to be used as the experimental data. The results of the experiment show that both the fractal dimension and information entropy present the same trend with the decrease of spatial resolution, and some inflection points appear at the same feature scales. Further analysis shows that these feature scales (corresponding to the inflection points) are related to the actual sizes of the geo-object, which results in fewer mixed pixels in the image, and these inflection points are significantly indicative of the observed features. Therefore, the experiment results indicate that the modified fractal methods are effective to reflect the pixel-based scale effect existing in remote sensing data and it is helpful to analyze the observation scale from different aspects. This research will ultimately benefit for remote sensing data selection and application.

Estimating Trabecular Bone Mechanical Properties From Non-Invasive Imaging

NASA Technical Reports Server (NTRS)

Hogan, Harry A.; Webster, Laurie

1997-01-01

An important component in developing countermeasures for maintaining musculoskeletal integrity during long-term space flight is an effective and meaningful method of monitoring skeletal condition. Magnetic resonance imaging (MRI) is an attractive non-invasive approach because it avoids the exposure to radiation associated with X-ray based imaging and also provides measures related to bone microstructure rather than just density. The purpose of the research for the 1996 Summer Faculty Fellowship period was to extend the usefulness of the MRI data to estimate the mechanical properties of trabecular bone. The main mechanical properties of interest are the elastic modulus and ultimate strength. Correlations are being investigated between these and fractal analysis parameters, MRI relaxation times, apparent densities, and bone mineral densities. Bone specimens from both human and equine donors have been studied initially to ensure high-quality MR images. Specimens were prepared and scanned from human proximal tibia bones as well as the equine distal radius. The quality of the images from the human bone appeared compromised due to freezing artifact, so only equine bone was included in subsequent procedures since these specimens could be acquired and imaged fresh before being frozen. MRI scans were made spanning a 3.6 cm length on each of 5 equine distal radius specimens. The images were then sent to Dr. Raj Acharya of the State University of New York at Buffalo for fractal analysis. Each piece was cut into 3 slabs approximately 1.2 cm thick and high-resolution contact radiographs were made to provide images for comparing fractal analysis with MR images. Dual energy X-ray absorptiometry (DEXA) scans were also made of each slab for subsequent bone mineral density determination. Slabs were cut into cubes for mechanical using a slow-speed diamond blade wafering saw (Buehler Isomet). The dimensions and wet weights of each cube specimen were measured and recorded. Wet weights were also recorded. Each specimen was labeled and marked to denote anatomic orientations, i.e. superior/inferior (S/I), media/lateral (M/L), and anterior/posterior (A/P). The actual locations of each cube cut were documented and images distributed to define ROI locations for other analyses (to Raj Acharya for fractal analysis, to Jon Richardson at Baylor College of Medicine for DEXA, and to Chen Lin at Baylor College of Medicine for T2* MRI analysis). Quasistatic mechanical testing consisted of compressive loading in all three mutually perpendicular anatomic directions. Cyclic loading was applied for 10 cycles to precondition the specimen and results calculated for the eleventh. For one of three directions tested on each specimen, the 10 cycles were followed with loading to failure. Testing is currently proceeding and once completed the results will be correlated with data from the other analyses. One of the main points of interest is the relationship between fractal dimension and mechanical properties. Throughout preparation and testing all specimens were maintained hydrated with physiological saline and stored frozen when not being used.

A new version of Visual tool for estimating the fractal dimension of images

NASA Astrophysics Data System (ADS)

Grossu, I. V.; Felea, D.; Besliu, C.; Jipa, Al.; Bordeianu, C. C.; Stan, E.; Esanu, T.

2010-04-01

This work presents a new version of a Visual Basic 6.0 application for estimating the fractal dimension of images (Grossu et al., 2009 [1]). The earlier version was limited to bi-dimensional sets of points, stored in bitmap files. The application was extended for working also with comma separated values files and three-dimensional images. New version program summaryProgram title: Fractal Analysis v02 Catalogue identifier: AEEG_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEEG_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 9999 No. of bytes in distributed program, including test data, etc.: 4 366 783 Distribution format: tar.gz Programming language: MS Visual Basic 6.0 Computer: PC Operating system: MS Windows 98 or later RAM: 30 M Classification: 14 Catalogue identifier of previous version: AEEG_v1_0 Journal reference of previous version: Comput. Phys. Comm. 180 (2009) 1999 Does the new version supersede the previous version?: Yes Nature of problem: Estimating the fractal dimension of 2D and 3D images. Solution method: Optimized implementation of the box-counting algorithm. Reasons for new version:The previous version was limited to bitmap image files. The new application was extended in order to work with objects stored in comma separated values (csv) files. The main advantages are: Easier integration with other applications (csv is a widely used, simple text file format); Less resources consumed and improved performance (only the information of interest, the "black points", are stored); Higher resolution (the points coordinates are loaded into Visual Basic double variables [2]); Possibility of storing three-dimensional objects (e.g. the 3D Sierpinski gasket). In this version the optimized box-counting algorithm [1] was extended to the three-dimensional case. Summary of revisions:The application interface was changed from SDI (single document interface) to MDI (multi-document interface). One form was added in order to provide a graphical user interface for the new functionalities (fractal analysis of 2D and 3D images stored in csv files). Additional comments: User friendly graphical interface; Easy deployment mechanism. Running time: In the first approximation, the algorithm is linear. References:[1] I.V. Grossu, C. Besliu, M.V. Rusu, Al. Jipa, C.C. Bordeianu, D. Felea, Comput. Phys. Comm. 180 (2009) 1999-2001.[2] F. Balena, Programming Microsoft Visual Basic 6.0, Microsoft Press, US, 1999.

Skin cancer texture analysis of OCT images based on Haralick, fractal dimension and the complex directional field features

NASA Astrophysics Data System (ADS)

Raupov, Dmitry S.; Myakinin, Oleg O.; Bratchenko, Ivan A.; Kornilin, Dmitry V.; Zakharov, Valery P.; Khramov, Alexander G.

2016-04-01

Optical coherence tomography (OCT) is usually employed for the measurement of tumor topology, which reflects structural changes of a tissue. We investigated the possibility of OCT in detecting changes using a computer texture analysis method based on Haralick texture features, fractal dimension and the complex directional field method from different tissues. These features were used to identify special spatial characteristics, which differ healthy tissue from various skin cancers in cross-section OCT images (B-scans). Speckle reduction is an important pre-processing stage for OCT image processing. In this paper, an interval type-II fuzzy anisotropic diffusion algorithm for speckle noise reduction in OCT images was used. The Haralick texture feature set includes contrast, correlation, energy, and homogeneity evaluated in different directions. A box-counting method is applied to compute fractal dimension of investigated tissues. Additionally, we used the complex directional field calculated by the local gradient methodology to increase of the assessment quality of the diagnosis method. The complex directional field (as well as the "classical" directional field) can help describe an image as set of directions. Considering to a fact that malignant tissue grows anisotropically, some principal grooves may be observed on dermoscopic images, which mean possible existence of principal directions on OCT images. Our results suggest that described texture features may provide useful information to differentiate pathological from healthy patients. The problem of recognition melanoma from nevi is decided in this work due to the big quantity of experimental data (143 OCT-images include tumors as Basal Cell Carcinoma (BCC), Malignant Melanoma (MM) and Nevi). We have sensitivity about 90% and specificity about 85%. Further research is warranted to determine how this approach may be used to select the regions of interest automatically.

Polarimetric Wavelet Fractal Remote Sensing Principles for Space Materials (Preprint)

DTIC Science & Technology

2012-06-04

previously introduced 9-10, 28. The combination of polarimetry and wavelet-fractal analysis yields enhanced knowledge of the spatial-temporal-frequency...applications in situations that require analysis over very short time durations or where information is localized, and have been combined with polarimetry ...and D.B. Chenault, “Near Infrared Imaging Polarimetry ”, Proc. SPIE 4481, pp. 30-31, 2001. [8] A.B. Mahler, P. Smith, R. Chipman, G. Smith, N

Fractal aggregates in tennis ball systems

NASA Astrophysics Data System (ADS)

Sabin, J.; Bandín, M.; Prieto, G.; Sarmiento, F.

2009-09-01

We present a new practical exercise to explain the mechanisms of aggregation of some colloids which are otherwise not easy to understand. We have used tennis balls to simulate, in a visual way, the aggregation of colloids under reaction-limited colloid aggregation (RLCA) and diffusion-limited colloid aggregation (DLCA) regimes. We have used the images of the cluster of balls, following Forrest and Witten's pioneering studies on the aggregation of smoke particles, to estimate their fractal dimension.

Fractal dimension analysis of weight-bearing bones of rats during skeletal unloading

NASA Technical Reports Server (NTRS)

Pornprasertsuk, S.; Ludlow, J. B.; Webber, R. L.; Tyndall, D. A.; Sanhueza, A. I.; Yamauchi, M.

2001-01-01

Fractal analysis was used to quantify changes in trabecular bone induced through the use of a rat tail-suspension model to simulate microgravity-induced osteopenia. Fractal dimensions were estimated from digitized radiographs obtained from tail-suspended and ambulatory rats. Fifty 4-month-old male Sprague-Dawley rats were divided into groups of 24 ambulatory (control) and 26 suspended (test) animals. Rats of both groups were killed after periods of 1, 4, and 8 weeks. Femurs and tibiae were removed and radiographed with standard intraoral films and digitized using a flatbed scanner. Square regions of interest were cropped at proximal, middle, and distal areas of each bone. Fractal dimensions were estimated from slopes of regression lines fitted to circularly averaged plots of log power vs. log spatial frequency. The results showed that the computed fractal dimensions were significantly greater for images of trabecular bones from tail-suspended groups than for ambulatory groups (p < 0.01) at 1 week. Periods between 1 and 4 weeks likewise yielded significantly different estimates (p < 0.05), consistent with an increase in bone loss. In the tibiae, the proximal regions of the suspended group produced significantly greater fractal dimensions than other regions (p < 0.05), which suggests they were more susceptible to unloading. The data are consistent with other studies demonstrating osteopenia in microgravity environments and the regional response to skeletal unloading. Thus, fractal analysis could be a useful technique to evaluate the structural changes of bone.

Investigation of non-premixed flame combustion characters in GO2/GH2 shear coaxial injectors using non-intrusive optical diagnostics

NASA Astrophysics Data System (ADS)

Dai, Jian; Yu, NanJia; Cai, GuoBiao

2015-12-01

Single-element combustor experiments are conducted for three shear coaxial geometry configuration injectors by using gaseous oxygen and gaseous hydrogen (GO2/GH2) as propellants. During the combustion process, several spatially and timeresolved non-intrusive optical techniques, such as OH planar laser induced fluorescence (PLIF), high speed imaging, and infrared imaging, are simultaneously employed to observe the OH radical concentration distribution, flame fluctuations, and temperature fields. The results demonstrate that the turbulent flow phenomenon of non-premixed flame exhibits a remarkable periodicity, and the mixing ratio becomes a crucial factor to influence the combustion flame length. The high speed and infrared images have a consistent temperature field trend. As for the OH-PLIF images, an intuitionistic local flame structure is revealed by single-shot instantaneous images. Furthermore, the means and standard deviations of OH radical intensity are acquired to provide statistical information regarding the flame, which may be helpful for validation of numerical simulations in future. Parameters of structure configurations, such as impinging angle and oxygen post thickness, play an important role in the reaction zone distribution. Based on a successful flame contour extraction method assembled with non-linear anisotropic diffusive filtering and variational level-set, it is possible to implement a fractal analysis to describe the fractal characteristics of the non-premixed flame contour. As a result, the flame front cannot be regarded as a fractal object. However, this turbulent process presents a self-similarity characteristic.

A multifractal approach to space-filling recovery for PET quantification.

PubMed

Willaime, Julien M Y; Aboagye, Eric O; Tsoumpas, Charalampos; Turkheimer, Federico E

2014-11-01

A new image-based methodology is developed for estimating the apparent space-filling properties of an object of interest in PET imaging without need for a robust segmentation step and used to recover accurate estimates of total lesion activity (TLA). A multifractal approach and the fractal dimension are proposed to recover the apparent space-filling index of a lesion (tumor volume, TV) embedded in nonzero background. A practical implementation is proposed, and the index is subsequently used with mean standardized uptake value (SUV mean) to correct TLA estimates obtained from approximate lesion contours. The methodology is illustrated on fractal and synthetic objects contaminated by partial volume effects (PVEs), validated on realistic (18)F-fluorodeoxyglucose PET simulations and tested for its robustness using a clinical (18)F-fluorothymidine PET test-retest dataset. TLA estimates were stable for a range of resolutions typical in PET oncology (4-6 mm). By contrast, the space-filling index and intensity estimates were resolution dependent. TLA was generally recovered within 15% of ground truth on postfiltered PET images affected by PVEs. Volumes were recovered within 15% variability in the repeatability study. Results indicated that TLA is a more robust index than other traditional metrics such as SUV mean or TV measurements across imaging protocols. The fractal procedure reported here is proposed as a simple and effective computational alternative to existing methodologies which require the incorporation of image preprocessing steps (i.e., partial volume correction and automatic segmentation) prior to quantification.

Three-dimensional fractal analysis of 99mTc-MAA SPECT images in chronic thromboembolic pulmonary hypertension for evaluation of response to balloon pulmonary angioplasty: association with pulmonary arterial pressure.

PubMed

Maruoka, Yasuhiro; Nagao, Michinobu; Baba, Shingo; Isoda, Takuro; Kitamura, Yoshiyuki; Yamazaki, Yuzo; Abe, Koichiro; Sasaki, Masayuki; Abe, Kohtaro; Honda, Hiroshi

2017-06-01

Balloon pulmonary angioplasty (BPA) is used for inoperable chronic thromboembolic pulmonary hypertension (CTEPH), but its effect cannot be evaluated noninvasively. We devised a noninvasive quantitative index of response to BPA using three-dimensional fractal analysis (3D-FA) of technetium-99m-macroaggregated albumin (Tc-MAA) single-photon emission computed tomography (SPECT). Forty CTEPH patients who underwent pulmonary perfusion scintigraphy and mean pulmonary arterial pressure (mPAP) measurement by right heart catheterization before and after BPA were studied. The total uptake volume (TUV) in bilateral lungs was determined from maximum intensity projection Tc-MAA SPECT images. Fractal dimension was assessed by 3D-FA. Parameters were compared before and after BPA, and between patients with post-BPA mPAP more than 30 mmHg and less than or equal to 30 mmHg. Receiver operating characteristic analysis was carried out. BPA significantly improved TUV (595±204-885±214 ml, P<0.001) and reduced the laterality of uptake (238±147-135±131 ml, P<0.001). Patients with poor therapeutic response (post-BPA mPAP≥30 mmHg, n=16) showed a significantly smaller TUV increase (P=0.044) and a significantly greater post-BPA fractal dimension (P<0.001) than the low-mPAP group. Fractal dimension correlated with mPAP values before and after BPA (P=0.013 and 0.001, respectively). A post-BPA fractal dimension threshold of 2.4 distinguished between BPA success and failure with 75% sensitivity, 79% specificity, 78% accuracy, and area under the curve of 0.85. 3D-FA using Tc-MAA SPECT pulmonary perfusion scintigraphy enables a noninvasive evaluation of the response of CTEPH patients to BPA.

A fractal derivative model for the characterization of anomalous diffusion in magnetic resonance imaging

NASA Astrophysics Data System (ADS)

Liang, Yingjie; Ye, Allen Q.; Chen, Wen; Gatto, Rodolfo G.; Colon-Perez, Luis; Mareci, Thomas H.; Magin, Richard L.

2016-10-01

Non-Gaussian (anomalous) diffusion is wide spread in biological tissues where its effects modulate chemical reactions and membrane transport. When viewed using magnetic resonance imaging (MRI), anomalous diffusion is characterized by a persistent or 'long tail' behavior in the decay of the diffusion signal. Recent MRI studies have used the fractional derivative to describe diffusion dynamics in normal and post-mortem tissue by connecting the order of the derivative with changes in tissue composition, structure and complexity. In this study we consider an alternative approach by introducing fractal time and space derivatives into Fick's second law of diffusion. This provides a more natural way to link sub-voxel tissue composition with the observed MRI diffusion signal decay following the application of a diffusion-sensitive pulse sequence. Unlike previous studies using fractional order derivatives, here the fractal derivative order is directly connected to the Hausdorff fractal dimension of the diffusion trajectory. The result is a simpler, computationally faster, and more direct way to incorporate tissue complexity and microstructure into the diffusional dynamics. Furthermore, the results are readily expressed in terms of spectral entropy, which provides a quantitative measure of the overall complexity of the heterogeneous and multi-scale structure of biological tissues. As an example, we apply this new model for the characterization of diffusion in fixed samples of the mouse brain. These results are compared with those obtained using the mono-exponential, the stretched exponential, the fractional derivative, and the diffusion kurtosis models. Overall, we find that the order of the fractal time derivative, the diffusion coefficient, and the spectral entropy are potential biomarkers to differentiate between the microstructure of white and gray matter. In addition, we note that the fractal derivative model has practical advantages over the existing models from the perspective of computational accuracy and efficiency.

Robust estimation of fractal measures for characterizing the structural complexity of the human brain: optimization and reproducibility

PubMed Central

Goñi, Joaquín; Sporns, Olaf; Cheng, Hu; Aznárez-Sanado, Maite; Wang, Yang; Josa, Santiago; Arrondo, Gonzalo; Mathews, Vincent P; Hummer, Tom A; Kronenberger, William G; Avena-Koenigsberger, Andrea; Saykin, Andrew J.; Pastor, María A.

2013-01-01

High-resolution isotropic three-dimensional reconstructions of human brain gray and white matter structures can be characterized to quantify aspects of their shape, volume and topological complexity. In particular, methods based on fractal analysis have been applied in neuroimaging studies to quantify the structural complexity of the brain in both healthy and impaired conditions. The usefulness of such measures for characterizing individual differences in brain structure critically depends on their within-subject reproducibility in order to allow the robust detection of between-subject differences. This study analyzes key analytic parameters of three fractal-based methods that rely on the box-counting algorithm with the aim to maximize within-subject reproducibility of the fractal characterizations of different brain objects, including the pial surface, the cortical ribbon volume, the white matter volume and the grey matter/white matter boundary. Two separate datasets originating from different imaging centers were analyzed, comprising, 50 subjects with three and 24 subjects with four successive scanning sessions per subject, respectively. The reproducibility of fractal measures was statistically assessed by computing their intra-class correlations. Results reveal differences between different fractal estimators and allow the identification of several parameters that are critical for high reproducibility. Highest reproducibility with intra-class correlations in the range of 0.9–0.95 is achieved with the correlation dimension. Further analyses of the fractal dimensions of parcellated cortical and subcortical gray matter regions suggest robustly estimated and region-specific patterns of individual variability. These results are valuable for defining appropriate parameter configurations when studying changes in fractal descriptors of human brain structure, for instance in studies of neurological diseases that do not allow repeated measurements or for disease-course longitudinal studies. PMID:23831414

On the fractal morphology of combustion-generated soot aggregates

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

Koylu, U.O.

1995-12-31

The fractal properties of soot aggregates were investigated using ex-situ and in-situ experimental methods as well as computer simulations. Ex-situ experiments involved thermophoretic sampling and analysis by transmission electron microscopy (TEM), while in-situ measurements employed angular static light scattering and data inversion based on Rayleigh-Debye-Gans (RDG) approximation. Computer simulations used a sequential algorithm which mimics mass fractal-like structures. So from a variety of hydrocarbon-fueled laminar and turbulent nonpremixed flame environments were considered in the present study. The TEM analysis of projected soot images sampled from fuel-rich conditions of buoyant and weakly-buoyant laminar flames indicated that the fractal dimension of sootmore » was relatively independent of position in flames, fuel type and flame condition. These measurements yielded an average fractal dimension of 1.8, although other structure parameters such as the primary particle diameters and number of primary particles in aggregates had wide range of values. Fractal prefactor (lacunarity) was also measured for soot sampled from the fuel-lean conditions of turbulent flames, considering the actual morphology by tilting the samples during TEM analysis. These measurements yielded a fractal dimension of 1.65 and a lacunarity of 8.5, with experimental uncertainties (95% confidence) of 0.08 and 0.5, respectively. Relationships between the actual and projected structure properties of soot were also developed by combining TEM observations with numerical simulations. Practical approximate formulae were suggested to find radius of gyration of an aggregate from its maximum dimension, and number of primary particles in an aggregate from projected area. Finally, the fractal dimension and lacunarity of soot were obtained using light scattering for the same conditions of the above TEM measurements.« less

The Application of Fractal and Multifractal Theory in Hydraulic-Flow-Unit Characterization and Permeability Estimation

NASA Astrophysics Data System (ADS)

Chen, X.; Yao, G.; Cai, J.

2017-12-01

Pore structure characteristics are important factors in influencing the fluid transport behavior of porous media, such as pore-throat ratio, pore connectivity and size distribution, moreover, wettability. To accurately characterize the diversity of pore structure among HFUs, five samples selected from different HFUs (porosities are approximately equal, however permeability varies widely) were chosen to conduct micro-computerized tomography test to acquire direct 3D images of pore geometries and to perform mercury injection experiments to obtain the pore volume-radii distribution. To characterize complex and high nonlinear pore structure of all samples, three classic fractal geometry models were applied. Results showed that each HFU has similar box-counting fractal dimension and generalized fractal dimension in the number-area model, but there are significant differences in multifractal spectrums. In the radius-volume model, there are three obvious linear segments, corresponding to three fractal dimension values, and the middle one is proved as the actual fractal dimension according to the maximum radius. In the number-radius model, the spherical-pore size distribution extracted by maximum ball algorithm exist a decrease in the number of small pores compared with the fractal power rate rather than the traditional linear law. Among the three models, only multifractal analysis can classify the HFUs accurately. Additionally, due to the tightness and low-permeability in reservoir rocks, connate water film existing in the inner surface of pore channels commonly forms bound water. The conventional model which is known as Yu-Cheng's model has been proved to be typically not applicable. Considering the effect of irreducible water saturation, an improved fractal permeability model was also deduced theoretically. The comparison results showed that the improved model can be applied to calculate permeability directly and accurately in such unconventional rocks.

Fractal lacunarity of trabecular bone and magnetic resonance imaging: New perspectives for osteoporotic fracture risk assessment

PubMed Central

Zaia, Annamaria

2015-01-01

Osteoporosis represents one major health condition for our growing elderly population. It accounts for severe morbidity and increased mortality in postmenopausal women and it is becoming an emerging health concern even in aging men. Screening of the population at risk for bone degeneration and treatment assessment of osteoporotic patients to prevent bone fragility fractures represent useful tools to improve quality of life in the elderly and to lighten the related socio-economic impact. Bone mineral density (BMD) estimate by means of dual-energy X-ray absorptiometry is normally used in clinical practice for osteoporosis diagnosis. Nevertheless, BMD alone does not represent a good predictor of fracture risk. From a clinical point of view, bone microarchitecture seems to be an intriguing aspect to characterize bone alteration patterns in aging and pathology. The widening into clinical practice of medical imaging techniques and the impressive advances in information technologies together with enhanced capacity of power calculation have promoted proliferation of new methods to assess changes of trabecular bone architecture (TBA) during aging and osteoporosis. Magnetic resonance imaging (MRI) has recently arisen as a useful tool to measure bone structure in vivo. In particular, high-resolution MRI techniques have introduced new perspectives for TBA characterization by non-invasive non-ionizing methods. However, texture analysis methods have not found favor with clinicians as they produce quite a few parameters whose interpretation is difficult. The introduction in biomedical field of paradigms, such as theory of complexity, chaos, and fractals, suggests new approaches and provides innovative tools to develop computerized methods that, by producing a limited number of parameters sensitive to pathology onset and progression, would speed up their application into clinical practice. Complexity of living beings and fractality of several physio-anatomic structures suggest fractal analysis as a promising approach to quantify morpho-functional changes in both aging and pathology. In this particular context, fractal lacunarity seems to be the proper tool to characterize TBA texture as it is able to describe both discontinuity of bone network and sizes of bone marrow spaces, whose changes are an index of bone fracture risk. In this paper, an original method of MRI texture analysis, based on TBA fractal lacunarity is described and discussed in the light of new perspectives for early diagnosis of osteoporotic fractures. PMID:25793162

Integrated quantitative fractal polarimetric analysis of monolayer lung cancer cells

NASA Astrophysics Data System (ADS)

Shrestha, Suman; Zhang, Lin; Quang, Tri; Farrahi, Tannaz; Narayan, Chaya; Deshpande, Aditi; Na, Ying; Blinzler, Adam; Ma, Junyu; Liu, Bo; Giakos, George C.

2014-05-01

Digital diagnostic pathology has become one of the most valuable and convenient advancements in technology over the past years. It allows us to acquire, store and analyze pathological information from the images of histological and immunohistochemical glass slides which are scanned to create digital slides. In this study, efficient fractal, wavelet-based polarimetric techniques for histological analysis of monolayer lung cancer cells will be introduced and different monolayer cancer lines will be studied. The outcome of this study indicates that application of fractal, wavelet polarimetric principles towards the analysis of squamous carcinoma and adenocarcinoma cancer cell lines may be proved extremely useful in discriminating among healthy and lung cancer cells as well as differentiating among different lung cancer cells.

Electromagnetic backscattering from one-dimensional drifting fractal sea surface II: Electromagnetic backscattering model

NASA Astrophysics Data System (ADS)

Tao, Xie; William, Perrie; Shang-Zhuo, Zhao; He, Fang; Wen-Jin, Yu; Yi-Jun, He

2016-07-01

Sea surface current has a significant influence on electromagnetic (EM) backscattering signals and may constitute a dominant synthetic aperture radar (SAR) imaging mechanism. An effective EM backscattering model for a one-dimensional drifting fractal sea surface is presented in this paper. This model is used to simulate EM backscattering signals from the drifting sea surface. Numerical results show that ocean currents have a significant influence on EM backscattering signals from the sea surface. The normalized radar cross section (NRCS) discrepancies between the model for a coupled wave-current fractal sea surface and the model for an uncoupled fractal sea surface increase with the increase of incidence angle, as well as with increasing ocean currents. Ocean currents that are parallel to the direction of the wave can weaken the EM backscattering signal intensity, while the EM backscattering signal is intensified by ocean currents propagating oppositely to the wave direction. The model presented in this paper can be used to study the SAR imaging mechanism for a drifting sea surface. Project supported by the National Natural Science Foundation of China (Grant No. 41276187), the Global Change Research Program of China (Grant No. 2015CB953901), the Priority Academic Program Development of Jiangsu Higher Education Institutions, China, the Program for the Innovation Research and Entrepreneurship Team in Jiangsu Province, China, the Canadian Program on Energy Research and Development, and the Canadian World Class Tanker Safety Service Program.

Fractal Characteristics of the Pore Network in Diatomites Using Mercury Porosimetry and Image Analysis

NASA Astrophysics Data System (ADS)

Stańczak, Grażyna; Rembiś, Marek; Figarska-Warchoł, Beata; Toboła, Tomasz

The complex pore space considerably affects the unique properties of diatomite and its significant potential for many industrial applications. The pore network in the diatomite from the Lower Miocene strata of the Skole nappe (the Jawornik deposit, SE Poland) has been investigated using a fractal approach. The fractal dimension of the pore-space volume was calculated using the Menger sponge as a model of a porous body and the mercury porosimetry data in a pore-throat diameter range between 10,000 and 10 nm. Based on the digital analyses of the two-dimensional images from thin sections taken under a scanning electron microscope at the backscattered electron mode at different magnifications, the authors tried to quantify the pore spaces of the diatomites using the box counting method. The results derived from the analyses of the pore-throat diameter distribution using mercury porosimetry have revealed that the pore space of the diatomite has the bifractal structure in two separated ranges of the pore-throat diameters considerably smaller than the pore-throat sizes corresponding to threshold pressures. Assuming that the fractal dimensions identified for the ranges of the smaller pore-throat diameters characterize the overall pore-throat network in the Jawornik diatomite, we can set apart the distribution of the pore-throat volume (necks) and the pore volume from the distribution of the pore-space volume (pores and necks together).

Bridging Three Orders of Magnitude: Multiple Scattered Waves Sense Fractal Microscopic Structures via Dispersion

NASA Astrophysics Data System (ADS)

Lambert, Simon A.; Näsholm, Sven Peter; Nordsletten, David; Michler, Christian; Juge, Lauriane; Serfaty, Jean-Michel; Bilston, Lynne; Guzina, Bojan; Holm, Sverre; Sinkus, Ralph

2015-08-01

Wave scattering provides profound insight into the structure of matter. Typically, the ability to sense microstructure is determined by the ratio of scatterer size to probing wavelength. Here, we address the question of whether macroscopic waves can report back the presence and distribution of microscopic scatterers despite several orders of magnitude difference in scale between wavelength and scatterer size. In our analysis, monosized hard scatterers 5 μ m in radius are immersed in lossless gelatin phantoms to investigate the effect of multiple reflections on the propagation of shear waves with millimeter wavelength. Steady-state monochromatic waves are imaged in situ via magnetic resonance imaging, enabling quantification of the phase velocity at a voxel size big enough to contain thousands of individual scatterers, but small enough to resolve the wavelength. We show in theory, experiments, and simulations that the resulting coherent superposition of multiple reflections gives rise to power-law dispersion at the macroscopic scale if the scatterer distribution exhibits apparent fractality over an effective length scale that is comparable to the probing wavelength. Since apparent fractality is naturally present in any random medium, microstructure can thereby leave its fingerprint on the macroscopically quantifiable power-law exponent. Our results are generic to wave phenomena and carry great potential for sensing microstructure that exhibits intrinsic fractality, such as, for instance, vasculature.

Fracture Surface Morphology and Impact Strength of Cellulose/PLA Composites.

PubMed

Gao, Honghong; Qiang, Tao

2017-06-07

Polylactide (PLA)-based composite materials reinforced with ball-milled celluloses were manufactured by extrusion blending followed by injection molding. Their surface morphology from impact fracture were imaged with scanning electron microscopy (SEM) and investigated by calculating their fractal dimensions. Then, linear regression was used to explore the relationship between fractal dimension and impact strength of the resultant cellulose/PLA composite materials. The results show that filling the ball-milled celluloses into PLA can improve the impact toughness of PLA by a minimum of 38%. It was demonstrated that the fracture pattern of the cellulose/PLA composite materials is different from that of pristine PLA. For the resultant composite materials, the fractal dimension of the impact fractured surfaces increased with increasing filling content and decreasing particle size of the ball-milled cellulose particles. There were highly positive correlations between fractal dimension of the fractured surfaces and impact strength of the cellulose/PLA composites. However, the linearity between fractal dimension and impact strength were different for the different methods, due to their different R-squared values. The approach presented in this work will help to understand the structure-property relationships of composite materials from a new perspective.

Fracture Surface Morphology and Impact Strength of Cellulose/PLA Composites

PubMed Central

Gao, Honghong; Qiang, Tao

2017-01-01

Polylactide (PLA)-based composite materials reinforced with ball-milled celluloses were manufactured by extrusion blending followed by injection molding. Their surface morphology from impact fracture were imaged with scanning electron microscopy (SEM) and investigated by calculating their fractal dimensions. Then, linear regression was used to explore the relationship between fractal dimension and impact strength of the resultant cellulose/PLA composite materials. The results show that filling the ball-milled celluloses into PLA can improve the impact toughness of PLA by a minimum of 38%. It was demonstrated that the fracture pattern of the cellulose/PLA composite materials is different from that of pristine PLA. For the resultant composite materials, the fractal dimension of the impact fractured surfaces increased with increasing filling content and decreasing particle size of the ball-milled cellulose particles. There were highly positive correlations between fractal dimension of the fractured surfaces and impact strength of the cellulose/PLA composites. However, the linearity between fractal dimension and impact strength were different for the different methods, due to their different R-squared values. The approach presented in this work will help to understand the structure–property relationships of composite materials from a new perspective. PMID:28772983

Fractality and growth of He bubbles in metals

NASA Astrophysics Data System (ADS)

Kajita, Shin; Ito, Atsushi M.; Ohno, Noriyasu

2017-08-01

Pinholes are formed on surfaces of metals by the exposure to helium plasmas, and they are regarded as the initial process of the growth of fuzzy nanostructures. In this study, number density of the pinholes is investigated in detail from the scanning electron microscope (SEM) micrographs of tungsten and tantalum exposed to the helium plasmas. A power law relation was identified between the number density and the size of pinholes. From the slope and the region where the power law was satisfied, the fractal dimension D and smin, which characterize the SEM images, are deduced. Parametric dependences and material dependence of D and smin are revealed. To explain the fractality, simple Monte-Carlo simulations including random walks of He atoms and absorption on bubble was introduced. It is shown that the initial position of the random walk is one of the key factors to deduce the fractality. The results indicated that new nucleations of bubbles are necessary to reproduce the number-density distribution of bubbles.

Microvascular fractal dimension predicts prognosis and response to chemotherapy in glioblastoma: an automatic image analysis study.

PubMed

Chen, Cong; He, Zhi-Cheng; Shi, Yu; Zhou, Wenchao; Zhang, Xia; Xiao, Hua-Liang; Wu, Hai-Bo; Yao, Xiao-Hong; Luo, Wan-Chun; Cui, You-Hong; Bao, Shideng; Kung, Hsiang-Fu; Bian, Xiu-Wu; Ping, Yi-Fang

2018-05-15

The microvascular profile has been included in the WHO glioma grading criteria. Nevertheless, microvessels in gliomas of the same WHO grade, e.g., WHO IV glioblastoma (GBM), exhibit heterogeneous and polymorphic morphology, whose possible clinical significance remains to be determined. In this study, we employed a fractal geometry-derived parameter, microvascular fractal dimension (mvFD), to quantify microvessel complexity and developed a home-made macro in Image J software to automatically determine mvFD from the microvessel-stained immunohistochemical images of GBM. We found that mvFD effectively quantified the morphological complexity of GBM microvasculature. Furthermore, high mvFD favored the survival of GBM patients as an independent prognostic indicator and predicted a better response to chemotherapy of GBM patients. When investigating the underlying relations between mvFD and tumor growth by deploying Ki67/mvFD as an index for microvasculature-normalized tumor proliferation, we discovered an inverse correlation between mvFD and Ki67/mvFD. Furthermore, mvFD inversely correlated with the expressions of a glycolytic marker, LDHA, which indicated poor prognosis of GBM patients. Conclusively, we developed an automatic approach for mvFD measurement, and demonstrated that mvFD could predict the prognosis and response to chemotherapy of GBM patients.

Mapping Transient Hyperventilation Induced Alterations with Estimates of the Multi-Scale Dynamics of BOLD Signal.

PubMed

Kiviniemi, Vesa; Remes, Jukka; Starck, Tuomo; Nikkinen, Juha; Haapea, Marianne; Silven, Olli; Tervonen, Osmo

2009-01-01

Temporal blood oxygen level dependent (BOLD) contrast signals in functional MRI during rest may be characterized by power spectral distribution (PSD) trends of the form 1/f(alpha). Trends with 1/f characteristics comprise fractal properties with repeating oscillation patterns in multiple time scales. Estimates of the fractal properties enable the quantification of phenomena that may otherwise be difficult to measure, such as transient, non-linear changes. In this study it was hypothesized that the fractal metrics of 1/f BOLD signal trends can map changes related to dynamic, multi-scale alterations in cerebral blood flow (CBF) after a transient hyperventilation challenge. Twenty-three normal adults were imaged in a resting-state before and after hyperventilation. Different variables (1/f trend constant alpha, fractal dimension D(f), and, Hurst exponent H) characterizing the trends were measured from BOLD signals. The results show that fractal metrics of the BOLD signal follow the fractional Gaussian noise model, even during the dynamic CBF change that follows hyperventilation. The most dominant effect on the fractal metrics was detected in grey matter, in line with previous hyperventilation vaso-reactivity studies. The alpha was able to differentiate also blood vessels from grey matter changes. D(f) was most sensitive to grey matter. H correlated with default mode network areas before hyperventilation but this pattern vanished after hyperventilation due to a global increase in H. In the future, resting-state fMRI combined with fractal metrics of the BOLD signal may be used for analyzing multi-scale alterations of cerebral blood flow.

Histomorphometric, fractal and lacunarity comparative analysis of sheep (Ovis aries), goat (Capra hircus) and roe deer (Capreolus capreolus) compact bone samples.

PubMed

Gudea, A I; Stefan, A C

2013-08-01

Quantitative and qualitative studies dealing with histomorphometry of the bone tissue play a new role in modern legal medicine/forensic medicine and archaeozoology nowadays. This study deals with the differences found in case of humerus and metapodial bones of recent sheep (Ovis aries), goat (Capra hircus) and roedeer (Capreolus capreolus) specimens, both from a qualitative point of view, but mainly from a quantitative perspective. A novel perspective given by the fractal analysis performed on the digital histological images is approached. This study shows that the qualitative assessment may not be a reliable one due to the close resemblance of the structures. From the quantitative perspective (several measurements performed on osteonal units and statistical processing of data),some of the elements measured show significant differences among 3 species(the primary osteonal diameter, etc.). The fractal analysis and the lacunarity of the images show a great deal of potential, proving that this type of analysis can be of great help in the separation of the material from this perspective.

Research on cloud background infrared radiation simulation based on fractal and statistical data

NASA Astrophysics Data System (ADS)

Liu, Xingrun; Xu, Qingshan; Li, Xia; Wu, Kaifeng; Dong, Yanbing

2018-02-01

Cloud is an important natural phenomenon, and its radiation causes serious interference to infrared detector. Based on fractal and statistical data, a method is proposed to realize cloud background simulation, and cloud infrared radiation data field is assigned using satellite radiation data of cloud. A cloud infrared radiation simulation model is established using matlab, and it can generate cloud background infrared images for different cloud types (low cloud, middle cloud, and high cloud) in different months, bands and sensor zenith angles.

Fusion of multiscale wavelet-based fractal analysis on retina image for stroke prediction.

PubMed

Che Azemin, M Z; Kumar, Dinesh K; Wong, T Y; Wang, J J; Kawasaki, R; Mitchell, P; Arjunan, Sridhar P

2010-01-01

In this paper, we present a novel method of analyzing retinal vasculature using Fourier Fractal Dimension to extract the complexity of the retinal vasculature enhanced at different wavelet scales. Logistic regression was used as a fusion method to model the classifier for 5-year stroke prediction. The efficacy of this technique has been tested using standard pattern recognition performance evaluation, Receivers Operating Characteristics (ROC) analysis and medical prediction statistics, odds ratio. Stroke prediction model was developed using the proposed system.

Skin cancer texture analysis of OCT images based on Haralick, fractal dimension, Markov random field features, and the complex directional field features

NASA Astrophysics Data System (ADS)

Raupov, Dmitry S.; Myakinin, Oleg O.; Bratchenko, Ivan A.; Zakharov, Valery P.; Khramov, Alexander G.

2016-10-01

In this paper, we propose a report about our examining of the validity of OCT in identifying changes using a skin cancer texture analysis compiled from Haralick texture features, fractal dimension, Markov random field method and the complex directional features from different tissues. Described features have been used to detect specific spatial characteristics, which can differentiate healthy tissue from diverse skin cancers in cross-section OCT images (B- and/or C-scans). In this work, we used an interval type-II fuzzy anisotropic diffusion algorithm for speckle noise reduction in OCT images. The Haralick texture features as contrast, correlation, energy, and homogeneity have been calculated in various directions. A box-counting method is performed to evaluate fractal dimension of skin probes. Markov random field have been used for the quality enhancing of the classifying. Additionally, we used the complex directional field calculated by the local gradient methodology to increase of the assessment quality of the diagnosis method. Our results demonstrate that these texture features may present helpful information to discriminate tumor from healthy tissue. The experimental data set contains 488 OCT-images with normal skin and tumors as Basal Cell Carcinoma (BCC), Malignant Melanoma (MM) and Nevus. All images were acquired from our laboratory SD-OCT setup based on broadband light source, delivering an output power of 20 mW at the central wavelength of 840 nm with a bandwidth of 25 nm. We obtained sensitivity about 97% and specificity about 73% for a task of discrimination between MM and Nevus.

A multifractal approach to space-filling recovery for PET quantification

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

Willaime, Julien M. Y., E-mail: julien.willaime@siemens.com; Aboagye, Eric O.; Tsoumpas, Charalampos

2014-11-01

Purpose: A new image-based methodology is developed for estimating the apparent space-filling properties of an object of interest in PET imaging without need for a robust segmentation step and used to recover accurate estimates of total lesion activity (TLA). Methods: A multifractal approach and the fractal dimension are proposed to recover the apparent space-filling index of a lesion (tumor volume, TV) embedded in nonzero background. A practical implementation is proposed, and the index is subsequently used with mean standardized uptake value (SUV {sub mean}) to correct TLA estimates obtained from approximate lesion contours. The methodology is illustrated on fractal andmore » synthetic objects contaminated by partial volume effects (PVEs), validated on realistic {sup 18}F-fluorodeoxyglucose PET simulations and tested for its robustness using a clinical {sup 18}F-fluorothymidine PET test–retest dataset. Results: TLA estimates were stable for a range of resolutions typical in PET oncology (4–6 mm). By contrast, the space-filling index and intensity estimates were resolution dependent. TLA was generally recovered within 15% of ground truth on postfiltered PET images affected by PVEs. Volumes were recovered within 15% variability in the repeatability study. Results indicated that TLA is a more robust index than other traditional metrics such as SUV {sub mean} or TV measurements across imaging protocols. Conclusions: The fractal procedure reported here is proposed as a simple and effective computational alternative to existing methodologies which require the incorporation of image preprocessing steps (i.e., partial volume correction and automatic segmentation) prior to quantification.« less

Cell type classifiers for breast cancer microscopic images based on fractal dimension texture analysis of image color layers.

PubMed

Jitaree, Sirinapa; Phinyomark, Angkoon; Boonyaphiphat, Pleumjit; Phukpattaranont, Pornchai

2015-01-01

Having a classifier of cell types in a breast cancer microscopic image (BCMI), obtained with immunohistochemical staining, is required as part of a computer-aided system that counts the cancer cells in such BCMI. Such quantitation by cell counting is very useful in supporting decisions and planning of the medical treatment of breast cancer. This study proposes and evaluates features based on texture analysis by fractal dimension (FD), for the classification of histological structures in a BCMI into either cancer cells or non-cancer cells. The cancer cells include positive cells (PC) and negative cells (NC), while the normal cells comprise stromal cells (SC) and lymphocyte cells (LC). The FD feature values were calculated with the box-counting method from binarized images, obtained by automatic thresholding with Otsu's method of the grayscale images for various color channels. A total of 12 color channels from four color spaces (RGB, CIE-L*a*b*, HSV, and YCbCr) were investigated, and the FD feature values from them were used with decision tree classifiers. The BCMI data consisted of 1,400, 1,200, and 800 images with pixel resolutions 128 × 128, 192 × 192, and 256 × 256, respectively. The best cross-validated classification accuracy was 93.87%, for distinguishing between cancer and non-cancer cells, obtained using the Cr color channel with window size 256. The results indicate that the proposed algorithm, based on fractal dimension features extracted from a color channel, performs well in the automatic classification of the histology in a BCMI. This might support accurate automatic cell counting in a computer-assisted system for breast cancer diagnosis. © Wiley Periodicals, Inc.

Rheological and fractal characteristics of unconditioned and conditioned water treatment residuals.

PubMed

Dong, Y J; Wang, Y L; Feng, J

2011-07-01

The rheological and fractal characteristics of raw (unconditioned) and conditioned water treatment residuals (WTRs) were investigated in this study. Variations in morphology, size, and image fractal dimensions of the flocs/aggregates in these WTR systems with increasing polymer doses were analyzed. The results showed that when the raw WTRs were conditioned with the polymer CZ8688, the optimum polymer dosage was observed at 24 kg/ton dry sludge. The average diameter of irregularly shaped flocs/aggregates in the WTR suspensions increased from 42.54 μm to several hundred micrometers with increasing polymer doses. Furthermore, the aggregates in the conditioned WTR system displayed boundary/surface and mass fractals. At the optimum polymer dosage, the aggregates formed had a volumetric average diameter of about 820.7 μm, with a one-dimensional fractal dimension of 1.01 and a mass fractal dimension of 2.74 on the basis of the image analysis. Rheological tests indicated that the conditioned WTRs at the optimum polymer dosage showed higher levels of shear-thinning behavior than the raw WTRs. Variations in the limiting viscosity (η(∞)) of conditioned WTRs with sludge content could be described by a linear equation, which were different from the often-observed empirical exponential relationship for most municipal sludge. With increasing temperature, the η(∞) of the raw WTRs decreased more rapidly than that of the raw WTRs. Good fitting results for the relationships between lgη(∞)∼T using the Arrhenius equation indicate that the WTRs had a much higher activation energy for viscosity of about 17.86-26.91 J/mol compared with that of anaerobic granular sludge (2.51 J/mol) (Mu and Yu, 2006). In addition, the Bingham plastic model adequately described the rheological behavior of the conditioned WTRs, whereas the rheology of the raw WTRs fit the Herschel-Bulkley model well at only certain sludge contents. Considering the good power-law relationships between the limiting viscosity and sludge content of the conditioned WTRs, their mass fractal dimensions were calculated through the models proposed by Shih et al. (1990), which were 2.48 for these conditioned WTR aggregates. The results demonstrate that conditioned WTRs behave like weak-link flocs/aggregates. Copyright © 2011 Elsevier Ltd. All rights reserved.

Effect of angle of deposition on the Fractal properties of ZnO thin film surface

NASA Astrophysics Data System (ADS)

Yadav, R. P.; Agarwal, D. C.; Kumar, Manvendra; Rajput, Parasmani; Tomar, D. S.; Pandey, S. N.; Priya, P. K.; Mittal, A. K.

2017-09-01

Zinc oxide (ZnO) thin films were prepared by atom beam sputtering at various deposition angles in the range of 20-75°. The deposited thin films were examined by glancing angle X-ray diffraction and atomic force microscopy (AFM). Scaling law analysis was performed on AFM images to show that the thin film surfaces are self-affine. Fractal dimension of each of the 256 vertical sections along the fast scan direction of a discretized surface, obtained from the AFM height data, was estimated using the Higuchi's algorithm. Hurst exponent was computed from the fractal dimension. The grain sizes, as determined by applying self-correlation function on AFM micrographs, varied with the deposition angle in the same manner as the Hurst exponent.

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

X-ray imaging of aggregation in silica and zeolitic precursors

NASA Astrophysics Data System (ADS)

Morrison, Graeme R.; Browne, Michael T.; Beelen, Theo P. M.; van Garderen, Harold F.

1993-01-01

The resolution available in the King's College London scanning transmission x-ray microscope (STXM) can be exploited to study aggregate structures over a length scale from 100 nm to 10 micrometers that overlaps with and complements that available from small-angle x-ray scattering (SAXS) data. It is then possible to use these combined sets of data to test between different growth models for the aggregates, using the fractal dimension of the structures as a way of distinguishing the different models. In this paper we show some of the first transmission x-ray images taken of silica gels and zeolite precursors, materials that are of great practical and economic importance for certain selective catalytic processes in the chemical industry, and yet for which there is still only limited understanding of the complicated processes involved in their preparation. These images reveal clearly the fractal aggregates that are formed by the specimens.

Beyond Fractals and 1/f Noise: Multifractal Analysis of Complex Physiological Time Series

NASA Astrophysics Data System (ADS)

Ivanov, Plamen Ch.; Amaral, Luis A. N.; Ashkenazy, Yosef; Stanley, H. Eugene; Goldberger, Ary L.; Hausdorff, Jeffrey M.; Yoneyama, Mitsuru; Arai, Kuniharu

2001-03-01

We investigate time series with 1/f-like spectra generated by two physiologic control systems --- the human heartbeat and human gait. We show that physiological fluctuations exhibit unexpected ``hidden'' structures often described by scaling laws. In particular, our studies indicate that when analyzed on different time scales the heartbeat fluctuations exhibit cascades of branching patterns with self-similar (fractal) properties, characterized by long-range power-law anticorrelations. We find that these scaling features change during sleep and wake phases, and with pathological perturbations. Further, by means of a new wavelet-based technique, we find evidence of multifractality in the healthy human heartbeat even under resting conditions, and show that the multifractal character and nonlinear properties of the healthy heart are encoded in the Fourier phases. We uncover a loss of multifractality for a life-threatening condition, congestive heart failure. In contrast to the heartbeat, we find that the interstride interval time series of healthy human gait, a voluntary process under neural regulation, is described by a single fractal dimension (such as classical 1/f noise) indicating monofractal behavior. Thus our approach can help distinguish physiological and physical signals with comparable frequency spectra and two-point correlations, and guide modeling of their control mechanisms.

Intelligent fuzzy approach for fast fractal image compression

NASA Astrophysics Data System (ADS)

Nodehi, Ali; Sulong, Ghazali; Al-Rodhaan, Mznah; Al-Dhelaan, Abdullah; Rehman, Amjad; Saba, Tanzila

2014-12-01

Fractal image compression (FIC) is recognized as a NP-hard problem, and it suffers from a high number of mean square error (MSE) computations. In this paper, a two-phase algorithm was proposed to reduce the MSE computation of FIC. In the first phase, based on edge property, range and domains are arranged. In the second one, imperialist competitive algorithm (ICA) is used according to the classified blocks. For maintaining the quality of the retrieved image and accelerating algorithm operation, we divided the solutions into two groups: developed countries and undeveloped countries. Simulations were carried out to evaluate the performance of the developed approach. Promising results thus achieved exhibit performance better than genetic algorithm (GA)-based and Full-search algorithms in terms of decreasing the number of MSE computations. The number of MSE computations was reduced by the proposed algorithm for 463 times faster compared to the Full-search algorithm, although the retrieved image quality did not have a considerable change.

Association of the Fractal Dimension of Retinal Arteries and Veins with Quantitative Brain MRI Measures in HIV-Infected and Uninfected Women

PubMed Central

Crystal, Howard A.; Holman, Susan; Lui, Yvonne W.; Baird, Alison E.; Yu, Hua; Klein, Ronald; Rojas-Soto, Diana Marcella; Gustafson, Deborah R.; Stebbins, Glenn T.

2016-01-01

Objective The fractal dimension of retinal arteries and veins is a measure of the complexity of the vascular tree. We hypothesized that retinal fractal dimension would be associated with brain volume and white matter integrity in HIV-infected women. Design Nested case-control within longitudinal cohort study. Methods Women were recruited from the Brooklyn site of the Women’s Interagency HIV study (WIHS); 34 HIV-infected and 21 HIV-uninfected women with analyzable MRIs and retinal photographs were included. Fractal dimension was determined using the SIVA software program on skeletonized retinal images. The relationship between predictors (retinal vascular measures) and outcomes (quantitative MRI measures) were analyzed with linear regression models. All models included age, intracranial volume, and both arterial and venous fractal dimension. Some models were adjusted for blood pressure, race/ethnicity, and HIV-infection. Results The women were 45.6 ± 7.3 years of age. Higher arterial dimension was associated with larger cortical volumes, but higher venous dimension was associated with smaller cortical volumes. In fully adjusted models, venous dimension was significantly associated with fractional anisotropy (standardized β = -0.41, p = 0.009) and total gray matter volume (β = -0.24, p = 0.03), and arterial dimension with mean diffusivity (β = -0.33,.p = 0.04) and fractional anisotropy (β = 0.34, p = 0.03). HIV-infection was not associated with any retinal or MRI measure. Conclusions Higher venous fractal dimension was associated with smaller cortical volumes and lower fractional anisotropy, whereas higher arterial fractal dimension was associated with the opposite patterns. Longitudinal studies are needed to validate this finding. PMID:27158911

A New Fractal Model of Chromosome and DNA Processes

NASA Astrophysics Data System (ADS)

Bouallegue, K.

Dynamic chromosome structure remains unknown. Can fractals and chaos be used as new tools to model, identify and generate a structure of chromosomes?Fractals and chaos offer a rich environment for exploring and modeling the complexity of nature. In a sense, fractal geometry is used to describe, model, and analyze the complex forms found in nature. Fractals have also been widely not only in biology but also in medicine. To this effect, a fractal is considered an object that displays self-similarity under magnification and can be constructed using a simple motif (an image repeated on ever-reduced scales).It is worth noting that the problem of identifying a chromosome has become a challenge to find out which one of the models it belongs to. Nevertheless, the several different models (a hierarchical coiling, a folded fiber, and radial loop) have been proposed for mitotic chromosome but have not reached a dynamic model yet.This paper is an attempt to solve topological problems involved in the model of chromosome and DNA processes. By combining the fractal Julia process and the numerical dynamical system, we have finally found out four main points. First, we have developed not only a model of chromosome but also a model of mitosis and one of meiosis. Equally important, we have identified the centromere position through the numerical model captured below. More importantly, in this paper, we have discovered the processes of the cell divisions of both mitosis and meiosis. All in all, the results show that this work could have a strong impact on the welfare of humanity and can lead to a cure of genetic diseases.

