NASA Technical Reports Server (NTRS)
Barnsley, Michael F.; Sloan, Alan D.
1989-01-01
Fractals are geometric or data structures which do not simplify under magnification. Fractal Image Compression is a technique which associates a fractal to an image. On the one hand, the fractal can be described in terms of a few succinct rules, while on the other, the fractal contains much or all of the image information. Since the rules are described with less bits of data than the image, compression results. Data compression with fractals is an approach to reach high compression ratios for large data streams related to images. The high compression ratios are attained at a cost of large amounts of computation. Both lossless and lossy modes are supported by the technique. The technique is stable in that small errors in codes lead to small errors in image data. Applications to the NASA mission are discussed.
Fractal images induce fractal pupil dilations and constrictions.
Moon, P; Muday, J; Raynor, S; Schirillo, J; Boydston, C; Fairbanks, M S; Taylor, R P
2014-09-01
Fractals are self-similar structures or patterns that repeat at increasingly fine magnifications. Research has revealed fractal patterns in many natural and physiological processes. This article investigates pupillary size over time to determine if their oscillations demonstrate a fractal pattern. We predict that pupil size over time will fluctuate in a fractal manner and this may be due to either the fractal neuronal structure or fractal properties of the image viewed. We present evidence that low complexity fractal patterns underlie pupillary oscillations as subjects view spatial fractal patterns. We also present evidence implicating the autonomic nervous system's importance in these patterns. Using the variational method of the box-counting procedure we demonstrate that low complexity fractal patterns are found in changes within pupil size over time in millimeters (mm) and our data suggest that these pupillary oscillation patterns do not depend on the fractal properties of the image viewed. PMID:24978815
NASA Astrophysics Data System (ADS)
Xie, Xufen; Wang, Hongyuan; Zhang, Wei
2015-11-01
This paper deals with the estimation of an in-orbit modulation transfer function (MTF) by a remote sensing image sequence, which is often difficult to measure because of a lack of suitable target images. A model is constructed which combines a fractal Brownian motion model that describes natural images stochastic fractal characteristics, with an inverse Fourier transform of an ideal remote sensing image amplitude spectrum. The model is used to decouple the blurring effect and an ideal natural image. Then, a model of MTF statistical estimation is built by standard deviation of the image sequence amplitude spectrum. Furthermore, model parameters are estimated by the ergodicity assumption of a remote sensing image sequence. Finally, the results of the statistical MTF estimation method are given and verified. The experimental results demonstrate that the method is practical and effective, and the relative deviation at the Nyquist frequency between the edge method and the method in this paper is less than 5.74%. The MTF estimation method is applicable for remote sensing image sequences and is not restricted by the characteristic target of images.
NASA Astrophysics Data System (ADS)
Jia, Peng; Cai, Dongmei; Wang, Dong
2014-11-01
A parallel blind deconvolution algorithm is presented. The algorithm contains the constraints of the point spread function (PSF) derived from the physical process of the imaging. Additionally, in order to obtain an effective restored image, the fractal energy ratio is used as an evaluation criterion to estimate the quality of the image. This algorithm is fine-grained parallelized to increase the calculation speed. Results of numerical experiments and real experiments indicate that this algorithm is effective.
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
Fractal calculus involving gauge function
NASA Astrophysics Data System (ADS)
Golmankhaneh, Alireza K.; Baleanu, Dumitru
2016-08-01
Henstock-Kurzweil integral or gauge integral is the generalization of the Riemann integral. The functions which are not integrable because of singularity in the senses of Lebesgue or Riemann are gauge integrable. In this manuscript, we have generalized Fα-calculus using the gauge integral method for the integrating of the functions on fractal set subset of real-line where they have singularities. The suggested new method leads to the wider class of functions on the fractal subset of real-line that are *Fα-integrable. Using gauge function we define *Fα-derivative of functions their Fα-derivative is not exist. The reported results can be used for generalizing the fundamental theorem of Fα-calculus.
Analysis on correlation imaging based on fractal interpolation
NASA Astrophysics Data System (ADS)
Li, Bailing; Zhang, Wenwen; Chen, Qian; Gu, Guohua
2015-10-01
One fractal interpolation algorithm has been discussed in detail and the statistical self-similarity characteristics of light field have been analized in correlated experiment. For the correlation imaging experiment in condition of low sampling frequent, an image analysis approach based on fractal interpolation algorithm is proposed. This approach aims to improve the resolution of original image which contains a fewer number of pixels and highlight the image contour feature which is fuzzy. By using this method, a new model for the light field has been established. For the case of different moments of the intensity in the receiving plane, the local field division also has been established and then the iterated function system based on the experimental data set can be obtained by choosing the appropriate compression ratio under a scientific error estimate. On the basis of the iterative function, an explicit fractal interpolation function expression is given out in this paper. The simulation results show that the correlation image reconstructed by fractal interpolation has good approximations to the original image. The number of pixels of image after interpolation is significantly increased. This method will effectively solve the difficulty of image pixel deficiency and significantly improved the outline of objects in the image. The rate of deviation as the parameter has been adopted in the paper in order to evaluate objectively the effect of the algorithm. To sum up, fractal interpolation method proposed in this paper not only keeps the overall image but also increases the local information of the original image.
Multi-Scale Fractal Analysis of Image Texture and Pattern
NASA Technical Reports Server (NTRS)
Emerson, Charles W.
1998-01-01
Fractals embody important ideas of self-similarity, in which the spatial behavior or appearance of a system is largely independent of scale. Self-similarity is defined as 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. An ideal fractal (or monofractal) curve or surface has a constant dimension over all scales, although it may not be an integer value. This is in contrast to Euclidean or topological dimensions, where discrete one, two, and three dimensions describe curves, planes, and volumes. 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. However, most geographical phenomena are not strictly self-similar at all scales, but they can often be modeled by a stochastic fractal in which the scaling and self-similarity properties of the fractal have inexact patterns that can be described by statistics. Stochastic fractal sets relax the monofractal self-similarity assumption and measure many scales and resolutions in order to represent the varying form of a phenomenon as a function of local variables across space. In image interpretation, pattern is defined as the overall spatial form of related features, and the repetition of certain forms is a characteristic pattern found in many cultural objects and some natural features. Texture is the visual impression of coarseness or smoothness caused by the variability or uniformity of image tone or color. A potential use of fractals concerns the analysis of image texture. In these situations it is commonly observed that the degree of roughness or inexactness in an image or surface is a function of scale and not of experimental technique. The fractal dimension of remote sensing data could yield quantitative insight on the spatial complexity and
Estimating fractal dimension of medical images
NASA Astrophysics Data System (ADS)
Penn, Alan I.; Loew, Murray H.
1996-04-01
Box counting (BC) is widely used to estimate the fractal dimension (fd) of medical images on the basis of a finite set of pixel data. The fd is then used as a feature to discriminate between healthy and unhealthy conditions. We show that BC is ineffective when used on small data sets and give examples of published studies in which researchers have obtained contradictory and flawed results by using BC to estimate the fd of data-limited medical images. We present a new method for estimating fd of data-limited medical images. In the new method, fractal interpolation functions (FIFs) are used to generate self-affine models of the underlying image; each model, upon discretization, approximates the original data points. The fd of each FIF is analytically evaluated. The mean of the fds of the FIFs is the estimate of the fd of the original data. The standard deviation of the fds of the FIFs is a confidence measure of the estimate. The goodness-of-fit of the discretized models to the original data is a measure of self-affinity of the original data. In a test case, the new method generated a stable estimate of fd of a rib edge in a standard chest x-ray; box counting failed to generate a meaningful estimate of the same image.
Pyramidal fractal dimension for high resolution images
NASA Astrophysics Data System (ADS)
Mayrhofer-Reinhartshuber, Michael; Ahammer, Helmut
2016-07-01
Fractal analysis (FA) should be able to yield reliable and fast results for high-resolution digital images to be applicable in fields that require immediate outcomes. Triggered by an efficient implementation of FA for binary images, we present three new approaches for fractal dimension (D) estimation of images that utilize image pyramids, namely, the pyramid triangular prism, the pyramid gradient, and the pyramid differences method (PTPM, PGM, PDM). We evaluated the performance of the three new and five standard techniques when applied to images with sizes up to 8192 × 8192 pixels. By using artificial fractal images created by three different generator models as ground truth, we determined the scale ranges with minimum deviations between estimation and theory. All pyramidal methods (PM) resulted in reasonable D values for images of all generator models. Especially, for images with sizes ≥1024 ×1024 pixels, the PMs are superior to the investigated standard approaches in terms of accuracy and computation time. A measure for the possibility to differentiate images with different intrinsic D values did show not only that the PMs are well suited for all investigated image sizes, and preferable to standard methods especially for larger images, but also that results of standard D estimation techniques are strongly influenced by the image size. Fastest results were obtained with the PDM and PGM, followed by the PTPM. In terms of absolute D values best performing standard methods were magnitudes slower than the PMs. Concluding, the new PMs yield high quality results in short computation times and are therefore eligible methods for fast FA of high-resolution images.
Pyramidal fractal dimension for high resolution images.