Fractal Analysis of Visual Search Activity for Mass Detection During Mammographic Screening

DOE PAGES

Alamudun, Folami T.; Yoon, Hong-Jun; Hudson, Kathy; ...

2017-02-21

Purpose: The objective of this study was to assess the complexity of human visual search activity during mammographic screening using fractal analysis and to investigate its relationship with case and reader characteristics. Methods: The study was performed for the task of mammographic screening with simultaneous viewing of four coordinated breast views as typically done in clinical practice. Eye-tracking data and diagnostic decisions collected for 100 mammographic cases (25 normal, 25 benign, 50 malignant) and 10 readers (three board certified radiologists and seven radiology residents), formed the corpus data for this study. The fractal dimension of the readers’ visual scanning patternsmore » was computed with the Minkowski–Bouligand box-counting method and used as a measure of gaze complexity. Individual factor and group-based interaction ANOVA analysis was performed to study the association between fractal dimension, case pathology, breast density, and reader experience level. The consistency of the observed trends depending on gaze data representation was also examined. Results: Case pathology, breast density, reader experience level, and individual reader differences are all independent predictors of the visual scanning pattern complexity when screening for breast cancer. No higher order effects were found to be significant. Conclusions: Fractal characterization of visual search behavior during mammographic screening is dependent on case properties and image reader characteristics.« less

Digenetic Changes in Macro- to Nano-Scale Porosity in the St. Peter Sandstone:L An (Ultra) Small Angle Neutron Scattering and Backscattered Electron Imagining Analysis

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

Anovitz, Lawrence; Cole, David; Rother, Gernot

2013-01-01

Small- and Ultra-Small Angle Neutron Scattering (SANS and USANS) provide powerful tools for quantitative analysis of porous rocks, yielding bulk statistical information over a wide range of length scales. This study utilized (U)SANS to characterize shallowly buried quartz arenites from the St. Peter Sandstone. Backscattered electron imaging was also used to extend the data to larger scales. These samples contain significant volumes of large-scale porosity, modified by quartz overgrowths, and neutron scattering results show significant sub-micron porosity. While previous scattering data from sandstones suggest scattering is dominated by surface fractal behavior over many orders of magnitude, careful analysis of ourmore » data shows both fractal and pseudo-fractal behavior. The scattering curves are composed of subtle steps, modeled as polydispersed assemblages of pores with log-normal distributions. However, in some samples an additional surface-fractal overprint is present, while in others there is no such structure, and scattering can be explained by summation of non-fractal structures. Combined with our work on other rock-types, these data suggest that microporosity is more prevalent, and may play a much more important role than previously thought in fluid/rock interactions.« less

Determination of Uniaxial Compressive Strength of Ankara Agglomerate Considering Fractal Geometry of Blocks

NASA Astrophysics Data System (ADS)

Coskun, Aycan; Sonmez, Harun; Ercin Kasapoglu, K.; Ozge Dinc, S.; Celal Tunusluoglu, M.

2010-05-01

The uniaxial compressive strength (UCS) of rock material is a crucial parameter to be used for design stages of slopes, tunnels and foundations to be constructed in/on geological medium. However, preparation of high quality cores from geological mixtures or fragmented rocks such as melanges, fault rocks, coarse pyroclastic rocks, breccias and sheared serpentinites is often extremely difficult. According to the studies performed in literature, this type of geological materials may be grouped as welded and unwelded birmocks. Success of preparation of core samples from welded bimrocks is slightly better than unwelded ones. Therefore, some studies performed on the welded bimrocks to understand the mechanical behavior of geological mixture materials composed of stronger and weaker components (Gokceoglu, 2002; Sonmez et al., 2004; Sonmez et al., 2006; Kahraman, et al., 2008). The overall strength of bimrocks are generally depends on strength contrast between blocks and matrix; types and strength of matrix; type, size, strength, shape and orientation of blocks and volumetric block proportion. In previously proposed prediction models, while UCS of unwelded bimrocks may be determined by decreasing the UCS of matrix considering the volumetric block proportion, the welded ones can be predicted by considering both UCS of matrix and blocks together (Lindquist, 1994; Lindquist and Goodman, 1994; Sonmez et al., 2006 and Sonmez et al., 2009). However, there is a few attempts were performed about the effect of blocks shape and orientation on the strength of bimrock (Linqduist, 1994 and Kahraman, et al., 2008). In this study, Ankara agglomerate, which is composed of andesite blocks and surrounded weak tuff matrix, was selected as study material. Image analyses were performed on bottom, top and side faces of cores to identify volumetric block portions. In addition to the image analyses, andesite blocks on bottom, top and side faces were digitized for determination of fractal dimensions. To determine fractal dimensions of more than hundred andesite blocks in cores, a computer program namely FRACRUN were developed. Fractal geometry has been used as practical and popular tool to define particularly irregular shaped bodies in literature since the theory of fractal was developed by Mandelbrot (1967) (Hyslip and Vallejo, 1997; Kruhl and Nega, 1996; Bagde etal., 2002; Gulbin and Evangulova, 2003; Pardini, 2003; Kolay and Kayabali, 2006; Hamdi, 2008; Zorlu, 2009 and Sezer, 2009). Although there are some methods to determine fractal dimensions, square grid-cell count method for 2D and segment count method for 1D were followed in the algorithm of FRACRUN. FRACRUN has capable of determine fractal dimensions of many closed polygons on a single surface. In the study, a database composed of uniaxial compressive strength, volumetric block proportion, fractal dimensions and number of blocks for each core was established. Finally, prediction models were developed by regression analyses and compared with the empirical equations proposed by Sonmez et al. (2006). Acknowledgement This study is a product of ongoing project supported by TUBITAK (The Scientific and Technological Research Council of Turkey - Project No: 108Y002). References Bagde, M.N., Raina, A.K., Chakraborty, A.K., Jethwa, J.L., 2002. Rock mass characterization by fractal dimension. Engineering Geology 63, 141-155. Gokceoglu, C., 2002. A fuzzy triangular chart to predict the uniaxial compressive strength of the Ankara agglomerates from their petrographic composition. Engineering Geology, 66 (1-2), 39-51. Gulbin, Y.L., Evangulova, E.B., 2003. Morphometry of quartz aggregates in granites: fractal images referring to nucleation and growth processes. Mathematical Geology 35 (7), 819-833 Hamdi, E., 2008. A fractal description of simulated 3D discontinuity networks. Rock Mechanics and Rock Engineering 41, 587-599. Hyslip, J.P., Vallejo, L.E., 1997. Fractals analysis of the roughness and size distribution of granular materials. Engineering Geology 48, 231-244. Kahraman, S., Alber, M., Fener, M. and Gunaydin, O. 2008. Evaluating the geomechanical properties of Misis fault breccia (Turkey). Int. J. Rock Mech. Min. Sci, 45, (8), 1469-1479. Kolay, E., Kayabali, K., 2006. Investigation of the effect of aggregate shape and surface roughness on the slake durability index using the fractal dimension approach. Engineering Geology 86, 271-294. Kruhl, J.H., Nega, M., 1996. The fractal shape of sutured quartz grain boundaries: application as a geothermometer. Geologische Rundschau 85, 38-43. Lindquist E.S. 1994. The strength, deformation properties of melange. PhD thesis, University of California, Berkeley, 1994. 264p. Lindquist E.S. and Goodman R.E. 1994. The strength and deformation properties of the physical model m!elange. In: Nelson PP, Laubach SE, editors. Proceedings of the First North American Rock Mechanics Conference (NARMS), Austin, Texas. Rotterdam: AA Balkema; 1994. Pardini, G., 2003. Fractal scaling of surface roughness in artificially weathered smectite rich soil regoliths. Geoderma 117, 157-167. Sezer E., 2009. A computer program for fractal dimension (FRACEK) with application on type of mass movement characterization. Computers and Geosciences (doi:10.1016/j.cageo.2009.04.006). Sonmez H, Tuncay E, and Gokceoglu C., 2004. Models to predict the uniaxial compressive strength and the modulus of elasticity for Ankara Agglomerate. Int. J. Rock Mech. Min. Sci., 41 (5), 717-729. Sonmez, H., Gokceoglu, C., Medley, E.W., Tuncay, E., and Nefeslioglu, H.A., 2006. Estimating the uniaxial compressive strength of a volcanic bimrock. Int. J. Rock Mech. Min. Sci., 43 (4), 554-561. Zorlu K., 2008. Description of the weathering states of building stones by fractal geometry and fuzzy inference system in the Olba ancient city (Southern Turkey). Engineering Geology 101 (2008) 124-133.

Quantification of ultrasonic texture intra-heterogeneity via volumetric stochastic modeling for tissue characterization.

PubMed

Al-Kadi, Omar S; Chung, Daniel Y F; Carlisle, Robert C; Coussios, Constantin C; Noble, J Alison

2015-04-01

Intensity variations in image texture can provide powerful quantitative information about physical properties of biological tissue. However, tissue patterns can vary according to the utilized imaging system and are intrinsically correlated to the scale of analysis. In the case of ultrasound, the Nakagami distribution is a general model of the ultrasonic backscattering envelope under various scattering conditions and densities where it can be employed for characterizing image texture, but the subtle intra-heterogeneities within a given mass are difficult to capture via this model as it works at a single spatial scale. This paper proposes a locally adaptive 3D multi-resolution Nakagami-based fractal feature descriptor that extends Nakagami-based texture analysis to accommodate subtle speckle spatial frequency tissue intensity variability in volumetric scans. Local textural fractal descriptors - which are invariant to affine intensity changes - are extracted from volumetric patches at different spatial resolutions from voxel lattice-based generated shape and scale Nakagami parameters. Using ultrasound radio-frequency datasets we found that after applying an adaptive fractal decomposition label transfer approach on top of the generated Nakagami voxels, tissue characterization results were superior to the state of art. Experimental results on real 3D ultrasonic pre-clinical and clinical datasets suggest that describing tumor intra-heterogeneity via this descriptor may facilitate improved prediction of therapy response and disease characterization. Copyright © 2014 The Authors. Published by Elsevier B.V. All rights reserved.

Spatial and radiometric characterization of multi-spectrum satellite images through multi-fractal analysis

NASA Astrophysics Data System (ADS)

Alonso, Carmelo; Tarquis, Ana M.; Zúñiga, Ignacio; Benito, Rosa M.

2017-03-01

Several studies have shown that vegetation indexes can be used to estimate root zone soil moisture. Earth surface images, obtained by high-resolution satellites, presently give a lot of information on these indexes, based on the data of several wavelengths. Because of the potential capacity for systematic observations at various scales, remote sensing technology extends the possible data archives from the present time to several decades back. Because of this advantage, enormous efforts have been made by researchers and application specialists to delineate vegetation indexes from local scale to global scale by applying remote sensing imagery. In this work, four band images have been considered, which are involved in these vegetation indexes, and were taken by satellites Ikonos-2 and Landsat-7 of the same geographic location, to study the effect of both spatial (pixel size) and radiometric (number of bits coding the image) resolution on these wavelength bands as well as two vegetation indexes: the Normalized Difference Vegetation Index (NDVI) and the Enhanced Vegetation Index (EVI). In order to do so, a multi-fractal analysis of these multi-spectral images was applied in each of these bands and the two indexes derived. The results showed that spatial resolution has a similar scaling effect in the four bands, but radiometric resolution has a larger influence in blue and green bands than in red and near-infrared bands. The NDVI showed a higher sensitivity to the radiometric resolution than EVI. Both were equally affected by the spatial resolution. From both factors, the spatial resolution has a major impact in the multi-fractal spectrum for all the bands and the vegetation indexes. This information should be taken in to account when vegetation indexes based on different satellite sensors are obtained.

Fractal Analysis of Radiologists Visual Scanning Pattern in Screening Mammography

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

Alamudun, Folami T; Yoon, Hong-Jun; Hudson, Kathy

2015-01-01

Several investigators have investigated radiologists visual scanning patterns with respect to features such as total time examining a case, time to initially hit true lesions, number of hits, etc. The purpose of this study was to examine the complexity of the radiologists visual scanning pattern when viewing 4-view mammographic cases, as they typically do in clinical practice. Gaze data were collected from 10 readers (3 breast imaging experts and 7 radiology residents) while reviewing 100 screening mammograms (24 normal, 26 benign, 50 malignant). The radiologists scanpaths across the 4 mammographic views were mapped to a single 2-D image plane. Then,more » fractal analysis was applied on the derived scanpaths using the box counting method. For each case, the complexity of each radiologist s scanpath was estimated using fractal dimension. The association between gaze complexity, case pathology, case density, and radiologist experience was evaluated using 3 factor fixed effects ANOVA. ANOVA showed that case pathology, breast density, and experience level are all independent predictors of the visual scanning pattern complexity. Visual scanning patterns are significantly different for benign and malignant cases than for normal cases as well as when breast parenchyma density changes.« less

Evaluation of Yogurt Microstructure Using Confocal Laser Scanning Microscopy and Image Analysis.

PubMed

Skytte, Jacob L; Ghita, Ovidiu; Whelan, Paul F; Andersen, Ulf; Møller, Flemming; Dahl, Anders B; Larsen, Rasmus

2015-06-01

The microstructure of protein networks in yogurts defines important physical properties of the yogurt and hereby partly its quality. Imaging this protein network using confocal scanning laser microscopy (CSLM) has shown good results, and CSLM has become a standard measuring technique for fermented dairy products. When studying such networks, hundreds of images can be obtained, and here image analysis methods are essential for using the images in statistical analysis. Previously, methods including gray level co-occurrence matrix analysis and fractal analysis have been used with success. However, a range of other image texture characterization methods exists. These methods describe an image by a frequency distribution of predefined image features (denoted textons). Our contribution is an investigation of the choice of image analysis methods by performing a comparative study of 7 major approaches to image texture description. Here, CSLM images from a yogurt fermentation study are investigated, where production factors including fat content, protein content, heat treatment, and incubation temperature are varied. The descriptors are evaluated through nearest neighbor classification, variance analysis, and cluster analysis. Our investigation suggests that the texton-based descriptors provide a fuller description of the images compared to gray-level co-occurrence matrix descriptors and fractal analysis, while still being as applicable and in some cases as easy to tune. © 2015 Institute of Food Technologists®

Effect of quartz overgrowth precipitation on the multiscale porosity of sandstone: A (U)SANS and imaging analysis

DOE PAGES

Anovitz, Lawrence M.; Cole, David R.; Jackson, Andrew J.; ...

2015-06-01

We have performed a series of experiments to understand the effects of quartz overgrowths on nanometer to centimeter scale pore structures of sandstones. Blocks from two samples of St. Peter Sandstone with different initial porosities (5.8 and 18.3%) were reacted from 3 days to 7.5 months at 100 and 200 °C in aqueous solutions supersaturated with respect to quartz by reaction with amorphous silica. Porosity in the resultant samples was analyzed using small and ultrasmall angle neutron scattering and scanning electron microscope/backscattered electron (SEM/BSE)-based image-scale processing techniques.Significant changes were observed in the multiscale pore structures. By three days much ofmore » the overgrowth in the low-porosity sample dissolved away. The reason for this is uncertain, but the overgrowths can be clearly distinguished from the original core grains in the BSE images. At longer times the larger pores are observed to fill with plate-like precipitates. As with the unreacted sandstones, porosity is a step function of size. Grain boundaries are typically fractal, but no evidence of mass fractal or fuzzy interface behavior was observed suggesting a structural difference between chemical and clastic sediments. After the initial loss of the overgrowths, image scale porosity (>~1 cm) decreases with time. Submicron porosity (typically ~25% of the total) is relatively constant or slightly decreasing in absolute terms, but the percent change is significant. Fractal dimensions decrease at larger scales, and increase at smaller scales with increased precipitation.« less

Age-dependence of power spectral density and fractal dimension of bone mineralized matrix in atomic force microscope topography images: potential correlates of bone tissue age and bone fragility in female femoral neck trabeculae

PubMed Central

Milovanovic, Petar; Djuric, Marija; Rakocevic, Zlatko

2012-01-01

There is an increasing interest in bone nano-structure, the ultimate goal being to reveal the basis of age-related bone fragility. In this study, power spectral density (PSD) data and fractal dimensions of the mineralized bone matrix were extracted from atomic force microscope topography images of the femoral neck trabeculae. The aim was to evaluate age-dependent differences in the mineralized matrix of human bone and to consider whether these advanced nano-descriptors might be linked to decreased bone remodeling observed by some authors and age-related decline in bone mechanical competence. The investigated bone specimens belonged to a group of young adult women (n = 5, age: 20–40 years) and a group of elderly women (n = 5, age: 70–95 years) without bone diseases. PSD graphs showed the roughness density distribution in relation to spatial frequency. In all cases, there was a fairly linear decrease in magnitude of the power spectra with increasing spatial frequencies. The PSD slope was steeper in elderly individuals (−2.374 vs. −2.066), suggesting the dominance of larger surface morphological features. Fractal dimension of the mineralized bone matrix showed a significant negative trend with advanced age, declining from 2.467 in young individuals to 2.313 in the elderly (r = 0.65, P = 0.04). Higher fractal dimension in young women reflects domination of smaller mineral grains, which is compatible with the more freshly remodeled structure. In contrast, the surface patterns in elderly individuals were indicative of older tissue age. Lower roughness and reduced structural complexity (decreased fractal dimension) of the interfibrillar bone matrix in the elderly suggest a decline in bone toughness, which explains why aged bone is more brittle and prone to fractures. PMID:22946475

Age-dependence of power spectral density and fractal dimension of bone mineralized matrix in atomic force microscope topography images: potential correlates of bone tissue age and bone fragility in female femoral neck trabeculae.

PubMed

Milovanovic, Petar; Djuric, Marija; Rakocevic, Zlatko

2012-11-01

There is an increasing interest in bone nano-structure, the ultimate goal being to reveal the basis of age-related bone fragility. In this study, power spectral density (PSD) data and fractal dimensions of the mineralized bone matrix were extracted from atomic force microscope topography images of the femoral neck trabeculae. The aim was to evaluate age-dependent differences in the mineralized matrix of human bone and to consider whether these advanced nano-descriptors might be linked to decreased bone remodeling observed by some authors and age-related decline in bone mechanical competence. The investigated bone specimens belonged to a group of young adult women (n = 5, age: 20-40 years) and a group of elderly women (n = 5, age: 70-95 years) without bone diseases. PSD graphs showed the roughness density distribution in relation to spatial frequency. In all cases, there was a fairly linear decrease in magnitude of the power spectra with increasing spatial frequencies. The PSD slope was steeper in elderly individuals (-2.374 vs. -2.066), suggesting the dominance of larger surface morphological features. Fractal dimension of the mineralized bone matrix showed a significant negative trend with advanced age, declining from 2.467 in young individuals to 2.313 in the elderly (r = 0.65, P = 0.04). Higher fractal dimension in young women reflects domination of smaller mineral grains, which is compatible with the more freshly remodeled structure. In contrast, the surface patterns in elderly individuals were indicative of older tissue age. Lower roughness and reduced structural complexity (decreased fractal dimension) of the interfibrillar bone matrix in the elderly suggest a decline in bone toughness, which explains why aged bone is more brittle and prone to fractures. © 2012 The Authors Journal of Anatomy © 2012 Anatomical Society.

Fractal analysis of plaque border, a novel method for the quantification of atherosclerotic plaque contour irregularity, is associated with pro-atherogenic plasma lipid profile in subjects with non-obstructive carotid stenoses.

PubMed

Moroni, Francesco; Magnoni, Marco; Vergani, Vittoria; Ammirati, Enrico; Camici, Paolo G

2018-01-01

Plaque border irregularity is a known imaging characteristic of vulnerable plaques, but its evaluation heavily relies on subjective evaluation and operator expertise. Aim of the present work is to propose a novel fractal-analysis based method for the quantification of atherosclerotic plaque border irregularity and assess its relation with cardiovascular risk factors. Forty-two asymptomatic subjects with carotid stenosis underwent ultrasound evaluation and assessment of cardiovascular risk factors. Total, low-density lipoprotein (LDL), high-density lipoprotein (HDL) plasma cholesterol and triglycerides concentrations were measured for each subject. Fractal analysis was performed in all the carotid segments affected by atherosclerosis, i.e. 147 segments. The resulting fractal dimension (FD) is a measure of irregularity of plaque profile on long axis view of the plaque. FD in the severest stenosis (main plaque FD,mFD) was 1.136±0.039. Average FD per patient (global FD,gFD) was 1.145±0.039. FD was independent of other plaque characteristics. mFD significantly correlated with plasma HDL (r = -0.367,p = 0.02) and triglycerides-to-HDL ratio (r = 0.480,p = 0.002). Fractal analysis is a novel, readily available, reproducible and inexpensive technique for the quantitative measurement of plaque irregularity. The correlation between low HDL levels and plaque FD suggests a role for HDL in the acquisition of morphologic features of plaque instability. Further studies are needed to validate the prognostic value of fractal analysis in carotid plaques evaluation.

Use of wavelet-packet transforms to develop an engineering model for multifractal characterization of mutation dynamics in pathological and nonpathological gene sequences

NASA Astrophysics Data System (ADS)

Walker, David Lee

1999-12-01

This study uses dynamical analysis to examine in a quantitative fashion the information coding mechanism in DNA sequences. This exceeds the simple dichotomy of either modeling the mechanism by comparing DNA sequence walks as Fractal Brownian Motion (fbm) processes. The 2-D mappings of the DNA sequences for this research are from Iterated Function System (IFS) (Also known as the ``Chaos Game Representation'' (CGR)) mappings of the DNA sequences. This technique converts a 1-D sequence into a 2-D representation that preserves subsequence structure and provides a visual representation. The second step of this analysis involves the application of Wavelet Packet Transforms, a recently developed technique from the field of signal processing. A multi-fractal model is built by using wavelet transforms to estimate the Hurst exponent, H. The Hurst exponent is a non-parametric measurement of the dynamism of a system. This procedure is used to evaluate gene- coding events in the DNA sequence of cystic fibrosis mutations. The H exponent is calculated for various mutation sites in this gene. The results of this study indicate the presence of anti-persistent, random walks and persistent ``sub-periods'' in the sequence. This indicates the hypothesis of a multi-fractal model of DNA information encoding warrants further consideration. This work examines the model's behavior in both pathological (mutations) and non-pathological (healthy) base pair sequences of the cystic fibrosis gene. These mutations both natural and synthetic were introduced by computer manipulation of the original base pair text files. The results show that disease severity and system ``information dynamics'' correlate. These results have implications for genetic engineering as well as in mathematical biology. They suggest that there is scope for more multi-fractal models to be developed.

Measuring surface topography by scanning electron microscopy. II. Analysis of three estimators of surface roughness in second dimension and third dimension.

PubMed

Bonetto, Rita Dominga; Ladaga, Juan Luis; Ponz, Ezequiel

2006-04-01

Scanning electron microscopy (SEM) is widely used in surface studies and continuous efforts are carried out in the search of estimators of different surface characteristics. By using the variogram, we developed two of these estimators that were used to characterize the surface roughness from the SEM image texture. One of the estimators is related to the crossover between fractal region at low scale and the periodic region at high scale, whereas the other estimator characterizes the periodic region. In this work, a full study of these estimators and the fractal dimension in two dimensions (2D) and three dimensions (3D) was carried out for emery papers. We show that the obtained fractal dimension with only one image is good enough to characterize the roughness surface because its behavior is similar to those obtained with 3D height data. We show also that the estimator that indicates the crossover is related to the minimum cell size in 2D and to the average particle size in 3D. The other estimator has different values for the three studied emery papers in 2D but it does not have a clear meaning, and these values are similar for those studied samples in 3D. Nevertheless, it indicates the formation tendency of compound cells. The fractal dimension values from the variogram and from an area versus step log-log graph were studied with 3D data. Both methods yield different values corresponding to different information from the samples.

Comparison of caprock pore networks which potentially will be impacted by carbon sequestration projects.

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

McCray, John; Navarre-Sitchler, Alexis; Mouzakis, Katherine

Injection of CO2 into underground rock formations can reduce atmospheric CO2 emissions. Caprocks present above potential storage formations are the main structural trap inhibiting CO2 from leaking into overlying aquifers or back to the Earth's surface. Dissolution and precipitation of caprock minerals resulting from reaction with CO2 may alter the pore network where many pores are of the micrometer to nanometer scale, thus altering the structural trapping potential of the caprock. However, the distribution, geometry and volume of pores at these scales are poorly characterized. In order to evaluate the overall risk of leakage of CO2 from storage formations, amore » first critical step is understanding the distribution and shape of pores in a variety of different caprocks. As the caprock is often comprised of mudstones, we analyzed samples from several mudstone formations with small angle neutron scattering (SANS) and high-resolution transmission electron microscopy (TEM) imaging to compare the pore networks. Mudstones were chosen from current or potential sites for carbon sequestration projects including the Marine Tuscaloosa Group, the Lower Tuscaloosa Group, the upper and lower shale members of the Kirtland Formation, and the Pennsylvanian Gothic shale. Expandable clay contents ranged from 10% to approximately 40% in the Gothic shale and Kirtland Formation, respectively. During SANS, neutrons effectively scatter from interfaces between materials with differing scattering length density (i.e., minerals and pores). The intensity of scattered neutrons, I(Q), where Q is the scattering vector, gives information about the volume and arrangement of pores in the sample. The slope of the scattering data when plotted as log I(Q) vs. log Q provides information about the fractality or geometry of the pore network. On such plots slopes from -2 to -3 represent mass fractals while slopes from -3 to -4 represent surface fractals. Scattering data showed surface fractal dimensions for the Kirtland formation and one sample from the Tuscaloosa formation close to 3, indicating very rough surfaces. In contrast, scattering data for the Gothic shale formation exhibited mass fractal behavior. In one sample of the Tuscaloosa formation the data are described by a surface fractal at low Q (larger pores) and a mass fractal at high Q (smaller pores), indicating two pore populations contributing to the scattering behavior. These small angle neutron scattering results, combined with high-resolution TEM imaging, provided a means for both qualitative and quantitative analysis of the differences in pore networks between these various mudstones.« less

A neural coding scheme reproducing foraging trajectories

NASA Astrophysics Data System (ADS)

Gutiérrez, Esther D.; Cabrera, Juan Luis

2015-12-01

The movement of many animals may follow Lévy patterns. The underlying generating neuronal dynamics of such a behavior is unknown. In this paper we show that a novel discovery of multifractality in winnerless competition (WLC) systems reveals a potential encoding mechanism that is translatable into two dimensional superdiffusive Lévy movements. The validity of our approach is tested on a conductance based neuronal model showing WLC and through the extraction of Lévy flights inducing fractals from recordings of rat hippocampus during open field foraging. Further insights are gained analyzing mice motor cortex neurons and non motor cell signals. The proposed mechanism provides a plausible explanation for the neuro-dynamical fundamentals of spatial searching patterns observed in animals (including humans) and illustrates an until now unknown way to encode information in neuronal temporal series.

Soil structure characterized using computed tomographic images

Treesearch

Zhanqi Cheng; Stephen H. Anderson; Clark J. Gantzer; J. W. Van Sambeek

2003-01-01

Fractal analysis of soil structure is a relatively new method for quantifying the effects of management systems on soil properties and quality. The objective of this work was to explore several methods of studying images to describe and quantify structure of soils under forest management. This research uses computed tomography and a topological method called Multiple...

Medical Image Compression Based on Vector Quantization with Variable Block Sizes in Wavelet Domain

PubMed Central

Jiang, Huiyan; Ma, Zhiyuan; Hu, Yang; Yang, Benqiang; Zhang, Libo

2012-01-01

An optimized medical image compression algorithm based on wavelet transform and improved vector quantization is introduced. The goal of the proposed method is to maintain the diagnostic-related information of the medical image at a high compression ratio. Wavelet transformation was first applied to the image. For the lowest-frequency subband of wavelet coefficients, a lossless compression method was exploited; for each of the high-frequency subbands, an optimized vector quantization with variable block size was implemented. In the novel vector quantization method, local fractal dimension (LFD) was used to analyze the local complexity of each wavelet coefficients, subband. Then an optimal quadtree method was employed to partition each wavelet coefficients, subband into several sizes of subblocks. After that, a modified K-means approach which is based on energy function was used in the codebook training phase. At last, vector quantization coding was implemented in different types of sub-blocks. In order to verify the effectiveness of the proposed algorithm, JPEG, JPEG2000, and fractal coding approach were chosen as contrast algorithms. Experimental results show that the proposed method can improve the compression performance and can achieve a balance between the compression ratio and the image visual quality. PMID:23049544

Medical image compression based on vector quantization with variable block sizes in wavelet domain.

PubMed

Jiang, Huiyan; Ma, Zhiyuan; Hu, Yang; Yang, Benqiang; Zhang, Libo

2012-01-01

An optimized medical image compression algorithm based on wavelet transform and improved vector quantization is introduced. The goal of the proposed method is to maintain the diagnostic-related information of the medical image at a high compression ratio. Wavelet transformation was first applied to the image. For the lowest-frequency subband of wavelet coefficients, a lossless compression method was exploited; for each of the high-frequency subbands, an optimized vector quantization with variable block size was implemented. In the novel vector quantization method, local fractal dimension (LFD) was used to analyze the local complexity of each wavelet coefficients, subband. Then an optimal quadtree method was employed to partition each wavelet coefficients, subband into several sizes of subblocks. After that, a modified K-means approach which is based on energy function was used in the codebook training phase. At last, vector quantization coding was implemented in different types of sub-blocks. In order to verify the effectiveness of the proposed algorithm, JPEG, JPEG2000, and fractal coding approach were chosen as contrast algorithms. Experimental results show that the proposed method can improve the compression performance and can achieve a balance between the compression ratio and the image visual quality.

Predicting Bone Mechanical Properties of Cancellous Bone from DXA, MRI, and Fractal Dimensional Measurements

NASA Technical Reports Server (NTRS)

Harrigan, Timothy P.; Ambrose, Catherine G.; Hogan, Harry A.; Shackleford, Linda; Webster, Laurie; LeBlanc, Adrian; Lin, Chen; Evans, Harlan

1997-01-01

This project was aimed at making predictions of bone mechanical properties from non-invasive DXA and MRI measurements. Given the bone mechanical properties, stress calculations can be made to compare normal bone stresses to the stresses developed in exercise countermeasures against bone loss during space flight. These calculations in turn will be used to assess whether mechanical factors can explain bone loss in space. In this study we assessed the use of T2(sup *) MRI imaging, DXA, and fractal dimensional analysis to predict strength and stiffness in cancellous bone.

Random-fractal Ansatz for the configurations of two-dimensional critical systems

NASA Astrophysics Data System (ADS)

Lee, Ching Hua; Ozaki, Dai; Matsueda, Hiroaki

2016-12-01

Critical systems have always intrigued physicists and precipitated the development of new techniques. Recently, there has been renewed interest in the information contained in the configurations of classical critical systems, whose computation do not require full knowledge of the wave function. Inspired by holographic duality, we investigated the entanglement properties of the classical configurations (snapshots) of the Potts model by introducing an Ansatz ensemble of random fractal images. By virtue of the central limit theorem, our Ansatz accurately reproduces the entanglement spectra of actual Potts snapshots without any fine tuning of parameters or artificial restrictions on ensemble choice. It provides a microscopic interpretation of the results of previous studies, which established a relation between the scaling behavior of snapshot entropy and the critical exponent. More importantly, it elucidates the role of ensemble disorder in restoring conformal invariance, an aspect previously ignored. Away from criticality, the breakdown of scale invariance leads to a renormalization of the parameter Σ in the random fractal Ansatz, whose variation can be used as an alternative determination of the critical exponent. We conclude by providing a recipe for the explicit construction of fractal unit cells consistent with a given scaling exponent.

EUS elastography (strain ratio) and fractal-based quantitative analysis for the diagnosis of solid pancreatic lesions.

PubMed

Carrara, Silvia; Di Leo, Milena; Grizzi, Fabio; Correale, Loredana; Rahal, Daoud; Anderloni, Andrea; Auriemma, Francesco; Fugazza, Alessandro; Preatoni, Paoletta; Maselli, Roberta; Hassan, Cesare; Finati, Elena; Mangiavillano, Benedetto; Repici, Alessandro

2018-06-01

EUS elastography is useful in characterizing solid pancreatic lesions (SPLs), and fractal analysis-based technology has been used to evaluate geometric complexity in oncology. The aim of this study was to evaluate EUS elastography (strain ratio) and fractal analysis for the characterization of SPLs. Consecutive patients with SPLs were prospectively enrolled between December 2015 and February 2017. Elastographic evaluation included parenchymal strain ratio (pSR) and wall strain ratio (wSR) and was performed with a new compact US processor. Elastographic images were analyzed using a computer program to determine the 3-dimensional histogram fractal dimension. A composite cytology/histology/clinical reference standard was used to assess sensitivity, specificity, positive predictive value, negative predictive value, and area under the receiver operating curve. Overall, 102 SPLs from 100 patients were studied. At final diagnosis, 69 (68%) were malignant and 33 benign. At elastography, both pSR and wSR appeared to be significantly higher in malignant as compared with benign SPLs (pSR, 24.5 vs 6.4 [P < .001]; wSR, 56.6 vs 15.3 [P < .001]). When the best cut-off levels of pSR and wSR at 9.10 and 16.2, respectively, were used, sensitivity, specificity, positive predictive value, negative predictive value, and area under the receiver operating curve were 88.4%, 78.8%, 89.7%, 76.9%, and 86.7% and 91.3%, 69.7%, 86.5%, 80%, and 85.7%, respectively. Fractal analysis showed a significant statistical difference (P = .0087) between the mean surface fractal dimension of malignant lesions (D = 2.66 ± .01) versus neuroendocrine tumor (D = 2.73 ± .03) and a statistical difference for all 3 channels red, green, and blue (P < .0001). EUS elastography with pSR and fractal-based analysis are useful in characterizing SPLs. (Clinical trial registration number: NCT02855151.). Copyright © 2018 American Society for Gastrointestinal Endoscopy. Published by Elsevier Inc. All rights reserved.

Exhaled Aerosol Pattern Discloses Lung Structural Abnormality: A Sensitivity Study Using Computational Modeling and Fractal Analysis

PubMed Central

Xi, Jinxiang; Si, Xiuhua A.; Kim, JongWon; Mckee, Edward; Lin, En-Bing

2014-01-01

Background Exhaled aerosol patterns, also called aerosol fingerprints, provide clues to the health of the lung and can be used to detect disease-modified airway structures. The key is how to decode the exhaled aerosol fingerprints and retrieve the lung structural information for a non-invasive identification of respiratory diseases. Objective and Methods In this study, a CFD-fractal analysis method was developed to quantify exhaled aerosol fingerprints and applied it to one benign and three malign conditions: a tracheal carina tumor, a bronchial tumor, and asthma. Respirations of tracer aerosols of 1 µm at a flow rate of 30 L/min were simulated, with exhaled distributions recorded at the mouth. Large eddy simulations and a Lagrangian tracking approach were used to simulate respiratory airflows and aerosol dynamics. Aerosol morphometric measures such as concentration disparity, spatial distributions, and fractal analysis were applied to distinguish various exhaled aerosol patterns. Findings Utilizing physiology-based modeling, we demonstrated substantial differences in exhaled aerosol distributions among normal and pathological airways, which were suggestive of the disease location and extent. With fractal analysis, we also demonstrated that exhaled aerosol patterns exhibited fractal behavior in both the entire image and selected regions of interest. Each exhaled aerosol fingerprint exhibited distinct pattern parameters such as spatial probability, fractal dimension, lacunarity, and multifractal spectrum. Furthermore, a correlation of the diseased location and exhaled aerosol spatial distribution was established for asthma. Conclusion Aerosol-fingerprint-based breath tests disclose clues about the site and severity of lung diseases and appear to be sensitive enough to be a practical tool for diagnosis and prognosis of respiratory diseases with structural abnormalities. PMID:25105680

A Brief Historical Introduction to Fractals and Fractal Geometry

ERIC Educational Resources Information Center

Debnath, Lokenath

2006-01-01

This paper deals with a brief historical introduction to fractals, fractal dimension and fractal geometry. Many fractals including the Cantor fractal, the Koch fractal, the Minkowski fractal, the Mandelbrot and Given fractal are described to illustrate self-similar geometrical figures. This is followed by the discovery of dynamical systems and…

Interactions between a fractal tree-like object and hydrodynamic turbulence: flow structure and characteristic mixing length

NASA Astrophysics Data System (ADS)

Meneveau, C. V.; Bai, K.; Katz, J.

2011-12-01

The vegetation canopy has a significant impact on various physical and biological processes such as forest microclimate, rainfall evaporation distribution and climate change. Most scaled laboratory experimental studies have used canopy element models that consist of rigid vertical strips or cylindrical rods that can be typically represented through only one or a few characteristic length scales, for example the diameter and height for cylindrical rods. However, most natural canopies and vegetation are highly multi-scale with branches and sub-branches, covering a wide range of length scales. Fractals provide a convenient idealization of multi-scale objects, since their multi-scale properties can be described in simple ways (Mandelbrot 1982). While fractal aspects of turbulence have been studied in several works in the past decades, research on turbulence generated by fractal objects started more recently. We present an experimental study of boundary layer flow over fractal tree-like objects. Detailed Particle-Image-Velocimetry (PIV) measurements are carried out in the near-wake of a fractal-like tree. The tree is a pre-fractal with five generations, with three branches and a scale reduction factor 1/2 at each generation. Its similarity fractal dimension (Mandelbrot 1982) is D ~ 1.58. Detailed mean velocity and turbulence stress profiles are documented, as well as their downstream development. We then turn attention to the turbulence mixing properties of the flow, specifically to the question whether a mixing length-scale can be identified in this flow, and if so, how it relates to the geometric length-scales in the pre-fractal object. Scatter plots of mean velocity gradient (shear) and Reynolds shear stress exhibit good linear relation at all locations in the flow. Therefore, in the transverse direction of the wake evolution, the Boussinesq eddy viscosity concept is appropriate to describe the mixing. We find that the measured mixing length increases with increasing streamwise locations. Conversely, the measured eddy viscosity and mixing length decrease with increasing elevation, which differs from eddy viscosity and mixing length behaviors of traditional boundary layers or canopies studied before. In order to find an appropriate length for the flow, several models based on the notion of superposition of scales are proposed and examined. One approach is based on spectral distributions. Another more practical approach is based on length-scale distributions evaluated using fractal geometry tools. These proposed models agree well with the measured mixing length. The results indicate that information about multi-scale clustering of branches as it occurs in fractals has to be incorporated into models of the mixing length for flows through canopies with multiple scales. The research is supported by National Science Foundation grant ATM-0621396 and AGS-1047550.

Beyond maximum entropy: Fractal pixon-based image reconstruction

NASA Technical Reports Server (NTRS)

Puetter, R. C.; Pina, R. K.

1994-01-01

We have developed a new Bayesian image reconstruction method that has been shown to be superior to the best implementations of other methods, including Goodness-of-Fit (e.g. Least-Squares and Lucy-Richardson) and Maximum Entropy (ME). Our new method is based on the concept of the pixon, the fundamental, indivisible unit of picture information. Use of the pixon concept provides an improved image model, resulting in an image prior which is superior to that of standard ME.

Temporal fractal analysis of the rs-BOLD signal identifies brain abnormalities in autism spectrum disorder.

PubMed

Dona, Olga; Hall, Geoffrey B; Noseworthy, Michael D

2017-01-01

Brain connectivity in autism spectrum disorders (ASD) has proven difficult to characterize due to the heterogeneous nature of the spectrum. Connectivity in the brain occurs in a complex, multilevel and multi-temporal manner, driving the fluctuations observed in local oxygen demand. These fluctuations can be characterized as fractals, as they auto-correlate at different time scales. In this study, we propose a model-free complexity analysis based on the fractal dimension of the rs-BOLD signal, acquired with magnetic resonance imaging. The fractal dimension can be interpreted as measure of signal complexity and connectivity. Previous studies have suggested that reduction in signal complexity can be associated with disease. Therefore, we hypothesized that a detectable difference in rs-BOLD signal complexity could be observed between ASD patients and Controls. Anatomical and functional data from fifty-five subjects with ASD (12.7 ± 2.4 y/o) and 55 age-matched (14.1 ± 3.1 y/o) healthy controls were accessed through the NITRC database and the ABIDE project. Subjects were scanned using a 3T GE Signa MRI and a 32-channel RF-coil. Axial FSPGR-3D images were used to prescribe rs-BOLD (TE/TR = 30/2000ms) where 300 time points were acquired. Motion correction was performed on the functional data and anatomical and functional images were aligned and spatially warped to the N27 standard brain atlas. Fractal analysis, performed on a grey matter mask, was done by estimating the Hurst exponent in the frequency domain using a power spectral density approach and refining the estimation in the time domain with de-trended fluctuation analysis and signal summation conversion methods. Voxel-wise fractal dimension (FD) was calculated for every subject in the control group and in the ASD group to create ROI-based Z-scores for the ASD patients. Voxel-wise validation of FD normality across controls was confirmed, and non-Gaussian voxels were eliminated from subsequent analysis. To maintain a 95% confidence level, only regions where Z-score values were at least 2 standard deviations away from the mean (i.e. where |Z| > 2.0) were included in the analysis. We found that the main regions, where signal complexity significantly decreased among ASD patients, were the amygdala (p = 0.001), the vermis (p = 0.02), the basal ganglia (p = 0.01) and the hippocampus (p = 0.02). No regions reported significant increase in signal complexity in this study. Our findings were correlated with ADIR and ADOS assessment tools, reporting the highest correlation with the ADOS metrics. Brain connectivity is best modeled as a complex system. Therefore, a measure of complexity as the fractal dimension of fluctuations in brain oxygen demand and utilization could provide important information about connectivity issues in ASD. Moreover, this technique can be used in the characterization of a single subject, with respect to controls, without the need for group analysis. Our novel approach provides an ideal avenue for personalized diagnostics, thus providing unique patient specific assessment that could help in individualizing treatments.

Radiomics-based differentiation of lung disease models generated by polluted air based on X-ray computed tomography data.

PubMed

Szigeti, Krisztián; Szabó, Tibor; Korom, Csaba; Czibak, Ilona; Horváth, Ildikó; Veres, Dániel S; Gyöngyi, Zoltán; Karlinger, Kinga; Bergmann, Ralf; Pócsik, Márta; Budán, Ferenc; Máthé, Domokos

2016-02-11

Lung diseases (resulting from air pollution) require a widely accessible method for risk estimation and early diagnosis to ensure proper and responsive treatment. Radiomics-based fractal dimension analysis of X-ray computed tomography attenuation patterns in chest voxels of mice exposed to different air polluting agents was performed to model early stages of disease and establish differential diagnosis. To model different types of air pollution, BALBc/ByJ mouse groups were exposed to cigarette smoke combined with ozone, sulphur dioxide gas and a control group was established. Two weeks after exposure, the frequency distributions of image voxel attenuation data were evaluated. Specific cut-off ranges were defined to group voxels by attenuation. Cut-off ranges were binarized and their spatial pattern was associated with calculated fractal dimension, then abstracted by the fractal dimension -- cut-off range mathematical function. Nonparametric Kruskal-Wallis (KW) and Mann-Whitney post hoc (MWph) tests were used. Each cut-off range versus fractal dimension function plot was found to contain two distinctive Gaussian curves. The ratios of the Gaussian curve parameters are considerably significant and are statistically distinguishable within the three exposure groups. A new radiomics evaluation method was established based on analysis of the fractal dimension of chest X-ray computed tomography data segments. The specific attenuation patterns calculated utilizing our method may diagnose and monitor certain lung diseases, such as chronic obstructive pulmonary disease (COPD), asthma, tuberculosis or lung carcinomas.

Experiments in encoding multilevel images as quadtrees

NASA Technical Reports Server (NTRS)

Lansing, Donald L.

1987-01-01

Image storage requirements for several encoding methods are investigated and the use of quadtrees with multigray level or multicolor images are explored. The results of encoding a variety of images having up to 256 gray levels using three schemes (full raster, runlength and quadtree) are presented. Although there is considerable literature on the use of quadtrees to store and manipulate binary images, their application to multilevel images is relatively undeveloped. The potential advantage of quadtree encoding is that an entire area with a uniform gray level may be encoded as a unit. A pointerless quadtree encoding scheme is described. Data are presented on the size of the quadtree required to encode selected images and on the relative storage requirements of the three encoding schemes. A segmentation scheme based on the statistical variation of gray levels within a quadtree quadrant is described. This parametric scheme may be used to control the storage required by an encoded image and to preprocess a scene for feature identification. Several sets of black and white and pseudocolor images obtained by varying the segmentation parameter are shown.

A neural coding scheme reproducing foraging trajectories

PubMed Central

Gutiérrez, Esther D.; Cabrera, Juan Luis

2015-01-01

The movement of many animals may follow Lévy patterns. The underlying generating neuronal dynamics of such a behavior is unknown. In this paper we show that a novel discovery of multifractality in winnerless competition (WLC) systems reveals a potential encoding mechanism that is translatable into two dimensional superdiffusive Lévy movements. The validity of our approach is tested on a conductance based neuronal model showing WLC and through the extraction of Lévy flights inducing fractals from recordings of rat hippocampus during open field foraging. Further insights are gained analyzing mice motor cortex neurons and non motor cell signals. The proposed mechanism provides a plausible explanation for the neuro-dynamical fundamentals of spatial searching patterns observed in animals (including humans) and illustrates an until now unknown way to encode information in neuronal temporal series. PMID:26648311

Learning to generate combinatorial action sequences utilizing the initial sensitivity of deterministic dynamical systems.

PubMed

Nishimoto, Ryu; Tani, Jun

2004-09-01

This study shows how sensory-action sequences of imitating finite state machines (FSMs) can be learned by utilizing the deterministic dynamics of recurrent neural networks (RNNs). Our experiments indicated that each possible combinatorial sequence can be recalled by specifying its respective initial state value and also that fractal structures appear in this initial state mapping after the learning converges. We also observed that the sequences of mimicking FSMs are encoded utilizing the transient regions rather than the invariant sets of the evolved dynamical systems of the RNNs.

A New Quantum Gray-Scale Image Encoding Scheme

NASA Astrophysics Data System (ADS)

Naseri, Mosayeb; Abdolmaleky, Mona; Parandin, Fariborz; Fatahi, Negin; Farouk, Ahmed; Nazari, Reza

2018-02-01

In this paper, a new quantum images encoding scheme is proposed. The proposed scheme mainly consists of four different encoding algorithms. The idea behind of the scheme is a binary key generated randomly for each pixel of the original image. Afterwards, the employed encoding algorithm is selected corresponding to the qubit pair of the generated randomized binary key. The security analysis of the proposed scheme proved its enhancement through both randomization of the generated binary image key and altering the gray-scale value of the image pixels using the qubits of randomized binary key. The simulation of the proposed scheme assures that the final encoded image could not be recognized visually. Moreover, the histogram diagram of encoded image is flatter than the original one. The Shannon entropies of the final encoded images are significantly higher than the original one, which indicates that the attacker can not gain any information about the encoded images. Supported by Kermanshah Branch, Islamic Azad University, Kermanshah, IRAN

Reliability of Using Retinal Vascular Fractal Dimension as a Biomarker in the Diabetic Retinopathy Detection

PubMed Central

Zhang, Jiong; Bekkers, Erik; Abbasi-Sureshjani, Samaneh

2016-01-01

The retinal fractal dimension (FD) is a measure of vasculature branching pattern complexity. FD has been considered as a potential biomarker for the detection of several diseases like diabetes and hypertension. However, conflicting findings were found in the reported literature regarding the association between this biomarker and diseases. In this paper, we examine the stability of the FD measurement with respect to (1) different vessel annotations obtained from human observers, (2) automatic segmentation methods, (3) various regions of interest, (4) accuracy of vessel segmentation methods, and (5) different imaging modalities. Our results demonstrate that the relative errors for the measurement of FD are significant and FD varies considerably according to the image quality, modality, and the technique used for measuring it. Automated and semiautomated methods for the measurement of FD are not stable enough, which makes FD a deceptive biomarker in quantitative clinical applications. PMID:27703803

Reliability of Using Retinal Vascular Fractal Dimension as a Biomarker in the Diabetic Retinopathy Detection.

PubMed

Huang, Fan; Dashtbozorg, Behdad; Zhang, Jiong; Bekkers, Erik; Abbasi-Sureshjani, Samaneh; Berendschot, Tos T J M; Ter Haar Romeny, Bart M

2016-01-01

The retinal fractal dimension (FD) is a measure of vasculature branching pattern complexity. FD has been considered as a potential biomarker for the detection of several diseases like diabetes and hypertension. However, conflicting findings were found in the reported literature regarding the association between this biomarker and diseases. In this paper, we examine the stability of the FD measurement with respect to (1) different vessel annotations obtained from human observers, (2) automatic segmentation methods, (3) various regions of interest, (4) accuracy of vessel segmentation methods, and (5) different imaging modalities. Our results demonstrate that the relative errors for the measurement of FD are significant and FD varies considerably according to the image quality, modality, and the technique used for measuring it. Automated and semiautomated methods for the measurement of FD are not stable enough, which makes FD a deceptive biomarker in quantitative clinical applications.

Function representation with circle inversion map systems

NASA Astrophysics Data System (ADS)

Boreland, Bryson; Kunze, Herb

2017-01-01

The fractals literature develops the now well-known concept of local iterated function systems (using affine maps) with grey-level maps (LIFSM) as an approach to function representation in terms of the associated fixed point of the so-called fractal transform. While originally explored as a method to achieve signal (and 2-D image) compression, more recent work has explored various aspects of signal and image processing using this machinery. In this paper, we develop a similar framework for function representation using circle inversion map systems. Given a circle C with centre õ and radius r, inversion with respect to C transforms the point p˜ to the point p˜', such that p˜ and p˜' lie on the same radial half-line from õ and d(õ, p˜)d(õ, p˜') = r2, where d is Euclidean distance. We demonstrate the results with an example.

Simultaneous transmission for an encrypted image and a double random-phase encryption key

NASA Astrophysics Data System (ADS)

Yuan, Sheng; Zhou, Xin; Li, Da-Hai; Zhou, Ding-Fu

2007-06-01

We propose a method to simultaneously transmit double random-phase encryption key and an encrypted image by making use of the fact that an acceptable decryption result can be obtained when only partial data of the encrypted image have been taken in the decryption process. First, the original image data are encoded as an encrypted image by a double random-phase encryption technique. Second, a double random-phase encryption key is encoded as an encoded key by the Rivest-Shamir-Adelman (RSA) public-key encryption algorithm. Then the amplitude of the encrypted image is modulated by the encoded key to form what we call an encoded image. Finally, the encoded image that carries both the encrypted image and the encoded key is delivered to the receiver. Based on such a method, the receiver can have an acceptable result and secure transmission can be guaranteed by the RSA cipher system.

Simultaneous transmission for an encrypted image and a double random-phase encryption key.

PubMed

Yuan, Sheng; Zhou, Xin; Li, Da-hai; Zhou, Ding-fu

2007-06-20

We propose a method to simultaneously transmit double random-phase encryption key and an encrypted image by making use of the fact that an acceptable decryption result can be obtained when only partial data of the encrypted image have been taken in the decryption process. First, the original image data are encoded as an encrypted image by a double random-phase encryption technique. Second, a double random-phase encryption key is encoded as an encoded key by the Rivest-Shamir-Adelman (RSA) public-key encryption algorithm. Then the amplitude of the encrypted image is modulated by the encoded key to form what we call an encoded image. Finally, the encoded image that carries both the encrypted image and the encoded key is delivered to the receiver. Based on such a method, the receiver can have an acceptable result and secure transmission can be guaranteed by the RSA cipher system.

Encoder: A Connectionist Model of How Learning to Visually Encode Fixated Text Images Improves Reading Fluency

ERIC Educational Resources Information Center

Martin, Gale L.

2004-01-01

This article proposes that visual encoding learning improves reading fluency by widening the span over which letters are recognized from a fixated text image so that fewer fixations are needed to cover a text line. Encoder is a connectionist model that learns to convert images like the fixated text images human readers encode into the…

Signal-to-noise ratio comparison of encoding methods for hyperpolarized noble gas MRI

NASA Technical Reports Server (NTRS)

Zhao, L.; Venkatesh, A. K.; Albert, M. S.; Panych, L. P.

2001-01-01

Some non-Fourier encoding methods such as wavelet and direct encoding use spatially localized bases. The spatial localization feature of these methods enables optimized encoding for improved spatial and temporal resolution during dynamically adaptive MR imaging. These spatially localized bases, however, have inherently reduced image signal-to-noise ratio compared with Fourier or Hadamad encoding for proton imaging. Hyperpolarized noble gases, on the other hand, have quite different MR properties compared to proton, primarily the nonrenewability of the signal. It could be expected, therefore, that the characteristics of image SNR with respect to encoding method will also be very different from hyperpolarized noble gas MRI compared to proton MRI. In this article, hyperpolarized noble gas image SNRs of different encoding methods are compared theoretically using a matrix description of the encoding process. It is shown that image SNR for hyperpolarized noble gas imaging is maximized for any orthonormal encoding method. Methods are then proposed for designing RF pulses to achieve normalized encoding profiles using Fourier, Hadamard, wavelet, and direct encoding methods for hyperpolarized noble gases. Theoretical results are confirmed with hyperpolarized noble gas MRI experiments. Copyright 2001 Academic Press.

Classification of microscopic images of breast tissue

NASA Astrophysics Data System (ADS)

Ballerini, Lucia; Franzen, Lennart

2004-05-01

Breast cancer is the most common form of cancer among women. The diagnosis is usually performed by the pathologist, that subjectively evaluates tissue samples. The aim of our research is to develop techniques for the automatic classification of cancerous tissue, by analyzing histological samples of intact tissue taken with a biopsy. In our study, we considered 200 images presenting four different conditions: normal tissue, fibroadenosis, ductal cancer and lobular cancer. Methods to extract features have been investigated and described. One method is based on granulometries, which are size-shape descriptors widely used in mathematical morphology. Applications of granulometries lead to distribution functions whose moments are used as features. A second method is based on fractal geometry, that seems very suitable to quantify biological structures. The fractal dimension of binary images has been computed using the euclidean distance mapping. Image classification has then been performed using the extracted features as input of a back-propagation neural network. A new method that combines genetic algorithms and morphological filters has been also investigated. In this case, the classification is based on a correlation measure. Very encouraging results have been obtained with pilot experiments using a small subset of images as training set. Experimental results indicate the effectiveness of the proposed methods. Cancerous tissue was correctly classified in 92.5% of the cases.

Using fractal analysis of thermal signatures for thyroid disease evaluation

NASA Astrophysics Data System (ADS)

Gavriloaia, Gheorghe; Sofron, Emil; Gavriloaia, Mariuca-Roxana; Ghemigean, Adina-Mariana

2010-11-01

The skin is the largest organ of the body and it protects against heat, light, injury and infection. Skin temperature is an important parameter for diagnosing diseases. Thermal analysis is non-invasive, painless, and relatively inexpensive, showing a great potential research. Since the thyroid regulates metabolic rate it is intimately connected to body temperature, more than, any modification of its function generates a specific thermal image on the neck skin. The shapes of thermal signatures are often irregular in size and shape. Euclidean geometry is not able to evaluate their shape for different thyroid diseases, and fractal geometry is used in this paper. Different thyroid diseases generate different shapes, and their complexity are evaluated by specific mathematical approaches, fractal analysis, in order to the evaluate selfsimilarity and lacunarity. Two kinds of thyroid diseases, hyperthyroidism and papillary cancer are analyzed in this paper. The results are encouraging and show the ability to continue research for thermal signature to be used in early diagnosis of thyroid diseases.

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

Alamudun, Folami T.; Yoon, Hong-Jun; Hudson, Kathy

Purpose: The objective of this study was to assess the complexity of human visual search activity during mammographic screening using fractal analysis and to investigate its relationship with case and reader characteristics. Methods: The study was performed for the task of mammographic screening with simultaneous viewing of four coordinated breast views as typically done in clinical practice. Eye-tracking data and diagnostic decisions collected for 100 mammographic cases (25 normal, 25 benign, 50 malignant) and 10 readers (three board certified radiologists and seven radiology residents), formed the corpus data for this study. The fractal dimension of the readers’ visual scanning patternsmore » was computed with the Minkowski–Bouligand box-counting method and used as a measure of gaze complexity. Individual factor and group-based interaction ANOVA analysis was performed to study the association between fractal dimension, case pathology, breast density, and reader experience level. The consistency of the observed trends depending on gaze data representation was also examined. Results: Case pathology, breast density, reader experience level, and individual reader differences are all independent predictors of the visual scanning pattern complexity when screening for breast cancer. No higher order effects were found to be significant. Conclusions: Fractal characterization of visual search behavior during mammographic screening is dependent on case properties and image reader characteristics.« less

Application of fractal and grey level co-occurrence matrix analysis in evaluation of brain corpus callosum and cingulum architecture.

PubMed

Pantic, Igor; Dacic, Sanja; Brkic, Predrag; Lavrnja, Irena; Pantic, Senka; Jovanovic, Tomislav; Pekovic, Sanja

2014-10-01

This aim of this study was to assess the discriminatory value of fractal and grey level co-occurrence matrix (GLCM) analysis methods in standard microscopy analysis of two histologically similar brain white mass regions that have different nerve fiber orientation. A total of 160 digital micrographs of thionine-stained rat brain white mass were acquired using a Pro-MicroScan DEM-200 instrument. Eighty micrographs from the anterior corpus callosum and eighty from the anterior cingulum areas of the brain were analyzed. The micrographs were evaluated using the National Institutes of Health ImageJ software and its plugins. For each micrograph, seven parameters were calculated: angular second moment, inverse difference moment, GLCM contrast, GLCM correlation, GLCM variance, fractal dimension, and lacunarity. Using the Receiver operating characteristic analysis, the highest discriminatory value was determined for inverse difference moment (IDM) (area under the receiver operating characteristic (ROC) curve equaled 0.925, and for the criterion IDM≤0.610 the sensitivity and specificity were 82.5 and 87.5%, respectively). Most of the other parameters also showed good sensitivity and specificity. The results indicate that GLCM and fractal analysis methods, when applied together in brain histology analysis, are highly capable of discriminating white mass structures that have different axonal orientation.

A Web platform for the interactive visualization and analysis of the 3D fractal dimension of MRI data.

PubMed

Jiménez, J; López, A M; Cruz, J; Esteban, F J; Navas, J; Villoslada, P; Ruiz de Miras, J

2014-10-01

This study presents a Web platform (http://3dfd.ujaen.es) for computing and analyzing the 3D fractal dimension (3DFD) from volumetric data in an efficient, visual and interactive way. The Web platform is specially designed for working with magnetic resonance images (MRIs) of the brain. The program estimates the 3DFD by calculating the 3D box-counting of the entire volume of the brain, and also of its 3D skeleton. All of this is done in a graphical, fast and optimized way by using novel technologies like CUDA and WebGL. The usefulness of the Web platform presented is demonstrated by its application in a case study where an analysis and characterization of groups of 3D MR images is performed for three neurodegenerative diseases: Multiple Sclerosis, Intrauterine Growth Restriction and Alzheimer's disease. To the best of our knowledge, this is the first Web platform that allows the users to calculate, visualize, analyze and compare the 3DFD from MRI images in the cloud. Copyright © 2014 Elsevier Inc. All rights reserved.

Fractal Analysis of Brain Blood Oxygenation Level Dependent (BOLD) Signals from Children with Mild Traumatic Brain Injury (mTBI).

PubMed

Dona, Olga; Noseworthy, Michael D; DeMatteo, Carol; Connolly, John F

2017-01-01

Conventional imaging techniques are unable to detect abnormalities in the brain following mild traumatic brain injury (mTBI). Yet patients with mTBI typically show delayed response on neuropsychological evaluation. Because fractal geometry represents complexity, we explored its utility in measuring temporal fluctuations of brain resting state blood oxygen level dependent (rs-BOLD) signal. We hypothesized that there could be a detectable difference in rs-BOLD signal complexity between healthy subjects and mTBI patients based on previous studies that associated reduction in signal complexity with disease. Fifteen subjects (13.4 ± 2.3 y/o) and 56 age-matched (13.5 ± 2.34 y/o) healthy controls were scanned using a GE Discovery MR750 3T MRI and 32-channel RF-coil. Axial FSPGR-3D images were used to prescribe rs-BOLD (TE/TR = 35/2000ms), acquired over 6 minutes. Motion correction was performed and anatomical and functional images were aligned and spatially warped to the N27 standard atlas. Fractal analysis, performed on grey matter, was done by estimating the Hurst exponent using de-trended fluctuation analysis and signal summation conversion methods. Voxel-wise fractal dimension (FD) was calculated for every subject in the control group to generate mean and standard deviation maps for regional Z-score analysis. Voxel-wise validation of FD normality across controls was confirmed, and non-Gaussian voxels (3.05% over the brain) were eliminated from subsequent analysis. For each mTBI patient, regions where Z-score values were at least 2 standard deviations away from the mean (i.e. where |Z| > 2.0) were identified. In individual patients the frequently affected regions were amygdala (p = 0.02), vermis(p = 0.03), caudate head (p = 0.04), hippocampus(p = 0.03), and hypothalamus(p = 0.04), all previously reported as dysfunctional after mTBI, but based on group analysis. It is well known that the brain is best modeled as a complex system. Therefore a measure of complexity using rs-BOLD signal FD could provide an additional method to grade and monitor mTBI. Furthermore, this approach can be personalized thus providing unique patient specific assessment.

Detecting Lung Diseases from Exhaled Aerosols: Non-Invasive Lung Diagnosis Using Fractal Analysis and SVM Classification

PubMed Central

Xi, Jinxiang; Zhao, Weizhong; Yuan, Jiayao Eddie; Kim, JongWon; Si, Xiuhua; Xu, Xiaowei

2015-01-01

Background Each lung structure exhales a unique pattern of aerosols, which can be used to detect and monitor lung diseases non-invasively. The challenges are accurately interpreting the exhaled aerosol fingerprints and quantitatively correlating them to the lung diseases. Objective and Methods In this study, we presented a paradigm of an exhaled aerosol test that addresses the above two challenges and is promising to detect the site and severity of lung diseases. This paradigm consists of two steps: image feature extraction using sub-regional fractal analysis and data classification using a support vector machine (SVM). Numerical experiments were conducted to evaluate the feasibility of the breath test in four asthmatic lung models. A high-fidelity image-CFD approach was employed to compute the exhaled aerosol patterns under different disease conditions. Findings By employing the 10-fold cross-validation method, we achieved 100% classification accuracy among four asthmatic models using an ideal 108-sample dataset and 99.1% accuracy using a more realistic 324-sample dataset. The fractal-SVM classifier has been shown to be robust, highly sensitive to structural variations, and inherently suitable for investigating aerosol-disease correlations. Conclusion For the first time, this study quantitatively linked the exhaled aerosol patterns with their underlying diseases and set the stage for the development of a computer-aided diagnostic system for non-invasive detection of obstructive respiratory diseases. PMID:26422016

Morphology and Fractal Characterization of Multiscale Pore Structures for Organic-Rich Lacustrine Shale Reservoirs

NASA Astrophysics Data System (ADS)

Wang, Yang; Wu, Caifang; Zhu, Yanming; Chen, Shangbin; Liu, Shimin; Zhang, Rui

Lacustrine shale gas has received considerable attention and has been playing an important role in unconventional natural gas production in China. In this study, multiple techniques, including total organic carbon (TOC) analysis, X-ray diffraction (XRD) analysis, field emission scanning electron microscopy (FE-SEM), helium pycnometry and low-pressure N2 adsorption have been applied to characterize the pore structure of lacustrine shale of Upper Triassic Yanchang Formation from the Ordos Basin. The results show that organic matter (OM) pores are the most important type dominating the pore system, while interparticle (interP) pores, intraparticle (intraP) and microfractures are also usually observed between or within different minerals. The shapes of OM pores are less complex compared with the other two pore types based on the Image-Pro Plus software analysis. In addition, the specific surface area ranges from 2.76m2/g to 10.26m2/g and the pore volume varies between 0.52m3/100g and 1.31m3/100g. Two fractal dimensions D1 and D2 were calculated using Frenkel-Halsey-Hill (FHH) method, with D1 varying between 2.510 and 2.632, and D2 varying between 2.617 and 2.814. Further investigation indicates that the fractal dimensions exhibit positive correlations with TOC contents, whereas there is no definite relationship observed between fractal dimensions and clay minerals. Meanwhile, the fractal dimensions increase with the increase in specific surface area, and is negatively correlated with the pore size.

Definition of fractal topography to essential understanding of scale-invariance

NASA Astrophysics Data System (ADS)

Jin, Yi; Wu, Ying; Li, Hui; Zhao, Mengyu; Pan, Jienan

2017-04-01

Fractal behavior is scale-invariant and widely characterized by fractal dimension. However, the cor-respondence between them is that fractal behavior uniquely determines a fractal dimension while a fractal dimension can be related to many possible fractal behaviors. Therefore, fractal behavior is independent of the fractal generator and its geometries, spatial pattern, and statistical properties in addition to scale. To mathematically describe fractal behavior, we propose a novel concept of fractal topography defined by two scale-invariant parameters, scaling lacunarity (P) and scaling coverage (F). The scaling lacunarity is defined as the scale ratio between two successive fractal generators, whereas the scaling coverage is defined as the number ratio between them. Consequently, a strictly scale-invariant definition for self-similar fractals can be derived as D = log F /log P. To reflect the direction-dependence of fractal behaviors, we introduce another parameter Hxy, a general Hurst exponent, which is analytically expressed by Hxy = log Px/log Py where Px and Py are the scaling lacunarities in the x and y directions, respectively. Thus, a unified definition of fractal dimension is proposed for arbitrary self-similar and self-affine fractals by averaging the fractal dimensions of all directions in a d-dimensional space, which . Our definitions provide a theoretical, mechanistic basis for understanding the essentials of the scale-invariant property that reduces the complexity of modeling fractals.

Advances in the Quantitative Characterization of the Shape of Ash-Sized Pyroclast Populations: Fractal Analyses Coupled to Micro- and Nano-Computed Tomography Techniques

NASA Astrophysics Data System (ADS)

Rausch, J.; Vonlanthen, P.; Grobety, B. H.

2014-12-01

The quantification of shape parameters in pyroclasts is fundamental to infer the dominant type of magma fragmentation (magmatic vs. phreatomagmatic), as well as the behavior of volcanic plumes and clouds in the atmosphere. In a case study aiming at reconstructing the fragmentation mechanisms triggering maar eruptions in two geologically and compositionally distinctive volcanic fields (West and East Eifel, Germany), the shapes of a large number of ash particle contours obtained from SEM images were analyzed by a dilation-based fractal method. Volcanic particle contours are pseudo-fractals showing mostly two distinct slopes in Richardson plots related to the fractal dimensions D1 (small-scale "textural" dimension) and D2 (large-scale "morphological" dimension). The validity of the data obtained from 2D sections was tested by analysing SEM micro-CT slices of one particle cut in different orientations and positions. Results for West Eifel maar particles yield large D1 values (> 1.023), resembling typical values of magmatic particles, which are characterized by a complex shape, especially at small scales. In contrast, the D1 values of ash particles from one East Eifel maar deposit are much smaller, coinciding with the fractal dimensions obtained from phreatomagmatic end-member particles. These quantitative morphological analyses suggest that the studied maar eruptions were triggered by two different fragmentation processes: phreatomagmatic in the East Eifel and magmatic in the West Eifel. The application of fractal analysis to quantitatively characterize the shape of pyroclasts and the linking of fractal dimensions to specific fragmentation processes has turned out to be a very promising tool for studying the fragmentation history of any volcanic eruption. The next step is to extend morphological analysis of volcanic particles to 3 dimensions. SEM micro-CT, already applied in this study, offers the required resolution, but is not suitable for the analysis of a large number of particles. Newly released nano CT-scanners, however, allows the simultaneous analysis of a statistically relevant number of particles (in the hundreds range). Preliminary results of a first trial will be presented.

Is the co-seismic slip distribution fractal?

NASA Astrophysics Data System (ADS)

Milliner, Christopher; Sammis, Charles; Allam, Amir; Dolan, James

2015-04-01

Co-seismic along-strike slip heterogeneity is widely observed for many surface-rupturing earthquakes as revealed by field and high-resolution geodetic methods. However, this co-seismic slip variability is currently a poorly understood phenomenon. Key unanswered questions include: What are the characteristics and underlying causes of along-strike slip variability? Do the properties of slip variability change from fault-to-fault, along-strike or at different scales? We cross-correlate optical, pre- and post-event air photos using the program COSI-Corr to measure the near-field, surface deformation pattern of the 1992 Mw 7.3 Landers and 1999 Mw 7.1 Hector Mine earthquakes in high-resolution. We produce the co-seismic slip profiles of both events from over 1,000 displacement measurements and observe consistent along-strike slip variability. Although the observed slip heterogeneity seems apparently complex and disordered, a spectral analysis reveals that the slip distributions are indeed self-affine fractal i.e., slip exhibits a consistent degree of irregularity at all observable length scales, with a 'short-memory' and is not random. We find a fractal dimension of 1.58 and 1.75 for the Landers and Hector Mine earthquakes, respectively, indicating that slip is more heterogeneous for the Hector Mine event. Fractal slip is consistent with both dynamic and quasi-static numerical simulations that use non-planar faults, which in turn causes heterogeneous along-strike stress, and we attribute the observed fractal slip to fault surfaces of fractal roughness. As fault surfaces are known to smooth over geologic time due to abrasional wear and fracturing, we also test whether the fractal properties of slip distributions alters between earthquakes from immature to mature fault systems. We will present results that test this hypothesis by using the optical image correlation technique to measure historic, co-seismic slip distributions of earthquakes from structurally mature, large cumulative displacement faults and compare these slip distributions to those from immature fault systems. Our results have fundamental implications for an understanding of slip heterogeneity and the behavior of the rupture process.

Automated selection of trabecular bone regions in knee radiographs.

PubMed

Podsiadlo, P; Wolski, M; Stachowiak, G W

2008-05-01

Osteoarthritic (OA) changes in knee joints can be assessed by analyzing the structure of trabecular bone (TB) in the tibia. This analysis is performed on TB regions selected manually by a human operator on x-ray images. Manual selection is time-consuming, tedious, and expensive. Even if a radiologist expert or highly trained person is available to select regions, high inter- and intraobserver variabilities are still possible. A fully automated image segmentation method was, therefore, developed to select the bone regions for numerical analyses of changes in bone structures. The newly developed method consists of image preprocessing, delineation of cortical bone plates (active shape model), and location of regions of interest (ROI). The method was trained on an independent set of 40 x-ray images. Automatically selected regions were compared to the "gold standard" that contains ROIs selected manually by a radiologist expert on 132 x-ray images. All images were acquired from subjects locked in a standardized standing position using a radiography rig. The size of each ROI is 12.8 x 12.8 mm. The automated method results showed a good agreement with the gold standard [similarity index (SI) = 0.83 (medial) and 0.81 (lateral) and the offset =[-1.78, 1.27]x[-0.65,0.26] mm (medial) and [-2.15, 1.59]x[-0.58, 0.52] mm (lateral)]. Bland and Altman plots were constructed for fractal signatures, and changes of fractal dimensions (FD) to region offsets calculated between the gold standard and automatically selected regions were calculated. The plots showed a random scatter and the 95% confidence intervals were (-0.006, 0.008) and (-0.001, 0.011). The changes of FDs to region offsets were less than 0.035. Previous studies showed that differences in FDs between non-OA and OA bone regions were greater than 0.05. ROIs were also selected by a second radiologist and then evaluated. Results indicated that the newly developed method could replace a human operator and produces bone regions with an accuracy that is sufficient for fractal analyses of bone texture.

Fractals: To Know, to Do, to Simulate.

ERIC Educational Resources Information Center

Talanquer, Vicente; Irazoque, Glinda

1993-01-01

Discusses the development of fractal theory and suggests fractal aggregates as an attractive alternative for introducing fractal concepts. Describes methods for producing metallic fractals and a computer simulation for drawing fractals. (MVL)

Single-shot imaging with higher-dimensional encoding using magnetic field monitoring and concomitant field correction.

PubMed

Testud, Frederik; Gallichan, Daniel; Layton, Kelvin J; Barmet, Christoph; Welz, Anna M; Dewdney, Andrew; Cocosco, Chris A; Pruessmann, Klaas P; Hennig, Jürgen; Zaitsev, Maxim

2015-03-01

PatLoc (Parallel Imaging Technique using Localized Gradients) accelerates imaging and introduces a resolution variation across the field-of-view. Higher-dimensional encoding employs more spatial encoding magnetic fields (SEMs) than the corresponding image dimensionality requires, e.g. by applying two quadratic and two linear spatial encoding magnetic fields to reconstruct a 2D image. Images acquired with higher-dimensional single-shot trajectories can exhibit strong artifacts and geometric distortions. In this work, the source of these artifacts is analyzed and a reliable correction strategy is derived. A dynamic field camera was built for encoding field calibration. Concomitant fields of linear and nonlinear spatial encoding magnetic fields were analyzed. A combined basis consisting of spherical harmonics and concomitant terms was proposed and used for encoding field calibration and image reconstruction. A good agreement between the analytical solution for the concomitant fields and the magnetic field simulations of the custom-built PatLoc SEM coil was observed. Substantial image quality improvements were obtained using a dynamic field camera for encoding field calibration combined with the proposed combined basis. The importance of trajectory calibration for single-shot higher-dimensional encoding is demonstrated using the combined basis including spherical harmonics and concomitant terms, which treats the concomitant fields as an integral part of the encoding. © 2014 Wiley Periodicals, Inc.

JPEG vs. JPEG 2000: an objective comparison of image encoding quality

NASA Astrophysics Data System (ADS)

Ebrahimi, Farzad; Chamik, Matthieu; Winkler, Stefan

2004-11-01

This paper describes an objective comparison of the image quality of different encoders. Our approach is based on estimating the visual impact of compression artifacts on perceived quality. We present a tool that measures these artifacts in an image and uses them to compute a prediction of the Mean Opinion Score (MOS) obtained in subjective experiments. We show that the MOS predictions by our proposed tool are a better indicator of perceived image quality than PSNR, especially for highly compressed images. For the encoder comparison, we compress a set of 29 test images with two JPEG encoders (Adobe Photoshop and IrfanView) and three JPEG2000 encoders (JasPer, Kakadu, and IrfanView) at various compression ratios. We compute blockiness, blur, and MOS predictions as well as PSNR of the compressed images. Our results show that the IrfanView JPEG encoder produces consistently better images than the Adobe Photoshop JPEG encoder at the same data rate. The differences between the JPEG2000 encoders in our test are less pronounced; JasPer comes out as the best codec, closely followed by IrfanView and Kakadu. Comparing the JPEG- and JPEG2000-encoding quality of IrfanView, we find that JPEG has a slight edge at low compression ratios, while JPEG2000 is the clear winner at medium and high compression ratios.

Encoding and decoding of digital spiral imaging based on bidirectional transformation of light's spatial eigenmodes.

PubMed

Zhang, Wuhong; Chen, Lixiang

2016-06-15

Digital spiral imaging has been demonstrated as an effective optical tool to encode optical information and retrieve topographic information of an object. Here we develop a conceptually new and concise scheme for optical image encoding and decoding toward free-space digital spiral imaging. We experimentally demonstrate that the optical lattices with ℓ=±50 orbital angular momentum superpositions and a clover image with nearly 200 Laguerre-Gaussian (LG) modes can be well encoded and successfully decoded. It is found that an image encoded/decoded with a two-index LG spectrum (considering both azimuthal and radial indices, ℓ and p) possesses much higher fidelity than that with a one-index LG spectrum (only considering the ℓ index). Our work provides an alternative tool for the image encoding/decoding scheme toward free-space optical communications.

Complementary-encoding holographic associative memory using a photorefractive crystal

NASA Astrophysics Data System (ADS)

Yuan, ShiFu; Wu, Minxian; Yan, Yingbai; Jin, Guofan

1996-06-01

We present a holographic implementation of accurate associative memory with only one holographic memory system. In the implementation, the stored and test images are coded by using complementary-encoding method. The recalled complete image is also a coded image that can be decoded with a decoding mask to get an original image or its complement image. The experiment shows that the complementary encoding can efficiently increase the addressing accuracy in a simple way. Instead of the above complementary-encoding method, a scheme that uses complementary area-encoding method is also proposed for the holographic implementation of gray-level image associative memory with accurate addressing.

Multifractal spectrum and lacunarity as measures of complexity of osseointegration.

PubMed

de Souza Santos, Daniel; Dos Santos, Leonardo Cavalcanti Bezerra; de Albuquerque Tavares Carvalho, Alessandra; Leão, Jair Carneiro; Delrieux, Claudio; Stosic, Tatijana; Stosic, Borko

2016-07-01

The goal of this study is to contribute to a better quantitative description of the early stages of osseointegration, by application of fractal, multifractal, and lacunarity analysis. Fractal, multifractal, and lacunarity analysis are performed on scanning electron microscopy (SEM) images of titanium implants that were first subjected to different treatment combinations of i) sand blasting, ii) acid etching, and iii) exposition to calcium phosphate, and were then submersed in a simulated body fluid (SBF) for 30 days. All the three numerical techniques are applied to the implant SEM images before and after SBF immersion, in order to provide a comprehensive set of common quantitative descriptors. It is found that implants subjected to different physicochemical treatments before submersion in SBF exhibit a rather similar level of complexity, while the great variety of crystal forms after SBF submersion reveals rather different quantitative measures (reflecting complexity), for different treatments. In particular, it is found that acid treatment, in most combinations with the other considered treatments, leads to a higher fractal dimension (more uniform distribution of crystals), lower lacunarity (lesser variation in gap sizes), and narrowing of the multifractal spectrum (smaller fluctuations on different scales). The current quantitative description has shown the capacity to capture the main features of complex images of implant surfaces, for several different treatments. Such quantitative description should provide a fundamental tool for future large scale systematic studies, considering the large variety of possible implant treatments and their combinations. Quantitative description of early stages of osseointegration on titanium implants with different treatments should help develop a better understanding of this phenomenon, in general, and provide basis for further systematic experimental studies. Clinical practice should benefit from such studies in the long term, by more ready access to implants of higher quality.

Visual communications and image processing '92; Proceedings of the Meeting, Boston, MA, Nov. 18-20, 1992

NASA Astrophysics Data System (ADS)

Maragos, Petros

The topics discussed at the conference include hierarchical image coding, motion analysis, feature extraction and image restoration, video coding, and morphological and related nonlinear filtering. Attention is also given to vector quantization, morphological image processing, fractals and wavelets, architectures for image and video processing, image segmentation, biomedical image processing, and model-based analysis. Papers are presented on affine models for motion and shape recovery, filters for directly detecting surface orientation in an image, tracking of unresolved targets in infrared imagery using a projection-based method, adaptive-neighborhood image processing, and regularized multichannel restoration of color images using cross-validation. (For individual items see A93-20945 to A93-20951)

Fractal Electronic Circuits Assembled From Nanoclusters

NASA Astrophysics Data System (ADS)

Fairbanks, M. S.; McCarthy, D.; Taylor, R. P.; Brown, S. A.

2009-07-01

Many patterns in nature can be described using fractal geometry. The effect of this fractal character is an array of properties that can include high internal connectivity, high dispersivity, and enhanced surface area to volume ratios. These properties are often desirable in applications and, consequently, fractal geometry is increasingly employed in technologies ranging from antenna to storm barriers. In this paper, we explore the application of fractal geometry to electrical circuits, inspired by the pervasive fractal structure of neurons in the brain. We show that, under appropriate growth conditions, nanoclusters of Sb form into islands on atomically flat substrates via a process close to diffusion-limited aggregation (DLA), establishing fractal islands that will form the basis of our fractal circuits. We perform fractal analysis of the islands to determine the spatial scaling properties (characterized by the fractal dimension, D) of the proposed circuits and demonstrate how varying growth conditions can affect D. We discuss fabrication approaches for establishing electrical contact to the fractal islands. Finally, we present fractal circuit simulations, which show that the fractal character of the circuit translates into novel, non-linear conduction properties determined by the circuit's D value.

Fractal dimension as an index of brain cortical changes throughout life.

PubMed

Kalmanti, Elina; Maris, Thomas G

2007-01-01

The fractal dimension (FD) of the cerebral cortex was measured in 93 individuals, aged from 3 months to 78 years, with normal brain MRI's in order to compare the convolutions of the cerebral cortex between genders and age groups. Image J, an image processing program, was used to skeletonize cerebral cortex and the box counting method applied. FDs on slices taken from left and right hemispheres were calculated. Our results showed a significant degree of lateralization in the left hemisphere. It appears that basal ganglia development, mainly in the left hemisphere, is heavily dependent upon age until puberty. In addition, both left and right cortex development equally depends on age until puberty, while the corresponding right hemisphere convolutions continue to develop until a later stage. An increased developmental activity appears between the ages of 1 and 15 years, indicating a significant brain remodelling during childhood and adolescence. In infancy, only changes in basal ganglia are observed, while the right hemisphere continues to remodel in adulthood.

Morphological characterization of diesel soot agglomerates based on the Beer-Lambert law

NASA Astrophysics Data System (ADS)

Lapuerta, Magín; Martos, Francisco J.; José Expósito, Juan

2013-03-01

A new method is proposed for the determination of the number of primary particles composing soot agglomerates emitted from diesel engines as well as their individual fractal dimension. The method is based on the Beer-Lambert law and it is applied to micro-photographs taken in high resolution transmission electron microscopy. Differences in the grey levels of the images lead to a more accurate estimation of the geometry of the agglomerate (in this case radius of gyration) than other methods based exclusively on the planar projections of the agglomerates. The method was validated by applying it to different images of the same agglomerate observed from different angles of incidence, and proving that the effect of the angle of incidence is minor, contrary to other methods. Finally, the comparisons with other methods showed that the size, number of primary particles and fractal dimension (the latter depending on the particle size) are usually underestimated when only planar projections of the agglomerates are considered.

Fractal-Based Image Compression

DTIC Science & Technology

1989-09-01

6. A Mercedes Benz symbol generated using an IFS code ................. 21 7. (a) U-A fern and (b) A-0 fern generated with RIFS codes...22 8. Construction of the Mercedes - Benz symbol using RIFS ................ 23 9. The regenerated perfect image of the Mercedes - Benz symbol using R IF...quite often, it cannot be done with a reasonable number of transforms. As an example, the Mercedes Benz symbol generated using an IFS code is illustrated

A fractal image analysis methodology for heat damage inspection in carbon fiber reinforced composites

NASA Astrophysics Data System (ADS)

Haridas, Aswin; Crivoi, Alexandru; Prabhathan, P.; Chan, Kelvin; Murukeshan, V. M.

2017-06-01

The use of carbon fiber-reinforced polymer (CFRP) composite materials in the aerospace industry have far improved the load carrying properties and the design flexibility of aircraft structures. A high strength to weight ratio, low thermal conductivity, and a low thermal expansion coefficient gives it an edge for applications demanding stringent loading conditions. Specifically, this paper focuses on the behavior of CFRP composites under stringent thermal loads. The properties of composites are largely affected by external thermal loads, especially when the loads are beyond the glass temperature, Tg, of the composite. Beyond this, the composites are subject to prominent changes in mechanical and thermal properties which may further lead to material decomposition. Furthermore, thermal damage formation being chaotic, a strict dimension cannot be associated with the formed damage. In this context, this paper focuses on comparing multiple speckle image analysis algorithms to effectively characterize the formed thermal damages on the CFRP specimen. This would provide us with a fast method for quantifying the extent of heat damage in carbon composites, thus reducing the required time for inspection. The image analysis methods used for the comparison include fractal dimensional analysis of the formed speckle pattern and analysis of number and size of various connecting elements in the binary image.

Effect of frying temperature and time on image characterizations of pellet snacks.

PubMed

Mohammadi Moghaddam, Toktam; BahramParvar, Maryam; Razavi, Seyed M A

2015-05-01

The development of non-destructive methods for the evaluation of food properties has important advantages for the food processing industries. So, the aim of this study was to evaluate the effects of frying temperature (150, 170, and 190 °C) and time (0.5, 1.5, 2.5, 3.5 and 4.5 min) on image properties (L*, a* and b*, fractal dimension, correlation, entropy, contrast and homogeneity) of pellet snacks. Textures were computed separately for eight channels (RGB, R, G, B, U, V, H and S). Enhancing the frying time from 0.5 min to 2.5 min increased the fractal dimension; but its increase from 2.5 min to 4.5 min could not expand the samples. Then, the highest volume of pellet snacks was observed at 2.5 min. Features derived from the image texture contained better information than color features. The best result was for U channel which showed that increasing the frying time increased the contrast, entropy and correlation. Developing the frying temperature up to 170 °C decreased contrast, entropy and correlation of images; however these factors were increased when frying temperature was 190 °C. These results were invert for homogeneity.

Music and fractals

NASA Astrophysics Data System (ADS)

Wuorinen, Charles

2015-03-01

Any of the arts may produce exemplars that have fractal characteristics. There may be fractal painting, fractal poetry, and the like. But these will always be specific instances, not necessarily displaying intrinsic properties of the art-medium itself. Only music, I believe, of all the arts possesses an intrinsically fractal character, so that its very nature is fractally determined. Thus, it is reasonable to assert that any instance of music is fractal...

Flow field topology of submerged jets with fractal generated turbulence

NASA Astrophysics Data System (ADS)

Cafiero, Gioacchino; Discetti, Stefano; Astarita, Tommaso

2015-11-01

Fractal grids (FGs) have been recently an object of numerous investigations due to the interesting capability of generating turbulence at multiple scales, thus paving the way to tune mixing and scalar transport. The flow field topology of a turbulent air jet equipped with a square FG is investigated by means of planar and volumetric particle image velocimetry. The comparison with the well-known features of a round jet without turbulence generators is also presented. The Reynolds number based on the nozzle exit section diameter for all the experiments is set to about 15 000. It is demonstrated that the presence of the grid enhances the entrainment rate and, as a consequence, the scalar transfer of the jet. Moreover, due to the effect of the jet external shear layer on the wake shed by the grid bars, the turbulence production region past the grid is significantly shortened with respect to the documented behavior of fractal grids in free-shear conditions. The organization of the large coherent structures in the FG case is also analyzed and discussed. Differently from the well-known generation of toroidal vortices due to the growth of azimuthal disturbances within the jet shear layer, the fractal grid introduces cross-wise disturbs which produce streamwise vortices; these structures, although characterized by a lower energy content, have a deeper streamwise penetration than the ring vortices, thus enhancing the entrainment process.

Hierarchical layered and semantic-based image segmentation using ergodicity map

NASA Astrophysics Data System (ADS)

Yadegar, Jacob; Liu, Xiaoqing

2010-04-01

Image segmentation plays a foundational role in image understanding and computer vision. Although great strides have been made and progress achieved on automatic/semi-automatic image segmentation algorithms, designing a generic, robust, and efficient image segmentation algorithm is still challenging. Human vision is still far superior compared to computer vision, especially in interpreting semantic meanings/objects in images. We present a hierarchical/layered semantic image segmentation algorithm that can automatically and efficiently segment images into hierarchical layered/multi-scaled semantic regions/objects with contextual topological relationships. The proposed algorithm bridges the gap between high-level semantics and low-level visual features/cues (such as color, intensity, edge, etc.) through utilizing a layered/hierarchical ergodicity map, where ergodicity is computed based on a space filling fractal concept and used as a region dissimilarity measurement. The algorithm applies a highly scalable, efficient, and adaptive Peano- Cesaro triangulation/tiling technique to decompose the given image into a set of similar/homogenous regions based on low-level visual cues in a top-down manner. The layered/hierarchical ergodicity map is built through a bottom-up region dissimilarity analysis. The recursive fractal sweep associated with the Peano-Cesaro triangulation provides efficient local multi-resolution refinement to any level of detail. The generated binary decomposition tree also provides efficient neighbor retrieval mechanisms for contextual topological object/region relationship generation. Experiments have been conducted within the maritime image environment where the segmented layered semantic objects include the basic level objects (i.e. sky/land/water) and deeper level objects in the sky/land/water surfaces. Experimental results demonstrate the proposed algorithm has the capability to robustly and efficiently segment images into layered semantic objects/regions with contextual topological relationships.

Effective degrees of freedom of a random walk on a fractal

NASA Astrophysics Data System (ADS)

Balankin, Alexander S.

2015-12-01

We argue that a non-Markovian random walk on a fractal can be treated as a Markovian process in a fractional dimensional space with a suitable metric. This allows us to define the fractional dimensional space allied to the fractal as the ν -dimensional space Fν equipped with the metric induced by the fractal topology. The relation between the number of effective spatial degrees of freedom of walkers on the fractal (ν ) and fractal dimensionalities is deduced. The intrinsic time of random walk in Fν is inferred. The Laplacian operator in Fν is constructed. This allows us to map physical problems on fractals into the corresponding problems in Fν. In this way, essential features of physics on fractals are revealed. Particularly, subdiffusion on path-connected fractals is elucidated. The Coulomb potential of a point charge on a fractal embedded in the Euclidean space is derived. Intriguing attributes of some types of fractals are highlighted.

An Approach to Study Elastic Vibrations of Fractal Cylinders

NASA Astrophysics Data System (ADS)

Steinberg, Lev; Zepeda, Mario

2016-11-01

This paper presents our study of dynamics of fractal solids. Concepts of fractal continuum and time had been used in definitions of a fractal body deformation and motion, formulation of conservation of mass, balance of momentum, and constitutive relationships. A linearized model, which was written in terms of fractal time and spatial derivatives, has been employed to study the elastic vibrations of fractal circular cylinders. Fractal differential equations of torsional, longitudinal and transverse fractal wave equations have been obtained and solution properties such as size and time dependence have been revealed.

Elasticity of fractal materials using the continuum model with non-integer dimensional space

NASA Astrophysics Data System (ADS)

Tarasov, Vasily E.

2015-01-01

Using a generalization of vector calculus for space with non-integer dimension, we consider elastic properties of fractal materials. Fractal materials are described by continuum models with non-integer dimensional space. A generalization of elasticity equations for non-integer dimensional space, and its solutions for the equilibrium case of fractal materials are suggested. Elasticity problems for fractal hollow ball and cylindrical fractal elastic pipe with inside and outside pressures, for rotating cylindrical fractal pipe, for gradient elasticity and thermoelasticity of fractal materials are solved.

Fractal vector optical fields.

PubMed

Pan, Yue; Gao, Xu-Zhen; Cai, Meng-Qiang; Zhang, Guan-Lin; Li, Yongnan; Tu, Chenghou; Wang, Hui-Tian

2016-07-15

We introduce the concept of a fractal, which provides an alternative approach for flexibly engineering the optical fields and their focal fields. We propose, design, and create a new family of optical fields-fractal vector optical fields, which build a bridge between the fractal and vector optical fields. The fractal vector optical fields have polarization states exhibiting fractal geometry, and may also involve the phase and/or amplitude simultaneously. The results reveal that the focal fields exhibit self-similarity, and the hierarchy of the fractal has the "weeding" role. The fractal can be used to engineer the focal field.

Human physiological benefits of viewing nature: EEG responses to exact and statistical fractal patterns.

PubMed

Hagerhall, C M; Laike, T; Küller, M; Marcheschi, E; Boydston, C; Taylor, R P

2015-01-01

Psychological and physiological benefits of viewing nature have been extensively studied for some time. More recently it has been suggested that some of these positive effects can be explained by nature's fractal properties. Virtually all studies on human responses to fractals have used stimuli that represent the specific form of fractal geometry found in nature, i.e. statistical fractals, as opposed to fractal patterns which repeat exactly at different scales. This raises the question of whether human responses like preference and relaxation are being driven by fractal geometry in general or by the specific form of fractal geometry found in nature. In this study we consider both types of fractals (statistical and exact) and morph one type into the other. Based on the Koch curve, nine visual stimuli were produced in which curves of three different fractal dimensions evolve gradually from an exact to a statistical fractal. The patterns were shown for one minute each to thirty-five subjects while qEEG was continuously recorded. The results showed that the responses to statistical and exact fractals differ, and that the natural form of the fractal is important for inducing alpha responses, an indicator of a wakefully relaxed state and internalized attention.

[Quantitative analysis method based on fractal theory for medical imaging of normal brain development in infants].

PubMed

Li, Heheng; Luo, Liangping; Huang, Li

2011-02-01

The present paper is aimed to study the fractal spectrum of the cerebral computerized tomography in 158 normal infants of different age groups, based on the calculation of chaotic theory. The distribution range of neonatal period was 1.88-1.90 (mean = 1.8913 +/- 0.0064); It reached a stable condition at the level of 1.89-1.90 during 1-12 months old (mean = 1.8927 +/- 0.0045); The normal range of 1-2 years old infants was 1.86-1.90 (mean = 1.8863 +/- 4 0.0085); It kept the invariance of the quantitative value among 1.88-1.91(mean = 1.8958 +/- 0.0083) during 2-3 years of age. ANOVA indicated there's no significant difference between boys and girls (F = 0.243, P > 0.05), but the difference of age groups was significant (F = 8.947, P < 0.001). The fractal dimension of cerebral computerized tomography in normal infants computed by box methods was maintained at an efficient stability from 1.86 to 1.91. It indicated that there exit some attractor modes in pediatric brain development.

Analysis of Texture Using the Fractal Model

NASA Technical Reports Server (NTRS)

Navas, William; Espinosa, Ramon Vasquez

1997-01-01

Properties such as the fractal dimension (FD) can be used for feature extraction and classification of regions within an image. The FD measures the degree of roughness of a surface, so this number is used to characterize a particular region, in order to differentiate it from another. There are two basic approaches discussed in the literature to measure FD: the blanket method, and the box counting method. Both attempt to measure FD by estimating the change in surface area with respect to the change in resolution. We tested both methods but box counting resulted computationally faster and gave better results. Differential Box Counting (DBC) was used to segment a collage containing three textures. The FD is independent of directionality and brightness so five features were used derived from the original image to account for directionality and gray level biases. FD can not be measured on a point, so we use a window that slides across the image giving values of FD to the pixel on the center of the window. Windowing blurs the boundaries of adjacent classes, so an edge-preserving, feature-smoothing algorithm is used to improve classification within segments and to make the boundaries sharper. Segmentation using DBC was 90.8910 accurate.

VESGEN Software for Mapping and Quantification of Vascular Regulators

NASA Technical Reports Server (NTRS)

Parsons-Wingerter, Patricia A.; Vickerman, Mary B.; Keith, Patricia A.

2012-01-01

VESsel GENeration (VESGEN) Analysis is an automated software that maps and quantifies effects of vascular regulators on vascular morphology by analyzing important vessel parameters. Quantification parameters include vessel diameter, length, branch points, density, and fractal dimension. For vascular trees, measurements are reported as dependent functions of vessel branching generation. VESGEN maps and quantifies vascular morphological events according to fractal-based vascular branching generation. It also relies on careful imaging of branching and networked vascular form. It was developed as a plug-in for ImageJ (National Institutes of Health, USA). VESGEN uses image-processing concepts of 8-neighbor pixel connectivity, skeleton, and distance map to analyze 2D, black-and-white (binary) images of vascular trees, networks, and tree-network composites. VESGEN maps typically 5 to 12 (or more) generations of vascular branching, starting from a single parent vessel. These generations are tracked and measured for critical vascular parameters that include vessel diameter, length, density and number, and tortuosity per branching generation. The effects of vascular therapeutics and regulators on vascular morphology and branching tested in human clinical or laboratory animal experimental studies are quantified by comparing vascular parameters with control groups. VESGEN provides a user interface to both guide and allow control over the users vascular analysis process. An option is provided to select a morphological tissue type of vascular trees, network or tree-network composites, which determines the general collections of algorithms, intermediate images, and output images and measurements that will be produced.

Iterated Function Systems in the Classroom

ERIC Educational Resources Information Center

Waiveris, Charles

2007-01-01

The title may appear daunting, but the exercises, which can be presented to students from middle school to graduate school, are not. The exercises center on creating fractal images in the xy-plane with free. easy-to-use software and questions appropriate to the level of the student.

Combining local scaling and global methods to detect soil pore space

NASA Astrophysics Data System (ADS)

Martin-Sotoca, Juan Jose; Saa-Requejo, Antonio; Grau, Juan B.; Tarquis, Ana M.

2017-04-01

The characterization of the spatial distribution of soil pore structures is essential to obtain different parameters that will influence in several models related to water flow and/or microbial growth processes. The first step in pore structure characterization is obtaining soil images that best approximate reality. Over the last decade, major technological advances in X-ray computed tomography (CT) have allowed for the investigation and reconstruction of natural porous media architectures at very fine scales. The subsequent step is delimiting the pore structure (pore space) from the CT soil images applying a thresholding. Many times we could find CT-scan images that show low contrast at the solid-void interface that difficult this step. Different delimitation methods can result in different spatial distributions of pores influencing the parameters used in the models. Recently, new local segmentation method using local greyscale value (GV) concentration variabilities, based on fractal concepts, has been presented. This method creates singularity maps to measure the GV concentration at each point. The C-A method was combined with the singularity map approach (Singularity-CA method) to define local thresholds that can be applied to binarize CT images. Comparing this method with classical methods, such as Otsu and Maximum Entropy, we observed that more pores can be detected mainly due to its ability to amplify anomalous concentrations. However, it delineated many small pores that were incorrect. In this work, we present an improve version of Singularity-CA method that avoid this problem basically combining it with the global classical methods. References Martín-Sotoca, J.J., A. Saa-Requejo, J.B. Grau, A.M. Tarquis. New segmentation method based on fractal properties using singularity maps. Geoderma, 287, 40-53, 2017. Martín-Sotoca, J.J, A. Saa-Requejo, J.B. Grau, A.M. Tarquis. Local 3D segmentation of soil pore space based on fractal properties using singularity maps. Geoderma, http://dx.doi.org/10.1016/j.geoderma.2016.11.029. Torre, Iván G., Juan C. Losada and A.M. Tarquis. Multiscaling properties of soil images. Biosystems Engineering, http://dx.doi.org/10.1016/j.biosystemseng.2016.11.006.

Efficacy of Distortion Correction on Diffusion Imaging: Comparison of FSL Eddy and Eddy_Correct Using 30 and 60 Directions Diffusion Encoding

PubMed Central

Yamada, Haruyasu; Abe, Osamu; Shizukuishi, Takashi; Kikuta, Junko; Shinozaki, Takahiro; Dezawa, Ko; Nagano, Akira; Matsuda, Masayuki; Haradome, Hiroki; Imamura, Yoshiki

2014-01-01

Diffusion imaging is a unique noninvasive tool to detect brain white matter trajectory and integrity in vivo. However, this technique suffers from spatial distortion and signal pileup or dropout originating from local susceptibility gradients and eddy currents. Although there are several methods to mitigate these problems, most techniques can be applicable either to susceptibility or eddy-current induced distortion alone with a few exceptions. The present study compared the correction efficiency of FSL tools, “eddy_correct” and the combination of “eddy” and “topup” in terms of diffusion-derived fractional anisotropy (FA). The brain diffusion images were acquired from 10 healthy subjects using 30 and 60 directions encoding schemes based on the electrostatic repulsive forces. For the 30 directions encoding, 2 sets of diffusion images were acquired with the same parameters, except for the phase-encode blips which had opposing polarities along the anteroposterior direction. For the 60 directions encoding, non–diffusion-weighted and diffusion-weighted images were obtained with forward phase-encoding blips and non–diffusion-weighted images with the same parameter, except for the phase-encode blips, which had opposing polarities. FA images without and with distortion correction were compared in a voxel-wise manner with tract-based spatial statistics. We showed that images corrected with eddy and topup possessed higher FA values than images uncorrected and corrected with eddy_correct with trilinear (FSL default setting) or spline interpolation in most white matter skeletons, using both encoding schemes. Furthermore, the 60 directions encoding scheme was superior as measured by increased FA values to the 30 directions encoding scheme, despite comparable acquisition time. This study supports the combination of eddy and topup as a superior correction tool in diffusion imaging rather than the eddy_correct tool, especially with trilinear interpolation, using 60 directions encoding scheme. PMID:25405472

Efficacy of distortion correction on diffusion imaging: comparison of FSL eddy and eddy_correct using 30 and 60 directions diffusion encoding.

PubMed

Yamada, Haruyasu; Abe, Osamu; Shizukuishi, Takashi; Kikuta, Junko; Shinozaki, Takahiro; Dezawa, Ko; Nagano, Akira; Matsuda, Masayuki; Haradome, Hiroki; Imamura, Yoshiki

2014-01-01

Diffusion imaging is a unique noninvasive tool to detect brain white matter trajectory and integrity in vivo. However, this technique suffers from spatial distortion and signal pileup or dropout originating from local susceptibility gradients and eddy currents. Although there are several methods to mitigate these problems, most techniques can be applicable either to susceptibility or eddy-current induced distortion alone with a few exceptions. The present study compared the correction efficiency of FSL tools, "eddy_correct" and the combination of "eddy" and "topup" in terms of diffusion-derived fractional anisotropy (FA). The brain diffusion images were acquired from 10 healthy subjects using 30 and 60 directions encoding schemes based on the electrostatic repulsive forces. For the 30 directions encoding, 2 sets of diffusion images were acquired with the same parameters, except for the phase-encode blips which had opposing polarities along the anteroposterior direction. For the 60 directions encoding, non-diffusion-weighted and diffusion-weighted images were obtained with forward phase-encoding blips and non-diffusion-weighted images with the same parameter, except for the phase-encode blips, which had opposing polarities. FA images without and with distortion correction were compared in a voxel-wise manner with tract-based spatial statistics. We showed that images corrected with eddy and topup possessed higher FA values than images uncorrected and corrected with eddy_correct with trilinear (FSL default setting) or spline interpolation in most white matter skeletons, using both encoding schemes. Furthermore, the 60 directions encoding scheme was superior as measured by increased FA values to the 30 directions encoding scheme, despite comparable acquisition time. This study supports the combination of eddy and topup as a superior correction tool in diffusion imaging rather than the eddy_correct tool, especially with trilinear interpolation, using 60 directions encoding scheme.

Effective degrees of freedom of a random walk on a fractal.

PubMed

Balankin, Alexander S

2015-12-01

We argue that a non-Markovian random walk on a fractal can be treated as a Markovian process in a fractional dimensional space with a suitable metric. This allows us to define the fractional dimensional space allied to the fractal as the ν-dimensional space F(ν) equipped with the metric induced by the fractal topology. The relation between the number of effective spatial degrees of freedom of walkers on the fractal (ν) and fractal dimensionalities is deduced. The intrinsic time of random walk in F(ν) is inferred. The Laplacian operator in F(ν) is constructed. This allows us to map physical problems on fractals into the corresponding problems in F(ν). In this way, essential features of physics on fractals are revealed. Particularly, subdiffusion on path-connected fractals is elucidated. The Coulomb potential of a point charge on a fractal embedded in the Euclidean space is derived. Intriguing attributes of some types of fractals are highlighted.

Aesthetic Responses to Exact Fractals Driven by Physical Complexity

PubMed Central

Bies, Alexander J.; Blanc-Goldhammer, Daryn R.; Boydston, Cooper R.; Taylor, Richard P.; Sereno, Margaret E.

2016-01-01

Fractals are physically complex due to their repetition of patterns at multiple size scales. Whereas the statistical characteristics of the patterns repeat for fractals found in natural objects, computers can generate patterns that repeat exactly. Are these exact fractals processed differently, visually and aesthetically, than their statistical counterparts? We investigated the human aesthetic response to the complexity of exact fractals by manipulating fractal dimensionality, symmetry, recursion, and the number of segments in the generator. Across two studies, a variety of fractal patterns were visually presented to human participants to determine the typical response to exact fractals. In the first study, we found that preference ratings for exact midpoint displacement fractals can be described by a linear trend with preference increasing as fractal dimension increases. For the majority of individuals, preference increased with dimension. We replicated these results for other exact fractal patterns in a second study. In the second study, we also tested the effects of symmetry and recursion by presenting asymmetric dragon fractals, symmetric dragon fractals, and Sierpinski carpets and Koch snowflakes, which have radial and mirror symmetry. We found a strong interaction among recursion, symmetry and fractal dimension. Specifically, at low levels of recursion, the presence of symmetry was enough to drive high preference ratings for patterns with moderate to high levels of fractal dimension. Most individuals required a much higher level of recursion to recover this level of preference in a pattern that lacked mirror or radial symmetry, while others were less discriminating. This suggests that exact fractals are processed differently than their statistical counterparts. We propose a set of four factors that influence complexity and preference judgments in fractals that may extend to other patterns: fractal dimension, recursion, symmetry and the number of segments in a pattern. Conceptualizations such as Berlyne’s and Redies’ theories of aesthetics also provide a suitable framework for interpretation of our data with respect to the individual differences that we detect. Future studies that incorporate physiological methods to measure the human aesthetic response to exact fractal patterns would further elucidate our responses to such timeless patterns. PMID:27242475

Paradigms of Complexity: Fractals and Structures in the Sciences

NASA Astrophysics Data System (ADS)

Novak, Miroslav M.