Mayrhofer-Reinhartshuber, Michael; Ahammer, Helmut
2016-07-01
Fractal analysis (FA) should be able to yield reliable and fast results for high-resolution digital images to be applicable in fields that require immediate outcomes. Triggered by an efficient implementation of FA for binary images, we present three new approaches for fractal dimension (D) estimation of images that utilize image pyramids, namely, the pyramid triangular prism, the pyramid gradient, and the pyramid differences method (PTPM, PGM, PDM). We evaluated the performance of the three new and five standard techniques when applied to images with sizes up to 8192 × 8192 pixels. By using artificial fractal images created by three different generator models as ground truth, we determined the scale ranges with minimum deviations between estimation and theory. All pyramidal methods (PM) resulted in reasonable D values for images of all generator models. Especially, for images with sizes ≥1024×1024 pixels, the PMs are superior to the investigated standard approaches in terms of accuracy and computation time. A measure for the possibility to differentiate images with different intrinsic D values did show not only that the PMs are well suited for all investigated image sizes, and preferable to standard methods especially for larger images, but also that results of standard D estimation techniques are strongly influenced by the image size. Fastest results were obtained with the PDM and PGM, followed by the PTPM. In terms of absolute D values best performing standard methods were magnitudes slower than the PMs. Concluding, the new PMs yield high quality results in short computation times and are therefore eligible methods for fast FA of high-resolution images. PMID:27475069
Chang, H T; Kuo, C J
1998-03-10
An optical parallel architecture for the random-iteration algorithm to decode a fractal image by use of iterated-function system (IFS) codes is proposed. The code value is first converted into transmittance in film or a spatial light modulator in the optical part of the system. With an optical-to-electrical converter, electrical-to-optical converter, and some electronic circuits for addition and delay, we can perform the contractive affine transformation (CAT) denoted in IFS codes. In the proposed decoding architecture all CAT's generate points (image pixels) in parallel, and these points then are joined for display purposes. Therefore the decoding speed is improved greatly compared with existing serial-decoding architectures. In addition, an error and stability analysis that considers nonperfect elements is presented for the proposed optical system. Finally, simulation results are given to validate the proposed architecture. PMID:18268718
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.
a Type of Fractal Interpolation Functions and Their Fractional Calculus
NASA Astrophysics Data System (ADS)
Liang, Yong-Shun; Zhang, Qi
2016-05-01
Combine Chebyshev systems with fractal interpolation, certain continuous functions have been approximated by fractal interpolation functions unanimously. Local structure of these fractal interpolation functions (FIF) has been discussed. The relationship between order of Riemann-Liouville fractional calculus and Box dimension of FIF has been investigated.
Fractal image compression: A resolution independent representation for imagery
NASA Technical Reports Server (NTRS)
Sloan, Alan D.
1993-01-01
A deterministic fractal is an image which has low information content and no inherent scale. Because of their low information content, deterministic fractals can be described with small data sets. They can be displayed at high resolution since they are not bound by an inherent scale. A remarkable consequence follows. Fractal images can be encoded at very high compression ratios. This fern, for example is encoded in less than 50 bytes and yet can be displayed at resolutions with increasing levels of detail appearing. The Fractal Transform was discovered in 1988 by Michael F. Barnsley. It is the basis for a new image compression scheme which was initially developed by myself and Michael Barnsley at Iterated Systems. The Fractal Transform effectively solves the problem of finding a fractal which approximates a digital 'real world image'.
Multi-Scale Fractal Analysis of Image Texture and Pattern
NASA Technical Reports Server (NTRS)
Emerson, Charles W.; Lam, Nina Siu-Ngan; Quattrochi, Dale A.
1999-01-01
Analyses of the fractal dimension of Normalized Difference Vegetation Index (NDVI) images of homogeneous land covers near Huntsville, Alabama revealed that the fractal dimension of an image of an agricultural land cover indicates greater complexity as pixel size increases, a forested land cover gradually grows smoother, and an urban image remains roughly self-similar over the range of pixel sizes analyzed (10 to 80 meters). A similar analysis of Landsat Thematic Mapper images of the East Humboldt Range in Nevada taken four months apart show a more complex relation between pixel size and fractal dimension. The major visible difference between the spring and late summer NDVI images is the absence of high elevation snow cover in the summer image. This change significantly alters the relation between fractal dimension and pixel size. The slope of the fractal dimension-resolution relation provides indications of how image classification or feature identification will be affected by changes in sensor spatial resolution.
Multi-Scale Fractal Analysis of Image Texture and Pattern
NASA Technical Reports Server (NTRS)
Emerson, Charles W.; Lam, Nina Siu-Ngan; Quattrochi, Dale A.
1999-01-01
Analyses of the fractal dimension of Normalized Difference Vegetation Index (NDVI) images of homogeneous land covers near Huntsville, Alabama revealed that the fractal dimension of an image of an agricultural land cover indicates greater complexity as pixel size increases, a forested land cover gradually grows smoother, and an urban image remains roughly self-similar over the range of pixel sizes analyzed (10 to 80 meters). A similar analysis of Landsat Thematic Mapper images of the East Humboldt Range in Nevada taken four months apart show a more complex relation between pixel size and fractal dimension. The major visible difference between the spring and late summer NDVI images of the absence of high elevation snow cover in the summer image. This change significantly alters the relation between fractal dimension and pixel size. The slope of the fractal dimensional-resolution relation provides indications of how image classification or feature identification will be affected by changes in sensor spatial resolution.
Smitha, K A; Gupta, A K; Jayasree, R S
2015-09-01
Glioma, the heterogeneous tumors originating from glial cells, generally exhibit varied grades and are difficult to differentiate using conventional MR imaging techniques. When this differentiation is crucial in the disease prognosis and treatment, even the advanced MR imaging techniques fail to provide a higher discriminative power for the differentiation of malignant tumor from benign ones. A powerful image processing technique applied to the imaging techniques is expected to provide a better differentiation. The present study focuses on the fractal analysis of fluid attenuation inversion recovery MR images, for the differentiation of glioma. For this, we have considered the most important parameters of fractal analysis, fractal dimension and lacunarity. While fractal analysis assesses the malignancy and complexity of a fractal object, lacunarity gives an indication on the empty space and the degree of inhomogeneity in the fractal objects. Box counting method with the preprocessing steps namely binarization, dilation and outlining was used to obtain the fractal dimension and lacunarity in glioma. Statistical analysis such as one-way analysis of variance and receiver operating characteristic (ROC) curve analysis helped to compare the mean and to find discriminative sensitivity of the results. It was found that the lacunarity of low and high grade gliomas vary significantly. ROC curve analysis between low and high grade glioma for fractal dimension and lacunarity yielded 70.3% sensitivity and 66.7% specificity and 70.3% sensitivity and 88.9% specificity, respectively. The study observes that fractal dimension and lacunarity increases with an increase in the grade of glioma and lacunarity is helpful in identifying most malignant grades. PMID:26305773
Kepler mission exoplanet transit data analysis using fractal imaging
NASA Astrophysics Data System (ADS)
Dehipawala, S.; Tremberger, G.; Majid, Y.; Holden, T.; Lieberman, D.; Cheung, T.
2012-10-01
The Kepler mission is designed to survey a fist-sized patch of the sky within the Milky Way galaxy for the discovery of exoplanets, with emphasis on near Earth-size exoplanets in or near the habitable zone. The Kepler space telescope would detect the brightness fluctuation of a host star and extract periodic dimming in the lightcurve caused by exoplanets that cross in front of their host star. The photometric data of a host star could be interpreted as an image where fractal imaging would be applicable. Fractal analysis could elucidate the incomplete data limitation posed by the data integration window. The fractal dimension difference between the lower and upper halves of the image could be used to identify anomalies associated with transits and stellar activity as the buried signals are expected to be in the lower half of such an image. Using an image fractal dimension resolution of 0.04 and defining the whole image fractal dimension as the Chi-square expected value of the fractal dimension, a p-value can be computed and used to establish a numerical threshold for decision making that may be useful in further studies of lightcurves of stars with candidate exoplanets. Similar fractal dimension difference approaches would be applicable to the study of photometric time series data via the Higuchi method. The correlated randomness of the brightness data series could be used to support inferences based on image fractal dimension differences. Fractal compression techniques could be used to transform a lightcurve image, resulting in a new image with a new fractal dimension value, but this method has been found to be ineffective for images with high information capacity. The three studied criteria could be used together to further constrain the Kepler list of candidate lightcurves of stars with possible exoplanets that may be planned for ground-based telescope confirmation.
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 cerebral surfaces using magnetic resonance images
Majumdar, S.; Prasad, R.R.
1988-11-01
The calculation of the fractal dimension of the surface bounded by the grey matter in the normal human brain using axial, sagittal, and coronal cross-sectional magnetic resonance (MR) images is presented. The fractal dimension in this case is a measure of the convolutedness of this cerebral surface. It is proposed that the fractal dimension, a feature that may be extracted from MR images, may potentially be used for image analysis, quantitative tissue characterization, and as a feature to monitor and identify cerebral abnormalities and developmental changes.
Evaluation of Two Fractal Methods for Magnetogram Image Analysis
NASA Technical Reports Server (NTRS)
Stark, B.; Adams, M.; Hathaway, D. H.; Hagyard, M. J.
1997-01-01
Fractal and multifractal techniques have been applied to various types of solar data to study the fractal properties of sunspots as well as the distribution of photospheric magnetic fields and the role of random motions on the solar surface in this distribution. Other research includes the investigation of changes in the fractal dimension as an indicator for solar flares. Here we evaluate the efficacy of two methods for determining the fractal dimension of an image data set: the Differential Box Counting scheme and a new method, the Jaenisch scheme. To determine the sensitivity of the techniques to changes in image complexity, various types of constructed images are analyzed. In addition, we apply this method to solar magnetogram data from Marshall Space Flight Centers vector magnetograph.