The Table of Contents for the book is as follows: * Preface * The Origin of Complexity (invited talk) * On the Existence of Spatially Uniform Scaling Laws in the Climate System * Multispectral Backscattering: A Fractal-Structure Probe * Small-Angle Multiple Scattering on a Fractal System of Point Scatterers * Symmetric Fractals Generated by Cellular Automata * Bispectra and Phase Correlations for Chaotic Dynamical Systems * Self-Organized Criticality Models of Neural Development * Altered Fractal and Irregular Heart Rate Behavior in Sick Fetuses * Extract Multiple Scaling in Long-Term Heart Rate Variability * A Semi-Continous Box Counting Method for Fractal Dimension Measurement of Short Single Dimension Temporal Signals - Preliminary Study * A Fractional Brownian Motion Model of Cracking * Self-Affine Scaling Studies on Fractography * Coarsening of Fractal Interfaces * A Fractal Model of Ocean Surface Superdiffusion * Stochastic Subsurface Flow and Transport in Fractal Fractal Conductivity Fields * Rendering Through Iterated Function Systems * The σ-Hull - The Hull Where Fractals Live - Calculating a Hull Bounded by Log Spirals to Solve the Inverse IFS-Problem by the Detected Orbits * On the Multifractal Properties of Passively Convected Scalar Fields * New Statistical Textural Transforms for Non-Stationary Signals: Application to Generalized Mutlifractal Analysis * Laplacian Growth of Parallel Needles: Their Mullins-Sekerka Instability * Entropy Dynamics Associated with Self-Organization * Fractal Properties in Economics (invited talk) * Fractal Approach to the Regional Seismic Event Discrimination Problem * Fractal and Topological Complexity of Radioactive Contamination * Pattern Selection: Nonsingular Saffman-Taylor Finger and Its Dynamic Evolution with Zero Surface Tension * A Family of Complex Wavelets for the Characterization of Singularities * Stabilization of Chaotic Amplitude Fluctuations in Multimode, Intracavity-Doubled Solid-State Lasers * Chaotic Dynamics of Elastic-Plastic Beams * The Riemann Non-Differentiable Function and Identities for the Gaussian Sums * Revealing the Multifractal Nature of Failure Sequence * The Fractal Nature of wood Revealed by Drying * Squaring the Circle: Diffusion Volume and Acoustic Behaviour of a Fractal Structure * Relationship Between Acupuncture Holographic Units and Fetus Development; Fractal Features of Two Acupuncture Holographic Unit Systems * The Fractal Properties of the Large-Scale Magnetic Fields on the Sun * Fractal Analysis of Tide Gauge Data * Author Index

Multi-fractal detrended texture feature for brain tumor classification

NASA Astrophysics Data System (ADS)

Reza, Syed M. S.; Mays, Randall; Iftekharuddin, Khan M.

2015-03-01

We propose a novel non-invasive brain tumor type classification using Multi-fractal Detrended Fluctuation Analysis (MFDFA) [1] in structural magnetic resonance (MR) images. This preliminary work investigates the efficacy of the MFDFA features along with our novel texture feature known as multifractional Brownian motion (mBm) [2] in classifying (grading) brain tumors as High Grade (HG) and Low Grade (LG). Based on prior performance, Random Forest (RF) [3] is employed for tumor grading using two different datasets such as BRATS-2013 [4] and BRATS-2014 [5]. Quantitative scores such as precision, recall, accuracy are obtained using the confusion matrix. On an average 90% precision and 85% recall from the inter-dataset cross-validation confirm the efficacy of the proposed method.

Broadband Focusing Acoustic Lens Based on Fractal Metamaterials

PubMed Central

Song, Gang Yong; Huang, Bei; Dong, Hui Yuan; Cheng, Qiang; Cui, Tie Jun

2016-01-01

Acoustic metamaterials are artificial structures which can manipulate sound waves through their unconventional effective properties. Different from the locally resonant elements proposed in earlier studies, we propose an alternate route to realize acoustic metamaterials with both low loss and large refractive indices. We describe a new kind of acoustic metamaterial element with the fractal geometry. Due to the self-similar properties of the proposed structure, broadband acoustic responses may arise within a broad frequency range, making it a good candidate for a number of applications, such as super-resolution imaging and acoustic tunneling. A flat acoustic lens is designed and experimentally verified using this approach, showing excellent focusing abilities from 2 kHz and 5 kHz in the measured results. PMID:27782216

Segmentation of anatomical branching structures based on texture features and conditional random field

NASA Astrophysics Data System (ADS)

Nuzhnaya, Tatyana; Bakic, Predrag; Kontos, Despina; Megalooikonomou, Vasileios; Ling, Haibin

2012-02-01

This work is a part of our ongoing study aimed at understanding a relation between the topology of anatomical branching structures with the underlying image texture. Morphological variability of the breast ductal network is associated with subsequent development of abnormalities in patients with nipple discharge such as papilloma, breast cancer and atypia. In this work, we investigate complex dependence among ductal components to perform segmentation, the first step for analyzing topology of ductal lobes. Our automated framework is based on incorporating a conditional random field with texture descriptors of skewness, coarseness, contrast, energy and fractal dimension. These features are selected to capture the architectural variability of the enhanced ducts by encoding spatial variations between pixel patches in galactographic image. The segmentation algorithm was applied to a dataset of 20 x-ray galactograms obtained at the Hospital of the University of Pennsylvania. We compared the performance of the proposed approach with fully and semi automated segmentation algorithms based on neural network classification, fuzzy-connectedness, vesselness filter and graph cuts. Global consistency error and confusion matrix analysis were used as accuracy measurements. For the proposed approach, the true positive rate was higher and the false negative rate was significantly lower compared to other fully automated methods. This indicates that segmentation based on CRF incorporated with texture descriptors has potential to efficiently support the analysis of complex topology of the ducts and aid in development of realistic breast anatomy phantoms.

Fractal-Based Image Compression

DTIC Science & Technology

1990-01-01

used Ziv - Lempel - experiments and for software development. Addi- Welch compression algorithm (ZLW) [51 [4] was used tional thanks to Roger Boss, Bill...vol17no. 6 (June 4) and with the minimum number of maps. [5] J. Ziv and A. Lempel , Compression of !ndivid- 5 Summary ual Sequences via Variable-Rate...transient and should be discarded. 2.5 Collage Theorem algorithm2 C3.2 Deterministic Algorithm for IFS Attractor For fast image compression the best

Verifying the Dependence of Fractal Coefficients on Different Spatial Distributions

NASA Astrophysics Data System (ADS)

Gospodinov, Dragomir; Marekova, Elisaveta; Marinov, Alexander

2010-01-01

A fractal distribution requires that the number of objects larger than a specific size r has a power-law dependence on the size N(r) = C/rD∝r-D where D is the fractal dimension. Usually the correlation integral is calculated to estimate the correlation fractal dimension of epicentres. A `box-counting' procedure could also be applied giving the `capacity' fractal dimension. The fractal dimension can be an integer and then it is equivalent to a Euclidean dimension (it is zero of a point, one of a segment, of a square is two and of a cube is three). In general the fractal dimension is not an integer but a fractional dimension and there comes the origin of the term `fractal'. The use of a power-law to statistically describe a set of events or phenomena reveals the lack of a characteristic length scale, that is fractal objects are scale invariant. Scaling invariance and chaotic behavior constitute the base of a lot of natural hazards phenomena. Many studies of earthquakes reveal that their occurrence exhibits scale-invariant properties, so the fractal dimension can characterize them. It has first been confirmed that both aftershock rate decay in time and earthquake size distribution follow a power law. Recently many other earthquake distributions have been found to be scale-invariant. The spatial distribution of both regional seismicity and aftershocks show some fractal features. Earthquake spatial distributions are considered fractal, but indirectly. There are two possible models, which result in fractal earthquake distributions. The first model considers that a fractal distribution of faults leads to a fractal distribution of earthquakes, because each earthquake is characteristic of the fault on which it occurs. The second assumes that each fault has a fractal distribution of earthquakes. Observations strongly favour the first hypothesis. The fractal coefficients analysis provides some important advantages in examining earthquake spatial distribution, which are:—Simple way to quantify scale-invariant distributions of complex objects or phenomena by a small number of parameters.—It is becoming evident that the applicability of fractal distributions to geological problems could have a more fundamental basis. Chaotic behaviour could underlay the geotectonic processes and the applicable statistics could often be fractal. The application of fractal distribution analysis has, however, some specific aspects. It is usually difficult to present an adequate interpretation of the obtained values of fractal coefficients for earthquake epicenter or hypocenter distributions. That is why in this paper we aimed at other goals—to verify how a fractal coefficient depends on different spatial distributions. We simulated earthquake spatial data by generating randomly points first in a 3D space - cube, then in a parallelepiped, diminishing one of its sides. We then continued this procedure in 2D and 1D space. For each simulated data set we calculated the points' fractal coefficient (correlation fractal dimension of epicentres) and then checked for correlation between the coefficients values and the type of spatial distribution. In that way one can obtain a set of standard fractal coefficients' values for varying spatial distributions. These then can be used when real earthquake data is analyzed by comparing the real data coefficients values to the standard fractal coefficients. Such an approach can help in interpreting the fractal analysis results through different types of spatial distributions.

3-D in vivo brain tumor geometry study by scaling analysis

NASA Astrophysics Data System (ADS)

Torres Hoyos, F.; Martín-Landrove, M.

2012-02-01

A new method, based on scaling analysis, is used to calculate fractal dimension and local roughness exponents to characterize in vivo 3-D tumor growth in the brain. Image acquisition was made according to the standard protocol used for brain radiotherapy and radiosurgery, i.e., axial, coronal and sagittal magnetic resonance T1-weighted images, and comprising the brain volume for image registration. Image segmentation was performed by the application of the k-means procedure upon contrasted images. We analyzed glioblastomas, astrocytomas, metastases and benign brain tumors. The results show significant variations of the parameters depending on the tumor stage and histological origin.

Fractal electrodynamics via non-integer dimensional space approach

NASA Astrophysics Data System (ADS)

Tarasov, Vasily E.

2015-09-01

Using the recently suggested vector calculus for non-integer dimensional space, we consider electrodynamics problems in isotropic case. This calculus allows us to describe fractal media in the framework of continuum models with non-integer dimensional space. We consider electric and magnetic fields of fractal media with charges and currents in the framework of continuum models with non-integer dimensional spaces. An application of the fractal Gauss's law, the fractal Ampere's circuital law, the fractal Poisson equation for electric potential, and equation for fractal stream of charges are suggested. Lorentz invariance and speed of light in fractal electrodynamics are discussed. An expression for effective refractive index of non-integer dimensional space is suggested.

Fractal nematic colloids

NASA Astrophysics Data System (ADS)

Hashemi, S. M.; Jagodič, U.; Mozaffari, M. R.; Ejtehadi, M. R.; Muševič, I.; Ravnik, M.

2017-01-01

Fractals are remarkable examples of self-similarity where a structure or dynamic pattern is repeated over multiple spatial or time scales. However, little is known about how fractal stimuli such as fractal surfaces interact with their local environment if it exhibits order. Here we show geometry-induced formation of fractal defect states in Koch nematic colloids, exhibiting fractal self-similarity better than 90% over three orders of magnitude in the length scales, from micrometers to nanometres. We produce polymer Koch-shaped hollow colloidal prisms of three successive fractal iterations by direct laser writing, and characterize their coupling with the nematic by polarization microscopy and numerical modelling. Explicit generation of topological defect pairs is found, with the number of defects following exponential-law dependence and reaching few 100 already at fractal iteration four. This work demonstrates a route for generation of fractal topological defect states in responsive soft matter.

Eddy current-nulled convex optimized diffusion encoding (EN-CODE) for distortion-free diffusion tensor imaging with short echo times.

PubMed

Aliotta, Eric; Moulin, Kévin; Ennis, Daniel B

2018-02-01

To design and evaluate eddy current-nulled convex optimized diffusion encoding (EN-CODE) gradient waveforms for efficient diffusion tensor imaging (DTI) that is free of eddy current-induced image distortions. The EN-CODE framework was used to generate diffusion-encoding waveforms that are eddy current-compensated. The EN-CODE DTI waveform was compared with the existing eddy current-nulled twice refocused spin echo (TRSE) sequence as well as monopolar (MONO) and non-eddy current-compensated CODE in terms of echo time (TE) and image distortions. Comparisons were made in simulations, phantom experiments, and neuro imaging in 10 healthy volunteers. The EN-CODE sequence achieved eddy current compensation with a significantly shorter TE than TRSE (78 versus 96 ms) and a slightly shorter TE than MONO (78 versus 80 ms). Intravoxel signal variance was lower in phantoms with EN-CODE than with MONO (13.6 ± 11.6 versus 37.4 ± 25.8) and not different from TRSE (15.1 ± 11.6), indicating good robustness to eddy current-induced image distortions. Mean fractional anisotropy values in brain edges were also significantly lower with EN-CODE than with MONO (0.16 ± 0.01 versus 0.24 ± 0.02, P < 1 x 10 -5 ) and not different from TRSE (0.16 ± 0.01 versus 0.16 ± 0.01, P = nonsignificant). The EN-CODE sequence eliminated eddy current-induced image distortions in DTI with a TE comparable to MONO and substantially shorter than TRSE. Magn Reson Med 79:663-672, 2018. © 2017 International Society for Magnetic Resonance in Medicine. © 2017 International Society for Magnetic Resonance in Medicine.

Three-Dimensional Surface Parameters and Multi-Fractal Spectrum of Corroded Steel

PubMed Central

Shanhua, Xu; Songbo, Ren; Youde, Wang

2015-01-01

To study multi-fractal behavior of corroded steel surface, a range of fractal surfaces of corroded surfaces of Q235 steel were constructed by using the Weierstrass-Mandelbrot method under a high total accuracy. The multi-fractal spectrum of fractal surface of corroded steel was calculated to study the multi-fractal characteristics of the W-M corroded surface. Based on the shape feature of the multi-fractal spectrum of corroded steel surface, the least squares method was applied to the quadratic fitting of the multi-fractal spectrum of corroded surface. The fitting function was quantitatively analyzed to simplify the calculation of multi-fractal characteristics of corroded surface. The results showed that the multi-fractal spectrum of corroded surface was fitted well with the method using quadratic curve fitting, and the evolution rules and trends were forecasted accurately. The findings can be applied to research on the mechanisms of corroded surface formation of steel and provide a new approach for the establishment of corrosion damage constitutive models of steel. PMID:26121468

Three-Dimensional Surface Parameters and Multi-Fractal Spectrum of Corroded Steel.

PubMed

Shanhua, Xu; Songbo, Ren; Youde, Wang

2015-01-01

To study multi-fractal behavior of corroded steel surface, a range of fractal surfaces of corroded surfaces of Q235 steel were constructed by using the Weierstrass-Mandelbrot method under a high total accuracy. The multi-fractal spectrum of fractal surface of corroded steel was calculated to study the multi-fractal characteristics of the W-M corroded surface. Based on the shape feature of the multi-fractal spectrum of corroded steel surface, the least squares method was applied to the quadratic fitting of the multi-fractal spectrum of corroded surface. The fitting function was quantitatively analyzed to simplify the calculation of multi-fractal characteristics of corroded surface. The results showed that the multi-fractal spectrum of corroded surface was fitted well with the method using quadratic curve fitting, and the evolution rules and trends were forecasted accurately. The findings can be applied to research on the mechanisms of corroded surface formation of steel and provide a new approach for the establishment of corrosion damage constitutive models of steel.

Body Image in Dyadic and Solitary Sexual Desire: The Role of Encoding Style and Distracting Thoughts.

PubMed

Dosch, Alessandra; Ghisletta, Paolo; Van der Linden, Martial

2016-01-01

This study explored the link between body image and desire to engage in sexual activity (dyadic and solitary desire) in adult women living in a long-term couple relationship. Moreover, it considered two psychological factors that may underlie such a link: the occurrence of body-related distracting thoughts during sexual activity and encoding style (i.e., the tendency to rely on preexisting internal schemata versus external information at encoding). A total of 53 women (29 to 47 years old) in heterosexual relationships completed questionnaires assessing sexual desire (dyadic, solitary), body image, body-related distracting thoughts during sexual activity, and encoding style. Results showed that poor body image was associated with low dyadic and solitary sexual desire. Body-related distracting thoughts during sexual activity mediated the link between body image and solitary (but not dyadic) sexual desire. Finally, the mediation of body-related distracting thoughts between body image and solitary sexual desire was moderated by encoding style. A negative body image promoted the occurrence of body-related distracting thoughts during sexual activity, especially in internal encoders. Our study highlights the importance of body image, distracting thoughts, and encoding style in women's solitary sexuality and suggests possible factors that may reduce the impact of those body-related factors in dyadic sexual desire.

Multidimensionally encoded magnetic resonance imaging.

PubMed

Lin, Fa-Hsuan

2013-07-01

Magnetic resonance imaging (MRI) typically achieves spatial encoding by measuring the projection of a q-dimensional object over q-dimensional spatial bases created by linear spatial encoding magnetic fields (SEMs). Recently, imaging strategies using nonlinear SEMs have demonstrated potential advantages for reconstructing images with higher spatiotemporal resolution and reducing peripheral nerve stimulation. In practice, nonlinear SEMs and linear SEMs can be used jointly to further improve the image reconstruction performance. Here, we propose the multidimensionally encoded (MDE) MRI to map a q-dimensional object onto a p-dimensional encoding space where p > q. MDE MRI is a theoretical framework linking imaging strategies using linear and nonlinear SEMs. Using a system of eight surface SEM coils with an eight-channel radiofrequency coil array, we demonstrate the five-dimensional MDE MRI for a two-dimensional object as a further generalization of PatLoc imaging and O-space imaging. We also present a method of optimizing spatial bases in MDE MRI. Results show that MDE MRI with a higher dimensional encoding space can reconstruct images more efficiently and with a smaller reconstruction error when the k-space sampling distribution and the number of samples are controlled. Copyright © 2012 Wiley Periodicals, Inc.

Depth to Curie temperature across the central Red Sea from magnetic data using the de-fractal method

NASA Astrophysics Data System (ADS)

Salem, Ahmed; Green, Chris; Ravat, Dhananjay; Singh, Kumar Hemant; East, Paul; Fairhead, J. Derek; Mogren, Saad; Biegert, Ed

2014-06-01

The central Red Sea rift is considered to be an embryonic ocean. It is characterised by high heat flow, with more than 90% of the heat flow measurements exceeding the world mean and high values extending to the coasts - providing good prospects for geothermal energy resources. In this study, we aim to map the depth to the Curie isotherm (580 °C) in the central Red Sea based on magnetic data. A modified spectral analysis technique, the “de-fractal spectral depth method” is developed and used to estimate the top and bottom boundaries of the magnetised layer. We use a mathematical relationship between the observed power spectrum due to fractal magnetisation and an equivalent random magnetisation power spectrum. The de-fractal approach removes the effect of fractal magnetisation from the observed power spectrum and estimates the parameters of depth to top and depth to bottom of the magnetised layer using iterative forward modelling of the power spectrum. We applied the de-fractal approach to 12 windows of magnetic data along a profile across the central Red Sea from onshore Sudan to onshore Saudi Arabia. The results indicate variable magnetic bottom depths ranging from 8.4 km in the rift axis to about 18.9 km in the marginal areas. Comparison of these depths with published Moho depths, based on seismic refraction constrained 3D inversion of gravity data, showed that the magnetic bottom in the rift area corresponds closely to the Moho, whereas in the margins it is considerably shallower than the Moho. Forward modelling of heat flow data suggests that depth to the Curie isotherm in the centre of the rift is also close to the Moho depth. Thus Curie isotherm depths estimated from magnetic data may well be imaging the depth to the Curie temperature along the whole profile. Geotherms constrained by the interpreted Curie isotherm depths have subsequently been calculated at three points across the rift - indicating the variation in the likely temperature profile with depth.

Fractal-like kinetics of intracellular enzymatic reactions: a chemical framework of endotoxin tolerance and a possible non-specific contribution of macromolecular crowding to cross-tolerance.

PubMed

Vasilescu, Catalin; Olteanu, Mircea; Flondor, Paul; Calin, George A

2013-09-14

The response to endotoxin (LPS), and subsequent signal transduction lead to the production of cytokines such as tumor necrosis factor-α (TNF-α) by innate immune cells. Cells or organisms pretreated with endotoxin enter into a transient state of hyporesponsiveness, referred to as endotoxin tolerance (ET) which represents a particular case of negative preconditioning. Despite recent progress in understanding the molecular basis of ET, there is no consensus yet on the primary mechanism responsible for ET and for the more complex cases of cross tolerance. In this study, we examined the consequences of the macromolecular crowding (MMC) and of fractal-like kinetics (FLK) of intracellular enzymatic reactions on the LPS signaling machinery. We hypothesized that this particular type of enzyme kinetics may explain the development of ET phenomenon. Our aim in the present study was to characterize the chemical kinetics framework in ET and determine whether fractal-like kinetics explains, at least in part, ET. We developed an ordinary differential equations (ODE) mathematical model that took into account the links between the MMC and the LPS signaling machinery leading to ET. We proposed that the intracellular fractal environment (MMC) contributes to ET and developed two mathematical models of enzyme kinetics: one based on Kopelman's fractal-like kinetics framework and the other based on Savageau's power law model. Kopelman's model provides a good image of the potential influence of a fractal intracellular environment (MMC) on ET. The Savageau power law model also partially explains ET. The computer simulations supported the hypothesis that MMC and FLK may play a role in ET. The model highlights the links between the organization of the intracellular environment, MMC and the LPS signaling machinery leading to ET. Our FLK-based model does not minimize the role of the numerous negative regulatory factors. It simply draws attention to the fact that macromolecular crowding can contribute significantly to the induction of ET by imposing geometric constrains and a particular chemical kinetic for the intracellular reactions.

Laser speckle imaging for lesion detection on tooth

NASA Astrophysics Data System (ADS)

Gavinho, Luciano G.; Silva, João. V. P.; Damazio, João. H.; Sfalcin, Ravana A.; Araujo, Sidnei A.; Pinto, Marcelo M.; Olivan, Silvia R. G.; Prates, Renato A.; Bussadori, Sandra K.; Deana, Alessandro M.

2018-02-01

Computer vision technologies for diagnostic imaging applied to oral lesions, specifically, carious lesions of the teeth, are in their early years of development. The relevance of this public problem, dental caries, worries countries around the world, as it affects almost the entire population, at least once in the life of each individual. The present work demonstrates current techniques for obtaining information about lesions on teeth by segmentation laser speckle imagens (LSI). Laser speckle image results from laser light reflection on a rough surface, and it was considered a noise but has important features that carry information about the illuminated surface. Even though these are basic images, only a few works have analyzed it by application of computer vision methods. In this article, we present the latest results of our group, in which Computer vision techniques were adapted to segment laser speckle images for diagnostic purposes. These methods are applied to the segmentation of images between healthy and lesioned regions of the tooth. These methods have proven to be effective in the diagnosis of early-stage lesions, often imperceptible in traditional diagnostic methods in the clinical practice. The first method uses first-order statistical models, segmenting the image by comparing the mean and standard deviation of the intensity of the pixels. The second method is based on the distance of the chi-square (χ2 ) between the histograms of the image, bringing a significant improvement in the precision of the diagnosis, while a third method introduces the use of fractal geometry, exposing, through of the fractal dimension, more precisely the difference between lesioned areas and healthy areas of a tooth compared to other methods of segmentation. So far, we can observe efficiency in the segmentation of the carious regions. A software was developed for the execution and demonstration of the applicability of the models

Method and apparatus for optical encoding with compressible imaging

NASA Technical Reports Server (NTRS)

Leviton, Douglas B. (Inventor)

2006-01-01

The present invention presents an optical encoder with increased conversion rates. Improvement in the conversion rate is a result of combining changes in the pattern recognition encoder's scale pattern with an image sensor readout technique which takes full advantage of those changes, and lends itself to operation by modern, high-speed, ultra-compact microprocessors and digital signal processors (DSP) or field programmable gate array (FPGA) logic elements which can process encoder scale images at the highest speeds. Through these improvements, all three components of conversion time (reciprocal conversion rate)--namely exposure time, image readout time, and image processing time--are minimized.

Determination of the spectral dependence of reduced scattering and quantitative second-harmonic generation imaging for detection of fibrillary changes in ovarian cancer

NASA Astrophysics Data System (ADS)

Campbell, Kirby R.; Tilbury, Karissa B.; Campagnola, Paul J.

2015-03-01

Here, we examine ovarian cancer extracellular matrix (ECM) modification by measuring the wavelength dependence of optical scattering measurements and quantitative second-harmonic generation (SHG) imaging metrics in the range of 800-1100 nm in order to determine fibrillary changes in ex vivo normal ovary, type I, and type II ovarian cancer. Mass fractals of the collagen fiber structure is analyzed based on a power law correlation function using spectral dependence measurements of the reduced scattering coefficient μs' where the mass fractal dimension is related to the power. Values of μs' are measured using independent methods of determining the values of μs and g by on-axis attenuation measurements using the Beer-Lambert Law and by fitting the angular distribution of scattering to the Henyey-Greenstein phase function, respectively. Quantitativespectral SHG imaging on the same tissues determines FSHG/BSHG creation ratios related to size and harmonophore distributions. Both techniques probe fibril packing order, but the optical scattering probes structures of sizes from about 50-2000 nm where SHG imaging - although only able to resolve individual fibers - builds contrast from the assembly of fibrils. Our findings suggest that type I ovarian tumor structure has the most ordered collagen fibers followed by normal ovary then type II tumors showing the least order.

Imaging surface contacts: Power law contact distributions and contact stresses in quartz, calcite, glass and acrylic plastic

USGS Publications Warehouse

Dieterich, J.H.; Kilgore, B.D.

1996-01-01

A procedure has been developed to obtain microscope images of regions of contact between roughened surfaces of transparent materials, while the surfaces are subjected to static loads or undergoing frictional slip. Static loading experiments with quartz, calcite, soda-lime glass and acrylic plastic at normal stresses to 30 MPa yield power law distributions of contact areas from the smallest contacts that can be resolved (3.5 ??m2) up to a limiting size that correlates with the grain size of the abrasive grit used to roughen the surfaces. In each material, increasing normal stress results in a roughly linear increase of the real area of contact. Mechanisms of contact area increase are by growth of existing contacts, coalescence of contacts and appearance of new contacts. Mean contacts stresses are consistent with the indentation strength of each material. Contact size distributions are insensitive to normal stress indicating that the increase of contact area is approximately self-similar. The contact images and contact distributions are modeled using simulations of surfaces with random fractal topographies. The contact process for model fractal surfaces is represented by the simple expedient of removing material at regions where surface irregularities overlap. Synthetic contact images created by this approach reproduce observed characteristics of the contacts and demonstrate that the exponent in the power law distributions depends on the scaling exponent used to generate the surface topography.

Fractal nematic colloids

PubMed Central

Hashemi, S. M.; Jagodič, U.; Mozaffari, M. R.; Ejtehadi, M. R.; Muševič, I.; Ravnik, M.

2017-01-01

Fractals are remarkable examples of self-similarity where a structure or dynamic pattern is repeated over multiple spatial or time scales. However, little is known about how fractal stimuli such as fractal surfaces interact with their local environment if it exhibits order. Here we show geometry-induced formation of fractal defect states in Koch nematic colloids, exhibiting fractal self-similarity better than 90% over three orders of magnitude in the length scales, from micrometers to nanometres. We produce polymer Koch-shaped hollow colloidal prisms of three successive fractal iterations by direct laser writing, and characterize their coupling with the nematic by polarization microscopy and numerical modelling. Explicit generation of topological defect pairs is found, with the number of defects following exponential-law dependence and reaching few 100 already at fractal iteration four. This work demonstrates a route for generation of fractal topological defect states in responsive soft matter. PMID:28117325

Hierarchical socioeconomic fractality: The rich, the poor, and the middle-class

NASA Astrophysics Data System (ADS)

Eliazar, Iddo; Cohen, Morrel H.

2014-05-01

Since the seminal work of the Italian economist Vilfredo Pareto, the study of wealth and income has been a topic of active scientific exploration engaging researches ranging from economics and political science to econophysics and complex systems. This paper investigates the intrinsic fractality of wealth and income. To that end we introduce and characterize three forms of socioeconomic scale-invariance-poor fractality, rich fractality, and middle-class fractality-and construct hierarchical fractal approximations of general wealth and income distributions, based on the stitching of these three forms of fractality. Intertwining the theoretical results with real-world empirical data we then establish that the three forms of socioeconomic fractality-amalgamated into a composite hierarchical structure-underlie the distributions of wealth and income in human societies. We further establish that the hierarchical socioeconomic fractality of wealth and income is also displayed by empirical rank distributions observed across the sciences.

Small-angle scattering from the Cantor surface fractal on the plane and the Koch snowflake

NASA Astrophysics Data System (ADS)

Cherny, Alexander Yu.; Anitas, Eugen M.; Osipov, Vladimir A.; Kuklin, Alexander I.

The small-angle scattering (SAS) from the Cantor surface fractal on the plane and Koch snowflake is considered. We develop the construction algorithm for the Koch snowflake, which makes possible the recurrence relation for the scattering amplitude. The surface fractals can be decomposed into a sum of surface mass fractals for arbitrary fractal iteration, which enables various approximations for the scattering intensity. It is shown that for the Cantor fractal, one can neglect with a good accuracy the correlations between the mass fractal amplitudes, while for the Koch snowflake, these correlations are important. It is shown that nevertheless, the correlations can be build in the mass fractal amplitudes, which explains the decay of the scattering intensity $I(q)\\sim q^{D_{\\mathrm{s}}-4}$ with $1 < D_{\\mathrm{s}} < 2$ being the fractal dimension of the perimeter. The curve $I(q)q^{4-D_{\\mathrm{s}}}$ is found to be log-periodic in the fractal region with the period equal to the scaling factor of the fractal. The log-periodicity arises from the self-similarity of sizes of basic structural units rather than from correlations between their distances. A recurrence relation is obtained for the radius of gyration of Koch snowflake, which is solved in the limit of infinite iterations. The present analysis allows us to obtain additional information from SAS data, such as the edges of the fractal regions, the fractal iteration number and the scaling factor.

Encoding plaintext by Fourier transform hologram in double random phase encoding using fingerprint keys

NASA Astrophysics Data System (ADS)

Takeda, Masafumi; Nakano, Kazuya; Suzuki, Hiroyuki; Yamaguchi, Masahiro

2012-09-01

It has been shown that biometric information can be used as a cipher key for binary data encryption by applying double random phase encoding. In such methods, binary data are encoded in a bit pattern image, and the decrypted image becomes a plain image when the key is genuine; otherwise, decrypted images become random images. In some cases, images decrypted by imposters may not be fully random, such that the blurred bit pattern can be partially observed. In this paper, we propose a novel bit coding method based on a Fourier transform hologram, which makes images decrypted by imposters more random. Computer experiments confirm that the method increases the randomness of images decrypted by imposters while keeping the false rejection rate as low as in the conventional method.

Automatic brain tumor detection in MRI: methodology and statistical validation

NASA Astrophysics Data System (ADS)

Iftekharuddin, Khan M.; Islam, Mohammad A.; Shaik, Jahangheer; Parra, Carlos; Ogg, Robert

2005-04-01

Automated brain tumor segmentation and detection are immensely important in medical diagnostics because it provides information associated to anatomical structures as well as potential abnormal tissue necessary to delineate appropriate surgical planning. In this work, we propose a novel automated brain tumor segmentation technique based on multiresolution texture information that combines fractal Brownian motion (fBm) and wavelet multiresolution analysis. Our wavelet-fractal technique combines the excellent multiresolution localization property of wavelets to texture extraction of fractal. We prove the efficacy of our technique by successfully segmenting pediatric brain MR images (MRIs) from St. Jude Children"s Research Hospital. We use self-organizing map (SOM) as our clustering tool wherein we exploit both pixel intensity and multiresolution texture features to obtain segmented tumor. Our test results show that our technique successfully segments abnormal brain tissues in a set of T1 images. In the next step, we design a classifier using Feed-Forward (FF) neural network to statistically validate the presence of tumor in MRI using both the multiresolution texture and the pixel intensity features. We estimate the corresponding receiver operating curve (ROC) based on the findings of true positive fractions and false positive fractions estimated from our classifier at different threshold values. An ROC, which can be considered as a gold standard to prove the competence of a classifier, is obtained to ascertain the sensitivity and specificity of our classifier. We observe that at threshold 0.4 we achieve true positive value of 1.0 (100%) sacrificing only 0.16 (16%) false positive value for the set of 50 T1 MRI analyzed in this experiment.

DETECTION OF SMALL-SCALE GRANULAR STRUCTURES IN THE QUIET SUN WITH THE NEW SOLAR TELESCOPE

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

Abramenko, V. I.; Yurchyshyn, V. B.; Goode, P. R.

2012-09-10

Results of a statistical analysis of solar granulation are presented. A data set of 36 images of a quiet-Sun area on the solar disk center was used. The data were obtained with the 1.6 m clear aperture New Solar Telescope at Big Bear Solar Observatory and with a broadband filter centered at the TiO (705.7 nm) spectral line. The very high spatial resolution of the data (diffraction limit of 77 km and pixel scale of 0.''0375) augmented by the very high image contrast (15.5% {+-} 0.6%) allowed us to detect for the first time a distinct subpopulation of mini-granular structures.more » These structures are dominant on spatial scales below 600 km. Their size is distributed as a power law with an index of -1.8 (which is close to the Kolmogorov's -5/3 law) and no predominant scale. The regular granules display a Gaussian (normal) size distribution with a mean diameter of 1050 km. Mini-granular structures contribute significantly to the total granular area. They are predominantly confined to the wide dark lanes between regular granules and often form chains and clusters, but different from magnetic bright points. A multi-fractality test reveals that the structures smaller than 600 km represent a multi-fractal, whereas on larger scales the granulation pattern shows no multi-fractality and can be considered as a Gaussian random field. The origin, properties, and role of the population of mini-granular structures in the solar magnetoconvection are yet to be explored.« less

The fractal forest: fractal geometry and applications in forest science.

Treesearch

Nancy D. Lorimer; Robert G. Haight; Rolfe A. Leary

1994-01-01

Fractal geometry is a tool for describing and analyzing irregularity. Because most of what we measure in the forest is discontinuous, jagged, and fragmented, fractal geometry has potential for improving the precision of measurement and description. This study reviews the literature on fractal geometry and its applications to forest measurements.

Reply to "Comment on 'Hydrodynamics of fractal continuum flow' and 'Map of fluid flow in fractal porous medium into fractal continuum flow'".

PubMed

Balankin, Alexander S; Elizarraraz, Benjamin Espinoza

2013-11-01

The aim of this Reply is to elucidate the difference between the fractal continuum models used in the preceding Comment and the models of fractal continuum flow which were put forward in our previous articles [Phys. Rev. E 85, 025302(R) (2012); 85, 056314 (2012)]. In this way, some drawbacks of the former models are highlighted. Specifically, inconsistencies in the definitions of the fractal derivative, the Jacobian of transformation, the displacement vector, and angular momentum are revealed. The proper forms of the Reynolds' transport theorem and angular momentum principle for the fractal continuum are reaffirmed in a more illustrative manner. Consequently, we emphasize that in the absence of any internal angular momentum, body couples, and couple stresses, the Cauchy stress tensor in the fractal continuum should be symmetric. Furthermore, we stress that the approach based on the Cartesian product measured and used in the preceding Comment cannot be employed to study the path-connected fractals, such as a flow in a fractally permeable medium. Thus, all statements of our previous works remain unchallenged.

The Fractal Behavior of Crystal Distribution of la Gloria Pluton, Chile

NASA Astrophysics Data System (ADS)

Gutiérrez, F. J.; Payacán, I. J.; Pasten, D.; Aravena, A.; Gelman, S. E.; Bachmann, O.; Parada, M. A.

2013-12-01

We utilize fractal analysis to study the spatial distributions of crystals in a 10 Ma granitic intrusion (La Gloria pluton) located in the central Chilean Andes. Previous work determined the crystal size distribution (CSD) and anisotropy of magnetic susceptibility (AMS) tensors throughout this pluton. Using orthogonal thin sections oriented along the AMS tensor axes, we have applied fractal analysis in three magmatic crystal families: plagioclase, ferromagnesian minerals (biotite and amphibole), and Fe-Ti oxides (magnetite with minor ilmenite). We find that plagioclase and ferromagnesian minerals have a Semi-logarithmic CSD (S-CSD), given by: log(n/n0)= -L/C (1) where n [mm-4], n0 [mm-4], L [mm] and C [mm] are crystal density, intercept (nucleation density; L=0), size of crystals (three axes) and characteristic length, respectively. In contrast, Fe-Ti oxides have a Fractal CSD (F-CSD, power law size distribution), given by: log(n)= - Dn log(L) + n1 (2) where Dn and n1 [log(mm-4)] are a non-dimensional proportionality constant and the logarithm of the initial crystallization density (n1 = log(n(L=1 mm))), respectively. Finally, we calculate the fractal dimension (D0) by applying the box-counting method on each crystal thin section image, using: log(N) = -D0 log(ɛ) (3) where N and ɛ are the number of boxes occupied by minerals and the length of the square box, respectively. Results indicate that D0 values (eq. 3) are well defined for all minerals, and are higher for plagioclase than for ferromagnesian minerals and lowest for Fe-Ti oxides. D0 values are correlated with n0 and -1/C for S-CSD (eq. 1), and with n1 values for F-CSD (eq. 2). These correlations between fractal dimensions with CSD parameters suggest crystal growth follows a fractal behaviour in magmatic systems. Fractal behaviour of CSD means that the spatial distribution of crystals follows an all-scale pattern as part of a self-organized magmatic system. We interpret S-CSD of plagioclase and ferromagnesian minerals as consequence of early to intermediate crystal growth, whereas F-CSD of magnetite is also a consequence of late magmatic equilibration by increasing of fine magnetite crystals (e.g. reaction of hornblende to magnetite plus actinolite, biotite and titanite). Acknowledgments. This research has been developed by the FONDECYT N°11100241 and PBCT-PDA07 projects granted by CONICYT (Chilean National Commission for Science and Technology). I.P. is supported by CONICYT magister grant N°22130729. F.G. and I.P. thank to FONDAP N°15090013 for supporting during the conference. D.P. acknowledges FONDECYT grant N° 3120237.

Image Segmentation via Fractal Dimension

DTIC Science & Technology

1987-12-01

Contipany, 1986. 7. Harrington, Steven. Computer Graphics A Programming Aproach. New York: McGrawU-Hill Book Company, 1987. 8. Norev, Moshe. Picture...ITEX TORHS conversion program . My fazily has been a constant source of relaxation and enoouragement, and I wish to thank them for their understanding...Conclusion 29.... ....................... 9........... . -11 III. Experimental Method 3..-.1..................... .. ....... -1 Overviev

Cortical complexity in bipolar disorder applying a spherical harmonics approach.

PubMed

Nenadic, Igor; Yotter, Rachel A; Dietzek, Maren; Langbein, Kerstin; Sauer, Heinrich; Gaser, Christian

2017-05-30

Recent studies using surface-based morphometry of structural magnetic resonance imaging data have suggested that some changes in bipolar disorder (BP) might be neurodevelopmental in origin. We applied a novel analysis of cortical complexity based on fractal dimensions in high-resolution structural MRI scans of 18 bipolar disorder patients and 26 healthy controls. Our region-of-interest based analysis revealed increases in fractal dimensions (in patients relative to controls) in left lateral orbitofrontal cortex and right precuneus, and decreases in right caudal middle frontal, entorhinal cortex, and right pars orbitalis, and left fusiform and posterior cingulate cortices. While our analysis is preliminary, it suggests that early neurodevelopmental pathologies might contribute to bipolar disorder, possibly through genetic mechanisms. Copyright © 2017 Elsevier Ireland Ltd. All rights reserved.

Response of fractal penetration of magnetic flux to disorder landscape in superconducting films

NASA Astrophysics Data System (ADS)

Ye, Zuxin; Li, Qiang; Si, W. D.; Suenaga, M.; Solovyov, V. F.; Johnson, P. D.

2005-10-01

Magnetic flux front and induction contours in superconducting YBa2Cu3O7-δ films with defect size stilde ξ (superconducting coherence length) and s≫ξ are studied by magneto-optical imaging. Robust self-affine spatial correlation was observed using scaling analysis in the small pinning disorder-dominated ( stilde ξ) films. The roughness exponent α was determined to be ˜0.66 , independent of numbers of defects (or the film thickness). When the disorder landscape also included a distribution of large defects (s≫ξ) , the flux front and induction contours exhibited self-similarity, with a fractal dimension D determined to be ˜1.33 using the box-counting method. The remarkably different flux penetration patterns were shown to be the manifestation of self-organized criticality at different length scales.

Application of fractal dimension method of functional MRI time-series to limbic dysregulation in anxiety study.

PubMed

Olejarczyk, Elzbieta

2007-01-01

Functional magnetic resonance imaging (fMRI) allows to investigate the amplitude of activation in neural networks of brain. In this work we present the results of fMRI time-series analysis performed to identify the process of dysregulation of dynamic interaction between different limbic system regions in healthy adults in state of increased anxiety. The results obtain for 65 healthy adults using nonlinear dynamics methods like fractal dimension confirm the key roles of the bilateral amygdala, bilateral hippocampus, BA9 (dorsolateral prefrontal cortex), and BA45 (ventromedial prefrontal cortex) in modulating emotional response in healthy adults. For different regions of interest (ROIs) significant correlations were found not only for the neutral respective rest but also for fear and angry contrasts.

Unsupervised segmentation of lung fields in chest radiographs using multiresolution fractal feature vector and deformable models.

PubMed

Lee, Wen-Li; Chang, Koyin; Hsieh, Kai-Sheng

2016-09-01

Segmenting lung fields in a chest radiograph is essential for automatically analyzing an image. We present an unsupervised method based on multiresolution fractal feature vector. The feature vector characterizes the lung field region effectively. A fuzzy c-means clustering algorithm is then applied to obtain a satisfactory initial contour. The final contour is obtained by deformable models. The results show the feasibility and high performance of the proposed method. Furthermore, based on the segmentation of lung fields, the cardiothoracic ratio (CTR) can be measured. The CTR is a simple index for evaluating cardiac hypertrophy. After identifying a suspicious symptom based on the estimated CTR, a physician can suggest that the patient undergoes additional extensive tests before a treatment plan is finalized.

Simulating and mapping spatial complexity using multi-scale techniques

USGS Publications Warehouse

De Cola, L.

1994-01-01

A central problem in spatial analysis is the mapping of data for complex spatial fields using relatively simple data structures, such as those of a conventional GIS. This complexity can be measured using such indices as multi-scale variance, which reflects spatial autocorrelation, and multi-fractal dimension, which characterizes the values of fields. These indices are computed for three spatial processes: Gaussian noise, a simple mathematical function, and data for a random walk. Fractal analysis is then used to produce a vegetation map of the central region of California based on a satellite image. This analysis suggests that real world data lie on a continuum between the simple and the random, and that a major GIS challenge is the scientific representation and understanding of rapidly changing multi-scale fields. -Author

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

NASA Technical Reports Server (NTRS)

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

1992-01-01

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

Fractal Bread.

ERIC Educational Resources Information Center

Esbenshade, Donald H., Jr.

1991-01-01

Develops the idea of fractals through a laboratory activity that calculates the fractal dimension of ordinary white bread. Extends use of the fractal dimension to compare other complex structures as other breads and sponges. (MDH)

Spatial encoding using the nonlinear field perturbations from magnetic materials.

PubMed

Karimi, Hirad; Dominguez-Viqueira, William; Cunningham, Charles H

2014-08-01

A proof-of-concept study was performed to assess the technical feasibility of using magnetic materials to generate spatial encoding fields. Spatially varying magnetic fields were generated by the placement of markers with different volume susceptibilities within the imaging volume. No linear gradients were used for spatial encoding during the signal acquisition. A signal-encoding model is described for reconstructing the images encoded with these field perturbations. Simulation and proof-of-concept experimental results are presented. Experiments were performed using field perturbations from a cylindrical marker as an example of the new encoding fields. Based on this experimental setup, annular rings were reconstructed from signals encoded with the new fields. Simulation results were presented for different acquisition parameters. Proof-of-concept was supported by the correspondence of regions in an image reconstructed from experimental data compared to those in a conventional gradient-echo image. Experimental results showed that inclusions of dimensions 1.5 mm in size could be resolved with the experimental setup. This study shows the technical feasibility of using magnetic markers to produce encoding fields. Magnetic materials will allow generating spatial encoding fields, which can be tailored to an imaging application with less complexity and at lower cost compared to the use of gradient inserts. Copyright © 2013 Wiley Periodicals, Inc.

Geometry of modified release formulations during dissolution--influence on performance of dosage forms with diclofenac sodium.

PubMed

Dorożyński, Przemysław; Kulinowski, Piotr; Jamróz, Witold; Juszczyk, Ewelina

2014-12-30

The objectives of the work included: presentation of magnetic resonance imaging (MRI) and fractal analysis based approach to comparison of dosage forms of different composition, structure, and assessment of the influence of the compositional factors i.e., matrix type, excipients etc., on properties and performance of the dosage form during drug dissolution. The work presents the first attempt to compare MRI data obtained for tablet formulations of different composition and characterized by distinct differences in hydration and drug dissolution mechanisms. The main difficulty, in such a case stems from differences in hydration behavior and tablet's geometry i.e., swelling, cracking, capping etc. A novel approach to characterization of matrix systems i.e., quantification of changes of geometrical complexity of the matrix shape during drug dissolution has been developed. Using three chosen commercial modified release tablet formulations with diclofenac sodium we present the method of parameterization of their geometrical complexity on the base of fractal analysis. The main result of the study is the correlation between the hydrating tablet behavior and drug dissolution - the increase of geometrical complexity expressed as fractal dimension relates to the increased variability of drug dissolution results. Copyright © 2014 Elsevier B.V. All rights reserved.

Renormalization Analysis of a Composite Ultrasonic Transducer with a Fractal Architecture

NASA Astrophysics Data System (ADS)

Algehyne, Ebrahem A.; Mulholland, Anthony J.

To ensure the safe operation of many safety critical structures such as nuclear plants, aircraft and oil pipelines, non-destructive imaging is employed using piezoelectric ultrasonic transducers. These sensors typically operate at a single frequency due to the restrictions imposed on their resonant behavior by the use of a single length scale in the design. To allow these transducers to transmit and receive more complex signals it would seem logical to use a range of length scales in the design so that a wide range of resonating frequencies will result. In this paper, we derive a mathematical model to predict the dynamics of an ultrasound transducer that achieves this range of length scales by adopting a fractal architecture. In fact, the device is modeled as a graph where the nodes represent segments of the piezoelectric and polymer materials. The electrical and mechanical fields that are contained within this graph are then expressed in terms of a finite element basis. The structure of the resulting discretized equations yields to a renormalization methodology which is used to derive expressions for the non-dimensionalized electrical impedance and the transmission and reception sensitivities. A comparison with a standard design shows some benefits of these fractal designs.

Investigation of novel fractal shape of the nano-aperture as a metasurface for bio sensing application

NASA Astrophysics Data System (ADS)

Heydari, Samaneh; Rastan, Iman; Parvin, Amin; Pirooj, Azadeh; Zarrabi, Ferdows B.

2017-01-01

Recently, nano-aperture is noticed due to its good transmission in the optical regime. Also, the nano-apertures are developed at the metasurface design for circular polarization; for this aim, various shapes of the nano-aperture are suggested. To reach this objective, we have developed a novel Jerusalem cross fractal shape for a mid-infrared application. We have simulated various formations of the nano-fractal Jerusalem cross based on a simple cross to show the effect of nano-aperture shape on electrical field enhancement in the near-field which is important in spectroscopy and optical imaging. In addition, we have used a single layer graphene over the aperture as a coat for making reconfigurable characteristic also creating a membrane for placement of nano-particle over the aperture. Implementation of the graphene is an amendment to the transfer of the nano-apertures. The biological materials with a thickness of 80 nm have been placed over the graphene layer and the Figures of Merits (FOM) have been obtained. Additionally, the prototype of nano-antenna is independent from incident wave polarization. The Finite Difference Time Domain (FDTD) calculations have been implemented in the simulation and modeling the nano-apertures.

A review on "A Novel Technique for Image Steganography Based on Block-DCT and Huffman Encoding"

NASA Astrophysics Data System (ADS)

Das, Rig; Tuithung, Themrichon

2013-03-01

This paper reviews the embedding and extraction algorithm proposed by "A. Nag, S. Biswas, D. Sarkar and P. P. Sarkar" on "A Novel Technique for Image Steganography based on Block-DCT and Huffman Encoding" in "International Journal of Computer Science and Information Technology, Volume 2, Number 3, June 2010" [3] and shows that the Extraction of Secret Image is Not Possible for the algorithm proposed in [3]. 8 bit Cover Image of size is divided into non joint blocks and a two dimensional Discrete Cosine Transformation (2-D DCT) is performed on each of the blocks. Huffman Encoding is performed on an 8 bit Secret Image of size and each bit of the Huffman Encoded Bit Stream is embedded in the frequency domain by altering the LSB of the DCT coefficients of Cover Image blocks. The Huffman Encoded Bit Stream and Huffman Table

Improvements in RF Shimming in High Field MRI Using High Permittivity Materials With Low Order Pre-Fractal Geometries.

PubMed

Schmidt, Rita; Webb, Andrew

2016-08-01

Ultra-high field MRI is an area of great interest for clinical research and basic science due to the increased signal-to-noise, spatial resolution and magnetic-susceptibility-based contrast. However, the fact that the electromagnetic wavelength in tissue is comparable to the relevant body dimensions means that the uniformity of the excitation field is much poorer than at lower field strengths. In addition to techniques such as transmit arrays, one simple but effective method to counteract this effect is to use high permittivity "pads". Very high permittivities enable thinner, flexible pads to be used, but the limiting factor is wavelength effects within the pads themselves, which can lead to image artifacts. So far, all studies have used simple continuous rectangular/circular pad geometries. In this work we investigate how the wavelength effects can be partially mitigated utilizing shaped pad with holes. Several arrangements have been simulated, including low order pre-fractal geometries, which maintain the overall coverage of the pad, but can provide better image homogeneity in the region of interest or higher sensitivity depending on the setup. Experimental data in the form of in vivo human images at 7T were acquired to validate the simulation results.

Anterior Chamber Angle Shape Analysis and Classification of Glaucoma in SS-OCT Images.

PubMed

Ni Ni, Soe; Tian, J; Marziliano, Pina; Wong, Hong-Tym

2014-01-01

Optical coherence tomography is a high resolution, rapid, and noninvasive diagnostic tool for angle closure glaucoma. In this paper, we present a new strategy for the classification of the angle closure glaucoma using morphological shape analysis of the iridocorneal angle. The angle structure configuration is quantified by the following six features: (1) mean of the continuous measurement of the angle opening distance; (2) area of the trapezoidal profile of the iridocorneal angle centered at Schwalbe's line; (3) mean of the iris curvature from the extracted iris image; (4) complex shape descriptor, fractal dimension, to quantify the complexity, or changes of iridocorneal angle; (5) ellipticity moment shape descriptor; and (6) triangularity moment shape descriptor. Then, the fuzzy k nearest neighbor (fkNN) classifier is utilized for classification of angle closure glaucoma. Two hundred and sixty-four swept source optical coherence tomography (SS-OCT) images from 148 patients were analyzed in this study. From the experimental results, the fkNN reveals the best classification accuracy (99.11 ± 0.76%) and AUC (0.98 ± 0.012) with the combination of fractal dimension and biometric parameters. It showed that the proposed approach has promising potential to become a computer aided diagnostic tool for angle closure glaucoma (ACG) disease.

Statistical and fractal analysis of autofluorescent myocardium images in posthumous diagnostics of acute coronary insufficiency

NASA Astrophysics Data System (ADS)

Boichuk, T. M.; Bachinskiy, V. T.; Vanchuliak, O. Ya.; Minzer, O. P.; Garazdiuk, M.; Motrich, A. V.