Liver ultrasound image classification by using fractal dimension of edge
NASA Astrophysics Data System (ADS)
Moldovanu, Simona; Bibicu, Dorin; Moraru, Luminita
2012-08-01
Medical ultrasound image edge detection is an important component in increasing the number of application of segmentation, and hence it has been subject of many studies in the literature. In this study, we have classified the liver ultrasound images (US) combining Canny and Sobel edge detectors with fractal analysis in order to provide an indicator about of the US images roughness. We intend to provide a classification rule of the focal liver lesions as: cirrhotic liver, liver hemangioma and healthy liver. For edges detection the Canny and Sobel operators were used. Fractal analyses have been applied for texture analysis and classification of focal liver lesions according to fractal dimension (FD) determined by using the Box Counting method. To assess the performance and accuracy rate of the proposed method the contrast-to-noise (CNR) is analyzed.
Wideband Fractal Antennas for Holographic Imaging and Rectenna Applications
Bunch, Kyle J.; McMakin, Douglas L.; Sheen, David M.
2008-04-18
At Pacific Northwest National Laboratory, wideband antenna arrays have been successfully used to reconstruct three-dimensional images at microwave and millimeter-wave frequencies. Applications of this technology have included portal monitoring, through-wall imaging, and weapons detection. Fractal antennas have been shown to have wideband characteristics due to their self-similar nature (that is, their geometry is replicated at different scales). They further have advantages in providing good characteristics in a compact configuration. We discuss the application of fractal antennas for holographic imaging. Simulation results will be presented. Rectennas are a specific class of antennas in which a received signal drives a nonlinear junction and is retransmitted at either a harmonic frequency or a demodulated frequency. Applications include tagging and tracking objects with a uniquely-responding antenna. It is of interest to consider fractal rectenna because the self-similarity of fractal antennas tends to make them have similar resonance behavior at multiples of the primary resonance. Thus, fractal antennas can be suited for applications in which a signal is reradiated at a harmonic frequency. Simulations will be discussed with this application in mind.
Fractal image perception provides novel insights into hierarchical cognition.
Martins, M J; Fischmeister, F P; Puig-Waldmüller, E; Oh, J; Geissler, A; Robinson, S; Fitch, W T; Beisteiner, R
2014-08-01
Hierarchical structures play a central role in many aspects of human cognition, prominently including both language and music. In this study we addressed hierarchy in the visual domain, using a novel paradigm based on fractal images. Fractals are self-similar patterns generated by repeating the same simple rule at multiple hierarchical levels. Our hypothesis was that the brain uses different resources for processing hierarchies depending on whether it applies a "fractal" or a "non-fractal" cognitive strategy. We analyzed the neural circuits activated by these complex hierarchical patterns in an event-related fMRI study of 40 healthy subjects. Brain activation was compared across three different tasks: a similarity task, and two hierarchical tasks in which subjects were asked to recognize the repetition of a rule operating transformations either within an existing hierarchical level, or generating new hierarchical levels. Similar hierarchical images were generated by both rules and target images were identical. We found that when processing visual hierarchies, engagement in both hierarchical tasks activated the visual dorsal stream (occipito-parietal cortex, intraparietal sulcus and dorsolateral prefrontal cortex). In addition, the level-generating task specifically activated circuits related to the integration of spatial and categorical information, and with the integration of items in contexts (posterior cingulate cortex, retrosplenial cortex, and medial, ventral and anterior regions of temporal cortex). These findings provide interesting new clues about the cognitive mechanisms involved in the generation of new hierarchical levels as required for fractals. PMID:24699014
Wideband fractal antennas for holographic imaging and rectenna applications
NASA Astrophysics Data System (ADS)
Bunch, Kyle J.; McMakin, Douglas L.; Sheen, David M.
2008-04-01
At Pacific Northwest National Laboratory, wideband antenna arrays have been successfully used to reconstruct three-dimensional images at microwave and millimeter-wave frequencies. Applications of this technology have included portal monitoring, through-wall imaging, and weapons detection. Fractal antennas have been shown to have wideband characteristics due to their self-similar nature (that is, their geometry is replicated at different scales). They further have advantages in providing good characteristics in a compact configuration. We discuss the application of fractal antennas for holographic imaging. Simulation results will be presented. Rectennas are a specific class of antennas in which a received signal drives a nonlinear junction and is retransmitted at either a harmonic frequency or a demodulated frequency. Applications include tagging and tracking objects with a uniquely-responding antenna. It is of interest to consider fractal rectenna because the self-similarity of fractal antennas tends to make them have similar resonance behavior at multiples of the primary resonance. Thus, fractal antennas can be suited for applications in which a signal is reradiated at a harmonic frequency. Simulations will be discussed with this application in mind.
Chaos-based encryption for fractal image coding
NASA Astrophysics Data System (ADS)
Yuen, Ching-Hung; Wong, Kwok-Wo
2012-01-01
A chaos-based cryptosystem for fractal image coding is proposed. The Rényi chaotic map is employed to determine the order of processing the range blocks and to generate the keystream for masking the encoded sequence. Compared with the standard approach of fractal image coding followed by the Advanced Encryption Standard, our scheme offers a higher sensitivity to both plaintext and ciphertext at a comparable operating efficiency. The keystream generated by the Rényi chaotic map passes the randomness tests set by the United States National Institute of Standards and Technology, and so the proposed scheme is sensitive to the key.
Fractal Analysis of Laplacian Pyramidal Filters Applied to Segmentation of Soil Images
de Castro, J.; Méndez, A.; Tarquis, A. M.
2014-01-01
The laplacian pyramid is a well-known technique for image processing in which local operators of many scales, but identical shape, serve as the basis functions. The required properties to the pyramidal filter produce a family of filters, which is unipara metrical in the case of the classical problem, when the length of the filter is 5. We pay attention to gaussian and fractal behaviour of these basis functions (or filters), and we determine the gaussian and fractal ranges in the case of single parameter a. These fractal filters loose less energy in every step of the laplacian pyramid, and we apply this property to get threshold values for segmenting soil images, and then evaluate their porosity. Also, we evaluate our results by comparing them with the Otsu algorithm threshold values, and conclude that our algorithm produce reliable test results. PMID:25114957
Fractal analysis of laplacian pyramidal filters applied to segmentation of soil images.
de Castro, J; Ballesteros, F; Méndez, A; Tarquis, A M
2014-01-01
The laplacian pyramid is a well-known technique for image processing in which local operators of many scales, but identical shape, serve as the basis functions. The required properties to the pyramidal filter produce a family of filters, which is unipara metrical in the case of the classical problem, when the length of the filter is 5. We pay attention to gaussian and fractal behaviour of these basis functions (or filters), and we determine the gaussian and fractal ranges in the case of single parameter a. These fractal filters loose less energy in every step of the laplacian pyramid, and we apply this property to get threshold values for segmenting soil images, and then evaluate their porosity. Also, we evaluate our results by comparing them with the Otsu algorithm threshold values, and conclude that our algorithm produce reliable test results. PMID:25114957
Fractal image analysis - Application to the topography of Oregon and synthetic images.
NASA Technical Reports Server (NTRS)
Huang, Jie; Turcotte, Donald L.
1990-01-01
Digitized topography for the state of Oregon has been used to obtain maps of fractal dimension and roughness amplitude. The roughness amplitude correlates well with variations in relief and is a promising parameter for the quantitative classification of landforms. The spatial variations in fractal dimension are low and show no clear correlation with different tectonic settings. For Oregon the mean fractal dimension from a two-dimensional spectral analysis is D = 2.586, and for a one-dimensional spectral analysis the mean fractal dimension is D = 1.487, which is close to the Brown noise value D = 1.5. Synthetic two-dimensional images have also been generated for a range of D values. For D = 2.6, the synthetic image has a mean one-dimensional spectral fractal dimension D = 1.58, which is consistent with the results for Oregon. This approach can be easily applied to any digitzed image that obeys fractal statistics.
Multi-Scale Fractal Analysis of Image Texture and Pattern
NASA Technical Reports Server (NTRS)
Emerson, Charles W.; Quattrochi, Dale A.; Luvall, Jeffrey C.
1997-01-01
Fractals embody important ideas of self-similarity, in which the spatial behavior or appearance of a system is largely scale-independent. Self-similarity is a property of curves or surfaces where each part is indistinguishable from the whole. The fractal dimension D of remote sensing data yields quantitative insight on the spatial complexity and information content contained within these data. Analyses of Normalized Difference Vegetation Index (NDVI) images of homogeneous land covers near Huntsville, Alabama revealed that the fractal dimension of an image of an agricultural land cover indicates greater complexity as pixel size increases, a forested land cover gradually grows smoother, and an urban image remains roughly self-similar over the range of pixel sizes analyzed(l0 to 80 meters). The forested scene behaves as one would expect-larger pixel sizes decrease the complexity of the image as individual clumps of trees are averaged into larger blocks. The increased complexity of the agricultural image with increasing pixel size results from the loss of homogeneous groups of pixels in the large fields to mixed pixels composed of varying combinations of NDVI values that correspond to roads and vegetation. The same process occur's in the urban image to some extent, but the lack of large, homogeneous areas in the high resolution NDVI image means the initially high D value is maintained as pixel size increases. The slope of the fractal dimension-resolution relationship provides indications of how image classification or feature identification will be affected by changes in sensor resolution.
ERIC Educational Resources Information Center
Jurgens, Hartmut; And Others
1990-01-01
The production and application of images based on fractal geometry are described. Discussed are fractal language groups, fractal image coding, and fractal dialects. Implications for these applications of geometry to mathematics education are suggested. (CW)
Fractal descriptors for discrimination of microscopy images of plant leaves
NASA Astrophysics Data System (ADS)
Silva, N. R.; Florindo, J. B.; Gómez, M. C.; Kolb, R. M.; Bruno, O. M.