2014-08-01

This research presents the results of investigation of laser polarization fluorescence of biological layers (histological sections of the myocardium). The polarized structure of autofluorescence imaging layers of biological tissues was detected and investigated. Proposed the model of describing the formation of polarization inhomogeneous of autofluorescence imaging biological optically anisotropic layers. On this basis, analytically and experimentally tested to justify the method of laser polarimetry autofluorescent. Analyzed the effectiveness of this method in the postmortem diagnosis of infarction. The objective criteria (statistical moments) of differentiation of autofluorescent images of histological sections myocardium were defined. The operational characteristics (sensitivity, specificity, accuracy) of these technique were determined.

Estimating Accurate Target Coordinates with Magnetic Resonance Images by Using Multiple Phase-Encoding Directions during Acquisition.

PubMed

Kim, Minsoo; Jung, Na Young; Park, Chang Kyu; Chang, Won Seok; Jung, Hyun Ho; Chang, Jin Woo

2018-06-01

Stereotactic procedures are image guided, often using magnetic resonance (MR) images limited by image distortion, which may influence targets for stereotactic procedures. The aim of this work was to assess methods of identifying target coordinates for stereotactic procedures with MR in multiple phase-encoding directions. In 30 patients undergoing deep brain stimulation, we acquired 5 image sets: stereotactic brain computed tomography (CT), T2-weighted images (T2WI), and T1WI in both right-to-left (RL) and anterior-to-posterior (AP) phase-encoding directions. Using CT coordinates as a reference, we analyzed anterior commissure and posterior commissure coordinates to identify any distortion relating to phase-encoding direction. Compared with CT coordinates, RL-directed images had more positive x-axis values (0.51 mm in T1WI, 0.58 mm in T2WI). AP-directed images had more negative y-axis values (0.44 mm in T1WI, 0.59 mm in T2WI). We adopted 2 methods to predict CT coordinates with MR image sets: parallel translation and selective choice of axes according to phase-encoding direction. Both were equally effective at predicting CT coordinates using only MR; however, the latter may be easier to use in clinical settings. Acquiring MR in multiple phase-encoding directions and selecting axes according to the phase-encoding direction allows identification of more accurate coordinates for stereotactic procedures. © 2018 S. Karger AG, Basel.

Influence of Turbulent Flow and Fractal Scaling on Effective Permeability of Fracture Network

NASA Astrophysics Data System (ADS)

Zhu, J.

2017-12-01

A new approach is developed to calculate hydraulic gradient dependent effective permeability of a fractal fracture network where both laminar and turbulent flows may occur in individual fractures. A critical fracture length is used to distinguish flow characteristics in individual fractures. The developed new solutions can be used for the case of a general scaling relationship, an extension to the linear scaling. We examine the impact on the effective permeability of the network of fractal fracture network characteristics, which include the fractal scaling coefficient and exponent, fractal dimension, ratio of minimum over maximum fracture lengths. Results demonstrate that the developed solution can explain more variations of the effective permeability in relation to the fractal dimensions estimated from the field observations. At high hydraulic gradient the effective permeability decreases with the fractal scaling exponent, but increases with the fractal scaling exponent at low gradient. The effective permeability increases with the scaling coefficient, fractal dimension, fracture length ratio and maximum fracture length.

Segmentation of singularity maps in the context of soil porosity

NASA Astrophysics Data System (ADS)

Martin-Sotoca, Juan J.; Saa-Requejo, Antonio; Grau, Juan; Tarquis, Ana M.

2016-04-01

Geochemical exploration have found with increasingly interests and benefits of using fractal (power-law) models to characterize geochemical distribution, including concentration-area (C-A) model (Cheng et al., 1994; Cheng, 2012) and concentration-volume (C-V) model (Afzal et al., 2011) just to name a few examples. These methods are based on the singularity maps of a measure that at each point define areas with self-similar properties that are shown in power-law relationships in Concentration-Area plots (C-A method). The C-A method together with the singularity map ("Singularity-CA" method) define thresholds that can be applied to segment the map. Recently, the "Singularity-CA" method has been applied to binarize 2D grayscale Computed Tomography (CT) soil images (Martin-Sotoca et al, 2015). Unlike image segmentation based on global thresholding methods, the "Singularity-CA" method allows to quantify the local scaling property of the grayscale value map in the space domain and determinate the intensity of local singularities. It can be used as a high-pass-filter technique to enhance high frequency patterns usually regarded as anomalies when applied to maps. In this work we will put special attention on how to select the singularity thresholds in the C-A plot to segment the image. We will compare two methods: 1) cross point of linear regressions and 2) Wavelets Transform Modulus Maxima (WTMM) singularity function detection. REFERENCES Cheng, Q., Agterberg, F. P. and Ballantyne, S. B. (1994). The separation of geochemical anomalies from background by fractal methods. Journal of Geochemical Exploration, 51, 109-130. Cheng, Q. (2012). Singularity theory and methods for mapping geochemical anomalies caused by buried sources and for predicting undiscovered mineral deposits in covered areas. Journal of Geochemical Exploration, 122, 55-70. Afzal, P., Fadakar Alghalandis, Y., Khakzad, A., Moarefvand, P. and Rashidnejad Omran, N. (2011) Delineation of mineralization zones in porphyry Cu deposits by fractal concentration-volume modeling. Journal of Geochemical Exploration, 108, 220-232. Martín-Sotoca, J. J., Tarquis, A. M., Saa-Requejo, A. and Grau, J. B. (2015). Pore detection in Computed Tomography (CT) soil images through singularity map analysis. Oral Presentation in PedoFract VIII Congress (June, La Coruña - Spain).

Characterization of Forested Landscapes From Remotely Sensed Data Using Fractals and Spatial Autocorrelation

NASA Technical Reports Server (NTRS)

Al-Hamdan, Mohammad Z.; Cruise, James F.; Rickman, Douglas L.; Quattrochi, Dale A.

2007-01-01

The characterization of forested areas is frequently required in resource management practice. Passive remotely sensed data, which are much more accessible and cost effective than are active data, have rarely, if ever, been used to characterize forest structure directly, but rather they usually focus on the estimation of indirect measurement of biomass or canopy coverage. In this study, some spatial analysis techniques are presented that might be employed with Landsat TM data to analyze forest structure characteristics. A case study is presented wherein fractal dimensions, along with a simple spatial autocorrelation technique (Moran s I), were related to stand density parameters of the Oakmulgee National Forest located in the southeastern United States (Alabama). The results of the case study presented herein have shown that as the percentage of smaller diameter trees becomes greater, and particularly if it exceeds 50%, then the canopy image obtained from Landsat TM data becomes sufficiently homogeneous so that the spatial indices reach their lower limits and thus are no longer determinative. It also appears, at least for the Oakmulgee forest, that the relationships between the spatial indices and forest class percentages within the boundaries can reasonably be considered linear. The linear relationship is much more pronounced in the sawtimber and saplings cases than in samples dominated by medium sized trees (poletimber). In addition, it also appears that, at least for the Oakmulgee forest, the relationships between the spatial indices and forest species groups (Hardwood and Softwood) percentages can reasonably be considered linear. The linear relationship is more pronounced in the forest species groups cases than in the forest classes cases. These results appear to indicate that both fractal dimensions and spatial autocorrelation indices hold promise as means of estimating forest stand characteristics from remotely sensed images. However, additional work is needed to confirm that the boundaries identified for Oakmulgee forest and the linear nature of the relationship between image complexity indices and forest characteristics are generally evident in other forests. In addition, the effects of other parameters such ,as topographic relief and image distortion due to sun angle and cloud cover, for example, need to be examined.

Probing the water distribution in porous model sands with two immiscible fluids: A nuclear magnetic resonance micro-imaging study

NASA Astrophysics Data System (ADS)

Lee, Bum Han; Lee, Sung Keun

2017-10-01

The effect of the structural heterogeneity of porous networks on the water distribution in porous media, initially saturated with immiscible fluid followed by increasing durations of water injection, remains one of the important problems in hydrology. The relationship among convergence rates (i.e., the rate of fluid saturation with varying injection time) and the macroscopic properties and structural parameters of porous media have been anticipated. Here, we used nuclear magnetic resonance (NMR) micro-imaging to obtain images (down to ∼50 μm resolution) of the distribution of water injected for varying durations into porous networks that were initially saturated with silicone oil. We then established the relationships among the convergence rates, structural parameters, and transport properties of porous networks. The volume fraction of the water phase increases as the water injection duration increases. The 3D images of the water distributions for silica gel samples are similar to those of the glass bead samples. The changes in water saturation (and the accompanying removal of silicone oil) and the variations in the volume fraction, specific surface area, and cube-counting fractal dimension of the water phase fit well with the single-exponential recovery function { f (t) = a [ 1 -exp (- λt) ] } . The asymptotic values (a, i.e., saturated value) of the properties of the volume fraction, specific surface area, and cube-counting fractal dimension of the glass bead samples were greater than those for the silica gel samples primarily because of the intrinsic differences in the porous networks and local distribution of the pore size and connectivity. The convergence rates of all of the properties are inversely proportional to the entropy length and permeability. Despite limitations of the current study, such as insufficient resolution and uncertainty for the estimated parameters due to sparsely selected short injection times, the observed trends highlight the first analyses of the cube-counting fractal dimension (and other structural properties) and convergence rates in porous networks consisting of two fluid components. These results indicate that the convergence rates correlate with the geometric factor that characterizes the porous networks and transport property of the porous networks.

WE-E-17A-06: Assessing the Scale of Tumor Heterogeneity by Complete Hierarchical Segmentation On MRI

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

Gensheimer, M; Trister, A; Ermoian, R

2014-06-15

Purpose: In many cancers, intratumoral heterogeneity exists in vascular and genetic structure. We developed an algorithm which uses clinical imaging to interrogate different scales of heterogeneity. We hypothesize that heterogeneity of perfusion at large distance scales may correlate with propensity for disease recurrence. We applied the algorithm to initial diagnosis MRI of rhabdomyosarcoma patients to predict recurrence. Methods: The Spatial Heterogeneity Analysis by Recursive Partitioning (SHARP) algorithm recursively segments the tumor image. The tumor is repeatedly subdivided, with each dividing line chosen to maximize signal intensity difference between the two subregions. This process continues to the voxel level, producing segmentsmore » at multiple scales. Heterogeneity is measured by comparing signal intensity histograms between each segmented region and the adjacent region. We measured the scales of contrast enhancement heterogeneity of the primary tumor in 18 rhabdomyosarcoma patients. Using Cox proportional hazards regression, we explored the influence of heterogeneity parameters on relapse-free survival (RFS). To compare with existing methods, fractal and Haralick texture features were also calculated. Results: The complete segmentation produced by SHARP allows extraction of diverse features, including the amount of heterogeneity at various distance scales, the area of the tumor with the most heterogeneity at each scale, and for a given point in the tumor, the heterogeneity at different scales. 10/18 rhabdomyosarcoma patients suffered disease recurrence. On contrast-enhanced MRI, larger scale of maximum signal intensity heterogeneity, relative to tumor diameter, predicted for shorter RFS (p=0.05). Fractal dimension, fractal fit, and three Haralick features did not predict RFS (p=0.09-0.90). Conclusion: SHARP produces an automatic segmentation of tumor regions and reports the amount of heterogeneity at various distance scales. In rhabdomyosarcoma, RFS was shorter when the primary tumor exhibited larger scale of heterogeneity on contrast-enhanced MRI. If validated on a larger dataset, this imaging biomarker could be useful to help personalize treatment.« less

[Reproducibility and accuracy in the morphometric and mechanical quantification of trabecular bone from 3 Tesla magnetic resonance images].

PubMed

Alberich-Bayarri, A; Martí-Bonmatí, L; Sanz-Requena, R; Sánchez-González, J; Hervás Briz, V; García-Martí, G; Pérez, M Á

2014-01-01

We used an animal model to analyze the reproducibility and accuracy of certain biomarkers of bone image quality in comparison to a gold standard of computed microtomography (μCT). We used magnetic resonance (MR) imaging and μCT to study the metaphyses of 5 sheep tibiae. The MR images (3 Teslas) were acquired with a T1-weighted gradient echo sequence and an isotropic spatial resolution of 180μm. The μCT images were acquired using a scanner with a spatial resolution of 7.5μm isotropic voxels. In the preparation of the images, we applied equalization, interpolation, and thresholding algorithms. In the quantitative analysis, we calculated the percentage of bone volume (BV/TV), the trabecular thickness (Tb.Th), the trabecular separation (Tb.Sp), the trabecular index (Tb.N), the 2D fractal dimension (D(2D)), the 3D fractal dimension (D(3D)), and the elastic module in the three spatial directions (Ex, Ey and Ez). The morphometric and mechanical quantification of trabecular bone by MR was very reproducible, with percentages of variation below 9% for all the parameters. Its accuracy compared to the gold standard (μCT) was high, with errors less than 15% for BV/TV, D(2D), D(3D), and E(app)x, E(app)y and E(app)z. Our experimental results in animals confirm that the parameters of BV/TV, D(2D), D(3D), and E(app)x, E(app)y and E(app)z obtained by MR have excellent reproducibility and accuracy and can be used as imaging biomarkers for the quality of trabecular bone. Copyright © 2013 SERAM. Published by Elsevier Espana. All rights reserved.

Emergence of fractal scaling in complex networks

NASA Astrophysics Data System (ADS)

Wei, Zong-Wen; Wang, Bing-Hong

2016-09-01

Some real-world networks are shown to be fractal or self-similar. It is widespread that such a phenomenon originates from the repulsion between hubs or disassortativity. Here we show that this common belief fails to capture the causality. Our key insight to address it is to pinpoint links critical to fractality. Those links with small edge betweenness centrality (BC) constitute a special architecture called fractal reference system, which gives birth to the fractal structure of those reported networks. In contrast, a small amount of links with high BC enable small-world effects, hiding the intrinsic fractality. With enough of such links removed, fractal scaling spontaneously arises from nonfractal networks. Our results provide a multiple-scale view on the structure and dynamics and place fractality as a generic organizing principle of complex networks on a firmer ground.

Image Understanding: Proceedings of a Workshop (14th) Held at Arlington, Virginia on 23 June 1983

DTIC Science & Technology

1983-06-01

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Band structures in fractal grading porous phononic crystals

NASA Astrophysics Data System (ADS)

Wang, Kai; Liu, Ying; Liang, Tianshu; Wang, Bin

2018-05-01

In this paper, a new grading porous structure is introduced based on a Sierpinski triangle routine, and wave propagation in this fractal grading porous phononic crystal is investigated. The influences of fractal hierarchy and porosity on the band structures in fractal graidng porous phononic crystals are clarified. Vibration modes of unit cell at absolute band gap edges are given to manifest formation mechanism of absolute band gaps. The results show that absolute band gaps are easy to form in fractal structures comparatively to the normal ones with the same porosity. Structures with higher fractal hierarchies benefit multiple wider absolute band gaps. This work provides useful guidance in design of fractal porous phononic crystals.

Fractals in geology and geophysics

NASA Technical Reports Server (NTRS)

Turcotte, Donald L.

1989-01-01

The definition of a fractal distribution is that the number of objects N with a characteristic size greater than r scales with the relation N of about r exp -D. The frequency-size distributions for islands, earthquakes, fragments, ore deposits, and oil fields often satisfy this relation. This application illustrates a fundamental aspect of fractal distributions, scale invariance. The requirement of an object to define a scale in photograhs of many geological features is one indication of the wide applicability of scale invariance to geological problems; scale invariance can lead to fractal clustering. Geophysical spectra can also be related to fractals; these are self-affine fractals rather than self-similar fractals. Examples include the earth's topography and geoid.

Comparison of two fractal interpolation methods

NASA Astrophysics Data System (ADS)

Fu, Yang; Zheng, Zeyu; Xiao, Rui; Shi, Haibo

2017-03-01

As a tool for studying complex shapes and structures in nature, fractal theory plays a critical role in revealing the organizational structure of the complex phenomenon. Numerous fractal interpolation methods have been proposed over the past few decades, but they differ substantially in the form features and statistical properties. In this study, we simulated one- and two-dimensional fractal surfaces by using the midpoint displacement method and the Weierstrass-Mandelbrot fractal function method, and observed great differences between the two methods in the statistical characteristics and autocorrelation features. From the aspect of form features, the simulations of the midpoint displacement method showed a relatively flat surface which appears to have peaks with different height as the fractal dimension increases. While the simulations of the Weierstrass-Mandelbrot fractal function method showed a rough surface which appears to have dense and highly similar peaks as the fractal dimension increases. From the aspect of statistical properties, the peak heights from the Weierstrass-Mandelbrot simulations are greater than those of the middle point displacement method with the same fractal dimension, and the variances are approximately two times larger. When the fractal dimension equals to 1.2, 1.4, 1.6, and 1.8, the skewness is positive with the midpoint displacement method and the peaks are all convex, but for the Weierstrass-Mandelbrot fractal function method the skewness is both positive and negative with values fluctuating in the vicinity of zero. The kurtosis is less than one with the midpoint displacement method, and generally less than that of the Weierstrass-Mandelbrot fractal function method. The autocorrelation analysis indicated that the simulation of the midpoint displacement method is not periodic with prominent randomness, which is suitable for simulating aperiodic surface. While the simulation of the Weierstrass-Mandelbrot fractal function method has strong periodicity, which is suitable for simulating periodic surface.

Iterative deep convolutional encoder-decoder network for medical image segmentation.

PubMed

Jung Uk Kim; Hak Gu Kim; Yong Man Ro

2017-07-01

In this paper, we propose a novel medical image segmentation using iterative deep learning framework. We have combined an iterative learning approach and an encoder-decoder network to improve segmentation results, which enables to precisely localize the regions of interest (ROIs) including complex shapes or detailed textures of medical images in an iterative manner. The proposed iterative deep convolutional encoder-decoder network consists of two main paths: convolutional encoder path and convolutional decoder path with iterative learning. Experimental results show that the proposed iterative deep learning framework is able to yield excellent medical image segmentation performances for various medical images. The effectiveness of the proposed method has been proved by comparing with other state-of-the-art medical image segmentation methods.

Effect of Drive Cycle and Gasoline Particulate Filter on the Size and Morphology of Soot Particles Emitted from a Gasoline-Direct-Injection Vehicle.

PubMed

Saffaripour, Meghdad; Chan, Tak W; Liu, Fengshan; Thomson, Kevin A; Smallwood, Gregory J; Kubsh, Joseph; Brezny, Rasto

2015-10-06

The size and morphology of particulate matter emitted from a light-duty gasoline-direct-injection (GDI) vehicle, over the FTP-75 and US06 transient drive cycles, have been characterized by transmission-electron-microscope (TEM) image analysis. To investigate the impact of gasoline particulate filters on particulate-matter emission, the results for the stock-GDI vehicle, that is, the vehicle in its original configuration, have been compared to the results for the same vehicle equipped with a catalyzed gasoline particulate filter (GPF). The stock-GDI vehicle emits graphitized fractal-like aggregates over all driving conditions. The mean projected area-equivalent diameter of these aggregates is in the 78.4-88.4 nm range and the mean diameter of primary particles varies between 24.6 and 26.6 nm. Post-GPF particles emitted over the US06 cycle appear to have an amorphous structure, and a large number of nucleation-mode particles, depicted as low-contrast ultrafine droplets, are observed in TEM images. This indicates the emission of a substantial amount of semivolatile material during the US06 cycle, most likely generated by the incomplete combustion of accumulated soot in the GPF during regeneration. The size of primary particles and soot aggregates does not vary significantly by implementing the GPF over the FTP-75 cycle; however, particles emitted by the GPF-equipped vehicle over the US06 cycle are about 20% larger than those emitted by the stock-GDI vehicle. This may be attributed to condensation of large amounts of organic material on soot aggregates. High-contrast spots, most likely solid nonvolatile cores, are observed within many of the nucleation-mode particles emitted over the US06 cycle by the GPF-equipped vehicle. These cores are either generated inside the engine or depict incipient soot particles which are partially carbonized in the exhaust line. The effect of drive cycle and the GPF on the fractal parameters of particles, such as fractal dimension and fractal prefactor, is insignificant.

Automated Image Analysis for the Detection of Benthic Crustaceans and Bacterial Mat Coverage Using the VENUS Undersea Cabled Network

PubMed Central

Aguzzi, Jacopo; Costa, Corrado; Robert, Katleen; Matabos, Marjolaine; Antonucci, Francesca; Juniper, S. Kim; Menesatti, Paolo

2011-01-01

The development and deployment of sensors for undersea cabled observatories is presently biased toward the measurement of habitat variables, while sensor technologies for biological community characterization through species identification and individual counting are less common. The VENUS cabled multisensory network (Vancouver Island, Canada) deploys seafloor camera systems at several sites. Our objective in this study was to implement new automated image analysis protocols for the recognition and counting of benthic decapods (i.e., the galatheid squat lobster, Munida quadrispina), as well as for the evaluation of changes in bacterial mat coverage (i.e., Beggiatoa spp.), using a camera deployed in Saanich Inlet (103 m depth). For the counting of Munida we remotely acquired 100 digital photos at hourly intervals from 2 to 6 December 2009. In the case of bacterial mat coverage estimation, images were taken from 2 to 8 December 2009 at the same time frequency. The automated image analysis protocols for both study cases were created in MatLab 7.1. Automation for Munida counting incorporated the combination of both filtering and background correction (Median- and Top-Hat Filters) with Euclidean Distances (ED) on Red-Green-Blue (RGB) channels. The Scale-Invariant Feature Transform (SIFT) features and Fourier Descriptors (FD) of tracked objects were then extracted. Animal classifications were carried out with the tools of morphometric multivariate statistic (i.e., Partial Least Square Discriminant Analysis; PLSDA) on Mean RGB (RGBv) value for each object and Fourier Descriptors (RGBv+FD) matrices plus SIFT and ED. The SIFT approach returned the better results. Higher percentages of images were correctly classified and lower misclassification errors (an animal is present but not detected) occurred. In contrast, RGBv+FD and ED resulted in a high incidence of records being generated for non-present animals. Bacterial mat coverage was estimated in terms of Percent Coverage and Fractal Dimension. A constant Region of Interest (ROI) was defined and background extraction by a Gaussian Blurring Filter was performed. Image subtraction within ROI was followed by the sum of the RGB channels matrices. Percent Coverage was calculated on the resulting image. Fractal Dimension was estimated using the box-counting method. The images were then resized to a dimension in pixels equal to a power of 2, allowing subdivision into sub-multiple quadrants. In comparisons of manual and automated Percent Coverage and Fractal Dimension estimates, the former showed an overestimation tendency for both parameters. The primary limitations on the automatic analysis of benthic images were habitat variations in sediment texture and water column turbidity. The application of filters for background corrections is a required preliminary step for the efficient recognition of animals and bacterial mat patches. PMID:22346657

Review of Random Phase Encoding in Volume Holographic Storage

PubMed Central

Su, Wei-Chia; Sun, Ching-Cherng

2012-01-01

Random phase encoding is a unique technique for volume hologram which can be applied to various applications such as holographic multiplexing storage, image encryption, and optical sensing. In this review article, we first review and discuss diffraction selectivity of random phase encoding in volume holograms, which is the most important parameter related to multiplexing capacity of volume holographic storage. We then review an image encryption system based on random phase encoding. The alignment of phase key for decryption of the encoded image stored in holographic memory is analyzed and discussed. In the latter part of the review, an all-optical sensing system implemented by random phase encoding and holographic interconnection is presented.

Order-fractal transitions in abstract paintings

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

Calleja, E.M. de la, E-mail: elsama79@gmail.com; Cervantes, F.; Calleja, J. de la

2016-08-15

In this study, we determined the degree of order for 22 Jackson Pollock paintings using the Hausdorff–Besicovitch fractal dimension. Based on the maximum value of each multi-fractal spectrum, the artworks were classified according to the year in which they were painted. It has been reported that Pollock’s paintings are fractal and that this feature was more evident in his later works. However, our results show that the fractal dimension of these paintings ranges among values close to two. We characterize this behavior as a fractal-order transition. Based on the study of disorder-order transition in physical systems, we interpreted the fractal-ordermore » transition via the dark paint strokes in Pollock’s paintings as structured lines that follow a power law measured by the fractal dimension. We determined self-similarity in specific paintings, thereby demonstrating an important dependence on the scale of observations. We also characterized the fractal spectrum for the painting entitled Teri’s Find. We obtained similar spectra for Teri’s Find and Number 5, thereby suggesting that the fractal dimension cannot be rejected completely as a quantitative parameter for authenticating these artworks. -- Highlights: •We determined the degree of order in Jackson Pollock paintings using the Hausdorff–Besicovitch dimension. •We detected a fractal-order transition from Pollock’s paintings between 1947 and 1951. •We suggest that Jackson Pollock could have painted Teri’s Find.« less

Fractality à la carte: a general particle aggregation model.

PubMed

Nicolás-Carlock, J R; Carrillo-Estrada, J L; Dossetti, V

2016-01-19

In nature, fractal structures emerge in a wide variety of systems as a local optimization of entropic and energetic distributions. The fractality of these systems determines many of their physical, chemical and/or biological properties. Thus, to comprehend the mechanisms that originate and control the fractality is highly relevant in many areas of science and technology. In studying clusters grown by aggregation phenomena, simple models have contributed to unveil some of the basic elements that give origin to fractality, however, the specific contribution from each of these elements to fractality has remained hidden in the complex dynamics. Here, we propose a simple and versatile model of particle aggregation that is, on the one hand, able to reveal the specific entropic and energetic contributions to the clusters' fractality and morphology, and, on the other, capable to generate an ample assortment of rich natural-looking aggregates with any prescribed fractal dimension.

Exploring fractal behaviour of blood oxygen saturation in preterm babies

NASA Astrophysics Data System (ADS)

Zahari, Marina; Hui, Tan Xin; Zainuri, Nuryazmin Ahmat; Darlow, Brian A.

2017-04-01

Recent evidence has been emerging that oxygenation instability in preterm babies could lead to an increased risk of retinal injury such as retinopathy of prematurity. There is a potential that disease severity could be better understood using nonlinear methods for time series data such as fractal theories [1]. Theories on fractal behaviours have been employed by researchers in various disciplines who were motivated to look into the behaviour or structure of irregular fluctuations in temporal data. In this study, an investigation was carried out to examine whether fractal behaviour could be detected in blood oxygen time series. Detection for the presence of fractals in oxygen data of preterm infants was performed using the methods of power spectrum, empirical probability distribution function and autocorrelation function. The results from these fractal identification methods indicate the possibility that these data exhibit fractal nature. Subsequently, a fractal framework for future research was suggested for oxygen time series.

Passenger flow analysis of Beijing urban rail transit network using fractal approach

NASA Astrophysics Data System (ADS)

Li, Xiaohong; Chen, Peiwen; Chen, Feng; Wang, Zijia

2018-04-01

To quantify the spatiotemporal distribution of passenger flow and the characteristics of an urban rail transit network, we introduce four radius fractal dimensions and two branch fractal dimensions by combining a fractal approach with passenger flow assignment model. These fractal dimensions can numerically describe the complexity of passenger flow in the urban rail transit network and its change characteristics. Based on it, we establish a fractal quantification method to measure the fractal characteristics of passenger follow in the rail transit network. Finally, we validate the reasonability of our proposed method by using the actual data of Beijing subway network. It has been shown that our proposed method can effectively measure the scale-free range of the urban rail transit network, network development and the fractal characteristics of time-varying passenger flow, which further provides a reference for network planning and analysis of passenger flow.

Poiseuille equation for steady flow of fractal fluid

NASA Astrophysics Data System (ADS)

Tarasov, Vasily E.

2016-07-01

Fractal fluid is considered in the framework of continuous models with noninteger dimensional spaces (NIDS). A recently proposed vector calculus in NIDS is used to get a description of fractal fluid flow in pipes with circular cross-sections. The Navier-Stokes equations of fractal incompressible viscous fluids are used to derive a generalization of the Poiseuille equation of steady flow of fractal media in pipe.

Fractal analysis for assessing tumour grade in microscopic images of breast tissue

NASA Astrophysics Data System (ADS)

Tambasco, Mauro; Costello, Meghan; Newcomb, Chris; Magliocco, Anthony M.

2007-03-01

In 2006, breast cancer is expected to continue as the leading form of cancer diagnosed in women, and the second leading cause of cancer mortality in this group. A method that has proven useful for guiding the choice of treatment strategy is the assessment of histological tumor grade. The grading is based upon the mitosis count, nuclear pleomorphism, and tubular formation, and is known to be subject to inter-observer variability. Since cancer grade is one of the most significant predictors of prognosis, errors in grading can affect patient management and outcome. Hence, there is a need to develop a breast cancer-grading tool that is minimally operator dependent to reduce variability associated with the current grading system, and thereby reduce uncertainty that may impact patient outcome. In this work, we explored the potential of a computer-based approach using fractal analysis as a quantitative measure of cancer grade for breast specimens. More specifically, we developed and optimized computational tools to compute the fractal dimension of low- versus high-grade breast sections and found them to be significantly different, 1.3+/-0.10 versus 1.49+/-0.10, respectively (Kolmogorov-Smirnov test, p<0.001). These results indicate that fractal dimension (a measure of morphologic complexity) may be a useful tool for demarcating low- versus high-grade cancer specimens, and has potential as an objective measure of breast cancer grade. Such prognostic value could provide more sensitive and specific information that would reduce inter-observer variability by aiding the pathologist in grading cancers.

Analysis of Resting-State fMRI Topological Graph Theory Properties in Methamphetamine Drug Users Applying Box-Counting Fractal Dimension.

PubMed

Siyah Mansoory, Meysam; Oghabian, Mohammad Ali; Jafari, Amir Homayoun; Shahbabaie, Alireza

2017-01-01

Graph theoretical analysis of functional Magnetic Resonance Imaging (fMRI) data has provided new measures of mapping human brain in vivo. Of all methods to measure the functional connectivity between regions, Linear Correlation (LC) calculation of activity time series of the brain regions as a linear measure is considered the most ubiquitous one. The strength of the dependence obligatory for graph construction and analysis is consistently underestimated by LC, because not all the bivariate distributions, but only the marginals are Gaussian. In a number of studies, Mutual Information (MI) has been employed, as a similarity measure between each two time series of the brain regions, a pure nonlinear measure. Owing to the complex fractal organization of the brain indicating self-similarity, more information on the brain can be revealed by fMRI Fractal Dimension (FD) analysis. In the present paper, Box-Counting Fractal Dimension (BCFD) is introduced for graph theoretical analysis of fMRI data in 17 methamphetamine drug users and 18 normal controls. Then, BCFD performance was evaluated compared to those of LC and MI methods. Moreover, the global topological graph properties of the brain networks inclusive of global efficiency, clustering coefficient and characteristic path length in addict subjects were investigated too. Compared to normal subjects by using statistical tests (P<0.05), topological graph properties were postulated to be disrupted significantly during the resting-state fMRI. Based on the results, analyzing the graph topological properties (representing the brain networks) based on BCFD is a more reliable method than LC and MI.

A fractal nature for polymerized laminin.

PubMed

Hochman-Mendez, Camila; Cantini, Marco; Moratal, David; Salmeron-Sanchez, Manuel; Coelho-Sampaio, Tatiana

2014-01-01

Polylaminin (polyLM) is a non-covalent acid-induced nano- and micro-structured polymer of the protein laminin displaying distinguished biological properties. Polylaminin stimulates neuritogenesis beyond the levels achieved by ordinary laminin and has been shown to promote axonal regeneration in animal models of spinal cord injury. Here we used confocal fluorescence microscopy (CFM), scanning electron microscopy (SEM) and atomic force microscopy (AFM) to characterize its three-dimensional structure. Renderization of confocal optical slices of immunostained polyLM revealed the aspect of a loose flocculated meshwork, which was homogeneously stained by the antibody. On the other hand, an ordinary matrix obtained upon adsorption of laminin in neutral pH (LM) was constituted of bulky protein aggregates whose interior was not accessible to the same anti-laminin antibody. SEM and AFM analyses revealed that the seed unit of polyLM was a flat polygon formed in solution whereas the seed structure of LM was highly heterogeneous, intercalating rod-like, spherical and thin spread lamellar deposits. As polyLM was visualized at progressively increasing magnifications, we observed that the morphology of the polymer was alike independently of the magnification used for the observation. A search for the Hausdorff dimension in images of the two matrices showed that polyLM, but not LM, presented fractal dimensions of 1.55, 1.62 and 1.70 after 1, 8 and 12 hours of adsorption, respectively. Data in the present work suggest that the intrinsic fractal nature of polymerized laminin can be the structural basis for the fractal-like organization of basement membranes in the neurogenic niches of the central nervous system.

Improving the signal subtle feature extraction performance based on dual improved fractal box dimension eigenvectors

NASA Astrophysics Data System (ADS)

Chen, Xiang; Li, Jingchao; Han, Hui; Ying, Yulong

2018-05-01

Because of the limitations of the traditional fractal box-counting dimension algorithm in subtle feature extraction of radiation source signals, a dual improved generalized fractal box-counting dimension eigenvector algorithm is proposed. First, the radiation source signal was preprocessed, and a Hilbert transform was performed to obtain the instantaneous amplitude of the signal. Then, the improved fractal box-counting dimension of the signal instantaneous amplitude was extracted as the first eigenvector. At the same time, the improved fractal box-counting dimension of the signal without the Hilbert transform was extracted as the second eigenvector. Finally, the dual improved fractal box-counting dimension eigenvectors formed the multi-dimensional eigenvectors as signal subtle features, which were used for radiation source signal recognition by the grey relation algorithm. The experimental results show that, compared with the traditional fractal box-counting dimension algorithm and the single improved fractal box-counting dimension algorithm, the proposed dual improved fractal box-counting dimension algorithm can better extract the signal subtle distribution characteristics under different reconstruction phase space, and has a better recognition effect with good real-time performance.

Multiple-image authentication with a cascaded multilevel architecture based on amplitude field random sampling and phase information multiplexing.

PubMed

Fan, Desheng; Meng, Xiangfeng; Wang, Yurong; Yang, Xiulun; Pan, Xuemei; Peng, Xiang; He, Wenqi; Dong, Guoyan; Chen, Hongyi

2015-04-10

A multiple-image authentication method with a cascaded multilevel architecture in the Fresnel domain is proposed, in which a synthetic encoded complex amplitude is first fabricated, and its real amplitude component is generated by iterative amplitude encoding, random sampling, and space multiplexing for the low-level certification images, while the phase component of the synthetic encoded complex amplitude is constructed by iterative phase information encoding and multiplexing for the high-level certification images. Then the synthetic encoded complex amplitude is iteratively encoded into two phase-type ciphertexts located in two different transform planes. During high-level authentication, when the two phase-type ciphertexts and the high-level decryption key are presented to the system and then the Fresnel transform is carried out, a meaningful image with good quality and a high correlation coefficient with the original certification image can be recovered in the output plane. Similar to the procedure of high-level authentication, in the case of low-level authentication with the aid of a low-level decryption key, no significant or meaningful information is retrieved, but it can result in a remarkable peak output in the nonlinear correlation coefficient of the output image and the corresponding original certification image. Therefore, the method realizes different levels of accessibility to the original certification image for different authority levels with the same cascaded multilevel architecture.

Staring 2-D hadamard transform spectral imager

DOEpatents

Gentry, Stephen M [Albuquerque, NM; Wehlburg, Christine M [Albuquerque, NM; Wehlburg, Joseph C [Albuquerque, NM; Smith, Mark W [Albuquerque, NM; Smith, Jody L [Albuquerque, NM

2006-02-07

A staring imaging system inputs a 2D spatial image containing multi-frequency spectral information. This image is encoded in one dimension of the image with a cyclic Hadamarid S-matrix. The resulting image is detecting with a spatial 2D detector; and a computer applies a Hadamard transform to recover the encoded image.

A fractal concentration area method for assigning a color palette for image representation

NASA Astrophysics Data System (ADS)

Cheng, Qiuming; Li, Qingmou

2002-05-01

Displaying the remotely sensed image with a proper color palette is the first task in any kind of image processing and pattern recognition in GIS and image processing environments. The purpose of displaying the image should be not only to provide a visual representation of the variance of the image, although this has been the primary objective of most conventional methods, but also the color palette should reflect real-world features on the ground which must be the primary objective of employing remotely sensed data. Although most conventional methods focus only on the first purpose of image representation, the concentration-area ( C- A plot) fractal method proposed in this paper aims to meet both purposes on the basis of pixel values and pixel value frequency distribution as well as spatial and geometrical properties of image patterns. The C- A method can be used to establish power-law relationships between the area A(⩾ s) with the pixel values greater than s and the pixel value s itself after plotting these values on log-log paper. A number of straight-line segments can be manually or automatically fitted to the points on the log-log paper, each representing a power-law relationship between the area A and the cutoff pixel value for s in a particular range. These straight-line segments can yield a group of cutoff values on the basis of which the image can be classified into discrete classes or zones. These zones usually correspond to the real-world features on the ground. A Windows program has been prepared in ActiveX format for implementing the C- A method and integrating it into other GIS and image processing systems. A case study of Landsat TM band 5 has been used to demonstrate the application of the method and the flexibility of the computer program.

Fractal analysis: A new tool in transient volcanic ash plume characterization.

NASA Astrophysics Data System (ADS)

Tournigand, Pierre-Yves; Peña Fernandez, Juan Jose; Taddeucci, Jacopo; Perugini, Diego; Sesterhenn, Jörn

2017-04-01

Transient volcanic plumes are time-dependent features generated by unstable eruptive sources. They represent a threat to human health and infrastructures, and a challenge to characterize due to their intrinsic instability. Plumes have been investigated through physical (e.g. visible, thermal, UV, radar imagery), experimental and numerical studies in order to provide new insights about their dynamics and better anticipate their behavior. It has been shown experimentally that plume dynamics is strongly dependent to source conditions and that plume shape evolution holds key to retrieve these conditions. In this study, a shape evolution analysis is performed on thermal high-speed videos of volcanic plumes from three different volcanoes Sakurajima (Japan), Stromboli (Italy) and Fuego (Guatemala), recorded with a FLIR SC655 thermal camera during several field campaigns between 2012 and 2016. To complete this dataset, three numerical gas-jet simulations at different Reynolds number (2000, 5000 and 10000) have been used in order to set reference values to the natural cases. Turbulent flow shapes are well known to feature scale-invariant structures and a high degree of complexity. For this reason we characterized the bi-dimensional shape of natural and synthetic plumes by using a fractal descriptor. Such method has been applied in other studies on experimental turbulent jets as well as on atmospheric clouds and have shown promising results. At each time-step plume contour has been manually outlined and measured using the box-counting method. This method consists in covering the image with squares of variable sizes and counting the number of squares containing the plume outline. The negative slope of the number of squares in function of their size in a log-log plot gives the fractal dimension of the plume at a given time. Preliminary results show an increase over time of the fractal dimension for natural volcanic plume as well as for the numerically simulated ones, but at varying rates. Increasing fractal dimension correspond to an increase in the overall complexity of plume shape and thus to an increase in flow turbulence over time. Accordingly, numerical simulations show that, fractal dimension increases faster with increasing Reynolds number. However, other parameters seem to play a role in volcanic plumes evolution. The features of the eruption source (e.g. vent number, size and shape, ejection duration, number and time interval between the different ejection pulses that characterize unsteady eruptions) seem also to have an effect on this time evolution with for example a single vent source generating a faster increase of the fractal dimension than in the case of a plume fed by several vents over time. This first attempt to use fractal analysis on volcanic plume could be the starting point towards a new kind of tools for volcanic plume characterization potentially giving an access to parameters so far unreachable by only using more traditional techniques. Fractal dimension analysis applied on volcanic plumes could directly link a shape evolution to source conditions and thus help to constrain uncertainties existing on such parameters.

A Comparison of Some of the Most Current Methods of Image Compression

DTIC Science & Technology

1993-06-01

found FrameMaker (available on the Sun) to be very flexible with imported files. It requires them to be in Raster format. 51 5. Access a. Fractal...account manager must set up a Sun account for access to FrameMaker , Sunvision, etc. Be sure to specify the utilities needed when signing up for an

Roughness Perception of Haptically Displayed Fractal Surfaces

NASA Technical Reports Server (NTRS)

Costa, Michael A.; Cutkosky, Mark R.; Lau, Sonie (Technical Monitor)

2000-01-01

Surface profiles were generated by a fractal algorithm and haptically rendered on a force feedback joystick, Subjects were asked to use the joystick to explore pairs of surfaces and report to the experimenter which of the surfaces they felt was rougher. Surfaces were characterized by their root mean square (RMS) amplitude and their fractal dimension. The most important factor affecting the perceived roughness of the fractal surfaces was the RMS amplitude of the surface. When comparing surfaces of fractal dimension 1.2-1.35 it was found that the fractal dimension was negatively correlated with perceived roughness.

A fractal growth model: Exploring the connection pattern of hubs in complex networks

NASA Astrophysics Data System (ADS)

Li, Dongyan; Wang, Xingyuan; Huang, Penghe

2017-04-01

Fractal is ubiquitous in many real-world networks. Previous researches showed that the strong disassortativity between the hub-nodes on all length scales was the key principle that gave rise to the fractal architecture of networks. Although fractal property emerged in some models, there were few researches about the fractal growth model and quantitative analyses about the strength of the disassortativity for fractal model. In this paper, we proposed a novel inverse renormalization method, named Box-based Preferential Attachment (BPA), to build the fractal growth models in which the Preferential Attachment was performed at box level. The proposed models provided a new framework that demonstrated small-world-fractal transition. Also, we firstly demonstrated the statistical characteristic of connection patterns of the hubs in fractal networks. The experimental results showed that, given proper growing scale and added edges, the proposed models could clearly show pure small-world or pure fractal or both of them. It also showed that the hub connection ratio showed normal distribution in many real-world networks. At last, the comparisons of connection pattern between the proposed models and the biological and technical networks were performed. The results gave useful reference for exploring the growth principle and for modeling the connection patterns for real-world networks.

Assessment of the spatial pattern of colorectal tumour perfusion estimated at perfusion CT using two-dimensional fractal analysis.

PubMed

Goh, Vicky; Sanghera, Bal; Wellsted, David M; Sundin, Josefin; Halligan, Steve

2009-06-01

The aim was to evaluate the feasibility of fractal analysis for assessing the spatial pattern of colorectal tumour perfusion at dynamic contrast-enhanced CT (perfusion CT). Twenty patients with colorectal adenocarcinoma underwent a 65-s perfusion CT study from which a perfusion parametric map was generated using validated commercial software. The tumour was identified by an experienced radiologist, segmented via thresholding and fractal analysis applied using in-house software: fractal dimension, abundance and lacunarity were assessed for the entire outlined tumour and for selected representative areas within the tumour of low and high perfusion. Comparison was made with ten patients with normal colons, processed in a similar manner, using two-way mixed analysis of variance with statistical significance at the 5% level. Fractal values were higher in cancer than normal colon (p < or = 0.001): mean (SD) 1.71 (0.07) versus 1.61 (0.07) for fractal dimension and 7.82 (0.62) and 6.89 (0.47) for fractal abundance. Fractal values were lower in 'high' than 'low' perfusion areas. Lacunarity curves were shifted to the right for cancer compared with normal colon. In conclusion, colorectal cancer mapped by perfusion CT demonstrates fractal properties. Fractal analysis is feasible, potentially providing a quantitative measure of the spatial pattern of tumour perfusion.

The role of the circadian system in fractal neurophysiological control

PubMed Central

Pittman-Polletta, Benjamin R.; Scheer, Frank A.J.L.; Butler, Matthew P.; Shea, Steven A.; Hu, Kun

2013-01-01

Many neurophysiological variables such as heart rate, motor activity, and neural activity are known to exhibit intrinsic fractal fluctuations - similar temporal fluctuation patterns at different time scales. These fractal patterns contain information about health, as many pathological conditions are accompanied by their alteration or absence. In physical systems, such fluctuations are characteristic of critical states on the border between randomness and order, frequently arising from nonlinear feedback interactions between mechanisms operating on multiple scales. Thus, the existence of fractal fluctuations in physiology challenges traditional conceptions of health and disease, suggesting that high levels of integrity and adaptability are marked by complex variability, not constancy, and are properties of a neurophysiological network, not individual components. Despite the subject's theoretical and clinical interest, the neurophysiological mechanisms underlying fractal regulation remain largely unknown. The recent discovery that the circadian pacemaker (suprachiasmatic nucleus) plays a crucial role in generating fractal patterns in motor activity and heart rate sheds an entirely new light on both fractal control networks and the function of this master circadian clock, and builds a bridge between the fields of circadian biology and fractal physiology. In this review, we sketch the emerging picture of the developing interdisciplinary field of fractal neurophysiology by examining the circadian system’s role in fractal regulation. PMID:23573942

A fractal analysis of quaternary, Cenozoic-Mesozoic, and Late Pennsylvanian sea level changes

NASA Technical Reports Server (NTRS)

Hsui, Albert T.; Rust, Kelly A.; Klein, George D.

1993-01-01

Sea level changes are related to both climatic variations and tectonic movements. The fractal dimensions of several sea level curves were compared to a modern climatic fractal dimension of 1.26 established for annual precipitation records. A similar fractal dimension (1.22) based on delta(O-18/O-16) in deep-sea sediments has been suggested to characterize climatic change during the past 2 m.y. Our analysis indicates that sea level changes over the past 150,000 to 250,000 years also exhibit comparable fractal dimensions. Sea level changes for periods longer than about 30 m.y. are found to produce fractal dimensions closer to unity and Missourian (Late Pennsylvanian) sea level changes yield a fractal dimension of 1.41. The fact that these sea level curves all possess fractal dimensions less than 1.5 indicates that sea level changes exhibit nonperiodic, long-run persistence. The different fractal dimensions calculated for the various time periods could be the result of a characteristic overprinting of the sediment recored by prevailing processes during deposition. For example, during the Quaternary, glacio-eustatic sea level changes correlate well with the present climatic signature. During the Missourian, however, mechanisms such as plate reorganization may have dominated, resulting in a significantly different fractal dimension.

Comparison of fractal dimensions based on segmented NDVI fields obtained from different remote sensors.

NASA Astrophysics Data System (ADS)

Alonso, C.; Benito, R. M.; Tarquis, A. M.

2012-04-01

Satellite image data have become an important source of information for monitoring vegetation and mapping land cover at several scales. Beside this, the distribution and phenology of vegetation is largely associated with climate, terrain characteristics and human activity. Various vegetation indices have been developed for qualitative and quantitative assessment of vegetation using remote spectral measurements. In particular, sensors with spectral bands in the red (RED) and near-infrared (NIR) lend themselves well to vegetation monitoring and based on them [(NIR - RED) / (NIR + RED)] Normalized Difference Vegetation Index (NDVI) has been widespread used. Given that the characteristics of spectral bands in RED and NIR vary distinctly from sensor to sensor, NDVI values based on data from different instruments will not be directly comparable. The spatial resolution also varies significantly between sensors, as well as within a given scene in the case of wide-angle and oblique sensors. As a result, NDVI values will vary according to combinations of the heterogeneity and scale of terrestrial surfaces and pixel footprint sizes. Therefore, the question arises as to the impact of differences in spectral and spatial resolutions on vegetation indices like the NDVI. The aim of this study is to establish a comparison between two different sensors in their NDVI values at different spatial resolutions. Scaling analysis and modeling techniques are increasingly understood to be the result of nonlinear dynamic mechanisms repeating scale after scale from large to small scales leading to non-classical resolution dependencies. In the remote sensing framework the main characteristic of sensors images is the high local variability in their values. This variability is a consequence of the increase in spatial and radiometric resolution that implies an increase in complexity that it is necessary to characterize. Fractal and multifractal techniques has been proven to be useful to extract such complexities from remote sensing images and will applied in this study to see the scaling behavior for each sensor in generalized fractal dimensions. The studied area is located in the provinces of Caceres and Salamanca (east of Iberia Peninsula) with an extension of 32 x 32 km2. The altitude in the area varies from 1,560 to 320 m, comprising natural vegetation in the mountain area (forest and bushes) and agricultural crops in the valleys. Scaling analysis were applied to Landsat-5 and MODIS TERRA to the normalized derived vegetation index (NDVI) on the same region with one day of difference, 13 and 12 of July 2003 respectively. From these images the area of interest was selected obtaining 1024 x 1024 pixels for Landsat image and 128 x 128 pixels for MODIS image. This implies that the resolution for MODIS is 250x250 m. and for Landsat is 30x30 m. From the reflectance data obtained from NIR and RED bands, NDVI was calculated for each image focusing this study on 0.2 to 0.5 ranges of values. Once that both NDVI fields were obtained several fractal dimensions were estimated in each one segmenting the values in 0.20-0.25, 0.25-0.30 and so on to rich 0.45-0.50. In all the scaling analysis the scale size length was expressed in meters, and not in pixels, to make the comparison between both sensors possible. Results are discussed. Acknowledgements This work has been supported by the Spanish MEC under Projects No. AGL2010-21501/AGR, MTM2009-14621 and i-MATH No. CSD2006-00032

Multimodal ophthalmic imaging using swept source spectrally encoded scanning laser ophthalmoscopy and optical coherence tomography

NASA Astrophysics Data System (ADS)

Malone, Joseph D.; El-Haddad, Mohamed T.; Tye, Logan A.; Majeau, Lucas; Godbout, Nicolas; Rollins, Andrew M.; Boudoux, Caroline; Tao, Yuankai K.

2016-03-01

Scanning laser ophthalmoscopy (SLO) and optical coherence tomography (OCT) benefit clinical diagnostic imaging in ophthalmology by enabling in vivo noninvasive en face and volumetric visualization of retinal structures, respectively. Spectrally encoding methods enable confocal imaging through fiber optics and reduces system complexity. Previous applications in ophthalmic imaging include spectrally encoded confocal scanning laser ophthalmoscopy (SECSLO) and a combined SECSLO-OCT system for image guidance, tracking, and registration. However, spectrally encoded imaging suffers from speckle noise because each spectrally encoded channel is effectively monochromatic. Here, we demonstrate in vivo human retinal imaging using a swept source spectrally encoded scanning laser ophthalmoscope and OCT (SSSESLO- OCT) at 1060 nm. SS-SESLO-OCT uses a shared 100 kHz Axsun swept source, shared scanner and imaging optics, and are detected simultaneously on a shared, dual channel high-speed digitizer. SESLO illumination and detection was performed using the single mode core and multimode inner cladding of a double clad fiber coupler, respectively, to preserve lateral resolution while improving collection efficiency and reducing speckle contrast at the expense of confocality. Concurrent en face SESLO and cross-sectional OCT images were acquired with 1376 x 500 pixels at 200 frames-per-second. Our system design is compact and uses a shared light source, imaging optics, and digitizer, which reduces overall system complexity and ensures inherent co-registration between SESLO and OCT FOVs. En face SESLO images acquired concurrent with OCT cross-sections enables lateral motion tracking and three-dimensional volume registration with broad applications in multivolume OCT averaging, image mosaicking, and intraoperative instrument tracking.

Single-shot spiral imaging enabled by an expanded encoding model: Demonstration in diffusion MRI.

PubMed

Wilm, Bertram J; Barmet, Christoph; Gross, Simon; Kasper, Lars; Vannesjo, S Johanna; Haeberlin, Max; Dietrich, Benjamin E; Brunner, David O; Schmid, Thomas; Pruessmann, Klaas P

2017-01-01

The purpose of this work was to improve the quality of single-shot spiral MRI and demonstrate its application for diffusion-weighted imaging. Image formation is based on an expanded encoding model that accounts for dynamic magnetic fields up to third order in space, nonuniform static B 0 , and coil sensitivity encoding. The encoding model is determined by B 0 mapping, sensitivity mapping, and concurrent field monitoring. Reconstruction is performed by iterative inversion of the expanded signal equations. Diffusion-tensor imaging with single-shot spiral readouts is performed in a phantom and in vivo, using a clinical 3T instrument. Image quality is assessed in terms of artefact levels, image congruence, and the influence of the different encoding factors. Using the full encoding model, diffusion-weighted single-shot spiral imaging of high quality is accomplished both in vitro and in vivo. Accounting for actual field dynamics, including higher orders, is found to be critical to suppress blurring, aliasing, and distortion. Enhanced image congruence permitted data fusion and diffusion tensor analysis without coregistration. Use of an expanded signal model largely overcomes the traditional vulnerability of spiral imaging with long readouts. It renders single-shot spirals competitive with echo-planar readouts and thus deploys shorter echo times and superior readout efficiency for diffusion imaging and further prospective applications. Magn Reson Med 77:83-91, 2017. © 2016 International Society for Magnetic Resonance in Medicine. © 2016 International Society for Magnetic Resonance in Medicine.

Modeling liver physiology: combining fractals, imaging and animation.