2014-03-01
This study proposes the application of fractal descriptors method to the discrimination of microscopy images of plant leaves. Fractal descriptors have demonstrated to be a powerful discriminative method in image analysis, mainly for the discrimination of natural objects. In fact, these descriptors express the spatial arrangement of pixels inside the texture under different scales and such arrangements are directly related to physical properties inherent to the material depicted in the image. Here, we employ the Bouligand-Minkowski descriptors. These are obtained by the dilation of a surface mapping the gray-level texture. The classification of the microscopy images is performed by the well-known Support Vector Machine (SVM) method and we compare the success rate with other literature texture analysis methods. The proposed method achieved a correctness rate of 89%, while the second best solution, the Co-occurrence descriptors, yielded only 78%. This clear advantage of fractal descriptors demonstrates the potential of such approach in the analysis of the plant microscopy images.
Advanced fractal approach for unsupervised classification of SAR images
NASA Astrophysics Data System (ADS)
Pant, Triloki; Singh, Dharmendra; Srivastava, Tanuja
2010-06-01
Unsupervised classification of Synthetic Aperture Radar (SAR) images is the alternative approach when no or minimum apriori information about the image is available. Therefore, an attempt has been made to develop an unsupervised classification scheme for SAR images based on textural information in present paper. For extraction of textural features two properties are used viz. fractal dimension D and Moran's I. Using these indices an algorithm is proposed for contextual classification of SAR images. The novelty of the algorithm is that it implements the textural information available in SAR image with the help of two texture measures viz. D and I. For estimation of D, the Two Dimensional Variation Method (2DVM) has been revised and implemented whose performance is compared with another method, i.e., Triangular Prism Surface Area Method (TPSAM). It is also necessary to check the classification accuracy for various window sizes and optimize the window size for best classification. This exercise has been carried out to know the effect of window size on classification accuracy. The algorithm is applied on four SAR images of Hardwar region, India and classification accuracy has been computed. A comparison of the proposed algorithm using both fractal dimension estimation methods with the K-Means algorithm is discussed. The maximum overall classification accuracy with K-Means comes to be 53.26% whereas overall classification accuracy with proposed algorithm is 66.16% for TPSAM and 61.26% for 2DVM.
Automatic classification for pathological prostate images based on fractal analysis.
Huang, Po-Whei; Lee, Cheng-Hsiung
2009-07-01
Accurate grading for prostatic carcinoma in pathological images is important to prognosis and treatment planning. Since human grading is always time-consuming and subjective, this paper presents a computer-aided system to automatically grade pathological images according to Gleason grading system which is the most widespread method for histological grading of prostate tissues. We proposed two feature extraction methods based on fractal dimension to analyze variations of intensity and texture complexity in regions of interest. Each image can be classified into an appropriate grade by using Bayesian, k-NN, and support vector machine (SVM) classifiers, respectively. Leave-one-out and k-fold cross-validation procedures were used to estimate the correct classification rates (CCR). Experimental results show that 91.2%, 93.7%, and 93.7% CCR can be achieved by Bayesian, k-NN, and SVM classifiers, respectively, for a set of 205 pathological prostate images. If our fractal-based feature set is optimized by the sequential floating forward selection method, the CCR can be promoted up to 94.6%, 94.2%, and 94.6%, respectively, using each of the above three classifiers. Experimental results also show that our feature set is better than the feature sets extracted from multiwavelets, Gabor filters, and gray-level co-occurrence matrix methods because it has a much smaller size and still keeps the most powerful discriminating capability in grading prostate images. PMID:19164082
Log-periodic route to fractal functions.
Gluzman, S; Sornette, D
2002-03-01
Log-periodic oscillations have been found to decorate the usual power-law behavior found to describe the approach to a critical point, when the continuous scale-invariance symmetry is partially broken into a discrete-scale invariance symmetry. For Ising or Potts spins with ferromagnetic interactions on hierarchical systems, the relative magnitude of the log-periodic corrections are usually very small, of order 10(-5). In growth processes [diffusion limited aggregation (DLA)], rupture, earthquake, and financial crashes, log-periodic oscillations with amplitudes of the order of 10% have been reported. We suggest a "technical" explanation for this 4 order-of-magnitude difference based on the property of the "regular function" g(x) embodying the effect of the microscopic degrees of freedom summed over in a renormalization group (RG) approach F(x)=g(x)+mu(-1)F(gamma x) of an observable F as a function of a control parameter x. For systems for which the RG equation has not been derived, the previous equation can be understood as a Jackson q integral, which is the natural tool for describing discrete-scale invariance. We classify the "Weierstrass-type" solutions of the RG into two classes characterized by the amplitudes A(n) of the power-law series expansion. These two classes are separated by a novel "critical" point. Growth processes (DLA), rupture, earthquake, and financial crashes thus seem to be characterized by oscillatory or bounded regular microscopic functions that lead to a slow power-law decay of A(n), giving strong log-periodic amplitudes. If in addition, the phases of A(n) are ergodic and mixing, the observable presents self-affine nondifferentiable properties. In contrast, the regular function of statistical physics models with "ferromagnetic"-type interactions at equilibrium involves unbound logarithms of polynomials of the control variable that lead to a fast exponential decay of A(n) giving weak log-periodic amplitudes and smoothed observables. PMID
ERIC Educational Resources Information Center
Osler, Thomas J.
1999-01-01
Because fractal images are by nature very complex, it can be inspiring and instructive to create the code in the classroom and watch the fractal image evolve as the user slowly changes some important parameter or zooms in and out of the image. Uses programming language that permits the user to store and retrieve a graphics image as a disk file.…
Aliasing removing of hyperspectral image based on fractal structure matching
NASA Astrophysics Data System (ADS)
Wei, Ran; Zhang, Ye; Zhang, Junping
2015-05-01
Due to the richness on high frequency components, hyperspectral image (HSI) is more sensitive to distortion like aliasing. Many methods aiming at removing such distortion have been proposed. However, seldom of them are suitable to HSI, due to low spatial resolution characteristic of HSI. Fortunately, HSI contains plentiful spectral information, which can be exploited to overcome such difficulties. Motivated by this, we proposed an aliasing removing method for HSI. The major differences between proposed and current methods is that proposed algorithm is able to utilize fractal structure information, thus the dilemma originated from low-resolution of HSI is solved. Experiments on real HSI data demonstrated subjectively and objectively that proposed method can not only remove annoying visual effect brought by aliasing, but also recover more high frequency component.
Lightning and the Heart: Fractal Behavior in Cardiac Function
BASSINGTHWAIGHTE, JAMES B.; van BEEK, J. H. G. M.
2010-01-01
Physical systems, from galactic clusters to diffusing molecules, often show fractal behavior. Likewise, living systems might often be well described by fractal algorithms. Such fractal descriptions in space and time imply that there is order in chaos, or put the other way around, chaotic dynamical systems in biology are more constrained and orderly than seen at first glance. The vascular network, the syncytium of cells, the processes of diffusion and transmembrane transport might be fractal features of the heart. These fractal features provide a basis which enables one to understand certain aspects of more global behavior such as atrial or ventricular fibrillation and perfusion heterogeneity. The heart might be regarded as a prototypical organ from these points of view. A particular example of the use of fractal geometry is in explaining myocardial flow heterogeneity via delivery of blood through an asymmetrical fractal branching network. PMID:21938081
Ising ferromagnet on a fractal family: Thermodynamical functions and scaling laws
NASA Astrophysics Data System (ADS)
Redinz, José Arnaldo; de Magalhães, Aglaé C. N.
1995-02-01
The Ising model with external magnetic field on infinitely ramified fractal lattices is studied. We derive exact expressions for the specific heat, spontaneous magnetization, and susceptibility. The critical exponents α, β, and γ corresponding to these respective thermal functions (at zero field) as well as the correlation length critical exponent ν are obtained. The hyperscaling law extended to fractals and the Rushbrooke scaling law are verified for these fractals.
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.
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.
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.
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.
Targets detection in smoke-screen image sequences using fractal and rough set theory
NASA Astrophysics Data System (ADS)
Yan, Xiaoke
2015-08-01
In this paper, a new algorithm for the detection of moving targets in smoke-screen image sequences is presented, which can combine three properties of pixel: grey, fractal dimensions and correlation between pixels by Rough Set. The first step is to locate and extract regions that may contain objects in an image by locally grey threshold technique. Secondly, the fractal dimensions of pixels are calculated, Smoke-Screen is done at different fractal dimensions. Finally, according to temporal and spatial correlations between different frames, the singular points can be filtered. The experimental results show that the algorithm can effectively increase detection probability and has robustness.
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
NASA Astrophysics Data System (ADS)
Boychuk, T. M.; Bodnar, B. M.; Vatamanesku, L. I.
2012-01-01
For the first time the complex correlation and fractal analysis was used for the investigation of microscopic images of both tissue images and hemangioma liquids. It was proposed a physical model of description of phase distributions formation of coherent radiation, which was transformed by optical anisotropic biological structures. The phase maps of laser radiation in the boundary diffraction zone were used as the main information parameter. The results of investigating the interrelation between the values of correlation (correlation area, asymmetry coefficient and autocorrelation function excess) and fractal (dispersion of logarithmic dependencies of power spectra) parameters are presented. They characterize the coordinate distributions of phase shifts in the points of laser images of histological sections of hemangioma, hemangioma blood smears and blood plasma with vascular system pathologies. The diagnostic criteria of hemangioma nascency are determined.
NASA Astrophysics Data System (ADS)
Boychuk, T. M.; Bodnar, B. M.; Vatamanesku, L. I.
2011-09-01
For the first time the complex correlation and fractal analysis was used for the investigation of microscopic images of both tissue images and hemangioma liquids. It was proposed a physical model of description of phase distributions formation of coherent radiation, which was transformed by optical anisotropic biological structures. The phase maps of laser radiation in the boundary diffraction zone were used as the main information parameter. The results of investigating the interrelation between the values of correlation (correlation area, asymmetry coefficient and autocorrelation function excess) and fractal (dispersion of logarithmic dependencies of power spectra) parameters are presented. They characterize the coordinate distributions of phase shifts in the points of laser images of histological sections of hemangioma, hemangioma blood smears and blood plasma with vascular system pathologies. The diagnostic criteria of hemangioma nascency are determined.
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.
A Lossless hybrid wavelet-fractal compression for welding radiographic images.
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. PMID:26890900
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.
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
Statistical fractal border features for MRI breast mass images
NASA Astrophysics Data System (ADS)
Penn, Alan I.; Bolinger, Lizann; Loew, Murray H.
1998-06-01
MRI has been proposed as an alternative method to mammography for detecting and staging breast cancer. Recent studies have shown that architectural features of breast masses may be useful in improving specificity. Since fractal dimension (fd) has been correlated with roughness, and border roughness is an indicator of malignancy, the fd of the mass border is a promising architectural feature for achieving improved specificity. Previous methods of estimating the fd of the mass border have been unreliable because of limited data or overlay restrictive assumptions of the fractal model. We present preliminary results of a statistical approach in which a sample space of fd estimates is generated from a family of self-affine fractal models. The fd of the mass border is then estimated from the statistics of the sample space.
Edge detection and image segmentation of space scenes using fractal analyses
NASA Technical Reports Server (NTRS)
Cleghorn, Timothy F.; Fuller, J. J.
1992-01-01
A method was developed for segmenting images of space scenes into manmade and natural components, using fractal dimensions and lacunarities. Calculations of these parameters are presented. Results are presented for a variety of aerospace images, showing that it is possible to perform edge detections of manmade objects against natural background such as those seen in an aerospace environment.
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.
NASA Astrophysics Data System (ADS)
Tremberger, George, Jr.; Flamholz, A.; Cheung, E.; Sullivan, R.; Subramaniam, R.; Schneider, P.; Brathwaite, G.; Boteju, J.; Marchese, P.; Lieberman, D.; Cheung, T.; Holden, Todd
2007-09-01
The absorption effect of the back surface boundary of a diffuse layer was studied via laser generated reflection speckle pattern. The spatial speckle intensity provided by a laser beam was measured. The speckle data were analyzed in terms of fractal dimension (computed by NIH ImageJ software via the box counting fractal method) and weak localization theory based on Mie scattering. Bar code imaging was modeled as binary absorption contrast and scanning resolution in millimeter range was achieved for diffusive layers up to thirty transport mean free path thick. Samples included alumina, porous glass and chicken tissue. Computer simulation was used to study the effect of speckle spatial distribution and observed fractal dimension differences were ascribed to variance controlled speckle sizes. Fractal dimension suppressions were observed in samples that had thickness dimensions around ten transport mean free path. Computer simulation suggested a maximum fractal dimension of about 2 and that subtracting information could lower fractal dimension. The fractal dimension was shown to be sensitive to sample thickness up to about fifteen transport mean free paths, and embedded objects which modified 20% or more of the effective thickness was shown to be detectable. The box counting fractal method was supplemented with the Higuchi data series fractal method and application to architectural distortion mammograms was demonstrated. The use of fractals in diffusive analysis would provide a simple language for a dialog between optics experts and mammography radiologists, facilitating the applications of laser diagnostics in tissues.
Improved triangular prism methods for fractal analysis of remotely sensed images
NASA Astrophysics Data System (ADS)
Zhou, Yu; Fung, Tung; Leung, Yee
2016-05-01
Feature extraction has been a major area of research in remote sensing, and fractal feature is a natural characterization of complex objects across scales. Extending on the modified triangular prism (MTP) method, we systematically discuss three factors closely related to the estimation of fractal dimensions of remotely sensed images. They are namely the (F1) number of steps, (F2) step size, and (F3) estimation accuracy of the facets' areas of the triangular prisms. Differing from the existing improved algorithms that separately consider these factors, we simultaneously take all factors to construct three new algorithms, namely the modification of the eight-pixel algorithm, the four corner and the moving-average MTP. Numerical experiments based on 4000 generated images show their superior performances over existing algorithms: our algorithms not only overcome the limitation of image size suffered by existing algorithms but also obtain similar average fractal dimension with smaller standard deviation, only 50% for images with high fractal dimensions. In the case of real-life application, our algorithms more likely obtain fractal dimensions within the theoretical range. Thus, the fractal nature uncovered by our algorithms is more reasonable in quantifying the complexity of remotely sensed images. Despite the similar performance of these three new algorithms, the moving-average MTP can mitigate the sensitivity of the MTP to noise and extreme values. Based on the numerical and real-life case study, we check the effect of the three factors, (F1)-(F3), and demonstrate that these three factors can be simultaneously considered for improving the performance of the MTP method.
ERIC Educational Resources Information Center
Barton, Ray
1990-01-01
Presented is an educational game called "The Chaos Game" which produces complicated fractal images. Two basic computer programs are included. The production of fractal images by the Sierpinski gasket and the Chaos Game programs is discussed. (CW)
Automatic Method to Classify Images Based on Multiscale Fractal Descriptors and Paraconsistent Logic
NASA Astrophysics Data System (ADS)
Pavarino, E.; Neves, L. A.; Nascimento, M. Z.; Godoy, M. F.; Arruda, P. F.; Neto, D. S.
2015-01-01
In this study is presented an automatic method to classify images from fractal descriptors as decision rules, such as multiscale fractal dimension and lacunarity. The proposed methodology was divided in three steps: quantification of the regions of interest with fractal dimension and lacunarity, techniques under a multiscale approach; definition of reference patterns, which are the limits of each studied group; and, classification of each group, considering the combination of the reference patterns with signals maximization (an approach commonly considered in paraconsistent logic). The proposed method was used to classify histological prostatic images, aiming the diagnostic of prostate cancer. The accuracy levels were important, overcoming those obtained with Support Vector Machine (SVM) and Best- first Decicion Tree (BFTree) classifiers. The proposed approach allows recognize and classify patterns, offering the advantage of giving comprehensive results to the specialists.
NASA Technical Reports Server (NTRS)
Huang, J.; Turcotte, D. L.
1989-01-01
The concept of fractal mapping is introduced and applied to digitized topography of Arizona. It is shown that the fractal statistics satisfy the topography of the state to a good approximation. The fractal dimensions and roughness amplitudes from subregions are used to construct maps of these quantities. It is found that the fractal dimension of actual two-dimensional topography is not affected by the adding unity to the fractal dimension of one-dimensional topographic tracks. In addition, consideration is given to the production of fractal maps from synthetically derived topography.
NASA Astrophysics Data System (ADS)
Bonifazi, Giuseppe
2002-05-01
Fractal geometry concerns the study of non-Euclidean geometrical figures generated by a recursive sequence of mathematical operations. These figures show self-similar features in the sense that their shape, at a certain scale, is equal to, or at least 'similar' to, the same shape of the figure at a different scale or resolution. This property of scale invariance often occurs also in some natural events. The basis of the method is the very comparison of the space covering of one of those geometrical constructions, the 'Sierpinski Carpet,' and the particles location and size distribution in the portion of surface acquired in the images. Fractal analysis method, consists in the study of the size distribution structure and disposition modalities. Such an approach was presented in this paper with reference to the characterization of airborne dust produced in working environment through the evaluation of particle size disposition and distribution over a surface. Such a behavior, in fact, was assumed to be strictly correlated with 1) material surface physical characteristics and 2) on the modalities by which the material is 'shot' on the dust sample holder (glass support). To get this goal, a 2D-Fractal extractor has been used, calibrated to different area thresholding values, as a result binary sample image changes, originating different fractal resolutions plotted for the residual background area (Richardson plot). Changing the lower size thresholding value of the 2D-Fractal extractor algorithm, means to change the starting point of fractal measurements; in such way, it has been looked for possible differences of powders in the lower dimensional classes. The rate by which the lowest part of the plot goes down to residual area equal to zero, together with fractal dimensions (low and high, depending on average material curve) and their precision (R2) of 'zero curve' (Richardson Plot with area thresholding value equal to zero, i.e. whole fractal distribution), can be used
Saremi, Saeed; Sejnowski, Terrence J
2016-05-01
Natural images are scale invariant with structures at all length scales.We formulated a geometric view of scale invariance in natural images using percolation theory, which describes the behavior of connected clusters on graphs.We map images to the percolation model by defining clusters on a binary representation for images. We show that critical percolating structures emerge in natural images and study their scaling properties by identifying fractal dimensions and exponents for the scale-invariant distributions of clusters. This formulation leads to a method for identifying clusters in images from underlying structures as a starting point for image segmentation. PMID:26415153
Saremi, Saeed; Sejnowski, Terrence J.