PubMed

Lin, Debbie W; Johnson, Scott; Hunt, C Anthony

2004-01-01

Physiological modeling of vascular and microvascular networks in several key human organ systems is critical for a deeper understanding of pharmacology and the effect of pharmacotherapies on disease. Like the lung and the kidney, the morphology of its vascular and microvascular system plays a major role in its functional capability. To understand liver function in absorption and metabolism of food and drugs, one must examine the morphology and physiology at both higher and lower level liver function. We have developed validated virtualized dynamic three dimensional (3D) models of liver secondary units and primary units by combining a number of different methods: three-dimensional rendering, fractals, and animation. We have simulated particle dynamics in the liver secondary unit. The resulting models are suitable for use in helping researchers easily visualize and gain intuition on results of in silico liver experiments.

Evidence of diffusive fractal aggregation of TiO2 nanoparticles by femtosecond laser ablation at ambient conditions

NASA Astrophysics Data System (ADS)

Celardo, G. L.; Archetti, D.; Ferrini, G.; Gavioli, L.; Pingue, P.; Cavaliere, E.

2017-01-01

The specific mechanisms which lead to the formation of fractal nanostructures by pulsed laser deposition remain elusive despite intense research efforts, motivated mainly by the technological interest in obtaining tailored nanostructures with simple and scalable production methods. Here we focus on fractal nanostructures of titanium dioxide, TiO2, a strategic material for many applications, obtained by femtosecond laser ablation at ambient conditions. We compare a theoretical model of fractal formation with experimental data. The comparison of theory and experiment confirms that fractal aggregates are formed after landing of the ablated material on the substrate surface by a simple diffusive mechanism. We model the fractal formation through extensive Monte Carlo simulations based on a set of minimal assumptions: TiO2 nanoparticles arrive already formed on the substrate, then they diffuse in a size/mass independent way and stick irreversibly upon touching, thus forming fractal clusters. Despite its simplicity, our model explains the main features of the fractal structures arising from the complex interaction of large TiO2 nanoparticles with different substrates. Indeed our model is able to reproduce both the fractal dimensions and the area distributions of the nanostructures for different densities of the ablated material. Finally we discuss the role of the thermal conductivity of the substrate and the laser fluence on the properties of the fractal nanostructures. Our results represent an advancement towards controlling the production of fractal nanostructures by pulsed laser deposition.

A fractal process of hydrogen diffusion in a-Si:H with exponential energy distribution

NASA Astrophysics Data System (ADS)

Hikita, Harumi; Ishikawa, Hirohisa; Morigaki, Kazuo

2017-04-01

Hydrogen diffusion in a-Si:H with exponential distribution of the states in energy exhibits the fractal structure. It is shown that a probability P(t) of the pausing time t has a form of tα (α: fractal dimension). It is shown that the fractal dimension α = Tr/T0 (Tr: hydrogen temperature, T0: a temperature corresponding to the width of exponential distribution of the states in energy) is in agreement with the Hausdorff dimension. A fractal graph for the case of α ≤ 1 is like the Cantor set. A fractal graph for the case of α > 1 is like the Koch curves. At α = ∞, hydrogen migration exhibits Brownian motion. Hydrogen diffusion in a-Si:H should be the fractal process.

Analysis of Fractional Flow for Transient Two-Phase Flow in Fractal Porous Medium

NASA Astrophysics Data System (ADS)

Lu, Ting; Duan, Yonggang; Fang, Quantang; Dai, Xiaolu; Wu, Jinsui

2016-03-01

Prediction of fractional flow in fractal porous medium is important for reservoir engineering and chemical engineering as well as hydrology. A physical conceptual fractional flow model of transient two-phase flow is developed in fractal porous medium based on the fractal characteristics of pore-size distribution and on the approximation that porous medium consist of a bundle of tortuous capillaries. The analytical expression for fractional flow for wetting phase is presented, and the proposed expression is the function of structural parameters (such as tortuosity fractal dimension, pore fractal dimension, maximum and minimum diameters of capillaries) and fluid properties (such as contact angle, viscosity and interfacial tension) in fractal porous medium. The sensitive parameters that influence fractional flow and its derivative are formulated, and their impacts on fractional flow are discussed.

[A method to estimate the short-term fractal dimension of heart rate variability based on wavelet transform].

PubMed

Zhonggang, Liang; Hong, Yan

2006-10-01

A new method of calculating fractal dimension of short-term heart rate variability signals is presented. The method is based on wavelet transform and filter banks. The implementation of the method is: First of all we pick-up the fractal component from HRV signals using wavelet transform. Next, we estimate the power spectrum distribution of fractal component using auto-regressive model, and we estimate parameter 7 using the least square method. Finally according to formula D = 2- (gamma-1)/2 estimate fractal dimension of HRV signal. To validate the stability and reliability of the proposed method, using fractional brown movement simulate 24 fractal signals that fractal value is 1.6 to validate, the result shows that the method has stability and reliability.

Spectrographic imaging system

DOEpatents

Morris, Michael D.; Treado, Patrick J.

1991-01-01

An imaging system for providing spectrographically resolved images. The system incorporates a one-dimensional spatial encoding mask which enables an image to be projected onto a two-dimensional image detector after spectral dispersion of the image. The dimension of the image which is lost due to spectral dispersion on the two-dimensional detector is recovered through employing a reverse transform based on presenting a multiplicity of different spatial encoding patterns to the image. The system is especially adapted for detecting Raman scattering of monochromatic light transmitted through or reflected from physical samples. Preferably, spatial encoding is achieved through the use of Hadamard mask which selectively transmits or blocks portions of the image from the sample being evaluated.

The Legacy of Benoit Mandelbrot in Geophysics

NASA Astrophysics Data System (ADS)

Turcotte, D. L.

2001-12-01

The concept of fractals (fractional dimension) was introduced by Benoit Mandelbrot in his famous 1967 Science paper. The initial application was to the length of the coastline of Britain. A milestone in the appreciation of the fractal concept by geophysicists was the Union session of the AGU on fractals led off by Benoit in 1986. Although fractals have found important applications in almost every branch of the physical, biological, and social sciences, fractals have been particularly useful in geophysics. Drainage networks are fractal. The frequency-magnitude distribution of earthquakes is fractal. The scale invariance of landscapes and many other geological processes is due to the applicability of power-law (fractal) distributions. Clouds are often fractal. Porosity distributions are fractal. In an almost independent line of research, Benoit in collaboration with James Wallace and others developed the concept of self-affine fractals. The original applications were primarily to time series in hydrology and built on the foundation laid by Henry Hurst. Fractional Gaussian noises and fractional Brownian motions are ubiquitous in geophysics. These are expressed in terms of the power-law relation between the power-spectral density S and frequency f, S ~ f{ β }, examples are β = 0 (white noise), β = 1 (1/f noise), β = 2 (Brownian motion). Of particular importance in geophysics are fractional noises with β = 0.5, these are stationary but have long-range persistent and have a Hurst exponent H = 0.7. Examples include river flows, tree rings, sunspots, varves, etc. Two of Benoit Mandelbrot's major contributions in geophysics as in other fields are: (1) an appreciation of the importance of fat-tail, power-law (fractal) distributions and (2) an appreciation of the importance of self-similar long-range persistence in both stationary time series (noises) and nonstationary time series (walks).

Spectrally-encoded color imaging

PubMed Central

Kang, DongKyun; Yelin, Dvir; Bouma, Brett E.; Tearney, Guillermo J.

2010-01-01

Spectrally-encoded endoscopy (SEE) is a technique for ultraminiature endoscopy that encodes each spatial location on the sample with a different wavelength. One limitation of previous incarnations of SEE is that it inherently creates monochromatic images, since the spectral bandwidth is expended in the spatial encoding process. Here we present a spectrally-encoded imaging system that has color imaging capability. The new imaging system utilizes three distinct red, green, and blue spectral bands that are configured to illuminate the grating at different incident angles. By careful selection of the incident angles, the three spectral bands can be made to overlap on the sample. To demonstrate the method, a bench-top system was built, comprising a 2400-lpmm grating illuminated by three 525-μm-diameter beams with three different spectral bands. Each spectral band had a bandwidth of 75 nm, producing 189 resolvable points. A resolution target, color phantoms, and excised swine small intestine were imaged to validate the system's performance. The color SEE system showed qualitatively and quantitatively similar color imaging performance to that of a conventional digital camera. PMID:19688002

White-Light Optical Information Processing and Holography.

DTIC Science & Technology

1984-06-22

Processing, Image Deblurring , Source Encoding, Signal Sampling, Coherence Measurement, Noise Performance, / Pseudocolor Encoding. , ’ ’ * .~ 10.ASS!RACT...o 2.1 Broad Spectral Band Color Image Deblurring .. . 4 2.2 Noise Performance ...... ...... .. . 4 2.3 Pseudocolor Encoding with Three Primary...spectra. This technique is particularly suitable for linear smeared color image deblurring . 2.2 Noise Performance In this period, we have also

Structure and properties of carbon black particles

NASA Astrophysics Data System (ADS)

Xu, Wei

Structure and properties of carbon black particles were investigated using atomic force microscopy, gas adsorption, Raman spectroscopy, and X-ray diffraction. Supplementary information was obtained using TEM and neutron scattering. The AFM imaging of carbon black aggregates provided qualitative visual information on their morphology, complementary to that obtained by 3-D modeling based on TEM images. Our studies showed that carbon black aggregates were relatively flat. The surface of all untreated carbon black particles was found to be rough and its fractal dimension was 2.2. Heating reduced the roughness and fractal dimension for all samples heat treated at above 1300 K to 2.0. Once the samples were heat treated rapid cooling did not affect the surface roughness. However, rapid cooling reduced crystallite sizes, and different Raman spectra were obtained for carbon blacks of various history of heat treatment. By analyzing the Raman spectra we determined the crystallite sizes and identified amorphous carbon. The concentration of amorphous carbon depends on hydrogen content. Once hydrogen was liberated at increased temperature, the concentration of amorphous carbon was reduced and crystallites started to grow. Properties of carbon blacks at high pressure were also studied. Hydrostatic pressure did not affect the size of the crystallites in carbon black particles. The pressure induced shift in Raman frequency of the graphitic component was a result of increased intermolecular forces and not smaller crystallites. Two methods of determining the fractal dimension, the FHH model and the yardstick technique based on the BET theory were used in the literature. Our study proved that the FHH model is sensitive to numerous assumptions and leads to wrong conclusions. On the other hand the yardstick method gave correct results, which agreed with the AFM results.

Fractal Dimension of Tc-99m DTPA GSA Estimates Pathologic Liver Injury due to Chemotherapy in Liver Cancer Patients.

PubMed

Hiroshima, Yukihiko; Shuto, Kiyohiko; Yamazaki, Kazuto; Kawaguchi, Daisuke; Yamada, Masatoshi; Kikuchi, Yutaro; Kasahara, Kohei; Murakami, Takashi; Hirano, Atsushi; Mori, Mikito; Kosugi, Chihiro; Matsuo, Kenichi; Ishida, Yasuo; Koda, Keiji; Tanaka, Kuniya

2016-12-01

Chemotherapy-induced liver injury after potent chemotherapy is a considerable problem in patients undergoing liver resection. The aim of this study was to assess the relationship between the fractal dimension (FD) of Tc-99m diethylenetriaminepentaacetic acid (DTPA) galactosyl human serum albumin (GSA) and pathologic change of liver parenchyma in liver cancer patients who have undergone chemotherapy. We examined 34 patients (10 female and 24 male; mean age, 68.5 years) who underwent hepatectomy. Hepatic injury was defined as steatosis more than 30 %, grade 2-3 sinusoidal dilation, and/or steatohepatitis Kleiner score ≥4. Fractal analysis was applied to all images of Tc-99m DTPA GSA using a plug-in tool on ImageJ software (NIH, Bethesda, MD). A differential box-counting method was applied, and FD was calculated as a heterogeneity parameter. Correlations between FD and clinicopathological variables were examined. FD values of patients with steatosis and steatohepatitis were significantly higher than those without (P > .001 and P > .001, respectively). There was no difference between the FD values of patients with and without sinusoidal dilatation (P = .357). Multivariate logistic regression showed FD as the only significant predictor for steatosis (P = .005; OR 36.5; 95 % CI 3.0-446.3) and steatohepatitis (P = .012; OR, 29.1; 95 % CI 2.1-400.1). FD of Tc-99m DTPA GSA was the significant predictor for fatty liver disease in patients who underwent chemotherapy. This new modality is able to differentiate steatohepatitis from steatosis; therefore, it may be useful for predicting chemotherapy-induced pathologic liver injury.

Iterons, fractals and computations of automata

NASA Astrophysics Data System (ADS)

Siwak, Paweł

1999-03-01

Processing of strings by some automata, when viewed on space-time (ST) diagrams, reveals characteristic soliton-like coherent periodic objects. They are inherently associated with iterations of automata mappings thus we call them the iterons. In the paper we present two classes of one-dimensional iterons: particles and filtrons. The particles are typical for parallel (cellular) processing, while filtrons, introduced in (32) are specific for serial processing of strings. In general, the images of iterated automata mappings exhibit not only coherent entities but also the fractals, and quasi-periodic and chaotic dynamics. We show typical images of such computations: fractals, multiplication by a number, and addition of binary numbers defined by a Turing machine. Then, the particles are presented as iterons generated by cellular automata in three computations: B/U code conversion (13, 29), majority classification (9), and in discrete version of the FPU (Fermi-Pasta-Ulam) dynamics (7, 23). We disclose particles by a technique of combinational recoding of ST diagrams (as opposed to sequential recoding). Subsequently, we recall the recursive filters based on FCA (filter cellular automata) window operators, and considered by Park (26), Ablowitz (1), Fokas (11), Fuchssteiner (12), Bruschi (5) and Jiang (20). We present the automata equivalents to these filters (33). Some of them belong to the class of filter automata introduced in (30). We also define and illustrate some properties of filtrons. Contrary to particles, the filtrons interact nonlocally in the sense that distant symbols may influence one another. Thus their interactions are very unusual. Some examples have been given in (32). Here we show new examples of filtron phenomena: multifiltron solitonic collisions, attracting and repelling filtrons, trapped bouncing filtrons (which behave like a resonance cavity) and quasi filtrons.

Multifractal and Singularity Maps of soil surface moisture distribution derived from 2D image analysis.

NASA Astrophysics Data System (ADS)

Cumbrera, Ramiro; Millán, Humberto; Martín-Sotoca, Juan Jose; Pérez Soto, Luis; Sanchez, Maria Elena; Tarquis, Ana Maria

2016-04-01

Soil moisture distribution usually presents extreme variation at multiple spatial scales. Image analysis could be a useful tool for investigating these spatial patterns of apparent soil moisture at multiple resolutions. The objectives of the present work were (i) to describe the local scaling of apparent soil moisture distribution and (ii) to define apparent soil moisture patterns from vertical planes of Vertisol pit images. Two soil pits (0.70 m long × 0.60 m width × 0.30 m depth) were excavated on a bare Mazic Pellic Vertisol. One was excavated in April/2011 and the other pit was established in May/2011 after 3 days of a moderate rainfall event. Digital photographs were taken from each Vertisol pit using a Kodak™ digital camera. The mean image size was 1600 × 945 pixels with one physical pixel ≈373 μm of the photographed soil pit. For more details see Cumbrera et al. (2012). Geochemical exploration have found with increasingly interests and benefits of using fractal (power-law) models to characterize geochemical distribution, using the concentration-area (C-A) model (Cheng et al., 1994; Cheng, 2012). This method is based on the singularity maps of a measure that at each point define areas with self-similar properties that are shown in power-law relationships in Concentration-Area plots (C-A method). The C-A method together with the singularity map ("Singularity-CA" method) define thresholds that can be applied to segment the map. We have applied it to each soil image. The results show that, in spite of some computational and practical limitations, image analysis of apparent soil moisture patterns could be used to study the dynamical change of soil moisture sampling in agreement with previous results (Millán et al., 2016). REFERENCES Cheng, Q., Agterberg, F. P. and Ballantyne, S. B. (1994). The separation of geochemical anomalies from background by fractal methods. Journal of Geochemical Exploration, 51, 109-130. Cheng, Q. (2012). Singularity theory and methods for mapping geochemical anomalies caused by buried sources and for predicting undiscovered mineral deposits in covered areas. Journal of Geochemical Exploration, 122, 55-70. Cumbrera, R., Ana M. Tarquis, Gabriel Gascó, Humberto Millán (2012) Fractal scaling of apparent soil moisture estimated from vertical planes of Vertisol pit images. Journal of Hydrology (452-453), 205-212. Martin Sotoca; J.J. Antonio Saa-Requejo, Juan Grau and Ana M. Tarquis (2016). Segmentation of singularity maps in the context of soil porosity. Geophysical Research Abstracts, 18, EGU2016-11402. Millán, H., Cumbrera, R. and Ana M. Tarquis (2016) Multifractal and Levy-stable statistics of soil surface moisture distribution derived from 2D image analysis. Applied Mathematical Modelling, 40(3), 2384-2395.

Fundamental Fractal Antenna Design Process

NASA Astrophysics Data System (ADS)

Zhu, L. P.; Kim, T. C.; Kakas, G. D.

2017-12-01

Antenna designers are always looking to come up with new ideas to push the envelope for new antennas, using a smaller volume while striving for higher bandwidth, wider bandwidth, and antenna gain. One proposed method of increasing bandwidth or shrinking antenna size is via the use of fractal geometry, which gives rise to fractal antennas. Fractals are those fun shapes that if one zooms in or zoom out, the structure is always the same. Design a new type of antenna based on fractal antenna design by utilize the Design of Experiment (DOE) will be shown in fractal antenna design process. Investigate conformal fractal antenna design for patterns, dimensions, and size, of the antenna but maintaining or improving the antenna performance. Research shows an antenna designer how to create basic requirements of the fractal antenna through a step by step process, and provides how to optimize the antenna design with the model prediction, lab measurement, and actual results from the compact range measurement on the antenna patterns.

Towards a physics on fractals: Differential vector calculus in three-dimensional continuum with fractal metric

NASA Astrophysics Data System (ADS)

Balankin, Alexander S.; Bory-Reyes, Juan; Shapiro, Michael

2016-02-01

One way to deal with physical problems on nowhere differentiable fractals is the mapping of these problems into the corresponding problems for continuum with a proper fractal metric. On this way different definitions of the fractal metric were suggested to account for the essential fractal features. In this work we develop the metric differential vector calculus in a three-dimensional continuum with a non-Euclidean metric. The metric differential forms and Laplacian are introduced, fundamental identities for metric differential operators are established and integral theorems are proved by employing the metric version of the quaternionic analysis for the Moisil-Teodoresco operator, which has been introduced and partially developed in this paper. The relations between the metric and conventional operators are revealed. It should be emphasized that the metric vector calculus developed in this work provides a comprehensive mathematical formalism for the continuum with any suitable definition of fractal metric. This offers a novel tool to study physics on fractals.

Quantum Image Processing and Its Application to Edge Detection: Theory and Experiment

NASA Astrophysics Data System (ADS)

Yao, Xi-Wei; Wang, Hengyan; Liao, Zeyang; Chen, Ming-Cheng; Pan, Jian; Li, Jun; Zhang, Kechao; Lin, Xingcheng; Wang, Zhehui; Luo, Zhihuang; Zheng, Wenqiang; Li, Jianzhong; Zhao, Meisheng; Peng, Xinhua; Suter, Dieter

2017-07-01

Processing of digital images is continuously gaining in volume and relevance, with concomitant demands on data storage, transmission, and processing power. Encoding the image information in quantum-mechanical systems instead of classical ones and replacing classical with quantum information processing may alleviate some of these challenges. By encoding and processing the image information in quantum-mechanical systems, we here demonstrate the framework of quantum image processing, where a pure quantum state encodes the image information: we encode the pixel values in the probability amplitudes and the pixel positions in the computational basis states. Our quantum image representation reduces the required number of qubits compared to existing implementations, and we present image processing algorithms that provide exponential speed-up over their classical counterparts. For the commonly used task of detecting the edge of an image, we propose and implement a quantum algorithm that completes the task with only one single-qubit operation, independent of the size of the image. This demonstrates the potential of quantum image processing for highly efficient image and video processing in the big data era.

Fractals, Coherence and Brain Dynamics

NASA Astrophysics Data System (ADS)

Vitiello, Giuseppe

2010-11-01

I show that the self-similarity property of deterministic fractals provides a direct connection with the space of the entire analytical functions. Fractals are thus described in terms of coherent states in the Fock-Bargmann representation. Conversely, my discussion also provides insights on the geometrical properties of coherent states: it allows to recognize, in some specific sense, fractal properties of coherent states. In particular, the relation is exhibited between fractals and q-deformed coherent states. The connection with the squeezed coherent states is also displayed. In this connection, the non-commutative geometry arising from the fractal relation with squeezed coherent states is discussed and the fractal spectral properties are identified. I also briefly discuss the description of neuro-phenomenological data in terms of squeezed coherent states provided by the dissipative model of brain and consider the fact that laboratory observations have shown evidence that self-similarity characterizes the brain background activity. This suggests that a connection can be established between brain dynamics and the fractal self-similarity properties on the basis of the relation discussed in this report between fractals and squeezed coherent states. Finally, I do not consider in this paper the so-called random fractals, namely those fractals obtained by randomization processes introduced in their iterative generation. Since self-similarity is still a characterizing property in many of such random fractals, my conjecture is that also in such cases there must exist a connection with the coherent state algebraic structure. In condensed matter physics, in many cases the generation by the microscopic dynamics of some kind of coherent states is involved in the process of the emergence of mesoscopic/macroscopic patterns. The discussion presented in this paper suggests that also fractal generation may provide an example of emergence of global features, namely long range correlation at mesoscopic/macroscopic level, from microscopic local deformation processes. In view of the wide spectrum of application of both, fractal studies and coherent state physics, spanning from solid state physics to laser physics, quantum optics, complex dynamical systems and biological systems, the results presented in the present report may lead to interesting practical developments in many research sectors.

Evolution of Fractal Parameters through Development Stage of Soil Crust

NASA Astrophysics Data System (ADS)

Ospina, Abelardo; Florentino, Adriana; Tarquis, Ana Maria

2016-04-01

Soil surface characteristics are subjected to changes driven by several interactions between water, air, biotic and abiotic components. One of the examples of such interactions is provided through biological soil crusts (BSC) in arid and semi-arid environments. BSC are communities composed of cyanobacteria, fungi, mosses, lichens, algae and liverworts covering the soil surface and play an important role in ecosystem functioning. The characteristics and formation of these BSC influence the soil hydrological balance, control the mass of eroded sediment, increase stability of soil surface, and influence plant productivity through the modification of nitrogen and carbon cycle. The site of this work is located at Quibor and Ojo de Agua (Lara state, Venezuela). The Quibor Depression in Venezuela is a major agricultural area being at semi-arid conditions and limited drainage favor the natural process of salinization. Additionally, the extension and intensification of agriculture has led to over-exploitation of groundwater in the past 30 years (Méndoza et al., 2013). The soil microbial crust develops initially on physical crusts which are mainly generated since wetting and drying, being a recurrent feature in the Quíbor arid zone. The microbiotic crust is organic, composed of macro organisms (bryophytes and lichens) and microorganisms (cyanobacteria, fungi algae, etc.); growing on the ground, forming a thickness no greater than 3 mm. For further details see Toledo and Florentino (2009). This study focus on characterize the development stage of the BSC based on image analysis. To this end, grayscale images of different types of biological soil crust at different stages where taken, each image corresponding to an area of 12.96 cm2 with a resolution of 1024x1024 pixels (Ospina et al., 2015). For each image lacunarity and fractal dimension through the differential box counting method were calculated. These were made with the software ImageJ/Fraclac (Karperien, 2013). REFERENCES Karperien, A. (2013). FracLac for ImageJ. Méndoza, B., Florentino, A., Hernández-Hernández, R.M., Aciego, J., Torres, D. and Vera, Elena. (2013). Biological attributes of two Quibor soils with addition of organic fertilizer and salt solutions. Revista Mexicana de Ciencias Agrícolas, 4(3), 409-421. Ospina, Abelardo, Adriana Florentino and Ana M. Tarquis (2015) Spatial Pattern of Biological Soil Crust with Fractal Geometry. Geophysical Research Abstracts, 17, EGU2015-15415-1 Toledo, V. and Florentino, A. (2009). The Microbiotic Crust On Soil. Revista de Investigación N° 68(33), 199-216.

The hippocampal formation participates in novel picture encoding: evidence from functional magnetic resonance imaging.

PubMed Central

Stern, C E; Corkin, S; González, R G; Guimaraes, A R; Baker, J R; Jennings, P J; Carr, C A; Sugiura, R M; Vedantham, V; Rosen, B R

1996-01-01

Considerable evidence exists to support the hypothesis that the hippocampus and related medial temporal lobe structures are crucial for the encoding and storage of information in long-term memory. Few human imaging studies, however, have successfully shown signal intensity changes in these areas during encoding or retrieval. Using functional magnetic resonance imaging (fMRI), we studied normal human subjects while they performed a novel picture encoding task. High-speed echo-planar imaging techniques evaluated fMRI signal changes throughout the brain. During the encoding of novel pictures, statistically significant increases in fMRI signal were observed bilaterally in the posterior hippocampal formation and parahippocampal gyrus and in the lingual and fusiform gyri. To our knowledge, this experiment is the first fMRI study to show robust signal changes in the human hippocampal region. It also provides evidence that the encoding of novel, complex pictures depends upon an interaction between ventral cortical regions, specialized for object vision, and the hippocampal formation and parahippocampal gyrus, specialized for long-term memory. Images Fig. 1 Fig. 3 PMID:8710927

Methods of nanoassembly of a fractal polymer and materials formed thereby

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

Newkome, George R; Moorefield, Charles N

2012-07-24

The invention relates to the formation of synthesized fractal constructs and the methods of chemical self-assembly for the preparation of a non-dendritic, nano-scale, fractal constructs or molecules. More particularly, the invention relates to fractal constructs formed by molecular self-assembly, to create synthetic, nanometer-scale fractal shapes. In an embodiment, a nanoscale Sierpinski hexagonal gasket is formed. This non-dendritic, perfectly self-similar fractal macromolecule is comprised of bisterpyridine building blocks that are bound together by coordination to 36 Ru and 6 Fe ions to form a nearly planar array of increasingly larger hexagons around a hollow center.

Methods of nanoassembly of a fractal polymer and materials formed thereby

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

Newkome, George R; Moorefield, Charles N

2014-09-23

The invention relates to the formation of synthesized fractal constructs and the methods of chemical self-assembly for the preparation of a non-dendritic, nano-scale, fractal constructs or molecules. More particularly, the invention relates to fractal constructs formed by molecular self-assembly, to create synthetic, nanometer-scale fractal shapes. In an embodiment, a nanoscale Sierpinski hexagonal gasket is formed. This non-dendritic, perfectly self-similar fractal macromolecule is comprised of bisterpyridine building blocks that are bound together by coordination to (36) Ru and (6) Fe ions to form a nearly planar array of increasingly larger hexagons around a hollow center.

Optimal spinneret layout in Von Koch curves of fractal theory based needleless electrospinning process

NASA Astrophysics Data System (ADS)

Yang, Wenxiu; Liu, Yanbo; Zhang, Ligai; Cao, Hong; Wang, Yang; Yao, Jinbo

2016-06-01

Needleless electrospinning technology is considered as a better avenue to produce nanofibrous materials at large scale, and electric field intensity and its distribution play an important role in controlling nanofiber diameter and quality of the nanofibrous web during electrospinning. In the current study, a novel needleless electrospinning method was proposed based on Von Koch curves of Fractal configuration, simulation and analysis on electric field intensity and distribution in the new electrospinning process were performed with Finite element analysis software, Comsol Multiphysics 4.4, based on linear and nonlinear Von Koch fractal curves (hereafter called fractal models). The result of simulation and analysis indicated that Second level fractal structure is the optimal linear electrospinning spinneret in terms of field intensity and uniformity. Further simulation and analysis showed that the circular type of Fractal spinneret has better field intensity and distribution compared to spiral type of Fractal spinneret in the nonlinear Fractal electrospinning technology. The electrospinning apparatus with the optimal Von Koch fractal spinneret was set up to verify the theoretical analysis results from Comsol simulation, achieving more uniform electric field distribution and lower energy cost, compared to the current needle and needleless electrospinning technologies.

Variability of fractal dimension of solar radio flux

NASA Astrophysics Data System (ADS)

Bhatt, Hitaishi; Sharma, Som Kumar; Trivedi, Rupal; Vats, Hari Om

2018-04-01

In the present communication, the variation of the fractal dimension of solar radio flux is reported. Solar radio flux observations on a day to day basis at 410, 1415, 2695, 4995, and 8800 MHz are used in this study. The data were recorded at Learmonth Solar Observatory, Australia from 1988 to 2009 covering an epoch of two solar activity cycles (22 yr). The fractal dimension is calculated for the listed frequencies for this period. The fractal dimension, being a measure of randomness, represents variability of solar radio flux at shorter time-scales. The contour plot of fractal dimension on a grid of years versus radio frequency suggests high correlation with solar activity. Fractal dimension increases with increasing frequency suggests randomness increases towards the inner corona. This study also shows that the low frequency is more affected by solar activity (at low frequency fractal dimension difference between solar maximum and solar minimum is 0.42) whereas, the higher frequency is less affected by solar activity (here fractal dimension difference between solar maximum and solar minimum is 0.07). A good positive correlation is found between fractal dimension averaged over all frequencies and yearly averaged sunspot number (Pearson's coefficient is 0.87).

Electromagnetism on anisotropic fractal media

NASA Astrophysics Data System (ADS)

Ostoja-Starzewski, Martin

2013-04-01

Basic equations of electromagnetic fields in anisotropic fractal media are obtained using a dimensional regularization approach. First, a formulation based on product measures is shown to satisfy the four basic identities of the vector calculus. This allows a generalization of the Green-Gauss and Stokes theorems as well as the charge conservation equation on anisotropic fractals. Then, pursuing the conceptual approach, we derive the Faraday and Ampère laws for such fractal media, which, along with two auxiliary null-divergence conditions, effectively give the modified Maxwell equations. Proceeding on a separate track, we employ a variational principle for electromagnetic fields, appropriately adapted to fractal media, so as to independently derive the same forms of these two laws. It is next found that the parabolic (for a conducting medium) and the hyperbolic (for a dielectric medium) equations involve modified gradient operators, while the Poynting vector has the same form as in the non-fractal case. Finally, Maxwell's electromagnetic stress tensor is reformulated for fractal systems. In all the cases, the derived equations for fractal media depend explicitly on fractal dimensions in three different directions and reduce to conventional forms for continuous media with Euclidean geometries upon setting these each of dimensions equal to unity.

The Fractal Patterns of Words in a Text: A Method for Automatic Keyword Extraction.

PubMed

Najafi, Elham; Darooneh, Amir H

2015-01-01

A text can be considered as a one dimensional array of words. The locations of each word type in this array form a fractal pattern with certain fractal dimension. We observe that important words responsible for conveying the meaning of a text have dimensions considerably different from one, while the fractal dimensions of unimportant words are close to one. We introduce an index quantifying the importance of the words in a given text using their fractal dimensions and then ranking them according to their importance. This index measures the difference between the fractal pattern of a word in the original text relative to a shuffled version. Because the shuffled text is meaningless (i.e., words have no importance), the difference between the original and shuffled text can be used to ascertain degree of fractality. The degree of fractality may be used for automatic keyword detection. Words with the degree of fractality higher than a threshold value are assumed to be the retrieved keywords of the text. We measure the efficiency of our method for keywords extraction, making a comparison between our proposed method and two other well-known methods of automatic keyword extraction.

The Fractal Patterns of Words in a Text: A Method for Automatic Keyword Extraction

PubMed Central

Najafi, Elham; Darooneh, Amir H.

2015-01-01

A text can be considered as a one dimensional array of words. The locations of each word type in this array form a fractal pattern with certain fractal dimension. We observe that important words responsible for conveying the meaning of a text have dimensions considerably different from one, while the fractal dimensions of unimportant words are close to one. We introduce an index quantifying the importance of the words in a given text using their fractal dimensions and then ranking them according to their importance. This index measures the difference between the fractal pattern of a word in the original text relative to a shuffled version. Because the shuffled text is meaningless (i.e., words have no importance), the difference between the original and shuffled text can be used to ascertain degree of fractality. The degree of fractality may be used for automatic keyword detection. Words with the degree of fractality higher than a threshold value are assumed to be the retrieved keywords of the text. We measure the efficiency of our method for keywords extraction, making a comparison between our proposed method and two other well-known methods of automatic keyword extraction. PMID:26091207

Externally Calibrated Parallel Imaging for 3D Multispectral Imaging Near Metallic Implants Using Broadband Ultrashort Echo Time Imaging

PubMed Central

Wiens, Curtis N.; Artz, Nathan S.; Jang, Hyungseok; McMillan, Alan B.; Reeder, Scott B.

2017-01-01

Purpose To develop an externally calibrated parallel imaging technique for three-dimensional multispectral imaging (3D-MSI) in the presence of metallic implants. Theory and Methods A fast, ultrashort echo time (UTE) calibration acquisition is proposed to enable externally calibrated parallel imaging techniques near metallic implants. The proposed calibration acquisition uses a broadband radiofrequency (RF) pulse to excite the off-resonance induced by the metallic implant, fully phase-encoded imaging to prevent in-plane distortions, and UTE to capture rapidly decaying signal. The performance of the externally calibrated parallel imaging reconstructions was assessed using phantoms and in vivo examples. Results Phantom and in vivo comparisons to self-calibrated parallel imaging acquisitions show that significant reductions in acquisition times can be achieved using externally calibrated parallel imaging with comparable image quality. Acquisition time reductions are particularly large for fully phase-encoded methods such as spectrally resolved fully phase-encoded three-dimensional (3D) fast spin-echo (SR-FPE), in which scan time reductions of up to 8 min were obtained. Conclusion A fully phase-encoded acquisition with broadband excitation and UTE enabled externally calibrated parallel imaging for 3D-MSI, eliminating the need for repeated calibration regions at each frequency offset. Significant reductions in acquisition time can be achieved, particularly for fully phase-encoded methods like SR-FPE. PMID:27403613

Quantification of left to right atrial shunts with velocity-encoded cine nuclear magnetic resonance imaging.

PubMed

Brenner, L D; Caputo, G R; Mostbeck, G; Steiman, D; Dulce, M; Cheitlin, M D; O'Sullivan, M; Higgins, C B

1992-11-01

The purpose of this study was to evaluate the ability of velocity-encoded nuclear magnetic resonance (NMR) imaging to quantify left to right intracardiac shunts in patients with an atrial septal defect. Quantification of intracardiac shunts is clinically important in planning therapy. Velocity-encoded NMR imaging was used to quantify stroke flow in the aorta and in the main pulmonary artery in a group of patients who were known to have an increased pulmonary to systemic flow ratio (Qp/Qs). The velocity-encoded NMR flow data were used to calculate Qp/Qs, and these values were compared with measurements of Qp/Qs obtained with oximetric data derived from cardiac catheterization and from stroke volume measurements of the two ventricles by using volumetric data from biphasic spin echo and cine NMR images obtained at end-diastole and end-systole. Two independent observers measured Qp/Qs by using velocity-encoded NMR imaging in 11 patients and found Qp/Qs ranging from 1.4:1 to 3.9:1. These measurements correlated well with both oximetric data (r = 0.91, SEE = 0.35) and ventricular volumetric data (r = 0.94, SEE = 0.30). Interobserver reproducibility for Qp/Qs by velocity-encoded NMR imaging was good (r = 0.97, SEE = 0.20). Velocity-encoded NMR imaging is an accurate and reproducible method for measuring Qp/Qs in left to right shunts. Because it is completely noninvasive, it can be used to monitor shunt volume over time.

Bilevel thresholding of sliced image of sludge floc.

PubMed

Chu, C P; Lee, D J

2004-02-15

This work examined the feasibility of employing various thresholding algorithms to determining the optimal bilevel thresholding value for estimating the geometric parameters of sludge flocs from the microtome sliced images and from the confocal laser scanning microscope images. Morphological information extracted from images depends on the bilevel thresholding value. According to the evaluation on the luminescence-inverted images and fractal curves (quadric Koch curve and Sierpinski carpet), Otsu's method yields more stable performance than other histogram-based algorithms and is chosen to obtain the porosity. The maximum convex perimeter method, however, can probe the shapes and spatial distribution of the pores among the biomass granules in real sludge flocs. A combined algorithm is recommended for probing the sludge floc structure.

Optical image encryption method based on incoherent imaging and polarized light encoding

NASA Astrophysics Data System (ADS)

Wang, Q.; Xiong, D.; Alfalou, A.; Brosseau, C.

2018-05-01

We propose an incoherent encoding system for image encryption based on a polarized encoding method combined with an incoherent imaging. Incoherent imaging is the core component of this proposal, in which the incoherent point-spread function (PSF) of the imaging system serves as the main key to encode the input intensity distribution thanks to a convolution operation. An array of retarders and polarizers is placed on the input plane of the imaging structure to encrypt the polarized state of light based on Mueller polarization calculus. The proposal makes full use of randomness of polarization parameters and incoherent PSF so that a multidimensional key space is generated to deal with illegal attacks. Mueller polarization calculus and incoherent illumination of imaging structure ensure that only intensity information is manipulated. Another key advantage is that complicated processing and recording related to a complex-valued signal are avoided. The encoded information is just an intensity distribution, which is advantageous for data storage and transition because information expansion accompanying conventional encryption methods is also avoided. The decryption procedure can be performed digitally or using optoelectronic devices. Numerical simulation tests demonstrate the validity of the proposed scheme.

Fractals in the Classroom

ERIC Educational Resources Information Center

Fraboni, Michael; Moller, Trisha

2008-01-01

Fractal geometry offers teachers great flexibility: It can be adapted to the level of the audience or to time constraints. Although easily explained, fractal geometry leads to rich and interesting mathematical complexities. In this article, the authors describe fractal geometry, explain the process of iteration, and provide a sample exercise.…

Some problems in fractal differential equations

NASA Astrophysics Data System (ADS)

Su, Weiyi

2016-06-01

Based upon the fractal calculus on local fields, or p-type calculus, or Gibbs-Butzer calculus ([1],[2]), we suggest a constructive idea for "fractal differential equations", beginning from some special examples to a general theory. However, this is just an original idea, it needs lots of later work to support. In [3], we show example "two dimension wave equations with fractal boundaries", and in this note, other examples, as well as an idea to construct fractal differential equations are shown.

Vector calculus in non-integer dimensional space and its applications to fractal media

NASA Astrophysics Data System (ADS)

Tarasov, Vasily E.

2015-02-01

We suggest a generalization of vector calculus for the case of non-integer dimensional space. The first and second orders operations such as gradient, divergence, the scalar and vector Laplace operators for non-integer dimensional space are defined. For simplification we consider scalar and vector fields that are independent of angles. We formulate a generalization of vector calculus for rotationally covariant scalar and vector functions. This generalization allows us to describe fractal media and materials in the framework of continuum models with non-integer dimensional space. As examples of application of the suggested calculus, we consider elasticity of fractal materials (fractal hollow ball and fractal cylindrical pipe with pressure inside and outside), steady distribution of heat in fractal media, electric field of fractal charged cylinder. We solve the correspondent equations for non-integer dimensional space models.

Fractal 1/f Dynamics Suggest Entanglement of Measurement and Human Performance

ERIC Educational Resources Information Center

Holden, John G.; Choi, Inhyun; Amazeen, Polemnia G.; Van Orden, Guy

2011-01-01

Variability of repeated measurements in human performances exhibits fractal 1/f noise. Yet the relative strength of this fractal pattern varies widely across conditions, tasks, and individuals. Four experiments illustrate how subtle details of the conditions of measurement change the fractal patterns observed across task conditions. The results…

Stories about Benoit

NASA Astrophysics Data System (ADS)

Frame, Michael; Cohen, Nathan

2015-03-01

The Yale University mathematics department hosted a memorial for Benoit on April 29 and 30, 2011. The first day of the meeting consisted of three technical talks on some aspects of fractals, Benoit's principal intellectual legacy. Bernard Sapoval spoke on fractals in physics, Peter Jones on fractals in mathematics, and Nassim Taleb on fractals in finance...

Fractals and the irreducibility of consciousness in plants and animals

PubMed Central

Gardiner, John

2013-01-01

In both plants and animals consciousness is fractal. Since fractals can only pass information in one direction it is impossible to extrapolate backward to find the rule that governs the fractal. Thus, similarly, it will be impossible to completely determine the rule or rules that govern consciousness. PMID:23759545

Fractals and the irreducibility of consciousness in plants and animals.

PubMed

Gardiner, John

2013-08-01

In both plants and animals consciousness is fractal. Since fractals can only pass information in one direction it is impossible to extrapolate backward to find the rule that governs the fractal. Thus, similarly, it will be impossible to completely determine the rule or rules that govern consciousness.

Fractal analysis of time varying data

DOEpatents

Vo-Dinh, Tuan; Sadana, Ajit

2002-01-01

Characteristics of time varying data, such as an electrical signal, are analyzed by converting the data from a temporal domain into a spatial domain pattern. Fractal analysis is performed on the spatial domain pattern, thereby producing a fractal dimension D.sub.F. The fractal dimension indicates the regularity of the time varying data.

Sensitivity quantification of remote detection NMR and MRI

NASA Astrophysics Data System (ADS)

Granwehr, J.; Seeley, J. A.

2006-04-01

A sensitivity analysis is presented of the remote detection NMR technique, which facilitates the spatial separation of encoding and detection of spin magnetization. Three different cases are considered: remote detection of a transient signal that must be encoded point-by-point like a free induction decay, remote detection of an experiment where the transient dimension is reduced to one data point like phase encoding in an imaging experiment, and time-of-flight (TOF) flow visualization. For all cases, the sensitivity enhancement is proportional to the relative sensitivity between the remote detector and the circuit that is used for encoding. It is shown for the case of an encoded transient signal that the sensitivity does not scale unfavorably with the number of encoded points compared to direct detection. Remote enhancement scales as the square root of the ratio of corresponding relaxation times in the two detection environments. Thus, remote detection especially increases the sensitivity of imaging experiments of porous materials with large susceptibility gradients, which cause a rapid dephasing of transverse spin magnetization. Finally, TOF remote detection, in which the detection volume is smaller than the encoded fluid volume, allows partial images corresponding to different time intervals between encoding and detection to be recorded. These partial images, which contain information about the fluid displacement, can be recorded, in an ideal case, with the same sensitivity as the full image detected in a single step with a larger coil.

Key management of the double random-phase-encoding method using public-key encryption

NASA Astrophysics Data System (ADS)

Saini, Nirmala; Sinha, Aloka

2010-03-01

Public-key encryption has been used to encode the key of the encryption process. In the proposed technique, an input image has been encrypted by using the double random-phase-encoding method using extended fractional Fourier transform. The key of the encryption process have been encoded by using the Rivest-Shamir-Adelman (RSA) public-key encryption algorithm. The encoded key has then been transmitted to the receiver side along with the encrypted image. In the decryption process, first the encoded key has been decrypted using the secret key and then the encrypted image has been decrypted by using the retrieved key parameters. The proposed technique has advantage over double random-phase-encoding method because the problem associated with the transmission of the key has been eliminated by using public-key encryption. Computer simulation has been carried out to validate the proposed technique.

Fractal and spectroscopic analysis of soot from internal combustion engines

NASA Astrophysics Data System (ADS)

Swapna, M. S.; Saritha Devi, H. V.; Raj, Vimal; Sankararaman, S.

2018-03-01

Today diesel engines are used worldwide for various applications and very importantly in transportation. Hydrocarbons are the most widespread precursors among carbon sources employed in the production of carbon nanotubes (CNTs). The aging of internal combustion engine is an important parameter in deciding the carbon emission and particulate matter due to incomplete combustion of fuel. In the present work, an attempt has been made for the effective utilization of the aged engines for potential applicationapplications in fuel cells and nanoelectronics. To analyze the impact of aging, the particulate matter rich in carbon content areis collected from diesel engines of different ages. The soot with CNTs is purified by the liquid phase oxidation method and analyzed by Field Emission Scanning Electron Microscopy, High-Resolution Transmission Electron Microscopy, Energy Dispersive Spectroscopy, UV-Visible spectroscopy, Raman spectroscopy and Thermogravimetric analysis. The SEM image contains self-similar patterns probing fractal analysis. The fractal dimensions of the samples are determined by the box counting method. We could find a greater amount of single-walled carbon nanotubes (SWCNTs) in the particulate matter emitted by aged diesel engines and thereby giving information about the combustion efficiency of the engine. The SWCNT rich sample finds a wide range of applicationapplications in nanoelectronics and thereby pointing a potential use of these aged engines.

Fractals in physiology and medicine

NASA Technical Reports Server (NTRS)

Goldberger, Ary L.; West, Bruce J.

1987-01-01

The paper demonstrates how the nonlinear concepts of fractals, as applied in physiology and medicine, can provide an insight into the organization of such complex structures as the tracheobronchial tree and heart, as well as into the dynamics of healthy physiological variability. Particular attention is given to the characteristics of computer-generated fractal lungs and heart and to fractal pathologies in these organs. It is shown that alterations in fractal scaling may underlie a number of pathophysiological disturbances, including sudden cardiac death syndromes.

Recent advances in coding theory for near error-free communications

NASA Technical Reports Server (NTRS)

Cheung, K.-M.; Deutsch, L. J.; Dolinar, S. J.; Mceliece, R. J.; Pollara, F.; Shahshahani, M.; Swanson, L.

1991-01-01

Channel and source coding theories are discussed. The following subject areas are covered: large constraint length convolutional codes (the Galileo code); decoder design (the big Viterbi decoder); Voyager's and Galileo's data compression scheme; current research in data compression for images; neural networks for soft decoding; neural networks for source decoding; finite-state codes; and fractals for data compression.

What does See the Impulse Acoustic Microscopy inside Nanocomposites?

NASA Astrophysics Data System (ADS)

Levin, V. M.; Petronyuk, Y. S.; Morokov, E. S.; Celzard, A.; Bellucci, S.; Kuzhir, P. P.

The paper presents results of studying bulk microstructure in carbon nanocomposites by impulse acoustic microscopy technique. Nanocomposite materials are in the focus of interest because of their outstanding properties in minimal nanofiller content. Large surface area and high superficial activity cause strong interaction between nanoparticles that can result in formation of fractal conglomerates. This paper involves results of the first direct observation of nanoparticle conglomerates inside the bulk of epoxy-carbon nanocomposites. Diverse types of carbon nanofiller have been under investigation. The impulse acoustic microscope SIAM-1 (Acoustic Microscopy Lab, IBCP RAS) has been employed for 3D imaging bulk microstructure and measuring elastic properties of the nanocomposite specimens. The range of 50-200 MHz allows observing microstructure inside the entire specimen bulk. Acoustic images are obtained in the ultramicroscopic regime; they are formed by the Rayleigh type scattered radiation. It has been found the high-resolution acoustic vision (impulse acoustic microscopy) is an efficient technique to observe mesostructure formed by fractal cluster inside nanocomposites. The clusterization takes its utmost form in nanocomposites with graphite nanoplatelets as nanofiller. The nanoparticles agglomerate into micron-sized conglomerates distributed randomly over the material. Mesostructure in nanocomposites filled with carbon nanotubes is alternation of regions with diverse density of nanotube packing. Regions with alternative density of CNT packing are clearly seen in acoustical images as neighboring pixels of various brightness.

Computerized morphometry as an aid in distinguishing recurrent versus nonrecurrent meningiomas.

PubMed

Noy, Shawna; Vlodavsky, Euvgeni; Klorin, Geula; Drumea, Karen; Ben Izhak, Ofer; Shor, Eli; Sabo, Edmond

2011-06-01

To use novel digital and morphometric methods to identify variables able to better predict the recurrence of intracranial meningiomas. Histologic images from 30 previously diagnosed meningioma tumors that recurred over 10 years of follow-up were consecutively selected from the Rambam Pathology Archives. Images were captured and morphometrically analyzed. Novel algorithms of digital pattern recognition using Fourier transformation and fractal and nuclear texture analyses were applied to evaluate the overall growth pattern complexity of the tumors, as well as the chromatin texture of individual tumor nuclei. The extracted parameters were then correlated with patient prognosis. Kaplan-Meier analyses revealed statistically significant associations between tumor morphometric parameters and recurrence times. Tumors with less nuclear orientation, more nuclear density, higher fractal dimension, and less regular chromatin textures tended to recur faster than those with a higher degree of nuclear order, less pattern complexity, lower density, and more homogeneous chromatin nuclear textures (p < 0.01). To our knowledge, these digital morphometric methods were used for the first time to accurately predict tumor recurrence in patients with intracranial meningiomas. The use of these methods may bring additional valuable information to the clinician regarding the optimal management of these patients.

Optical information authentication using compressed double-random-phase-encoded images and quick-response codes.

PubMed

Wang, Xiaogang; Chen, Wen; Chen, Xudong

2015-03-09

In this paper, we develop a new optical information authentication system based on compressed double-random-phase-encoded images and quick-response (QR) codes, where the parameters of optical lightwave are used as keys for optical decryption and the QR code is a key for verification. An input image attached with QR code is first optically encoded in a simplified double random phase encoding (DRPE) scheme without using interferometric setup. From the single encoded intensity pattern recorded by a CCD camera, a compressed double-random-phase-encoded image, i.e., the sparse phase distribution used for optical decryption, is generated by using an iterative phase retrieval technique with QR code. We compare this technique to the other two methods proposed in literature, i.e., Fresnel domain information authentication based on the classical DRPE with holographic technique and information authentication based on DRPE and phase retrieval algorithm. Simulation results show that QR codes are effective on improving the security and data sparsity of optical information encryption and authentication system.

[Features of fractal dynamics EEG of alpha-rhythm in patients with neurotic and neurosis-like disorders].

PubMed

Shul'ts, E V; Baburin, I N; Karavaeva, T A; Karvasarskiĭ, B D; Slezin, V B

2011-01-01

Fifty-five patients with neurotic and neurosis-like disorders and 20 healthy controls, aged 17-64 years, have been examined. The basic research method was electroencephalography (EEG) with the fractal analysis of alpha power fluctuations. In patients, the changes in the fractal structure were of the same direction: the decrease of fractal indexes of low-frequency fluctuations and the increase of fractal indexes of mid-frequency fluctuations. Patients with neurosis-like disorders, in comparison to those with neurotic disorders, were characterized by more expressed (quantitative) changes in fractal structures of more extended character. It suggests the presence of deeper pathological changes in patients with neurosis-like disorders.

Transport properties of electrons in fractal magnetic-barrier structures

NASA Astrophysics Data System (ADS)

Sun, Lifeng; Fang, Chao; Guo, Yong

2010-09-01

Quantum transport properties in fractal magnetically modulated structures are studied by the transfer-matrix method. It is found that the transmission spectra depend sensitively not only on the incident energy and the direction of the wave vector but also on the stage of the fractal structures. Resonance splitting, enhancement, and position shift of the resonance peaks under different magnetic modulation are observed at four different fractal stages, and the relationship between the conductance in the fractal structure and magnetic modulation is also revealed. The results indicate the spectra of the transmission can be considered as fingerprints for the fractal structures, which show the subtle correspondence between magnetic structures and transport behaviors.

Deep Marginalized Sparse Denoising Auto-Encoder for Image Denoising

NASA Astrophysics Data System (ADS)

Ma, Hongqiang; Ma, Shiping; Xu, Yuelei; Zhu, Mingming

2018-01-01

Stacked Sparse Denoising Auto-Encoder (SSDA) has been successfully applied to image denoising. As a deep network, the SSDA network with powerful data feature learning ability is superior to the traditional image denoising algorithms. However, the algorithm has high computational complexity and slow convergence rate in the training. To address this limitation, we present a method of image denoising based on Deep Marginalized Sparse Denoising Auto-Encoder (DMSDA). The loss function of Sparse Denoising Auto-Encoder is marginalized so that it satisfies both sparseness and marginality. The experimental results show that the proposed algorithm can not only outperform SSDA in the convergence speed and training time, but also has better denoising performance than the current excellent denoising algorithms, including both the subjective and objective evaluation of image denoising.