2016-01-01
Natural images are scale invariant with structures at all length scales. We formulated a geometric view of scale invariance in natural images using percolation theory, which describes the behavior of connected clusters on graphs. We map images to the percolation model by defining clusters on a binary representation for images. We show that critical percolating structures emerge in natural images and study their scaling properties by identifying fractal dimensions and exponents for the scale-invariant distributions of clusters. This formulation leads to a method for identifying clusters in images from underlying structures as a starting point for image segmentation. PMID:26415153
Fractal methods for extracting artificial objects from the unmanned aerial vehicle images
NASA Astrophysics Data System (ADS)
Markov, Eugene
2016-04-01
Unmanned aerial vehicles (UAVs) have become used increasingly in earth surface observations, with a special interest put into automatic modes of environmental control and recognition of artificial objects. Fractal methods for image processing well detect the artificial objects in digital space images but were not applied previously to the UAV-produced imagery. Parameters of photography, on-board equipment, and image characteristics differ considerably for spacecrafts and UAVs. Therefore, methods that work properly with space images can produce different results for the UAVs. In this regard, testing the applicability of fractal methods for the UAV-produced images and determining the optimal range of parameters for these methods represent great interest. This research is dedicated to the solution of this problem. Specific features of the earth's surface images produced with UAVs are described in the context of their interpretation and recognition. Fractal image processing methods for extracting artificial objects are described. The results of applying these methods to the UAV images are presented.
Plant Identification Based on Leaf Midrib Cross-Section Images Using Fractal Descriptors
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. PMID:26091501
Differential Diagnosis: Shape and Function, Fractal Tools in the Pathology Lab.
Bianciardi, Giorgio
2015-10-01
Fractal analysis is a useful objective tool in describing complexity of shapes and signals providing information for understanding pathological changes. We present fractal approaches and software used in our pathology laboratory to analyze shapes of tumors in tissues and cells, to evaluate the microvessel network complexity in hereditary diseases or the complexity of the surface of blood cells in atherosclerosis-linked condition, as well to analyze function in vasculopathic subjects by chaotic analysis of electrocardiographic signals, in order to perform differential diagnosis. The fractal parameters appear to converge towards distinct values in pathological conditions compared to healthy, approaching the characteristics values of a percolation process or the diffusion-limited aggregation process, respectively: a bifurcation that allows to support the diagnostic process of the pathologist in his daily work. These methods, presented here as a kind of a cookbook ready for the pathologist, are low cost and not time consuming. PMID:26375935
Radial distribution function for hard spheres in fractal dimensions: A heuristic approximation
NASA Astrophysics Data System (ADS)
Santos, Andrés; de Haro, Mariano López
2016-06-01
Analytic approximations for the radial distribution function, the structure factor, and the equation of state of hard-core fluids in fractal dimension d (1 ≤d ≤3 ) are developed as heuristic interpolations from the knowledge of the exact and Percus-Yevick results for the hard-rod and hard-sphere fluids, respectively. In order to assess their value, such approximate results are compared with those of recent Monte Carlo simulations and numerical solutions of the Percus-Yevick equation for a fractal dimension [M. Heinen et al., Phys. Rev. Lett. 115, 097801 (2015), 10.1103/PhysRevLett.115.097801], a good agreement being observed.
Alzheimer's Disease Detection in Brain Magnetic Resonance Images Using Multiscale Fractal Analysis
Lahmiri, Salim; Boukadoum, Mounir
2013-01-01
We present a new automated system for the detection of brain magnetic resonance images (MRI) affected by Alzheimer's disease (AD). The MRI is analyzed by means of multiscale analysis (MSA) to obtain its fractals at six different scales. The extracted fractals are used as features to differentiate healthy brain MRI from those of AD by a support vector machine (SVM) classifier. The result of classifying 93 brain MRIs consisting of 51 images of healthy brains and 42 of brains affected by AD, using leave-one-out cross-validation method, yielded 99.18% ± 0.01 classification accuracy, 100% sensitivity, and 98.20% ± 0.02 specificity. These results and a processing time of 5.64 seconds indicate that the proposed approach may be an efficient diagnostic aid for radiologists in the screening for AD. PMID:24967286
a New Class of Fractal Interpolation Surfaces Based on Functional Values
NASA Astrophysics Data System (ADS)
Chand, A. K. B.; Vijender, N.
2016-02-01
Fractal interpolation is a modern technique for fitting of smooth/non-smooth data. Based on only functional values, we develop two types of 𝒞1-rational fractal interpolation surfaces (FISs) on a rectangular grid in the present paper that contain scaling factors in both directions and two types of positive real parameters which are referred as shape parameters. The graphs of these 𝒞1-rational FISs are the attractors of suitable rational iterated function systems (IFSs) in ℝ3 which use a collection of rational IFSs in the x-direction and y-direction and hence these FISs are self-referential in nature. Using upper bounds of the interpolation error of the x-direction and y-direction fractal interpolants along the grid lines, we study the convergence results of 𝒞1-rational FISs toward the original function. A numerical illustration is provided to explain the visual quality of our rational FISs. An extra feature of these fractal surface schemes is that it allows subsequent interactive alteration of the shape of the surfaces by changing the scaling factors and shape parameters.
A formal link of anticipatory mental imaging with fractal features of biological time
NASA Astrophysics Data System (ADS)
Bounias, Michel; Bonaly, André
2001-06-01
Previous works have supported the proposition that biological organisms are endowed with perceptive functions based of fixed points in mental chaining sequences (Bounias and Bonaly, 1997). Former conjectures proposed that memory could be fractal (Dubois, 1990; Bonaly, 1989, 1994) and that the biological time, standing at the intersection of the arrows of past events and of future events, exhibit some similarity with the construction of a Koch-like structure (Bonaly, 2000). A formal examination of the biological system of perception let now appear that the perception of time occurs at the intersection of two consecutive fixed point sequences. Therefore, time-flow is mapped by sequences of fixed points of which each is the convergence value of sequences of neuronal configurations. Since the latter are indexed by the ordered sequences of closed Poincaré sections determining the physical arrow of time (Bonaly and Bounias, 1995), there exists a surjective Lipschitz-Hölder mapping of physical time onto system-perceived time. The succession of consecutive fixed points of the perceptive sequence in turn constitute a sequence whose properties account for the apparent continuity of time-perception, in the same time as they fulfill the basically nonlinearity of time as a general parameter. A generator polygon is shown to be constituted by four sides: (i) the interval between two consecutive bursts of perceptions provides the base, with a projection paralleling the arrow of physical time; (ii) the top is constituted by the sequence of repeated fixed points accounting for the mental image got from the first burst, and further maintained up to the formation of the next fixed point; (iii) the first lateral side is the difference (Lk-1 to Lk) between the measure (L) of neuronal chains leading to the first image a(uk), and: (iv) the second lateral side is the difference of measure between Lk and Lk+1. The equation of the system is therefore of the incursive type, and this
NASA Astrophysics Data System (ADS)
Ahammer, Helmut; DeVaney, Trevor T. J.
2004-03-01
The boundary of a fractal object, represented in a two-dimensional space, is theoretically a line with an infinitely small width. In digital images this boundary or contour is limited to the pixel resolution of the image and the width of the line commonly depends on the edge detection algorithm used. The Minkowski dimension was evaluated by using three different edge detection algorithms (Sobel, Roberts, and Laplace operator). These three operators were investigated because they are very widely used and because their edge detection result is very distinct concerning the line width. Very common fractals (Sierpinski carpet and Koch islands) were investigated as well as the binary images from a cancer invasion assay taken with a confocal laser scanning microscope. The fractal dimension is directly proportional to the width of the contour line and the fact, that in practice very often the investigated objects are fractals only within a limited resolution range is considered too.
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
Multi-modal multi-fractal boundary encoding in object-based image compression
NASA Astrophysics Data System (ADS)
Schmalz, Mark S.
2006-08-01
The compact representation of region boundary contours is key to efficient representation and compression of digital images using object-based compression (OBC). In OBC, regions are coded in terms of their texture, color, and shape. Given the appropriate representation scheme, high compression ratios (e.g., 500:1 <= CR <= 2,500:1) have been reported for selected images. Because a region boundary is often represented with more parameters than the region contents, it is crucial to maximize the boundary compression ratio by reducing these parameters. Researchers have elsewhere shown that cherished boundary encoding techniques such as chain coding, simplicial complexes, or quadtrees, to name but a few, are inadequate to support OBC within the aforementioned CR range. Several existing compression standards such as MPEG support efficient boundary representation, but do not necessarily support OBC at CR >= 500:1 . Siddiqui et al. exploited concepts from fractal geometry to encode and compress region boundaries based on fractal dimension, reporting CR = 286.6:1 in one test. However, Siddiqui's algorithm is costly and appears to contain ambiguities. In this paper, we first discuss fractal dimension and OBC compression ratio, then enhance Siddiqui's algorithm, achieving significantly higher CR for a wide variety of boundary types. In particular, our algorithm smoothes a region boundary B, then extracts its inflection or control points P, which are compactly represented. The fractal dimension D is computed locally for the detrended B. By appropriate subsampling, one efficiently segments disjoint clusters of D values subject to a preselected tolerance, thereby partitioning B into a multifractal. This is accomplished using four possible compression modes. In contrast, previous researchers have characterized boundary variance with one fractal dimension, thereby producing a monofractal. At its most complex, the compressed representation contains P, a spatial marker, and a D value
Fractal analyses of osseous healing using Tuned Aperture Computed Tomography images
Seyedain, Ali; Webber, Richard L.; Nair, Umadevi P.; Piesco, Nicholas P.; Agarwal, Sudha; Mooney, Mark P.; Gröndahl, Hans-Göran
2016-01-01
The aim of this study was to evaluate osseous healing in mandibular defects using fractal analyses on conventional radiographs and tuned aperture computed tomography (TACT; OrthoTACT, Instrumentarium Imaging, Helsinki, Finland) images. Eighty test sites on the inferior margins of rabbit mandibles were subject to lesion induction and treated with one of the following: no treatment (controls); osteoblasts only; polymer matrix only; or osteoblast-polymer matrix (OPM) combination. Images were acquired using conventional radiography and TACT, including unprocessed TACT (TACT-U) and iteratively restored TACT (TACT-IR). Healing was followed up over time and images acquired at 3, 6, 9, and 12 weeks post-surgery. Fractal dimension (FD) was computed within regions of interest in the defects using the TACT workbench. Results were analyzed for effects produced by imaging modality, treatment modality, time after surgery and lesion location. Histomorphometric data were available to assess ground truth. Significant differences (p < 0.0001) were noted based on imaging modality with TACT-IR recording the highest mean fractal dimension (MFD), followed by TACT-U and conventional images, in that order. Sites treated with OPM recorded the highest MFDs among all treatment modalities (p < 0.0001). The highest MFD based on time was recorded at 3 weeks and differed significantly with 12 weeks (p < 0.035). Correlation of FD with results of histomorphometric data was high (r = 0.79; p < 0.001). The FD computed on TACT-IR showed the highest correlation with histomorphometric data, thus establishing the fact TACT is a more efficient and accurate imaging modality for quantification of osseous changes within healing bony defects. PMID:11519567
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.