Fractal dimension analysis of complexity in Ligeti piano pieces

NASA Astrophysics Data System (ADS)

Bader, Rolf

2005-04-01

Fractal correlation dimensional analysis has been performed with whole solo piano pieces by Gyrgy Ligeti at every 50ms interval of the pieces. The resulting curves of development of complexity represented by the fractal dimension showed up a very reasonable correlation with the perceptional density of events during these pieces. The seventh piece of Ligeti's ``Musica ricercata'' was used as a test case. Here, each new part of the piece was followed by an increase of the fractal dimension because of the increase of information at the part changes. The second piece ``Galamb borong,'' number seven of the piano Etudes was used, because Ligeti wrote these Etudes after studying fractal geometry. Although the piece is not fractal in the strict mathematical sense, the overall structure of the psychoacoustic event-density as well as the detailed event development is represented by the fractal dimension plot.

a Fractal Permeability Model Coupling Boundary-Layer Effect for Tight Oil Reservoirs

NASA Astrophysics Data System (ADS)

Wang, Fuyong; Liu, Zhichao; Jiao, Liang; Wang, Congle; Guo, Hu

A fractal permeability model coupling non-flowing boundary-layer effect for tight oil reservoirs was proposed. Firstly, pore structures of tight formations were characterized with fractal theory. Then, with the empirical equation of boundary-layer thickness, Hagen-Poiseuille equation and fractal theory, a fractal torturous capillary tube model coupled with boundary-layer effect was developed, and verified with experimental data. Finally, the parameters influencing effective liquid permeability were quantitatively investigated. The research results show that effective liquid permeability of tight formations is not only decided by pore structures, but also affected by boundary-layer distributions, and effective liquid permeability is the function of fluid type, fluid viscosity, pressure gradient, fractal dimension, tortuosity fractal dimension, minimum pore radius and maximum pore radius. For the tight formations dominated with nanoscale pores, boundary-layer effect can significantly reduce effective liquid permeability, especially under low pressure gradient.

Fractal characterization of fracture surfaces in concrete

USGS Publications Warehouse

Saouma, V.E.; Barton, C.C.; Gamaleldin, N.A.

1990-01-01

Fractal geometry is used to characterize the roughness of cracked concrete surfaces through a specially built profilometer, and the fractal dimension is subsequently correlated to the fracture toughness and direction of crack propagation. Preliminary results indicate that the fracture surface is indeed fractal over two orders of magnitudes with a dimension of approximately 1.20. ?? 1990.

a Fractal Analysis for Net Present Value of Multi-Stage Hydraulic Fractured Horizontal Well

NASA Astrophysics Data System (ADS)

Lu, Hong-Lin; Zhang, Ji-Jun; Tan, Xiao-Hua; Li, Xiao-Ping; Zhao, Jia-Hui

Because of the low permeability, multi-stage hydraulic fractured horizontal wells (MHFHWs) occupy a dominant position among production wells in tight gas reservoir. However, net present value (NPV) estimation method for MHFHW in tight gas reservoirs often ignores the effect of heterogeneity in microscopic pore structure. Apart from that, a new fractal model is presented for NPV of MHFHW, based on the fractal expressions of formation parameters. First, with the aid of apparent permeability model, a pseudo pressure expression considering both reservoir fractal features and slippage effect is derived, contributing to establish the productivity model. Secondly, economic assessment method is built based on the fractal productivity model, in order to obtain the NPV of MHFHW. Thirdly, the type curves are illustrated and the influences of different fractal parameters are discussed. The pore fractal dimensions Df and the capillary tortuosity fractal dimensions DT have significant effects on the NPV of an MHFHW. Finally, the proposed model in this paper provides a new methodology for analyzing and predicting the NPV of an MHFHW and may be conducive to a better understanding of the optimal design of MHFHW.

Fractal Theory and Field Cover Experiments: Implications for the Fractal Characteristics and Radon Diffusion Behavior of Soils and Rocks.

PubMed

Tan, Wanyu; Li, Yongmei; Tan, Kaixuan; Duan, Xianzhe; Liu, Dong; Liu, Zehua

2016-12-01

Radon diffusion and transport through different media is a complex process affected by many factors. In this study, the fractal theories and field covering experiments were used to study the fractal characteristics of particle size distribution (PSD) of six kinds of geotechnical materials (e.g., waste rock, sand, laterite, kaolin, mixture of sand and laterite, and mixture of waste rock and laterite) and their effects on radon diffusion. In addition, the radon diffusion coefficient and diffusion length were calculated. Moreover, new formulas for estimating diffusion coefficient and diffusion length functional of fractal dimension d of PSD were proposed. These results demonstrate the following points: (1) the fractal dimension d of the PSD can be used to characterize the property of soils and rocks in the studies of radon diffusion behavior; (2) the diffusion coefficient and diffusion length decrease with increasing fractal dimension of PSD; and (3) the effectiveness of final covers in reducing radon exhalation of uranium tailings impoundments can be evaluated on the basis of the fractal dimension of PSD of materials.

Anisotropic fractal media by vector calculus in non-integer dimensional space

NASA Astrophysics Data System (ADS)

Tarasov, Vasily E.

2014-08-01

A review of different approaches to describe anisotropic fractal media is proposed. In this paper, differentiation and integration non-integer dimensional and multi-fractional spaces are considered as tools to describe anisotropic fractal materials and media. We suggest a generalization of vector calculus for non-integer dimensional space by using a product measure method. The product of fractional and non-integer dimensional spaces allows us to take into account the anisotropy of the fractal media in the framework of continuum models. The integration over non-integer-dimensional spaces is considered. In this paper differential operators of first and second orders for fractional space and non-integer dimensional space are suggested. The differential operators are defined as inverse operations to integration in spaces with non-integer dimensions. Non-integer dimensional space that is product of spaces with different dimensions allows us to give continuum models for anisotropic type of the media. The Poisson's equation for fractal medium, the Euler-Bernoulli fractal beam, and the Timoshenko beam equations for fractal material are considered as examples of application of suggested generalization of vector calculus for anisotropic fractal materials and media.

Delay-Encoded Harmonic Imaging (DE-HI) in Multiplane-Wave Compounding.

PubMed

Gong, Ping; Song, Pengfei; Chen, Shigao

2017-04-01

The development of ultrafast ultrasound imaging brings great opportunities to improve imaging technologies such as shear wave elastography and ultrafast Doppler imaging. In ultrafast imaging, several tilted plane or diverging wave images are coherently combined to form a compounded image, leading to trade-offs among image signal-to-noise ratio (SNR), resolution, and post-compounded frame rate. Multiplane wave (MW) imaging is proposed to solve this trade-off by encoding multiple plane waves with Hadamard matrix during one transmission event (i.e. pulse-echo event), to improve image SNR without sacrificing the resolution or frame rate. However, it suffers from stronger reverberation artifacts in B-mode images compared to standard plane wave compounding due to longer transmitted pulses. If harmonic imaging can be combined with MW imaging, the reverberation artifacts and other clutter noises such as sidelobes and multipath scattering clutters should be suppressed. The challenge, however, is that the Hadamard codes used in MW imaging cannot encode the 2 nd harmonic component by inversing the pulse polarity. In this paper, we propose a delay-encoded harmonic imaging (DE-HI) technique to encode the 2 nd harmonic with a one quarter period delay calculated at the transmit center frequency, rather than reversing the pulse polarity during multiplane wave emissions. Received DE-HI signals can then be decoded in the frequency domain to recover the signals as in single plane wave emissions, but mainly with improved SNR at the 2 nd harmonic component instead of the fundamental component. DE-HI was tested experimentally with a point target, a B-mode imaging phantom, and in-vivo human liver imaging. Improvements in image contrast-to-noise ratio (CNR), spatial resolution, and lesion-signal-to-noise ratio ( l SNR) have been achieved compared to standard plane wave compounding, MW imaging, and standard harmonic imaging (maximal improvement of 116% on CNR and 115% on l SNR as compared to standard HI around 55 mm depth in the B-mode imaging phantom study). The potential high frame rate and the stability of encoding and decoding processes of DE-HI were also demonstrated, which made DE-HI promising for a wide spectrum of imaging applications.

A novel attack method about double-random-phase-encoding-based image hiding method

NASA Astrophysics Data System (ADS)

Xu, Hongsheng; Xiao, Zhijun; Zhu, Xianchen

2018-03-01

By using optical image processing techniques, a novel text encryption and hiding method applied by double-random phase-encoding technique is proposed in the paper. The first step is that the secret message is transformed into a 2-dimension array. The higher bits of the elements in the array are used to fill with the bit stream of the secret text, while the lower bits are stored specific values. Then, the transformed array is encoded by double random phase encoding technique. Last, the encoded array is embedded on a public host image to obtain the image embedded with hidden text. The performance of the proposed technique is tested via analytical modeling and test data stream. Experimental results show that the secret text can be recovered either accurately or almost accurately, while maintaining the quality of the host image embedded with hidden data by properly selecting the method of transforming the secret text into an array and the superimposition coefficient.

Prediction of pork quality parameters by applying fractals and data mining on MRI.

PubMed

Caballero, Daniel; Pérez-Palacios, Trinidad; Caro, Andrés; Amigo, José Manuel; Dahl, Anders B; ErsbØll, Bjarne K; Antequera, Teresa

2017-09-01

This work firstly investigates the use of MRI, fractal algorithms and data mining techniques to determine pork quality parameters non-destructively. The main objective was to evaluate the capability of fractal algorithms (Classical Fractal algorithm, CFA; Fractal Texture Algorithm, FTA and One Point Fractal Texture Algorithm, OPFTA) to analyse MRI in order to predict quality parameters of loin. In addition, the effect of the sequence acquisition of MRI (Gradient echo, GE; Spin echo, SE and Turbo 3D, T3D) and the predictive technique of data mining (Isotonic regression, IR and Multiple linear regression, MLR) were analysed. Both fractal algorithm, FTA and OPFTA are appropriate to analyse MRI of loins. The sequence acquisition, the fractal algorithm and the data mining technique seems to influence on the prediction results. For most physico-chemical parameters, prediction equations with moderate to excellent correlation coefficients were achieved by using the following combinations of acquisition sequences of MRI, fractal algorithms and data mining techniques: SE-FTA-MLR, SE-OPFTA-IR, GE-OPFTA-MLR, SE-OPFTA-MLR, with the last one offering the best prediction results. Thus, SE-OPFTA-MLR could be proposed as an alternative technique to determine physico-chemical traits of fresh and dry-cured loins in a non-destructive way with high accuracy. Copyright © 2017. Published by Elsevier Ltd.

The fractal nature of vacuum arc cathode spots

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

Anders, Andre

2005-05-27

Cathode spot phenomena show many features of fractals, for example self-similar patterns in the emitted light and arc erosion traces. Although there have been hints on the fractal nature of cathode spots in the literature, the fractal approach to spot interpretation is underutilized. In this work, a brief review of spot properties is given, touching the differences between spot type 1 (on cathodes surfaces with dielectric layers) and spot type 2 (on metallic, clean surfaces) as well as the known spot fragment or cell structure. The basic properties of self-similarity, power laws, random colored noise, and fractals are introduced. Severalmore » points of evidence for the fractal nature of spots are provided. Specifically power laws are identified as signature of fractal properties, such as spectral power of noisy arc parameters (ion current, arc voltage, etc) obtained by fast Fourier transform. It is shown that fractal properties can be observed down to the cutoff by measurement resolution or occurrence of elementary steps in physical processes. Random walk models of cathode spot motion are well established: they go asymptotically to Brownian motion for infinitesimal step width. The power spectrum of the arc voltage noise falls as 1/f {sup 2}, where f is frequency, supporting a fractal spot model associated with Brownian motion.« less

Directional fractal signature methods for trabecular bone texture in hand radiographs: Data from the Osteoarthritis Initiative

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

Wolski, M., E-mail: marcin.wolski@curtin.edu.au; Podsiadlo, P.; Stachowiak, G. W.

Purpose: To develop directional fractal signature methods for the analysis of trabecular bone (TB) texture in hand radiographs. Problems associated with the small size of hand bones and the orientation of fingers were addressed. Methods: An augmented variance orientation transform (AVOT) and a quadrant rotating grid (QRG) methods were developed. The methods calculate fractal signatures (FSs) in different directions. Unlike other methods they have the search region adjusted according to the size of bone region of interest (ROI) to be analyzed and they produce FSs defined with respect to any chosen reference direction, i.e., they work for arbitrary orientation ofmore » fingers. Five parameters at scales ranging from 2 to 14 pixels (depending on image size and method) were derived from rose plots of Hurst coefficients, i.e., FS in dominating roughness (FS{sub Sta}), vertical (FS{sub V}) and horizontal (FS{sub H}) directions, aspect ratio (StrS), and direction signatures (StdS), respectively. The accuracy in measuring surface roughness and isotropy/anisotropy was evaluated using 3600 isotropic and 800 anisotropic fractal surface images of sizes between 20 × 20 and 64 × 64 pixels. The isotropic surfaces had FDs ranging from 2.1 to 2.9 in steps of 0.1, and the anisotropic surfaces had two dominating directions of 30° and 120°. The methods were used to find differences in hand TB textures between 20 matched pairs of subjects with (cases: approximate Kellgren-Lawrence (KL) grade ≥2) and without (controls: approximate KL grade <2) radiographic hand osteoarthritis (OA). The OA Initiative public database was used and 20 × 20 pixel bone ROIs were selected on 5th distal and middle phalanges. The performance of the AVOT and QRG methods was compared against a variance orientation transform (VOT) method developed earlier [M. Wolski, P. Podsiadlo, and G. W. Stachowiak, “Directional fractal signature analysis of trabecular bone: evaluation of different methods to detect early osteoarthritis in knee radiographs,” Proc. Inst. Mech. Eng., Part H 223, 211–236 (2009)]. Results: The AVOT method correctly quantified the isotropic and anisotropic surfaces for all image sizes and scales. Values of FS{sub Sta} were significantly different (P < 0.05) between the isotropic surfaces. Using the VOT and QRG methods no differences were found at large scales for the isotropic surfaces that are smaller than 64 × 64 and 48 × 48 pixels, respectively, and at some scales for the anisotropic surfaces with size 48 × 48 pixels. Compared to controls, using the AVOT and QRG methods the authors found that OA TB textures were less rough (P < 0.05) in the dominating and horizontal directions (i.e., lower FS{sub Sta} and FS{sub H}), rougher in the vertical direction (i.e., higher FS{sub V}) and less anisotropic (i.e., higher StrS) than controls. No differences were found using the VOT method. Conclusions: The AVOT method is well suited for the analysis of bone texture in hand radiographs and it could be potentially useful for early detection and prediction of hand OA.« less

Space-time encoding for high frame rate ultrasound imaging.

PubMed

Misaridis, Thanassis X; Jensen, Jørgen A

2002-05-01

Frame rate in ultrasound imaging can be dramatically increased by using sparse synthetic transmit aperture (STA) beamforming techniques. The two main drawbacks of the method are the low signal-to-noise ratio (SNR) and the motion artifacts, that degrade the image quality. In this paper we propose a spatio-temporal encoding for STA imaging based on simultaneous transmission of two quasi-orthogonal tapered linear FM signals. The excitation signals are an up- and a down-chirp with frequency division and a cross-talk of -55 dB. The received signals are first cross-correlated with the appropriate code, then spatially decoded and finally beamformed for each code, yielding two images per emission. The spatial encoding is a Hadamard encoding previously suggested by Chiao et al. [in: Proceedings of the IEEE Ultrasonics Symposium, 1997, p. 1679]. The Hadamard matrix has half the size of the transmit element groups, due to the orthogonality of the temporal encoded wavefronts. Thus, with this method, the frame rate is doubled compared to previous systems. Another advantage is the utilization of temporal codes which are more robust to attenuation. With the proposed technique it is possible to obtain images dynamically focused in both transmit and receive with only two firings. This reduces the problem of motion artifacts. The method has been tested with extensive simulations using Field II. Resolution and SNR are compared with uncoded STA imaging and conventional phased-array imaging. The range resolution remains the same for coded STA imaging with four emissions and is slightly degraded for STA imaging with two emissions due to the -55 dB cross-talk between the signals. The additional proposed temporal encoding adds more than 15 dB on the SNR gain, yielding a SNR at the same order as in phased-array imaging.

Quantitative assessment of early diabetic retinopathy using fractal analysis.

PubMed

Cheung, Ning; Donaghue, Kim C; Liew, Gerald; Rogers, Sophie L; Wang, Jie Jin; Lim, Shueh-Wen; Jenkins, Alicia J; Hsu, Wynne; Li Lee, Mong; Wong, Tien Y

2009-01-01

Fractal analysis can quantify the geometric complexity of the retinal vascular branching pattern and may therefore offer a new method to quantify early diabetic microvascular damage. In this study, we examined the relationship between retinal fractal dimension and retinopathy in young individuals with type 1 diabetes. We conducted a cross-sectional study of 729 patients with type 1 diabetes (aged 12-20 years) who had seven-field stereoscopic retinal photographs taken of both eyes. From these photographs, retinopathy was graded according to the modified Airlie House classification, and fractal dimension was quantified using a computer-based program following a standardized protocol. In this study, 137 patients (18.8%) had diabetic retinopathy signs; of these, 105 had mild retinopathy. Median (interquartile range) retinal fractal dimension was 1.46214 (1.45023-1.47217). After adjustment for age, sex, diabetes duration, A1C, blood pressure, and total cholesterol, increasing retinal vascular fractal dimension was significantly associated with increasing odds of retinopathy (odds ratio 3.92 [95% CI 2.02-7.61] for fourth versus first quartile of fractal dimension). In multivariate analysis, each 0.01 increase in retinal vascular fractal dimension was associated with a nearly 40% increased odds of retinopathy (1.37 [1.21-1.56]). This association remained after additional adjustment for retinal vascular caliber. Greater retinal fractal dimension, representing increased geometric complexity of the retinal vasculature, is independently associated with early diabetic retinopathy signs in type 1 diabetes. Fractal analysis of fundus photographs may allow quantitative measurement of early diabetic microvascular damage.

The fractal geometry of life.

PubMed

Losa, Gabriele A

2009-01-01

The extension of the concepts of Fractal Geometry (Mandelbrot [1983]) toward the life sciences has led to significant progress in understanding complex functional properties and architectural / morphological / structural features characterising cells and tissues during ontogenesis and both normal and pathological development processes. It has even been argued that fractal geometry could provide a coherent description of the design principles underlying living organisms (Weibel [1991]). Fractals fulfil a certain number of theoretical and methodological criteria including a high level of organization, shape irregularity, functional and morphological self-similarity, scale invariance, iterative pathways and a peculiar non-integer fractal dimension [FD]. Whereas mathematical objects are deterministic invariant or self-similar over an unlimited range of scales, biological components are statistically self-similar only within a fractal domain defined by upper and lower limits, called scaling window, in which the relationship between the scale of observation and the measured size or length of the object can be established (Losa and Nonnenmacher [1996]). Selected examples will contribute to depict complex biological shapes and structures as fractal entities, and also to show why the application of the fractal principle is valuable for measuring dimensional, geometrical and functional parameters of cells, tissues and organs occurring within the vegetal and animal realms. If the criteria for a strict description of natural fractals are met, then it follows that a Fractal Geometry of Life may be envisaged and all natural objects and biological systems exhibiting self-similar patterns and scaling properties may be considered as belonging to the new subdiscipline of "fractalomics".

Fractal Characteristics of Pores in Taiyuan Formation Shale from Hedong Coal Field, China

NASA Astrophysics Data System (ADS)

Li, Kunjie; Zeng, Fangui; Cai, Jianchao; Sheng, Guanglong; Xia, Peng; Zhang, Kun

For the purpose of investigating the fractal characteristics of pores in Taiyuan formation shale, a series of qualitative and quantitative experiments were conducted on 17 shale samples from well HD-1 in Hedong coal field of North China. The results of geochemical experiments show that Total organic carbon (TOC) varies from 0.67% to 5.32% and the organic matters are in the high mature or over mature stage. The shale samples consist mainly of clay minerals and quartz with minor pyrite and carbonates. The FE-SEM images indicate that three types of pores, organic-related pores, inorganic-related pores and micro-fractures related pores, are developed well, and a certain number of intragranular pores are found inside quartz and carbonates formed by acid liquid corrosion. The pore size distributions (PSDs) broadly range from several to hundreds nanometers, but most pores are smaller than 10nm. As the result of different adsorption features at relative pressure (0-0.5) and (0.5-1) on the N2 adsorption isotherm, two fractal dimensions D1 and D2 were obtained with the Frenkel-Halsey-Hill (FHH) model. D1 and D2 vary from 2.4227 to 2.6219 and from 2.6049 to 2.7877, respectively. Both TOC and brittle minerals have positive effect on D1 and D2, whereas clay minerals, have a negative influence on them. The fractal dimensions are also influenced by the pore structure parameters, such as the specific surface area, BJH pore volume, etc. Shale samples with higher D1 could provide more adsorption sites leading to a greater methane adsorption capacity, whereas shale samples with higher D2 have little influence on methane adsorption capacity.

Investigation of the Fractal Geometry of Tundra Lake Patterns using Historical Topographic Maps and Satellite Imagery.

NASA Astrophysics Data System (ADS)

Kariyawasam, T.; Essa, A.; Gong, M.; Sudakov, I.

2017-12-01

Greenhouse gas emissions from tundra lakes are a significant positive feedback to the atmosphere in a changing climate as a pronounced growth of the numbers of tundra lake patterns has been observed in the Arctic region. Detailed knowledge of spatial dynamics of lake patterns in a changing arctic tundra landscape and their geometrical properties is therefore potentially valuable, in order to understand and accurately model the sources of greenhouse gas emissions from boreal permafrost. Our goal is to use a collection of historical topographic maps and satellite imagery of tundra lakes to conduct computational image analyses for examining spatial dynamics of Tundra lake patterns. Our approach is based upon analyzing area-perimeter data of thousands of tundra lakes to compute the fractal dimension to study the tundra lake pattern geometry, which have been used to classify pollen grains by textual patterning (Mander, 2016), vegetation in dryland ecosystems (Mander, 2017) and melt pond patterns (Hohenegger, 2012). By analyzing area - perimeter data for over 900 lakes we find that for both historical topographic maps and current satellite imagery, the fractal dimension D is stable at 1.6 for Tundra lakes with area less than about 100km2. For Tundra lake sizes bigger than 100 km2 fractal dimension takes values close to 2 and less than one indicative of structural changes in Tundra lake pattern geometry. Furthermore the current study did not reveal any percolation transition above some critical threshold in Tundra lake evolution. The results of the study will provide scientists with new data on these aspects of tundra lakes to help characterize the geomorphology of spatial patterns in arctic tundra lakes.

Image barcodes

NASA Astrophysics Data System (ADS)

Damera-Venkata, Niranjan; Yen, Jonathan

2003-01-01

A Visually significant two-dimensional barcode (VSB) developed by Shaked et. al. is a method used to design an information carrying two-dimensional barcode, which has the appearance of a given graphical entity such as a company logo. The encoding and decoding of information using the VSB, uses a base image with very few graylevels (typically only two). This typically requires the image histogram to be bi-modal. For continuous-tone images such as digital photographs of individuals, the representation of tone or "shades of gray" is not only important to obtain a pleasing rendition of the face, but in most cases, the VSB renders these images unrecognizable due to its inability to represent true gray-tone variations. This paper extends the concept of a VSB to an image bar code (IBC). We enable the encoding and subsequent decoding of information embedded in the hardcopy version of continuous-tone base-images such as those acquired with a digital camera. The encoding-decoding process is modeled by robust data transmission through a noisy print-scan channel that is explicitly modeled. The IBC supports a high information capacity that differentiates it from common hardcopy watermarks. The reason for the improved image quality over the VSB is a joint encoding/halftoning strategy based on a modified version of block error diffusion. Encoder stability, image quality vs. information capacity tradeoffs and decoding issues with and without explicit knowledge of the base-image are discussed.

Externally calibrated parallel imaging for 3D multispectral imaging near metallic implants using broadband ultrashort echo time imaging.

PubMed

Wiens, Curtis N; Artz, Nathan S; Jang, Hyungseok; McMillan, Alan B; Reeder, Scott B

2017-06-01

To develop an externally calibrated parallel imaging technique for three-dimensional multispectral imaging (3D-MSI) in the presence of metallic implants. A fast, ultrashort echo time (UTE) calibration acquisition is proposed to enable externally calibrated parallel imaging techniques near metallic implants. The proposed calibration acquisition uses a broadband radiofrequency (RF) pulse to excite the off-resonance induced by the metallic implant, fully phase-encoded imaging to prevent in-plane distortions, and UTE to capture rapidly decaying signal. The performance of the externally calibrated parallel imaging reconstructions was assessed using phantoms and in vivo examples. Phantom and in vivo comparisons to self-calibrated parallel imaging acquisitions show that significant reductions in acquisition times can be achieved using externally calibrated parallel imaging with comparable image quality. Acquisition time reductions are particularly large for fully phase-encoded methods such as spectrally resolved fully phase-encoded three-dimensional (3D) fast spin-echo (SR-FPE), in which scan time reductions of up to 8 min were obtained. A fully phase-encoded acquisition with broadband excitation and UTE enabled externally calibrated parallel imaging for 3D-MSI, eliminating the need for repeated calibration regions at each frequency offset. Significant reductions in acquisition time can be achieved, particularly for fully phase-encoded methods like SR-FPE. Magn Reson Med 77:2303-2309, 2017. © 2016 International Society for Magnetic Resonance in Medicine. © 2016 International Society for Magnetic Resonance in Medicine.

Virtually distortion-free imaging system for large field, high resolution lithography

DOEpatents

Hawryluk, A.M.; Ceglio, N.M.

1993-01-05

Virtually distortion free large field high resolution imaging is performed using an imaging system which contains large field distortion or field curvature. A reticle is imaged in one direction through the optical system to form an encoded mask. The encoded mask is then imaged back through the imaging system onto a wafer positioned at the reticle position.

Virtually distortion-free imaging system for large field, high resolution lithography

DOEpatents

Hawryluk, Andrew M.; Ceglio, Natale M.

1993-01-01

Virtually distortion free large field high resolution imaging is performed using an imaging system which contains large field distortion or field curvature. A reticle is imaged in one direction through the optical system to form an encoded mask. The encoded mask is then imaged back through the imaging system onto a wafer positioned at the reticle position.

The Effect of Impeller Type on Floc Size and Structure during Shear-Induced Flocculation

PubMed

Spicer; Keller; Pratsinis

1996-12-01

The effect of impeller type and shear rate on the evolution of floc size and structure during shear-induced flocculation of polystyrene particles with aluminum sulfate is investigated by image analysis. One radial flow (six-blade Rushton turbine) and two axial flow (three-blade fluid foil, four-blade 45° pitch) impeller configurations are examined. The steady state average floc size is shown to depend on the frequency of recirculation to the impeller zone and its characteristic velocity gradient. The concepts of fractal geometry are used to characterize the floc structure. For all impellers, the two-dimensional floc fractal dimension, Dpf, increases during floc growth, indicating formation of more open structures. Later on, Dpf levels off at a steady state value as breakage becomes significant and the floc size distribution approaches steady state. The shear rate does not affect the steady state Dpf of the flocs within experimental uncertainty.

Chimera states in brain networks: Empirical neural vs. modular fractal connectivity

NASA Astrophysics Data System (ADS)

Chouzouris, Teresa; Omelchenko, Iryna; Zakharova, Anna; Hlinka, Jaroslav; Jiruska, Premysl; Schöll, Eckehard

2018-04-01

Complex spatiotemporal patterns, called chimera states, consist of coexisting coherent and incoherent domains and can be observed in networks of coupled oscillators. The interplay of synchrony and asynchrony in complex brain networks is an important aspect in studies of both the brain function and disease. We analyse the collective dynamics of FitzHugh-Nagumo neurons in complex networks motivated by its potential application to epileptology and epilepsy surgery. We compare two topologies: an empirical structural neural connectivity derived from diffusion-weighted magnetic resonance imaging and a mathematically constructed network with modular fractal connectivity. We analyse the properties of chimeras and partially synchronized states and obtain regions of their stability in the parameter planes. Furthermore, we qualitatively simulate the dynamics of epileptic seizures and study the influence of the removal of nodes on the network synchronizability, which can be useful for applications to epileptic surgery.

Scaling in geology: landforms and earthquakes.

PubMed Central

Turcotte, D L

1995-01-01

Landforms and earthquakes appear to be extremely complex; yet, there is order in the complexity. Both satisfy fractal statistics in a variety of ways. A basic question is whether the fractal behavior is due to scale invariance or is the signature of a broadly applicable class of physical processes. Both landscape evolution and regional seismicity appear to be examples of self-organized critical phenomena. A variety of statistical models have been proposed to model landforms, including diffusion-limited aggregation, self-avoiding percolation, and cellular automata. Many authors have studied the behavior of multiple slider-block models, both in terms of the rupture of a fault to generate an earthquake and in terms of the interactions between faults associated with regional seismicity. The slider-block models exhibit a remarkably rich spectrum of behavior; two slider blocks can exhibit low-order chaotic behavior. Large numbers of slider blocks clearly exhibit self-organized critical behavior. Images Fig. 6 PMID:11607562

Correlation estimation and performance optimization for distributed image compression

NASA Astrophysics Data System (ADS)

He, Zhihai; Cao, Lei; Cheng, Hui

2006-01-01

Correlation estimation plays a critical role in resource allocation and rate control for distributed data compression. A Wyner-Ziv encoder for distributed image compression is often considered as a lossy source encoder followed by a lossless Slepian-Wolf encoder. The source encoder consists of spatial transform, quantization, and bit plane extraction. In this work, we find that Gray code, which has been extensively used in digital modulation, is able to significantly improve the correlation between the source data and its side information. Theoretically, we analyze the behavior of Gray code within the context of distributed image compression. Using this theoretical model, we are able to efficiently allocate the bit budget and determine the code rate of the Slepian-Wolf encoder. Our experimental results demonstrate that the Gray code, coupled with accurate correlation estimation and rate control, significantly improves the picture quality, by up to 4 dB, over the existing methods for distributed image compression.

Fractal tomography and its application in 3D vision

NASA Astrophysics Data System (ADS)

Trubochkina, N.

2018-01-01

A three-dimensional artistic fractal tomography method that implements a non-glasses 3D visualization of fractal worlds in layered media is proposed. It is designed for the glasses-free 3D vision of digital art objects and films containing fractal content. Prospects for the development of this method in art galleries and the film industry are considered.

Electro-chemical manifestation of nanoplasmonics in fractal media

NASA Astrophysics Data System (ADS)

Baskin, Emmanuel; Iomin, Alexander

2013-06-01

Electrodynamics of composite materials with fractal geometry is studied in the framework of fractional calculus. This consideration establishes a link between fractal geometry of the media and fractional integrodifferentiation. The photoconductivity in the vicinity of the electrode-electrolyte fractal interface is studied. The methods of fractional calculus are employed to obtain an analytical expression for the giant local enhancement of the optical electric field inside the fractal composite structure at the condition of the surface plasmon excitation. This approach makes it possible to explain experimental data on photoconductivity in the nano-electrochemistry.

Study on Conversion Between Momentum and Contrarian Based on Fractal Game

NASA Astrophysics Data System (ADS)

Wu, Xu; Song, Guanghui; Deng, Yan; Xu, Lin

2015-06-01

Based on the fractal game which is performed by the majority and the minority, the fractal market theory (FMT) is employed to describe the features of investors' decision-making. Accordingly, the process of fractal games is formed in order to analyze the statistical features of conversion between momentum and contrarian. The result shows that among three fractal game mechanisms, the statistical feature of simulated return rate series is much more similar to log returns on actual series. In addition, the conversion between momentum and contrarian is also extremely similar to real situation, which can reflect the effectiveness of using fractal game in analyzing the conversion between momentum and contrarian. Moreover, it also provides decision-making reference which helps investors develop effective investment strategy.

Numerical study of electromagnetic scattering from one-dimensional nonlinear fractal sea surface

NASA Astrophysics Data System (ADS)

Xie, Tao; He, Chao; William, Perrie; Kuang, Hai-Lan; Zou, Guang-Hui; Chen, Wei

2010-02-01

In recent years, linear fractal sea surface models have been developed for the sea surface in order to establish an electromagnetic backscattering model. Unfortunately, the sea surface is always nonlinear, particularly at high sea states. We present a nonlinear fractal sea surface model and derive an electromagnetic backscattering model. Using this model, we numerically calculate the normalized radar cross section (NRCS) of a nonlinear sea surface. Comparing the averaged NRCS between linear and nonlinear fractal models, we show that the NRCS of a linear fractal sea surface underestimates the NRCS of the real sea surface, especially for sea states with high fractal dimensions, and for dominant ocean surface gravity waves that are either very short or extremely long.

Binary image encryption in a joint transform correlator scheme by aid of run-length encoding and QR code

NASA Astrophysics Data System (ADS)

Qin, Yi; Wang, Zhipeng; Wang, Hongjuan; Gong, Qiong

2018-07-01

We propose a binary image encryption method in joint transform correlator (JTC) by aid of the run-length encoding (RLE) and Quick Response (QR) code, which enables lossless retrieval of the primary image. The binary image is encoded with RLE to obtain the highly compressed data, and then the compressed binary image is further scrambled using a chaos-based method. The compressed and scrambled binary image is then transformed into one QR code that will be finally encrypted in JTC. The proposed method successfully, for the first time to our best knowledge, encodes a binary image into a QR code with the identical size of it, and therefore may probe a new way for extending the application of QR code in optical security. Moreover, the preprocessing operations, including RLE, chaos scrambling and the QR code translation, append an additional security level on JTC. We present digital results that confirm our approach.

Implementation of digital image encryption algorithm using logistic function and DNA encoding

NASA Astrophysics Data System (ADS)

Suryadi, MT; Satria, Yudi; Fauzi, Muhammad

2018-03-01

Cryptography is a method to secure information that might be in form of digital image. Based on past research, in order to increase security level of chaos based encryption algorithm and DNA based encryption algorithm, encryption algorithm using logistic function and DNA encoding was proposed. Digital image encryption algorithm using logistic function and DNA encoding use DNA encoding to scramble the pixel values into DNA base and scramble it in DNA addition, DNA complement, and XOR operation. The logistic function in this algorithm used as random number generator needed in DNA complement and XOR operation. The result of the test show that the PSNR values of cipher images are 7.98-7.99 bits, the entropy values are close to 8, the histogram of cipher images are uniformly distributed and the correlation coefficient of cipher images are near 0. Thus, the cipher image can be decrypted perfectly and the encryption algorithm has good resistance to entropy attack and statistical attack.

An edge preserving differential image coding scheme

NASA Technical Reports Server (NTRS)

Rost, Martin C.; Sayood, Khalid

1992-01-01

Differential encoding techniques are fast and easy to implement. However, a major problem with the use of differential encoding for images is the rapid edge degradation encountered when using such systems. This makes differential encoding techniques of limited utility, especially when coding medical or scientific images, where edge preservation is of utmost importance. A simple, easy to implement differential image coding system with excellent edge preservation properties is presented. The coding system can be used over variable rate channels, which makes it especially attractive for use in the packet network environment.

Data Embedding for Covert Communications, Digital Watermarking, and Information Augmentation

DTIC Science & Technology

2000-03-01

proposed an image authentication algorithm based on the fragility of messages embedded in digital images using LSB encoding. In [Walt95], he proposes...Invertibility 2/ 3 SAMPLE DATA EMBEDDING TECHNIQUES 23 3.1 SPATIAL TECHNIQUES 23 LSB Encoding in Intensity Images 23 Data embedding...ATTACK 21 FIGURE 6. EFFECTS OF LSB ENCODING 25 FIGURE 7. ALGORITHM FOR EZSTEGO 28 FIGURE 8. DATA EMBEDDING IN THE FREQUENCY DOMAIN 30 FIGURE 9

Encoding processes during retrieval tasks.

PubMed

Buckner, R L; Wheeler, M E; Sheridan, M A

2001-04-01

Episodic memory encoding is pervasive across many kinds of task and often arises as a secondary processing effect in tasks that do not require intentional memorization. To illustrate the pervasive nature of information processing that leads to episodic encoding, a form of incidental encoding was explored based on the "Testing" phenomenon: The incidental-encoding task was an episodic memory retrieval task. Behavioral data showed that performing a memory retrieval task was as effective as intentional instructions at promoting episodic encoding. During fMRI imaging, subjects viewed old and new words and indicated whether they remembered them. Relevant to encoding, the fate of the new words was examined using a second, surprise test of recognition after the imaging session. fMRI analysis of those new words that were later remembered revealed greater activity in left frontal regions than those that were later forgotten - the same pattern of results as previously observed for traditional incidental and intentional episodic encoding tasks. This finding may offer a partial explanation for why repeated testing improves memory performance. Furthermore, the observation of correlates of episodic memory encoding during retrieval tasks challenges some interpretations that arise from direct comparisons between "encoding tasks" and "retrieval tasks" in imaging data. Encoding processes and their neural correlates may arise in many tasks, even those nominally labeled as retrieval tasks by the experimenter.

Fractual interrelationships in field and seismic data. Final report

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

NONE

1997-01-07

Fractals provide a description of physical patterns over a range of scales in both time and space. Studies presented herein examine the fractal characteristics of various geological variables such as deformed bed-lengths, fold relief, seismic reflection arrival time variations, drainage and topographic patterns, and fracture systems. The studies are also extended to consider the possibility that the fractal characteristics of these variables are interrelated. Fractal interrelationships observed in these studies provide a method for relating variations in the fractal characteristics of seismic reflection events from reservoir intervals to the fractal characteristics of reservoir fracture systems, faults, and fold distributions. Themore » work is motivated by current exploration and development interests to detect fractured reservoirs and to accurately predict flow rates and flow patterns within the fractured reservoir. Accurate prediction requires an understanding of several reservoir properties including the fractal geometry of the reservoir fracture network. Results of these studies provide a method to remotely assess the fractal characteristics of a fractured reservoir, and help guide field development activities. The most significant outgrowth of this research is that the fractal properties of structural relief inferred from seismic data and structural cross sections provide a quantitative means to characterize and compare complex structural patterns. Production from fractured reservoirs is the result of complex structural and stratigraphic controls; hence, the import of fractal characterization to the assessment of fractured reservoirs lies in its potential to quantitatively define interrelationships between subtle structural variation and production. The potential uses are illustrated using seismic data from the Granny Creek oil field in the Appalachian Plateau.« less

Fractal density modeling of crustal heterogeneity from the KTB deep hole

NASA Astrophysics Data System (ADS)

Chen, Guoxiong; Cheng, Qiuming

2017-03-01

Fractal or multifractal concepts have significantly enlightened our understanding of crustal heterogeneity. Much attention has focused on 1/f scaling natures of physicochemical heterogeneity of Earth crust from fractal increment perspective. In this study, fractal density model from fractal clustering point of view is used to characterize the scaling behaviors of heterogeneous sources recorded at German Continental Deep Drilling Program (KTB) main hole, and of special contribution is the local and global multifractal analysis revisited by using Haar wavelet transform (HWT). Fractal density modeling of mass accumulation generalizes the unit of rock density from integer (e.g., g/cm3) to real numbers (e.g., g/cmα), so that crustal heterogeneities with respect to source accumulation are quantified by singularity strength of fractal density in α-dimensional space. From that perspective, we found that the bulk densities of metamorphic rocks exhibit fractal properties but have a weak multifractality, decreasing with the depth. The multiscaling natures of chemical logs also have been evidenced, and the observed distinct fractal laws for mineral contents are related to their different geochemical behaviors within complex lithological context. Accordingly, scaling distributions of mineral contents have been recognized as a main contributor to the multifractal natures of heterogeneous density for low-porosity crystalline rocks. This finally allows us to use de Wijs cascade process to explain the mechanism of fractal density. In practice, the proposed local singularity analysis based on HWT is suggested as an attractive high-pass filtering to amplify weak signatures of well logs as well as to delineate microlithological changes.

Estimation of soil saturated hydraulic conductivity by artificial neural networks ensemble in smectitic soils

NASA Astrophysics Data System (ADS)

Sedaghat, A.; Bayat, H.; Safari Sinegani, A. A.

2016-03-01

The saturated hydraulic conductivity ( K s ) of the soil is one of the main soil physical properties. Indirect estimation of this parameter using pedo-transfer functions (PTFs) has received considerable attention. The Purpose of this study was to improve the estimation of K s using fractal parameters of particle and micro-aggregate size distributions in smectitic soils. In this study 260 disturbed and undisturbed soil samples were collected from Guilan province, the north of Iran. The fractal model of Bird and Perrier was used to compute the fractal parameters of particle and micro-aggregate size distributions. The PTFs were developed by artificial neural networks (ANNs) ensemble to estimate K s by using available soil data and fractal parameters. There were found significant correlations between K s and fractal parameters of particles and microaggregates. Estimation of K s was improved significantly by using fractal parameters of soil micro-aggregates as predictors. But using geometric mean and geometric standard deviation of particles diameter did not improve K s estimations significantly. Using fractal parameters of particles and micro-aggregates simultaneously, had the most effect in the estimation of K s . Generally, fractal parameters can be successfully used as input parameters to improve the estimation of K s in the PTFs in smectitic soils. As a result, ANNs ensemble successfully correlated the fractal parameters of particles and micro-aggregates to K s .

Investigation of diamond wheel topography in Elliptical Ultrasonic Assisted Grinding (EUAG) of monocrystal sapphire using fractal analysis method.

PubMed

Wang, Qiuyan; Zhao, Wenxiang; Liang, Zhiqiang; Wang, Xibin; Zhou, Tianfeng; Wu, Yongbo; Jiao, Li

2018-03-01

The wear behaviors of grinding wheel have significant influence on the work-surface topography. However, a comprehensive and quantitative method is lacking for evaluating the wear conditions of grinding wheel. In this paper, a fractal analysis method is used to investigate the wear behavior of resin-bonded diamond wheel in Elliptical Ultrasonic Assisted Grinding (EUAG) of monocrystal sapphire, and a series of experiments on EUAG and conventional grinding (CG) are performed. The results show that the fractal dimension of grinding wheel topography is highly correlated to the wear behavior, i.e., grain fracture, grain pullout, and wheel loading. An increase in cutting edge density on the wheel surface results in an increase of the fractal dimension, but an increase in the grain pullout and wheel loading results in a decrease in the fractal dimension. The wheel topography in EUAG has a higher fractal dimension than that in CG before 60 passes due to better self-sharpening behavior, and then has a smaller fractal dimension because of more serious wheel loadings after 60 passes. By angle-dependent distribution analysis of profile fractal dimensions, the wheel surface topography is transformed from isotropic to anisotropic. These indicated that the fractal analysis method could be further used in monitoring of a grinding wheel performance in EUAG. Copyright © 2017 Elsevier B.V. All rights reserved.

Not just fractal surfaces, but surface fractal aggregates: Derivation of the expression for the structure factor and its applications

NASA Astrophysics Data System (ADS)

Besselink, R.; Stawski, T. M.; Van Driessche, A. E. S.; Benning, L. G.

2016-12-01

Densely packed surface fractal aggregates form in systems with high local volume fractions of particles with very short diffusion lengths, which effectively means that particles have little space to move. However, there are no prior mathematical models, which would describe scattering from such surface fractal aggregates and which would allow the subdivision between inter- and intraparticle interferences of such aggregates. Here, we show that by including a form factor function of the primary particles building the aggregate, a finite size of the surface fractal interfacial sub-surfaces can be derived from a structure factor term. This formalism allows us to define both a finite specific surface area for fractal aggregates and the fraction of particle interfacial sub-surfaces at the perimeter of an aggregate. The derived surface fractal model is validated by comparing it with an ab initio approach that involves the generation of a "brick-in-a-wall" von Koch type contour fractals. Moreover, we show that this approach explains observed scattering intensities from in situ experiments that followed gypsum (CaSO4 ṡ 2H2O) precipitation from highly supersaturated solutions. Our model of densely packed "brick-in-a-wall" surface fractal aggregates may well be the key precursor step in the formation of several types of mosaic- and meso-crystals.

a Fractal Network Model for Fractured Porous Media

NASA Astrophysics Data System (ADS)

Xu, Peng; Li, Cuihong; Qiu, Shuxia; Sasmito, Agus Pulung

2016-04-01

The transport properties and mechanisms of fractured porous media are very important for oil and gas reservoir engineering, hydraulics, environmental science, chemical engineering, etc. In this paper, a fractal dual-porosity model is developed to estimate the equivalent hydraulic properties of fractured porous media, where a fractal tree-like network model is used to characterize the fracture system according to its fractal scaling laws and topological structures. The analytical expressions for the effective permeability of fracture system and fractured porous media, tortuosity, fracture density and fraction are derived. The proposed fractal model has been validated by comparisons with available experimental data and numerical simulation. It has been shown that fractal dimensions for fracture length and aperture have significant effect on the equivalent hydraulic properties of fractured porous media. The effective permeability of fracture system can be increased with the increase of fractal dimensions for fracture length and aperture, while it can be remarkably lowered by introducing tortuosity at large branching angle. Also, a scaling law between the fracture density and fractal dimension for fracture length has been found, where the scaling exponent depends on the fracture number. The present fractal dual-porosity model may shed light on the transport physics of fractured porous media and provide theoretical basis for oil and gas exploitation, underground water, nuclear waste disposal and geothermal energy extraction as well as chemical engineering, etc.

Langevin Equation on Fractal Curves

NASA Astrophysics Data System (ADS)

Satin, Seema; Gangal, A. D.

2016-07-01

We analyze random motion of a particle on a fractal curve, using Langevin approach. This involves defining a new velocity in terms of mass of the fractal curve, as defined in recent work. The geometry of the fractal curve, plays an important role in this analysis. A Langevin equation with a particular model of noise is proposed and solved using techniques of the Fα-Calculus.

ABC of multi-fractal spacetimes and fractional sea turtles

NASA Astrophysics Data System (ADS)

Calcagni, Gianluca

2016-04-01

We clarify what it means to have a spacetime fractal geometry in quantum gravity and show that its properties differ from those of usual fractals. A weak and a strong definition of multi-scale and multi-fractal spacetimes are given together with a sketch of the landscape of multi-scale theories of gravitation. Then, in the context of the fractional theory with q-derivatives, we explore the consequences of living in a multi-fractal spacetime. To illustrate the behavior of a non-relativistic body, we take the entertaining example of a sea turtle. We show that, when only the time direction is fractal, sea turtles swim at a faster speed than in an ordinary world, while they swim at a slower speed if only the spatial directions are fractal. The latter type of geometry is the one most commonly found in quantum gravity. For time-like fractals, relativistic objects can exceed the speed of light, but strongly so only if their size is smaller than the range of particle-physics interactions. We also find new results about log-oscillating measures, the measure presentation and their role in physical observations and in future extensions to nowhere-differentiable stochastic spacetimes.

Anisotropic fractal media by vector calculus in non-integer dimensional space

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

Tarasov, Vasily E., E-mail: tarasov@theory.sinp.msu.ru

2014-08-15

A review of different approaches to describe anisotropic fractal media is proposed. In this paper, differentiation and integration non-integer dimensional and multi-fractional spaces are considered as tools to describe anisotropic fractal materials and media. We suggest a generalization of vector calculus for non-integer dimensional space by using a product measure method. The product of fractional and non-integer dimensional spaces allows us to take into account the anisotropy of the fractal media in the framework of continuum models. The integration over non-integer-dimensional spaces is considered. In this paper differential operators of first and second orders for fractional space and non-integer dimensionalmore » space are suggested. The differential operators are defined as inverse operations to integration in spaces with non-integer dimensions. Non-integer dimensional space that is product of spaces with different dimensions allows us to give continuum models for anisotropic type of the media. The Poisson's equation for fractal medium, the Euler-Bernoulli fractal beam, and the Timoshenko beam equations for fractal material are considered as examples of application of suggested generalization of vector calculus for anisotropic fractal materials and media.« less

Fractal dust constrains the collisional history of comets

NASA Astrophysics Data System (ADS)

Fulle, M.; Blum, J.

2017-07-01

The fractal dust particles observed by Rosetta cannot form in the physical conditions observed today in comet 67P/Churyumov-Gerasimenko (67P hereinafter), being instead consistent with models of the pristine dust aggregates coagulated in the solar nebula. Since bouncing collisions in the protoplanetary disc restructure fractals into compact aggregates (pebbles), the only way to preserve fractals in a comet is the gentle gravitational collapse of a mixture of pebbles and fractals, which must occur before their mutual collision speeds overcome ≈1 m s-1. This condition fixes the pebble radius to ≲1 cm, as confirmed by Comet Nucleus Infrared and Visible Analyser onboard Philae. Here, we show that the flux of fractal particles measured by Rosetta constrains the 67P nucleus in a random packing of cm-sized pebbles, with all the voids among them filled by fractal particles. This structure is inconsistent with any catastrophic collision, which would have compacted or dispersed most fractals, thus leaving empty most voids in the reassembled nucleus. Comets are less numerous than current estimates, as confirmed by lacking small craters on Pluto and Charon. Bilobate comets accreted at speeds <1 m s-1 from cometesimals born in the same disc stream.

Detecting fractal power-law long-range dependence in pre-sliced cooked pork ham surface intensity patterns using Detrended Fluctuation Analysis.

PubMed

Valous, Nektarios A; Drakakis, Konstantinos; Sun, Da-Wen

2010-10-01

The visual texture of pork ham slices reveals information about the different qualities and perceived image heterogeneity, which is encapsulated as spatial variations in geometry and spectral characteristics. Detrended Fluctuation Analysis (DFA) detects long-range correlations in nonstationary spatial sequences, by a self-similarity scaling exponent alpha. In the current work, the aim is to investigate the usefulness of alpha, using different colour channels (R, G, B, L*, a*, b*, H, S, V, and Grey), as a quantitative descriptor of visual texture in sliced ham surface patterns for the detection of long-range correlations in unidimensional spatial series of greyscale intensity pixel values at 0 degrees , 30 degrees , 45 degrees , 60 degrees , and 90 degrees rotations. Images were acquired from three qualities of pre-sliced pork ham, typically consumed in Ireland (200 slices per quality). Results indicated that the DFA approach can be used to characterize and quantify the textural appearance of the three ham qualities, for different image orientations, with a global scaling exponent. The spatial series extracted from the ham images display long-range dependence, indicating an average behaviour around 1/f-noise. Results indicate that alpha has a universal character in quantifying the visual texture of ham surface intensity patterns, with no considerable crossovers that alter the behaviour of the fluctuations. Fractal correlation properties can thus be a useful metric for capturing information embedded in the visual texture of hams. Copyright (c) 2010 The American Meat Science Association. Published by Elsevier Ltd. All rights reserved.

Fractal Geometry in the Arts: AN Overview across the Different Cultures

NASA Astrophysics Data System (ADS)

Sala, Nicoletta

Fractal, in mathematics, is a geometric shape that is complex and detailed in structure at any level of magnification. The word "fractal" was coined less than thirty years ago by one of history's most creative and mathematicians, Benoit Mandelbrot, whose work, The Fractal Geometry of Nature, first introduced and explained concepts underlying this new vision of the geometry. Although other mathematical thinkers like Georg Cantor (1845-1918), Felix Hausdorff (1868-1942), Gaston Julia (1893-1978), Helge von Koch (1870-1924), Giuseppe Peano (1858-1932), Lewis Richardson (1891-1953), Waclaw Sierpinski (1882-1969) and others had attained isolated insights of fractal understanding, such ideas were largely ignored until Mandelbrot's genius forged them at a single blow into a gorgeously coherent and fascinating discipline. Fractal geometry is applied in different field now: engineering, physics, chemistry, biology, and architecture. The aim of this paper is to introduce an approach where the arts are analysed using a fractal point of view.

Fractal continuum model for tracer transport in a porous medium.

PubMed

Herrera-Hernández, E C; Coronado, M; Hernández-Coronado, H

2013-12-01

A model based on the fractal continuum approach is proposed to describe tracer transport in fractal porous media. The original approach has been extended to treat tracer transport and to include systems with radial and uniform flow, which are cases of interest in geoscience. The models involve advection due to the fluid motion in the fractal continuum and dispersion whose mathematical expression is taken from percolation theory. The resulting advective-dispersive equations are numerically solved for continuous and for pulse tracer injection. The tracer profile and the tracer breakthrough curve are evaluated and analyzed in terms of the fractal parameters. It has been found in this work that anomalous transport frequently appears, and a condition on the fractal parameter values to predict when sub- or superdiffusion might be expected has been obtained. The fingerprints of fractality on the tracer breakthrough curve in the explored parameter window consist of an early tracer breakthrough and long tail curves for the spherical and uniform flow cases, and symmetric short tailed curves for the radial flow case.

A new numerical approximation of the fractal ordinary differential equation

NASA Astrophysics Data System (ADS)

Atangana, Abdon; Jain, Sonal

2018-02-01

The concept of fractal medium is present in several real-world problems, for instance, in the geological formation that constitutes the well-known subsurface water called aquifers. However, attention has not been quite devoted to modeling for instance, the flow of a fluid within these media. We deem it important to remind the reader that the concept of fractal derivative is not to represent the fractal sharps but to describe the movement of the fluid within these media. Since this class of ordinary differential equations is highly complex to solve analytically, we present a novel numerical scheme that allows to solve fractal ordinary differential equations. Error analysis of the method is also presented. Application of the method and numerical approximation are presented for fractal order differential equation. The stability and the convergence of the numerical schemes are investigated in detail. Also some exact solutions of fractal order differential equations are presented and finally some numerical simulations are presented.

Temporal fractals in seabird foraging behaviour: diving through the scales of time

PubMed Central

MacIntosh, Andrew J. J.; Pelletier, Laure; Chiaradia, Andre; Kato, Akiko; Ropert-Coudert, Yan

2013-01-01

Animal behaviour exhibits fractal structure in space and time. Fractal properties in animal space-use have been explored extensively under the Lévy flight foraging hypothesis, but studies of behaviour change itself through time are rarer, have typically used shorter sequences generated in the laboratory, and generally lack critical assessment of their results. We thus performed an in-depth analysis of fractal time in binary dive sequences collected via bio-logging from free-ranging little penguins (Eudyptula minor) across full-day foraging trips (216 data points; 4 orders of temporal magnitude). Results from 4 fractal methods show that dive sequences are long-range dependent and persistent across ca. 2 orders of magnitude. This fractal structure correlated with trip length and time spent underwater, but individual traits had little effect. Fractal time is a fundamental characteristic of penguin foraging behaviour, and its investigation is thus a promising avenue for research on interactions between animals and their environments. PMID:23703258

Perceptual and Physiological Responses to Jackson Pollock's Fractals

PubMed Central

Taylor, Richard P.; Spehar, Branka; Van Donkelaar, Paul; Hagerhall, Caroline M.

2011-01-01

Fractals have been very successful in quantifying the visual complexity exhibited by many natural patterns, and have captured the imagination of scientists and artists alike. Our research has shown that the poured patterns of the American abstract painter Jackson Pollock are also fractal. This discovery raises an intriguing possibility – are the visual characteristics of fractals responsible for the long-term appeal of Pollock's work? To address this question, we have conducted 10 years of scientific investigation of human response to fractals and here we present, for the first time, a review of this research that examines the inter-relationship between the various results. The investigations include eye tracking, visual preference, skin conductance, and EEG measurement techniques. We discuss the artistic implications of the positive perceptual and physiological responses to fractal patterns. PMID:21734876

Fractal fluctuations in gaze speed visual search.

PubMed

Stephen, Damian G; Anastas, Jason

2011-04-01

Visual search involves a subtle coordination of visual memory and lower-order perceptual mechanisms. Specifically, the fluctuations in gaze may provide support for visual search above and beyond what may be attributed to memory. Prior research indicates that gaze during search exhibits fractal fluctuations, which allow for a wide sampling of the field of view. Fractal fluctuations constitute a case of fast diffusion that may provide an advantage in exploration. We present reanalyses of eye-tracking data collected by Stephen and Mirman (Cognition, 115, 154-165, 2010) for single-feature and conjunction search tasks. Fluctuations in gaze during these search tasks were indeed fractal. Furthermore, the degree of fractality predicted decreases in reaction time on a trial-by-trial basis. We propose that fractality may play a key role in explaining the efficacy of perceptual exploration.

A conservation law, entropy principle and quantization of fractal dimensions in hadron interactions

NASA Astrophysics Data System (ADS)

Zborovský, I.

2018-04-01

Fractal self-similarity of hadron interactions demonstrated by the z-scaling of inclusive spectra is studied. The scaling regularity reflects fractal structure of the colliding hadrons (or nuclei) and takes into account general features of fragmentation processes expressed by fractal dimensions. The self-similarity variable z is a function of the momentum fractions x1 and x2 of the colliding objects carried by the interacting hadron constituents and depends on the momentum fractions ya and yb of the scattered and recoil constituents carried by the inclusive particle and its recoil counterpart, respectively. Based on entropy principle, new properties of the z-scaling concept are found. They are conservation of fractal cumulativity in hadron interactions and quantization of fractal dimensions characterizing hadron structure and fragmentation processes at a constituent level.

Relationship between the anomalous diffusion and the fractal dimension of the environment

NASA Astrophysics Data System (ADS)

Zhokh, Alexey; Trypolskyi, Andrey; Strizhak, Peter

2018-03-01

In this letter, we provide an experimental study highlighting a relation between the anomalous diffusion and the fractal dimension of the environment using the methanol anomalous transport through the porous solid pellets with various pores geometries and different chemical compositions. The anomalous diffusion exponent was derived from the non-integer order of the time-fractional diffusion equation that describes the methanol anomalous transport through the solid media. The surface fractal dimension was estimated from the nitrogen adsorption isotherms using the Frenkel-Halsey-Hill method. Our study shows that decreasing the fractal dimension leads to increasing the anomalous diffusion exponent, whereas the anomalous diffusion constant is independent on the fractal dimension. We show that the obtained results are in a good agreement with the anomalous diffusion model on a fractal mesh.

A Fractal Dimension Survey of Active Region Complexity

NASA Technical Reports Server (NTRS)

McAteer, R. T. James; Gallagher, Peter; Ireland, Jack

2005-01-01

A new approach to quantifying the magnetic complexity of active regions using a fractal dimension measure is presented. This fully-automated approach uses full disc MDI magnetograms of active regions from a large data set (2742 days of the SoHO mission; 9342 active regions) to compare the calculated fractal dimension to both Mount Wilson classification and flare rate. The main Mount Wilson classes exhibit no distinct fractal dimension distribution, suggesting a self-similar nature of all active regions. Solar flare productivity exhibits an increase in both the frequency and GOES X-ray magnitude of flares from regions with higher fractal dimensions. Specifically a lower threshold fractal dimension of 1.2 and 1.25 exists as a necessary, but not sufficient, requirement for an active region to produce M- and X-class flares respectively .

A Tutorial Review on Fractal Spacetime and Fractional Calculus

NASA Astrophysics Data System (ADS)

He, Ji-Huan

2014-11-01

This tutorial review of fractal-Cantorian spacetime and fractional calculus begins with Leibniz's notation for derivative without limits which can be generalized to discontinuous media like fractal derivative and q-derivative of quantum calculus. Fractal spacetime is used to elucidate some basic properties of fractal which is the foundation of fractional calculus, and El Naschie's mass-energy equation for the dark energy. The variational iteration method is used to introduce the definition of fractional derivatives. Fractal derivative is explained geometrically and q-derivative is motivated by quantum mechanics. Some effective analytical approaches to fractional differential equations, e.g., the variational iteration method, the homotopy perturbation method, the exp-function method, the fractional complex transform, and Yang-Laplace transform, are outlined and the main solution processes are given.

Fractal-Based Image Compression, II

DTIC Science & Technology

1990-06-01

data for figure 3 ----------------------------------- 10 iv 1. INTRODUCTION The need for data compression is not new. With humble beginnings such as...the use of acronyms and abbreviations in spoken and written word, the methods for data compression became more advanced as the need for information...grew. The Morse code, developed because of the need for faster telegraphy, was an early example of a data compression technique. Largely because of the

Drawing dynamical and parameters planes of iterative families and methods.

PubMed

Chicharro, Francisco I; Cordero, Alicia; Torregrosa, Juan R

2013-01-01

The complex dynamical analysis of the parametric fourth-order Kim's iterative family is made on quadratic polynomials, showing the MATLAB codes generated to draw the fractal images necessary to complete the study. The parameter spaces associated with the free critical points have been analyzed, showing the stable (and unstable) regions where the selection of the parameter will provide us the excellent schemes (or dreadful ones).

Self-Calibrating Wave-Encoded Variable-Density Single-Shot Fast Spin Echo Imaging.

PubMed

Chen, Feiyu; Taviani, Valentina; Tamir, Jonathan I; Cheng, Joseph Y; Zhang, Tao; Song, Qiong; Hargreaves, Brian A; Pauly, John M; Vasanawala, Shreyas S

2018-04-01

It is highly desirable in clinical abdominal MR scans to accelerate single-shot fast spin echo (SSFSE) imaging and reduce blurring due to T 2 decay and partial-Fourier acquisition. To develop and investigate the clinical feasibility of wave-encoded variable-density SSFSE imaging for improved image quality and scan time reduction. Prospective controlled clinical trial. With Institutional Review Board approval and informed consent, the proposed method was assessed on 20 consecutive adult patients (10 male, 10 female, range, 24-84 years). A wave-encoded variable-density SSFSE sequence was developed for clinical 3.0T abdominal scans to enable high acceleration (3.5×) with full-Fourier acquisitions by: 1) introducing wave encoding with self-refocusing gradient waveforms to improve acquisition efficiency; 2) developing self-calibrated estimation of wave-encoding point-spread function and coil sensitivity to improve motion robustness; and 3) incorporating a parallel imaging and compressed sensing reconstruction to reconstruct highly accelerated datasets. Image quality was compared pairwise with standard Cartesian acquisition independently and blindly by two radiologists on a scale from -2 to 2 for noise, contrast, confidence, sharpness, and artifacts. The average ratio of scan time between these two approaches was also compared. A Wilcoxon signed-rank tests with a P value under 0.05 considered statistically significant. Wave-encoded variable-density SSFSE significantly reduced the perceived noise level and improved the sharpness of the abdominal wall and the kidneys compared with standard acquisition (mean scores 0.8, 1.2, and 0.8, respectively, P < 0.003). No significant difference was observed in relation to other features (P = 0.11). An average of 21% decrease in scan time was achieved using the proposed method. Wave-encoded variable-density sampling SSFSE achieves improved image quality with clinically relevant echo time and reduced scan time, thus providing a fast and robust approach for clinical SSFSE imaging. 1 Technical Efficacy: Stage 6 J. Magn. Reson. Imaging 2018;47:954-966. © 2017 International Society for Magnetic Resonance in Medicine.

Editorial

NASA Astrophysics Data System (ADS)

Liu, Shuai

Fractal represents a special feature of nature and functional objects. However, fractal based computing can be applied to many research domains because of its fixed property resisted deformation, variable parameters and many unpredictable changes. Theoretical research and practical application of fractal based computing have been hotspots for 30 years and will be continued. There are many pending issues awaiting solutions in this domain, thus this thematic issue containing 14 papers publishes the state-of-the-art developments in theorem and application of fractal based computing, including mathematical analysis and novel engineering applications. The topics contain fractal and multifractal features in application and solution of nonlinear odes and equation.

Cascade model for fluvial geomorphology

NASA Technical Reports Server (NTRS)

Newman, W. I.; Turcotte, D. L.

1990-01-01

Erosional landscapes are generally scale invariant and fractal. Spectral studies provide quantitative confirmation of this statement. Linear theories of erosion will not generate scale-invariant topography. In order to explain the fractal behavior of landscapes a modified Fourier series has been introduced that is the basis for a renormalization approach. A nonlinear dynamical model has been introduced for the decay of the modified Fourier series coefficients that yield a fractal spectra. It is argued that a physical basis for this approach is that a fractal (or nearly fractal) distribution of storms (floods) continually renews erosional features on all scales.

Mass fractal dimension and spectral dimension to characterize different horizons in La Herreria (Sierra de Guadarrama, Spain)

NASA Astrophysics Data System (ADS)

Inclan, Rosa Maria

2016-04-01

Knowledge on three dimensional soil pore architecture is important to improve our understanding of the factors that control a number of critical soil processes as it controls biological, chemical and physical processes at various scales. Computed Tomography (CT) images provide increasingly reliable information about the geometry of pores and solids in soils at very small scale with the benefit that is a non-invasive technique. Fractal formalism has revealed as a useful tool in these cases where highly complex and heterogeneous meda are studied. One of these quantifications is mass dimension (Dm) and spectral dimension (d) applied to describe the water and gas diffusion coefficients in soils (Tarquis et al., 2012). In this work, intact soil samples were collected from the first three horizons of La Herreria soil. This station is located in the lowland mountain area of Sierra de Guadarrama (Santolaria et al., 2015) and it represents a highly degraded type of site as a result of the livestock keeping. The 3D images, of 45.1 micro-m resolution (256x256x256 voxels), were obtained and then binarized following the singularity-CA method (Martín-Sotoca et al. 2016). Based on these images Dm and d were estimated. The results showed an statistical difference in porosity, Dm and d for each horizon. This fact has a direct implication in diffusion parameters for a pore network modeling based on both fractal dimensions. These soil parameters will constitute a basis for site characterization for further studies regarding soil degradation; determining the interaction between soil, plant and atmosphere with respect to human induced activities as well as the basis for several nitrogen and carbon cycles modeling. References Martin Sotoca; J.J. Ana M. Tarquis, Antonio Saa Requejo, and Juan B. Grau (2016). Pore detection in Computed Tomography (CT) soil 3D images using singularity map analysis. Geophysical Research Abstracts, 18, EGU2016-829. Santolaria-Canales, Edmundo and the GuMNet Consortium Team (2015). GuMNet - Guadarrama Monitoring Network. Installation and set up of a high altitude monitoring network, north of Madrid. Spain. Geophysical Research Abstracts, 17, EGU2015-13989-2. Tarquis, A. M., Sanchez, M. E., Antón, J. M., Jimenez, J., Saa-Requejo, A., Andina, D., & Crawford, J. W. (2012). Variation in spectral and mass dimension on three-dimensional soil image processing. Soil Science, 177(2), 88-97. Web: http://www.ucm.es/gumnet/

Results for diffusion-weighted imaging with a fourth-channel gradient insert.

PubMed

Feldman, Rebecca E; Scholl, Timothy J; Alford, Jamu K; Handler, William B; Harris, Chad T; Chronik, Blaine A

2011-12-01

Diffusion-weighted imaging suffers from motion artifacts and relatively low signal quality due to the long echo times required to permit the diffusion encoding. We investigated the inclusion of a noncylindrical fourth gradient coil, dedicated entirely to diffusion encoding, into the imaging system. Standard three-axis whole body gradients were used during image acquisition, but we designed and constructed an insert coil to perform diffusion encodings. We imaged three phantoms on a 3-T system with a range of diffusion coefficients. Using the insert gradient, we were able to encode b values of greater than 1300 s/mm(2) with an echo time of just 83 ms. Images obtained using the insert gradient had higher signal to noise ratios than those obtained using the whole body gradient: at 500 s/mm(2) there was a 18% improvement in signal to noise ratio, at 1000 s/mm(2) there was a 39% improvement in signal to noise ratio, and at 1350 s/mm(2) there was a 56% improvement in signal to noise ratio. Using the insert gradient, we were capable of doing diffusion encoding at high b values by using relatively short echo times. Copyright © 2011 Wiley Periodicals, Inc.

Simultaneous multiplexing and encoding of multiple images based on a double random phase encryption system

NASA Astrophysics Data System (ADS)

Alfalou, Ayman; Mansour, Ali

2009-09-01

Nowadays, protecting information is a major issue in any transmission system, as showed by an increasing number of research papers related to this topic. Optical encoding methods, such as a Double Random Phase encryption system i.e. DRP, are widely used and cited in the literature. DRP systems have very simple principle and they are easily applicable to most images (B&W, gray levels or color). Moreover, some applications require an enhanced encoding level based on multiencryption scheme and including biometric keys (as digital fingerprints). The enhancement should be done without increasing transmitted or stored information. In order to achieve that goal, a new approach for simultaneous multiplexing & encoding of several target images is developed in this manuscript. By introducing two additional security levels, our approach enhances the security level of a classic "DRP" system. Our first security level consists in using several independent image-keys (randomly and structurally) along with a new multiplexing algorithm. At this level, several target images (multiencryption) are used. This part can reduce needed information (encoding information). At the second level a standard DRP system is included. Finally, our approach can detect if any vandalism attempt has been done on transmitted encrypted images.

Accelerated radial Fourier-velocity encoding using compressed sensing.

PubMed

Hilbert, Fabian; Wech, Tobias; Hahn, Dietbert; Köstler, Herbert

2014-09-01

Phase Contrast Magnetic Resonance Imaging (MRI) is a tool for non-invasive determination of flow velocities inside blood vessels. Because Phase Contrast MRI only measures a single mean velocity per voxel, it is only applicable to vessels significantly larger than the voxel size. In contrast, Fourier Velocity Encoding measures the entire velocity distribution inside a voxel, but requires a much longer acquisition time. For accurate diagnosis of stenosis in vessels on the scale of spatial resolution, it is important to know the velocity distribution of a voxel. Our aim was to determine velocity distributions with accelerated Fourier Velocity Encoding in an acquisition time required for a conventional Phase Contrast image. We imaged the femoral artery of healthy volunteers with ECG-triggered, radial CINE acquisition. Data acquisition was accelerated by undersampling, while missing data were reconstructed by Compressed Sensing. Velocity spectra of the vessel were evaluated by high resolution Phase Contrast images and compared to spectra from fully sampled and undersampled Fourier Velocity Encoding. By means of undersampling, it was possible to reduce the scan time for Fourier Velocity Encoding to the duration required for a conventional Phase Contrast image. Acquisition time for a fully sampled data set with 12 different Velocity Encodings was 40 min. By applying a 12.6-fold retrospective undersampling, a data set was generated equal to 3:10 min acquisition time, which is similar to a conventional Phase Contrast measurement. Velocity spectra from fully sampled and undersampled Fourier Velocity Encoded images are in good agreement and show the same maximum velocities as compared to velocity maps from Phase Contrast measurements. Compressed Sensing proved to reliably reconstruct Fourier Velocity Encoded data. Our results indicate that Fourier Velocity Encoding allows an accurate determination of the velocity distribution in vessels in the order of the voxel size. Thus, compared to normal Phase Contrast measurements delivering only mean velocities, no additional scan time is necessary to retrieve meaningful velocity spectra in small vessels. Copyright © 2013. Published by Elsevier GmbH.

Fractal Interrelationships in Field and Seismic Data

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

Wilson, T.H.; Dominic, Jovita; Halverson, Joel

1997-10-01

Size scaling interrelationships are evaluated in this study using a fractal model. Fractal models of several geologic variables are examined and include fracture patterns, reflection travel times, structural relief, drainage, topographic relief and active fault patterns. The fractal properties of structural relief inferred from seismic data and structural cross sections provide a quantitative means to characterize and compare complex structural patterns. Studies were conducted using seismic data from the Granny Creek oil field in the Appalachian Plateau. Previous studies of the field reveal that subtle detached structures present on the limb of a larger structure are associated with enhanced productionmore » from the field. Vertical increases of fractal dimension across the zone of detachment provide a measure of the extent to which detachment has occurred. The increases of fractal dimension are greatest in the more productive areas of the field. A result with equally important ramifications is that fracture systems do not appear to be intrinsically fractal as is often suggested in the literature. While examples of nearly identical patterns can be found at different scales supporting the idea of self-similarity, these examples are often taken from different areas and from different lithologies. Examination of fracture systems at different scales in the Valley and Ridge Province suggest that their distribution become increasingly sparse with scale reduction, and therefore are dissimilar or non-fractal. Box counting data in all cases failed to yield a fractal regime. The results obtained from this analysis bring into question the general applicability of reservoir simulations employing fractal models of fracture distribution. The same conclusions were obtained from the analysis of 1D fracture patterns such as those that might appear in a horizontal well.« less

Ulam method and fractal Weyl law for Perron-Frobenius operators

NASA Astrophysics Data System (ADS)

Ermann, L.; Shepelyansky, D. L.

2010-06-01

We use the Ulam method to study spectral properties of the Perron-Frobenius operators of dynamical maps in a chaotic regime. For maps with absorption we show numerically that the spectrum is characterized by the fractal Weyl law recently established for nonunitary operators describing poles of quantum chaotic scattering with the Weyl exponent ν = d-1, where d is the fractal dimension of corresponding strange set of trajectories nonescaping in future times. In contrast, for dissipative maps we numerically find the Weyl exponent ν = d/2 where d is the fractal dimension of strange attractor. The Weyl exponent can be also expressed via the relation ν = d0/2 where d0 is the fractal dimension of the invariant sets. We also discuss the properties of eigenvalues and eigenvectors of such operators characterized by the fractal Weyl law.

Correlation of Fractal Dimension Values with Implant Insertion Torque and Resonance Frequency Values at Implant Recipient Sites.

PubMed

Suer, Berkay Tolga; Yaman, Zekai; Buyuksarac, Bora

2016-01-01

Fractal analysis is a mathematical method used to describe the internal architecture of complex structures such as trabecular bone. Fractal analysis of panoramic radiographs of implant recipient sites could help to predict the quality of the bone prior to implant placement. This study investigated the correlations between the fractal dimension values obtained from panoramic radiographs and the insertion torque and resonance frequency values of mandibular implants. Thirty patients who received a total of 55 implants of the same brand, diameter, and length in the mandibular premolar and molar regions were included in the study. The same surgical procedures were applied to each patient, and the insertion torque and resonance frequency values were recorded for each implant at the time of placement. The radiographic fractal dimensions of the alveolar bone in the implant recipient area were calculated from preoperative panoramic radiographs using a box-counting algorithm. The insertion torque and resonance frequency values were compared with the fractal dimension values using the Spearman test. All implants were successful, and none were lost during the follow-up period. Linear correlations were observed between the fractal dimension and resonance frequency, between the fractal dimension and insertion torque, and between resonance frequency and insertion torque. These results suggest that the noninvasive measurement of the fractal dimension from panoramic radiographs might help to predict the bone quality, and thus the primary stability of dental implants, before implant surgery.

Fractal Patterns of Neural Activity Exist within the Suprachiasmatic Nucleus and Require Extrinsic Network Interactions

PubMed Central

Hu, Kun; Meijer, Johanna H.; Shea, Steven A.; vanderLeest, Henk Tjebbe; Pittman-Polletta, Benjamin; Houben, Thijs; van Oosterhout, Floor; Deboer, Tom; Scheer, Frank A. J. L.

2012-01-01

The mammalian central circadian pacemaker (the suprachiasmatic nucleus, SCN) contains thousands of neurons that are coupled through a complex network of interactions. In addition to the established role of the SCN in generating rhythms of ∼24 hours in many physiological functions, the SCN was recently shown to be necessary for normal self-similar/fractal organization of motor activity and heart rate over a wide range of time scales—from minutes to 24 hours. To test whether the neural network within the SCN is sufficient to generate such fractal patterns, we studied multi-unit neural activity of in vivo and in vitro SCNs in rodents. In vivo SCN-neural activity exhibited fractal patterns that are virtually identical in mice and rats and are similar to those in motor activity at time scales from minutes up to 10 hours. In addition, these patterns remained unchanged when the main afferent signal to the SCN, namely light, was removed. However, the fractal patterns of SCN-neural activity are not autonomous within the SCN as these patterns completely broke down in the isolated in vitro SCN despite persistence of circadian rhythmicity. Thus, SCN-neural activity is fractal in the intact organism and these fractal patterns require network interactions between the SCN and extra-SCN nodes. Such a fractal control network could underlie the fractal regulation observed in many physiological functions that involve the SCN, including motor control and heart rate regulation. PMID:23185285

Two-dimensional imaging in a lightweight portable MRI scanner without gradient coils.

PubMed

Cooley, Clarissa Zimmerman; Stockmann, Jason P; Armstrong, Brandon D; Sarracanie, Mathieu; Lev, Michael H; Rosen, Matthew S; Wald, Lawrence L

2015-02-01

As the premiere modality for brain imaging, MRI could find wider applicability if lightweight, portable systems were available for siting in unconventional locations such as intensive care units, physician offices, surgical suites, ambulances, emergency rooms, sports facilities, or rural healthcare sites. We construct and validate a truly portable (<100 kg) and silent proof-of-concept MRI scanner which replaces conventional gradient encoding with a rotating lightweight cryogen-free, low-field magnet. When rotated about the object, the inhomogeneous field pattern is used as a rotating spatial encoding magnetic field (rSEM) to create generalized projections which encode the iteratively reconstructed two-dimensional (2D) image. Multiple receive channels are used to disambiguate the nonbijective encoding field. The system is validated with experimental images of 2D test phantoms. Similar to other nonlinear field encoding schemes, the spatial resolution is position dependent with blurring in the center, but is shown to be likely sufficient for many medical applications. The presented MRI scanner demonstrates the potential for portability by simultaneously relaxing the magnet homogeneity criteria and eliminating the gradient coil. This new architecture and encoding scheme shows convincing proof of concept images that are expected to be further improved with refinement of the calibration and methodology. © 2014 Wiley Periodicals, Inc.

2D Imaging in a Lightweight Portable MRI Scanner without Gradient Coils

PubMed Central

Cooley, Clarissa Zimmerman; Stockmann, Jason P.; Armstrong, Brandon D.; Sarracanie, Mathieu; Lev, Michael H.; Rosen, Matthew S.; Wald, Lawrence L.

2014-01-01

Purpose As the premiere modality for brain imaging, MRI could find wider applicability if lightweight, portable systems were available for siting in unconventional locations such as Intensive Care Units, physician offices, surgical suites, ambulances, emergency rooms, sports facilities, or rural healthcare sites. Methods We construct and validate a truly portable (<100kg) and silent proof-of-concept MRI scanner which replaces conventional gradient encoding with a rotating lightweight cryogen-free, low-field magnet. When rotated about the object, the inhomogeneous field pattern is used as a rotating Spatial Encoding Magnetic field (rSEM) to create generalized projections which encode the iteratively reconstructed 2D image. Multiple receive channels are used to disambiguate the non-bijective encoding field. Results The system is validated with experimental images of 2D test phantoms. Similar to other non-linear field encoding schemes, the spatial resolution is position dependent with blurring in the center, but is shown to be likely sufficient for many medical applications. Conclusion The presented MRI scanner demonstrates the potential for portability by simultaneously relaxing the magnet homogeneity criteria and eliminating the gradient coil. This new architecture and encoding scheme shows convincing proof of concept images that are expected to be further improved with refinement of the calibration and methodology. PMID:24668520

Comprehensive Fractal Description of Porosity of Coal of Different Ranks

PubMed Central

Ren, Jiangang; Zhang, Guocheng; Song, Zhimin; Liu, Gaofeng; Li, Bing

2014-01-01

We selected, as the objects of our research, lignite from the Beizao Mine, gas coal from the Caiyuan Mine, coking coal from the Xiqu Mine, and anthracite from the Guhanshan Mine. We used the mercury intrusion method and the low-temperature liquid nitrogen adsorption method to analyze the structure and shape of the coal pores and calculated the fractal dimensions of different aperture segments in the coal. The experimental results show that the fractal dimension of the aperture segment of lignite, gas coal, and coking coal with an aperture of greater than or equal to 10 nm, as well as the fractal dimension of the aperture segment of anthracite with an aperture of greater than or equal to 100 nm, can be calculated using the mercury intrusion method; the fractal dimension of the coal pore, with an aperture range between 2.03 nm and 361.14 nm, can be calculated using the liquid nitrogen adsorption method, of which the fractal dimensions bounded by apertures of 10 nm and 100 nm are different. Based on these findings, we defined and calculated the comprehensive fractal dimensions of the coal pores and achieved the unity of fractal dimensions for full apertures of coal pores, thereby facilitating, overall characterization for the heterogeneity of the coal pore structure. PMID:24955407

Fractal Characteristics of Soil Retention Curve and Particle Size Distribution with Different Vegetation Types in Mountain Areas of Northern China.

PubMed

Niu, Xiang; Gao, Peng; Wang, Bing; Liu, Yu

2015-12-03

Based on fractal theory, the fractal characteristics of soil particle size distribution (PSD) and soil water retention curve (WRC) under the five vegetation types were studied in the mountainous land of Northern China. Results showed that: (1) the fractal parameters of soil PSD and soil WRC varied greatly under each different vegetation type, with Quercus acutissima Carr. and Robina pseudoacacia Linn. mixed plantation (QRM) > Pinus thunbergii Parl. and Pistacia chinensis Bunge mixed plantation (PPM) > Pinus thunbergii Parl. (PTP) > Juglans rigia Linn. (JRL) > abandoned grassland (ABG); (2) the soil fractal dimensions of woodlands (QRM, PPM, PTP and JRL) were significantly higher than that in ABG, and mixed forests (QRM and PPM) were higher than that in pure forests (PTP and JRL); (3) the fractal dimension of soil was positively correlated with the silt and clay content but negatively correlated with the sand content; and (4) the fractal dimension of soil PSD was positively correlated with the soil WRC. These indicated that the fractal parameters of soil PSD and soil WRC could act as quantitative indices to reflect the physical properties of the soil, and could be used to describe the influences of the Return Farmland to Forests Projects on soil structure.

Effects of Anisotropy on Scalar Field Ghost Dark Energy and the Non-Equilibrium Thermodynamics in Fractal Cosmology

NASA Astrophysics Data System (ADS)

Najafi, A.; Hossienkhani, H.

2017-10-01

Since the fractal cosmology has been created in early universe, therefore their models were mostly isotropic. The majority of previous studies had been based on FRW universe, while in the early universe, the best model for describing fractal cosmology is actually the anisotropic universe. Therefore in this work, by assuming the anisotropic universe, the cosmological implications of ghost and generalized ghost dark energy models with dark matter in fractal cosmology has been discussed. Moreover, the different kinds of dark energy models such as quintessence and tachyon field, with the generalized ghost dark energy in fractal universe has been investigated. In addition, we have reconstructed the Hubble parameter, H, the energy density, ρ, the deceleration parameter, q, the equations of state parameter, {ω }{{}D}, for both ghost and generalized ghost dark energy models. This correspondence allows us to reconstruct the potential and the dynamics of a fractal canonical scalar field according to the evolution of generalized ghost dark energy density. Eventually, thermodynamics of the cosmological apparent horizon in fractal cosmology was investigated and the validity of the Generalized second law of thermodynamics (GSLT) have been examined in an anisotropic universe. The results show the influence of the anisotropy on the GSLT of thermodynamics in a fractal cosmology.

Evolving random fractal Cantor superlattices for the infrared using a genetic algorithm

PubMed Central

Bossard, Jeremy A.; Lin, Lan; Werner, Douglas H.

2016-01-01

Ordered and chaotic superlattices have been identified in Nature that give rise to a variety of colours reflected by the skin of various organisms. In particular, organisms such as silvery fish possess superlattices that reflect a broad range of light from the visible to the UV. Such superlattices have previously been identified as ‘chaotic’, but we propose that apparent ‘chaotic’ natural structures, which have been previously modelled as completely random structures, should have an underlying fractal geometry. Fractal geometry, often described as the geometry of Nature, can be used to mimic structures found in Nature, but deterministic fractals produce structures that are too ‘perfect’ to appear natural. Introducing variability into fractals produces structures that appear more natural. We suggest that the ‘chaotic’ (purely random) superlattices identified in Nature are more accurately modelled by multi-generator fractals. Furthermore, we introduce fractal random Cantor bars as a candidate for generating both ordered and ‘chaotic’ superlattices, such as the ones found in silvery fish. A genetic algorithm is used to evolve optimal fractal random Cantor bars with multiple generators targeting several desired optical functions in the mid-infrared and the near-infrared. We present optimized superlattices demonstrating broadband reflection as well as single and multiple pass bands in the near-infrared regime. PMID:26763335

Fractal Characteristics of Soil Retention Curve and Particle Size Distribution with Different Vegetation Types in Mountain Areas of Northern China

PubMed Central

Niu, Xiang; Gao, Peng; Wang, Bing; Liu, Yu

2015-01-01

Based on fractal theory, the fractal characteristics of soil particle size distribution (PSD) and soil water retention curve (WRC) under the five vegetation types were studied in the mountainous land of Northern China. Results showed that: (1) the fractal parameters of soil PSD and soil WRC varied greatly under each different vegetation type, with Quercus acutissima Carr. and Robina pseudoacacia Linn. mixed plantation (QRM) > Pinus thunbergii Parl. and Pistacia chinensis Bunge mixed plantation (PPM) > Pinus thunbergii Parl. (PTP) > Juglans rigia Linn. (JRL) > abandoned grassland (ABG); (2) the soil fractal dimensions of woodlands (QRM, PPM, PTP and JRL) were significantly higher than that in ABG, and mixed forests (QRM and PPM) were higher than that in pure forests (PTP and JRL); (3) the fractal dimension of soil was positively correlated with the silt and clay content but negatively correlated with the sand content; and (4) the fractal dimension of soil PSD was positively correlated with the soil WRC. These indicated that the fractal parameters of soil PSD and soil WRC could act as quantitative indices to reflect the physical properties of the soil, and could be used to describe the influences of the Return Farmland to Forests Projects on soil structure. PMID:26633458

Effect of fractal silver electrodes on charge collection and light distribution in semiconducting organic polymer films

DOE PAGES

Chamousis, Rachel L.; Chang, Lilian; Watterson, William J.; ...

2014-08-21

Living organisms use fractal structures to optimize material and energy transport across regions of differing size scales. Here we test the effect of fractal silver electrodes on light distribution and charge collection in organic semiconducting polymer films made of P3HT and PCBM. The semiconducting polymers were deposited onto electrochemically grown fractal silver structures (5000 nm × 500 nm; fractal dimension of 1.71) with PEDOT:PSS as hole-selective interlayer. The fractal silver electrodes appear black due to increased horizontal light scattering, which is shown to improve light absorption in the polymer. According to surface photovoltage spectroscopy, fractal silver electrodes outperform the flatmore » electrodes when the BHJ film thickness is large (>400 nm, 0.4 V photovoltage). Photocurrents of up to 200 microamperes cm -2 are generated from the bulk heterojunction (BHJ) photoelectrodes under 435 nm LED (10–20 mW cm -2) illumination in acetonitrile solution containing 0.005 M ferrocenium hexafluorophosphate as the electron acceptor. In conclusion, the low IPCE values (0.3–0.7%) are due to slow electron transfer to ferrocenium ion and due to shunting along the large metal–polymer interface. Overall, this work provides an initial assessment of the potential of fractal electrodes for organic photovoltaic cells.« less

Power Scaling of the Mainland Shoreline of the Atlantic Coast of the United States

NASA Astrophysics Data System (ADS)

Vasko, E.; Barton, C. C.; Geise, G. R.; Rizki, M. M.

2017-12-01

The fractal dimension of the mainland shoreline of the Atlantic coast of the United Stated from Maine to Homestead, FL has been measured in 1000 km increments using the box-counting method. The shoreline analyzed is the NOAA Medium Resolution Shoreline (https://shoreline.noaa.gov/data/datasheets/medres.html). The shoreline was reconstituted into sequentially numbered X-Y coordinate points in UTM Zone 18N which are spaced 50 meters apart, as measured continuously along the shoreline. We created a MATLAB computer code to measure the fractal dimension by box counting while "walking" along the shoreline. The range of box sizes is 0.7 to 450 km. The fractal dimension ranges from 1.0 to1.5 along the mainland shoreline of the Atlantic coast. The fractal dimension is compared with beach particle sizes (bedrock outcrop, cobbles, pebbles, sand, clay), tidal range, rate of sea level rise, rate and direction of vertical crustal movement, and wave energy, looking for correlation with the measured fractal dimensions. The results show a correlation between high fractal dimensions (1.3 - 1.4) and tectonically emergent coasts, and low fractal dimensions (1.0 - 1.2) along submergent and stable coastal regions. Fractal dimension averages 1.3 along shorelines with shoreline protection structures such as seawalls, jetties, and groins.

Radiographic applications of spatial frequency multiplexing

NASA Technical Reports Server (NTRS)

Macovski, A.

1981-01-01

The application of spacial frequency encoding techniques which allow different regions of the X-ray spectrum to be encoded on conventional radiographs was studied. Clinical considerations were reviewed, as were experimental studies involving the encoding and decoding of X-ray images at different energies and the subsequent processing of the data to produce images of specific materials in the body.

Compressed domain indexing of losslessly compressed images

NASA Astrophysics Data System (ADS)

Schaefer, Gerald

2001-12-01

Image retrieval and image compression have been pursued separately in the past. Only little research has been done on a synthesis of the two by allowing image retrieval to be performed directly in the compressed domain of images without the need to uncompress them first. In this paper methods for image retrieval in the compressed domain of losslessly compressed images are introduced. While most image compression techniques are lossy, i.e. discard visually less significant information, lossless techniques are still required in fields like medical imaging or in situations where images must not be changed due to legal reasons. The algorithms in this paper are based on predictive coding methods where a pixel is encoded based on the pixel values of its (already encoded) neighborhood. The first method is based on an understanding that predictively coded data is itself indexable and represents a textural description of the image. The second method operates directly on the entropy encoded data by comparing codebooks of images. Experiments show good image retrieval results for both approaches.

Fractal Risk Assessment of ISS Propulsion Module in Meteoroid and Orbital Debris Environments

NASA Technical Reports Server (NTRS)

Mog, Robert A.

2001-01-01

A unique and innovative risk assessment of the International Space Station (ISS) Propulsion Module is conducted using fractal modeling of the Module's response to the meteoroid and orbital debris environments. Both the environment models and structural failure modes due to the resultant hypervelocity impact phenomenology, as well as Module geometry, are investigated for fractal applicability. The fractal risk assessment methodology could produce a greatly simplified alternative to current methodologies, such as BUMPER analyses, while maintaining or increasing the number of complex scenarios that can be assessed. As a minimum, this innovative fractal approach will provide an independent assessment of existing methodologies in a unique way.

Scattering from fractals

NASA Astrophysics Data System (ADS)

Hurd, Alan J.

The realization that structures in Nature often can be described by Mandelbrot's fractals has led to a revolution in many areas of physics. The interaction of waves with fractal systems has, understandably, become intensely studied since scattering is the method of choice to probe delicate fractal structures such as chainlike particle aggregates. Not all of these waves are electromagnetic. Neutron scattering, for example, is an important complementary tool to structural studies by X-ray and light scattering. Since the phenomenology of small-angle neutron scattering (SANS), as it is applied to fractal systems, is identical to that of small-angle X-ray scattering (SAXS), it falls within the scope of this paper.

Thermodynamics of photons on fractals.

PubMed

Akkermans, Eric; Dunne, Gerald V; Teplyaev, Alexander

2010-12-03

A thermodynamical treatment of a massless scalar field (a photon) confined to a fractal spatial manifold leads to an equation of state relating pressure to internal energy, PV(s) = U/d(s), where d(s) is the spectral dimension and V(s) defines the "spectral volume." For regular manifolds, V(s) coincides with the usual geometric spatial volume, but on a fractal this is not necessarily the case. This is further evidence that on a fractal, momentum space can have a different dimension than position space. Our analysis also provides a natural definition of the vacuum (Casimir) energy of a fractal. We suggest ways that these unusual properties might be probed experimentally.

Fractals in biology and medicine

NASA Technical Reports Server (NTRS)

Havlin, S.; Buldyrev, S. V.; Goldberger, A. L.; Mantegna, R. N.; Ossadnik, S. M.; Peng, C. K.; Simons, M.; Stanley, H. E.

1995-01-01

Our purpose is to describe some recent progress in applying fractal concepts to systems of relevance to biology and medicine. We review several biological systems characterized by fractal geometry, with a particular focus on the long-range power-law correlations found recently in DNA sequences containing noncoding material. Furthermore, we discuss the finding that the exponent alpha quantifying these long-range correlations ("fractal complexity") is smaller for coding than for noncoding sequences. We also discuss the application of fractal scaling analysis to the dynamics of heartbeat regulation, and report the recent finding that the normal heart is characterized by long-range "anticorrelations" which are absent in the diseased heart.

Chaos, Fractals, and Polynomials.

ERIC Educational Resources Information Center

Tylee, J. Louis; Tylee, Thomas B.

1996-01-01

Discusses chaos theory; linear algebraic equations and the numerical solution of polynomials, including the use of the Newton-Raphson technique to find polynomial roots; fractals; search region and coordinate systems; convergence; and generating color fractals on a computer. (LRW)

Effortful Retrieval Reduces Hippocampal Activity and Impairs Incidental Encoding

PubMed Central

Reas, Emilie T.; Brewer, James B.

2014-01-01

Functional imaging studies frequently report that the hippocampus is engaged by successful episodic memory retrieval. However, considering that concurrent encoding of the background environment occurs during retrieval and influences medial temporal lobe activity, it is plausible that hippocampal encoding functions are reduced with increased attentional engagement during effortful retrieval. Expanding upon evidence that retrieval efforts suppress activity in hippocampal regions implicated in encoding, this study examines the influence of retrieval effort on encoding performance and the interactive effects of encoding and retrieval on hippocampal and neocortical activity. Functional magnetic resonance imaging was conducted while subjects performed a word recognition task with incidental picture encoding. Both lower memory strength and increased search duration were associated with encoding failure and reduced hippocampal and default network activity. Activity in the anterior hippocampus tracked encoding, which was more strongly deactivated when incidental encoding was unsuccessful. These findings highlight potential contributions from background encoding processes to hippocampal activations during neuroimaging studies of episodic memory retrieval. PMID:23378272

Visualization of information with an established order

DOEpatents

Wong, Pak Chung [Richland, WA; Foote, Harlan P [Richmond, WA; Thomas, James J [Richland, WA; Wong, Kwong-Kwok [Sugar Land, TX

2007-02-13

Among the embodiments of the present invention is a system including one or more processors operable to access data representative of a biopolymer sequence of monomer units. The one or more processors are further operable to establish a pattern corresponding to at least one fractal curve and generate one or more output signals corresponding to a number of image elements each representative of one of the monomer units. Also included is a display device responsive to the one or more output signals to visualize the biopolymer sequence by displaying the image elements in accordance with the pattern.

Experimental confirmation of long-memory correlations in star-wander data.

PubMed

Zunino, Luciano; Gulich, Damián; Funes, Gustavo; Ziad, Aziz

2014-07-01

In this Letter we have analyzed the temporal correlations of the angle-of-arrival fluctuations of stellar images. Experimentally measured data were carefully examined by implementing multifractal detrended fluctuation analysis. This algorithm is able to discriminate the presence of fractal and multifractal structures in recorded time sequences. We have confirmed that turbulence-degraded stellar wavefronts are compatible with a long-memory correlated monofractal process. This experimental result is quite significant for the accurate comprehension and modeling of the atmospheric turbulence effects on the stellar images. It can also be of great utility within the adaptive optics field.

Influence of the artificial saliva storage on 3-D surface texture characteristics of contemporary dental nanocomposites.

PubMed

Ţălu, Ştefan; Bramowicz, Miroslaw; Kulesza, Slawomir; Lainović, Tijana; Vilotić, Marko; Blažić, Larisa

2016-11-01

The aim of this study was to analyse the influence of the artificial saliva on a three-dimensional (3-D) surface texture of contemporary dental composites. The representatives of four composites types were tested: nanofilled (Filtek Ultimate Body, FUB), nanohybrid (Filtek Z550, FZ550), microfilled (Gradia Direct, GD) and microhybrid (Filtek Z250, FZ250). The specimens were polymerised and polished by the multistep protocol (SuperSnap, Shofu). Their surface was examined, before and after 3 weeks' exposure to artificial saliva storage. The surface texture was analysed using the atomic force microscope (AFM). The obtained images were processed to calculate the areal autocorrelation function (AACF), anisotropy ratio S tr (texture aspect ratio), and structure function (SF). The log-log plots of SF were used to calculate fractal properties, such as fractal dimension D, and pseudo-topothesy K. The analysis showed changes in surface anisotropy ratio S tr values, which became higher, whereas the S q roughness (root-mean-square) reduced after the artificial saliva storage. All the samples exhibited bifractal structure before the saliva treatment, but only half of them remained bifractal afterwards (GD, FZ250), whereas the other half turned into a monofractal (FUB, FZ550). The cube-count fractal dimension D cc was found to be material- and treatment-insensitive. © 2016 The Authors Journal of Microscopy © 2016 Royal Microscopical Society.

Variation of quantitative emphysema measurements from CT scans

NASA Astrophysics Data System (ADS)

Keller, Brad M.; Reeves, Anthony P.; Henschke, Claudia I.; Barr, R. Graham; Yankelevitz, David F.

2008-03-01

Emphysema is a lung disease characterized by destruction of the alveolar air sacs and is associated with long-term respiratory dysfunction. CT scans allow for imaging of the anatomical basis of emphysema, and several measures have been introduced for the quantification of the extent of disease. In this paper we compare these measures for repeatability over time. The measures of interest in this study are emphysema index, mean lung density, histogram percentile, and the fractal dimension. To allow for direct comparisons, the measures were normalized to a 0-100 scale. These measures have been computed for a set of 2,027 scan pairs in which the mean interval between scans was 1.15 years (σ: 93 days). These independent pairs were considered with respect to three different scanning conditions (a) 223 pairs where both were scanned with a 5 mm slice thickness protocol, (b) 695 with the first scanned with the 5 mm protocol and the second with a 1.25 mm protocol, and (c) 1109 pairs scanned both times using a 1.25 mm protocol. We found that average normalized emphysema index and histogram percentiles scores increased by 5.9 and 11 points respectively, while the fractal dimension showed stability with a mean difference of 1.2. We also found, a 7 point bias introduced for emphysema index under condition (b), and that the fractal dimension measure is least affected by scanner parameter changes.

Fractal and Fourier analysis of the hepatic sinusoidal network in normal and cirrhotic rat liver

PubMed Central

Gaudio, Eugenio; Chaberek, Slawomir; Montella, Andrea; Pannarale, Luigi; Morini, Sergio; Novelli, Gilnardo; Borghese, Federica; Conte, Davide; Ostrowski, Kazimierz

2005-01-01

The organization of the hepatic microvascular network has been widely studied in recent years, especially with regard to cirrhosis. This research has enabled us to recognize the distinctive vascular patterns in the cirrhotic liver, compared with the normal liver, which may explain the cause of liver dysfunction and failure. The aim of this study was to compare normal and cirrhotic rat livers by means of a quantitative mathematical approach based on fractal and Fourier analyses performed on photomicrographs and therefore on discriminant analysis. Vascular corrosion casts of livers belonging to the following three experimental groups were studied by scanning electron microscopy: normal rats, CCl4-induced cirrhotic rats and cirrhotic rats after ligation of the bile duct. Photomicrographs were taken at a standard magnification; these images were used for the mathematical analysis. Our experimental design found that use of these different analyses reaches an efficiency of over 94%. Our analyses demonstrated a higher complexity of the normal hepatic sinusoidal network in comparison with the cirrhotic network. In particular, the morphological changes were more marked in the animals with bile duct-ligation cirrhosis compared with animals with CCl4-induced cirrhosis. The present findings based on fractal and Fourier analysis could increase our understanding of the pathophysiological alterations of the liver, and may have a diagnostic value in future clinical research. PMID:16050897

A simple method for estimating the size of nuclei on fractal surfaces

NASA Astrophysics Data System (ADS)

Zeng, Qiang

2017-10-01

Determining the size of nuclei on complex surfaces remains a big challenge in aspects of biological, material and chemical engineering. Here the author reported a simple method to estimate the size of the nuclei in contact with complex (fractal) surfaces. The established approach was based on the assumptions of contact area proportionality for determining nucleation density and the scaling congruence between nuclei and surfaces for identifying contact regimes. It showed three different regimes governing the equations for estimating the nucleation site density. Nuclei in the size large enough could eliminate the effect of fractal structure. Nuclei in the size small enough could lead to the independence of nucleation site density on fractal parameters. Only when nuclei match the fractal scales, the nucleation site density is associated with the fractal parameters and the size of the nuclei in a coupling pattern. The method was validated by the experimental data reported in the literature. The method may provide an effective way to estimate the size of nuclei on fractal surfaces, through which a number of promising applications in relative fields can be envisioned.

A stress sensitivity model for the permeability of porous media based on bi-dispersed fractal theory

NASA Astrophysics Data System (ADS)

Tan, X.-H.; Liu, C.-Y.; Li, X.-P.; Wang, H.-Q.; Deng, H.

A stress sensitivity model for the permeability of porous media based on bidispersed fractal theory is established, considering the change of the flow path, the fractal geometry approach and the mechanics of porous media. It is noted that the two fractal parameters of the porous media construction perform differently when the stress changes. The tortuosity fractal dimension of solid cluster DcTσ become bigger with an increase of stress. However, the pore fractal dimension of solid cluster Dcfσ and capillary bundle Dpfσ remains the same with an increase of stress. The definition of normalized permeability is introduced for the analyzation of the impacts of stress sensitivity on permeability. The normalized permeability is related to solid cluster tortuosity dimension, pore fractal dimension, solid cluster maximum diameter, Young’s modulus and Poisson’s ratio. Every parameter has clear physical meaning without the use of empirical constants. Predictions of permeability of the model is accordant with the obtained experimental data. Thus, the proposed model can precisely depict the flow of fluid in porous media under stress.

Diagnostics of multi-fractality of magnetized plasma inside coronal holes and quiet sun areas

NASA Astrophysics Data System (ADS)

Abramenko, Valentyna

Turbulent and multi-fractal properties of magnetized plasma in solar Coronal Holes (CHs) and Quiet Sun (QS) photosphere were explored using high-resolution magnetograms measured with the New Solar Telescope (NST) at the Big Bear Solar Observatory (BBSO, USA), Hinode/SOT and SDO/HMI instruments. Distribution functions of size and magnetic flux measured for small-scale magnetic elements follow the log-normal law, which implies multi-fractal organization of the magnetic field and the absence of a unique power law for all scales. The magnetograms show multi-fractality in CHs on scales 400 - 10000 km, which becomes better pronounced as the spatial resolution of data improves. Photospheric granulation measured with NST exhibits multi-fractal properties on very small scales of 50 - 600 km. While multi-fractal nature of solar active regions is well known, newly established multi-fractality of weakest magnetic fields on the solar surface, i.e., in CHs and QS, leads us to a conclusion that the entire variety of solar magnetic fields is generated by a unique nonlinear dynamical process.

Symmetric encryption algorithms using chaotic and non-chaotic generators: A review

PubMed Central

Radwan, Ahmed G.; AbdElHaleem, Sherif H.; Abd-El-Hafiz, Salwa K.

2015-01-01

This paper summarizes the symmetric image encryption results of 27 different algorithms, which include substitution-only, permutation-only or both phases. The cores of these algorithms are based on several discrete chaotic maps (Arnold’s cat map and a combination of three generalized maps), one continuous chaotic system (Lorenz) and two non-chaotic generators (fractals and chess-based algorithms). Each algorithm has been analyzed by the correlation coefficients between pixels (horizontal, vertical and diagonal), differential attack measures, Mean Square Error (MSE), entropy, sensitivity analyses and the 15 standard tests of the National Institute of Standards and Technology (NIST) SP-800-22 statistical suite. The analyzed algorithms include a set of new image encryption algorithms based on non-chaotic generators, either using substitution only (using fractals) and permutation only (chess-based) or both. Moreover, two different permutation scenarios are presented where the permutation-phase has or does not have a relationship with the input image through an ON/OFF switch. Different encryption-key lengths and complexities are provided from short to long key to persist brute-force attacks. In addition, sensitivities of those different techniques to a one bit change in the input parameters of the substitution key as well as the permutation key are assessed. Finally, a comparative discussion of this work versus many recent research with respect to the used generators, type of encryption, and analyses is presented to highlight the strengths and added contribution of this paper. PMID:26966561

Environmental Assessment and Monitoring with ICAMS (Image Characterization and Modeling System) Using Multiscale Remote-Sensing Data

NASA Technical Reports Server (NTRS)

Lam, N.; Qiu, H.-I.; Quattrochi, Dale A.; Zhao, Wei

1997-01-01

With the rapid increase in spatial data, especially in the NASA-EOS (Earth Observing System) era, it is necessary to develop efficient and innovative tools to handle and analyze these data so that environmental conditions can be assessed and monitored. A main difficulty facing geographers and environmental scientists in environmental assessment and measurement is that spatial analytical tools are not easily accessible. We have recently developed a remote sensing/GIS software module called Image Characterization and Modeling System (ICAMS) to provide specialized spatial analytical tools for the measurement and characterization of satellite and other forms of spatial data. ICAMS runs on both the Intergraph-MGE and Arc/info UNIX and Windows-NT platforms. The main techniques in ICAMS include fractal measurement methods, variogram analysis, spatial autocorrelation statistics, textural measures, aggregation techniques, normalized difference vegetation index (NDVI), and delineation of land/water and vegetated/non-vegetated boundaries. In this paper, we demonstrate the main applications of ICAMS on the Intergraph-MGE platform using Landsat Thematic Mapper images from the city of Lake Charles, Louisiana. While the utilities of ICAMS' spatial measurement methods (e.g., fractal indices) in assessing environmental conditions remain to be researched, making the software available to a wider scientific community can permit the techniques in ICAMS to be evaluated and used for a diversity of applications. The findings from these various studies should lead to improved algorithms and more reliable models for environmental assessment and monitoring.