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.
Zone specific fractal dimension of retinal images as predictor of stroke incidence.
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. PMID:25485298
Zone Specific Fractal Dimension of Retinal Images as Predictor of Stroke Incidence
Kumar, Dinesh Kant; Hao, Hao; Unnikrishnan, Premith; 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. PMID:25485298
Using fractal compression scheme to embed a digital signature into an image
NASA Astrophysics Data System (ADS)
Puate, Joan; Jordan, Frederic D.
1997-01-01
With the increase in the number of digital networks and recording devices, digital images appear to be a material, especially still images, whose ownership is widely threatened due to the availability of simple, rapid and perfect duplication and distribution means. It is in this context that several European projects are devoted to finding a technical solution which, as it applies to still images, introduces a code or watermark into the image data itself. This watermark should not only allow one to determine the owner of the image, but also respect its quality and be difficult to revoke. An additional requirement is that the code should be retrievable by the only mean of the protected information. In this paper, we propose a new scheme based on fractal coding and decoding. In general terms, a fractal coder exploits the spatial redundancy within the image by establishing a relationship between its different parts. We describe a way to use this relationship as a means of embedding a watermark. Tests have been performed in order to measure the robustness of the technique against JPEG conversion and low pass filtering. In both cases, very promising results have been obtained.
Landmine detection using IR image segmentation by means of fractal dimension analysis
NASA Astrophysics Data System (ADS)
Abbate, Horacio A.; Gambini, Juliana; Delrieux, Claudio; Castro, Eduardo H.
2009-05-01
This work is concerned with buried landmines detection by long wave infrared images obtained during the heating or cooling of the soil and a segmentation process of the images. The segmentation process is performed by means of a local fractal dimension analysis (LFD) as a feature descriptor. We use two different LFD estimators, box-counting dimension (BC), and differential box counting dimension (DBC). These features are computed in a per pixel basis, and the set of features is clusterized by means of the K-means method. This segmentation technique produces outstanding results, with low computational cost.
Bells Galore: Oscillations and circle-map dynamics from space-filling fractal functions
Puente, C.E.; Cortis, A.; Sivakumar, B.
2008-10-15
The construction of a host of interesting patterns over one and two dimensions, as transformations of multifractal measures via fractal interpolating functions related to simple affine mappings, is reviewed. It is illustrated that, while space-filling fractal functions most commonly yield limiting Gaussian distribution measures (bells), there are also situations (depending on the affine mappings parameters) in which there is no limit. Specifically, the one-dimensional case may result in oscillations between two bells, whereas the two-dimensional case may give rise to unexpected circle map dynamics of an arbitrary number of two-dimensional circular bells. It is also shown that, despite the multitude of bells over two dimensions, whose means dance making regular polygons or stars inscribed on a circle, the iteration of affine maps yields exotic kaleidoscopes that decompose such an oscillatory pattern in a way that is similar to the many cases that converge to a single bell.
Badea, Alexandru Florin; Lupsor Platon, Monica; Crisan, Maria; Cattani, Carlo; Badea, Iulia; Pierro, Gaetano; Sannino, Gianpaolo; Baciut, Grigore
2013-01-01
The geometry of some medical images of tissues, obtained by elastography and ultrasonography, is characterized in terms of complexity parameters such as the fractal dimension (FD). It is well known that in any image there are very subtle details that are not easily detectable by the human eye. However, in many cases like medical imaging diagnosis, these details are very important since they might contain some hidden information about the possible existence of certain pathological lesions like tissue degeneration, inflammation, or tumors. Therefore, an automatic method of analysis could be an expedient tool for physicians to give a faultless diagnosis. The fractal analysis is of great importance in relation to a quantitative evaluation of "real-time" elastography, a procedure considered to be operator dependent in the current clinical practice. Mathematical analysis reveals significant discrepancies among normal and pathological image patterns. The main objective of our work is to demonstrate the clinical utility of this procedure on an ultrasound image corresponding to a submandibular diffuse pathology. PMID:23762183
Radial distribution function for hard spheres in fractal dimensions: A heuristic approximation.
Santos, Andrés; de Haro, Mariano López
2016-06-01
Analytic approximations for the radial distribution function, the structure factor, and the equation of state of hard-core fluids in fractal dimension d (1≤d≤3) are developed as heuristic interpolations from the knowledge of the exact and Percus-Yevick results for the hard-rod and hard-sphere fluids, respectively. In order to assess their value, such approximate results are compared with those of recent Monte Carlo simulations and numerical solutions of the Percus-Yevick equation for a fractal dimension [M. Heinen et al., Phys. Rev. Lett. 115, 097801 (2015)PRLTAO0031-900710.1103/PhysRevLett.115.097801], a good agreement being observed. PMID:27415227
NASA Astrophysics Data System (ADS)
Mukhopadhyay, Sabyasachi; Das, Nandan K.; Pradhan, Asima; Ghosh, Nirmalya; Panigrahi, Prasanta K.
2014-02-01
The objective of the present work is to diagnose pre-cancer by wavelet transform and multi-fractal de-trended fluctuation analysis of DIC images of normal and different grades of cancer tissues. Our DIC imaging and fluctuation analysis methods (Discrete and continuous wavelet transform, MFDFA) confirm the ability to diagnose and detect the early stage of cancer in cervical tissue.
Azevedo-Marques, P M; Spagnoli, H F; Frighetto-Pereira, L; Menezes-Reis, R; Metzner, G A; Rangayyan, R M; Nogueira-Barbosa, M H
2015-08-01
Fractures with partial collapse of vertebral bodies are generically referred to as "vertebral compression fractures" or VCFs. VCFs can have different etiologies comprising trauma, bone failure related to osteoporosis, or metastatic cancer affecting bone. VCFs related to osteoporosis (benign fractures) and to cancer (malignant fractures) are commonly found in the elderly population. In the clinical setting, the differentiation between benign and malignant fractures is complex and difficult. This paper presents a study aimed at developing a system for computer-aided diagnosis to help in the differentiation between malignant and benign VCFs in magnetic resonance imaging (MRI). We used T1-weighted MRI of the lumbar spine in the sagittal plane. Images from 47 consecutive patients (31 women, 16 men, mean age 63 years) were studied, including 19 malignant fractures and 54 benign fractures. Spectral and fractal features were extracted from manually segmented images of 73 vertebral bodies with VCFs. The classification of malignant vs. benign VCFs was performed using the k-nearest neighbor classifier with the Euclidean distance. Results obtained show that combinations of features derived from Fourier and wavelet transforms, together with the fractal dimension, were able to obtain correct classification rate up to 94.7% with area under the receiver operating characteristic curve up to 0.95. PMID:26736364
Evaluation of super-resolution imager with binary fractal test target
NASA Astrophysics Data System (ADS)
Landeau, Stéphane
2014-10-01
Today, new generation of powerful non-linear image processing are used for real time super-resolution or noise reduction. Optronic imagers with such features are becoming difficult to assess, because spatial resolution and sensitivity are now related to scene content. Many algorithms include regularization process, which usually reduces image complexity to enhance spread edges or contours. Small important scene details can be then deleted by this kind of processing. In this paper, a binary fractal test target is presented, with a structured clutter pattern and an interesting autosimilarity multi-scale property. The apparent structured clutter of this test target gives a trade-off between a white noise, unlikely in real scenes, and very structured targets like MTF targets. Together with the fractal design of the target, an assessment method has been developed to evaluate automatically the non-linear effects on the acquired and processed image of the imager. The calculated figure of merit is to be directly comparable to the linear Fourier MTF. For this purpose the Haar wavelet elements distributed spatially and at different scales on the target are assimilated to the sine Fourier cycles at different frequencies. The probability of correct resolution indicates the ability to read correct Haar contrast among all Haar wavelet elements with a position constraint. For the method validation, a simulation of two different imager types has been done, a well-sampled linear system and an under-sampled one, coupled with super-resolution or noise reduction algorithms. The influence of the target contrast on the figures of merit is analyzed. Finally, the possible introduction of this new figure of merit in existing analytical range performance models, such as TRM4 (Fraunhofer IOSB) or NVIPM (NVESD) is discussed. Benefits and limitations of the method are also compared to the TOD (TNO) evaluation method.
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.
NASA Astrophysics Data System (ADS)
Popescu, Dan P.; Flueraru, Costel; Mao, Youxin; Chang, Shoude; Sowa, Michael G.
2010-02-01
Two methods for analyzing OCT images of arterial tissues are tested. These methods are applied toward two types of samples: segments of arteries collected from atherosclerosis-prone Watanabe heritable hyper-lipidemic rabbits and pieces of porcine left descending coronary arteries without atherosclerosis. The first method is based on finding the attenuation coefficients for the OCT signal that propagates through various regions of the tissue. The second method involves calculating the fractal dimensions of the OCT signal textures in the regions of interest identified within the acquired images. A box-counting algorithm is used for calculating the fractal dimensions. Both parameters, the attenuation coefficient as well as the fractal dimension correlate very well with the anatomical features of both types of samples.
Medical image retrieval and analysis by Markov random fields and multi-scale fractal dimension.
Backes, André Ricardo; Gerhardinger, Leandro Cavaleri; Batista Neto, João do Espírito Santo; Bruno, Odemir Martinez
2015-02-01
Many Content-based Image Retrieval (CBIR) systems and image analysis tools employ color, shape and texture (in a combined fashion or not) as attributes, or signatures, to retrieve images from databases or to perform image analysis in general. Among these attributes, texture has turned out to be the most relevant, as it allows the identification of a larger number of images of a different nature. This paper introduces a novel signature which can be used for image analysis and retrieval. It combines texture with complexity extracted from objects within the images. The approach consists of a texture segmentation step, modeled as a Markov Random Field process, followed by the estimation of the complexity of each computed region. The complexity is given by a Multi-scale Fractal Dimension. Experiments have been conducted using an MRI database in both pattern recognition and image retrieval contexts. The results show the accuracy of the proposed method in comparison with other traditional texture descriptors and also indicate how the performance changes as the level of complexity is altered. PMID:25586375
Medical image retrieval and analysis by Markov random fields and multi-scale fractal dimension
NASA Astrophysics Data System (ADS)
Backes, André Ricardo; Cavaleri Gerhardinger, Leandro; do Espírito Santo Batista Neto, João; Martinez Bruno, Odemir
2015-02-01
Many Content-based Image Retrieval (CBIR) systems and image analysis tools employ color, shape and texture (in a combined fashion or not) as attributes, or signatures, to retrieve images from databases or to perform image analysis in general. Among these attributes, texture has turned out to be the most relevant, as it allows the identification of a larger number of images of a different nature. This paper introduces a novel signature which can be used for image analysis and retrieval. It combines texture with complexity extracted from objects within the images. The approach consists of a texture segmentation step, modeled as a Markov Random Field process, followed by the estimation of the complexity of each computed region. The complexity is given by a Multi-scale Fractal Dimension. Experiments have been conducted using an MRI database in both pattern recognition and image retrieval contexts. The results show the accuracy of the proposed method in comparison with other traditional texture descriptors and also indicate how the performance changes as the level of complexity is altered.
NASA Astrophysics Data System (ADS)
Yang, Y.; Li, H. T.; Han, Y. S.; Gu, H. Y.
2015-06-01
Image segmentation is the foundation of further object-oriented image analysis, understanding and recognition. It is one of the key technologies in high resolution remote sensing applications. In this paper, a new fast image segmentation algorithm for high resolution remote sensing imagery is proposed, which is based on graph theory and fractal net evolution approach (FNEA). Firstly, an image is modelled as a weighted undirected graph, where nodes correspond to pixels, and edges connect adjacent pixels. An initial object layer can be obtained efficiently from graph-based segmentation, which runs in time nearly linear in the number of image pixels. Then FNEA starts with the initial object layer and a pairwise merge of its neighbour object with the aim to minimize the resulting summed heterogeneity. Furthermore, according to the character of different features in high resolution remote sensing image, three different merging criterions for image objects based on spectral and spatial information are adopted. Finally, compared with the commercial remote sensing software eCognition, the experimental results demonstrate that the efficiency of the algorithm has significantly improved, and the result can maintain good feature boundaries.
Fractal dimensions of wave functions and local spectral measures on the Fibonacci chain
NASA Astrophysics Data System (ADS)
Macé, Nicolas; Jagannathan, Anuradha; Piéchon, Frédéric
2016-05-01
We present a theoretical framework for understanding the wave functions and spectrum of an extensively studied paradigm for quasiperiodic systems, namely the Fibonacci chain. Our analytical results, which are obtained in the limit of strong modulation of the hopping amplitudes, are in good agreement with published numerical data. In the perturbative limit, we show a symmetry of wave functions under permutation of site and energy indices. We compute the wave-function renormalization factors and from them deduce analytical expressions for the fractal exponents corresponding to individual wave functions, as well as their global averages. The multifractality of wave functions is seen to appear at next-to-leading order in ρ . Exponents for the local spectral density are given, in extremely good accord with numerical calculations. Interestingly, our analytical results for exponents are observed to describe the system rather well even for values of ρ well outside the domain of applicability of perturbation theory.
Kamiya, Akira; Takahashi, Tatsuhisa
2007-06-01
The branching systems in our body (vascular and bronchial trees) and those in the environment (plant trees and river systems) are characterized by a fractal nature: the self-similarity in the bifurcation pattern. They increase their branch density toward terminals according to a power function with the exponent called fractal dimension (D). From a stochastic model based-on this feature, we formulated the fractal-based integrals to calculate such morphological parameters as aggregated branch length, surface area, and content volume for any given range of radius (r). It was followed by the derivation of branch number and cross-sectional area, by virtue of the logarithmic sectioning of the r axis and of the branch radius-length relation also given by a power function of r with an exponent (alpha). These derivatives allowed us to quantify various hydrodynamic parameters of vascular and bronchial trees as fluid conduit systems, including the individual branch flow rate, mean flow velocity, wall shear rate and stress, internal pressure, and circumferential tension. The validity of these expressions was verified by comparing the outcomes with actual data measured in vivo in the vascular beds. From additional analyses of the terminal branch number, we found a simple equation relating the exponent (m) of the empirical power law (Murray's so-called cube law) to the other exponents as (m=D+alpha). Finally, allometric studies of mammalian vascular trees revealed uniform and scale-independent distributions of terminal arterioles in organs, which afforded an infarct index, reflecting the severity of tissue damage following arterial infarction. PMID:17347385
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.
Characterizing Hyperspectral Imagery (AVIRIS) Using Fractal Technique
NASA Technical Reports Server (NTRS)
Qiu, Hong-Lie; Lam, Nina Siu-Ngan; Quattrochi, Dale
1997-01-01
With the rapid increase in hyperspectral data acquired by various experimental hyperspectral imaging sensors, it is necessary to develop efficient and innovative tools to handle and analyze these data. The objective of this study is to seek effective spatial analytical tools for summarizing the spatial patterns of hyperspectral imaging data. In this paper, we (1) examine how fractal dimension D changes across spectral bands of hyperspectral imaging data and (2) determine the relationships between fractal dimension and image content. It has been documented that fractal dimension changes across spectral bands for the Landsat-TM data and its value [(D)] is largely a function of the complexity of the landscape under study. The newly available hyperspectral imaging data such as that from the Airborne Visible Infrared Imaging Spectrometer (AVIRIS) which has 224 bands, covers a wider spectral range with a much finer spectral resolution. Our preliminary result shows that fractal dimension values of AVIRIS scenes from the Santa Monica Mountains in California vary between 2.25 and 2.99. However, high fractal dimension values (D > 2.8) are found only from spectral bands with high noise level and bands with good image quality have a fairly stable dimension value (D = 2.5 - 2.6). This suggests that D can also be used as a summary statistics to represent the image quality or content of spectral bands.
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)
Generalized functional formulation for multi-fractal representation of basin hydraulic geometry
NASA Astrophysics Data System (ADS)
Kim, JongChun; Paik, Kyungrock
2015-04-01
Natural rivers exhibit power-functional variability in their width, depth, and velocity with flow discharge (Leopold and Maddock, 1953). This relation named hydraulic geometry has been empirically supported by many field studies across the world (e.g., Leopold et al., 1964; Stall and Fok, 1968). The relationship appears either at a fixed cross-section, showing temporal variability, or along a downstream direction across an entire basin, showing spatial variability, the latter named downstream or basin hydraulic geometry. Theoretical studies that attempt to explain the power-law phenomenon (fractal), have assumed that the watershed is homogeneous hydrologically and geologically. Nevertheless, real watersheds are often subject to spatially heterogeneous conditions, due to various reasons including partial area storm coverage (Sólyom and Tucker, 2004) and transmission losses on bed and banks (Lane et al., 1997). In this setting, hydraulic geometry relationships are likely to deviate from monotonic power-law relationship and to follow rather more complex multi-fractal characteristics. In fact, deviation from single power-law was reported for at-a-station relationship of midwest rivers in US (Dodov and Foufoula-Georgiou, 2004). In the case of downstream variation, we identify significant multi-fractal characteristics over the Colorado River basin where strong heterogeneity in geological and hydrological settings presents. Conventional power-law hydraulic geometry relationships cannot express the functional variability for these cases. Motivated by this fact, we generalize the hydraulic geometry functional formulation in this study to express multi-fractal relationships. To do so, we couple the formulation of Paik and Kumar (2004), which generalized at-a-station and downstream relationships, with the formulation of Dodov and Foufoula-Georgiou (2004) which was proposed for multi-scaling in at-a-station relationship. The proposed formulation is successfully evaluated with
Electronic states on a fractal: Exact Green's-function renormalization approach
NASA Astrophysics Data System (ADS)
Andrade, R. F. S.; Schellnhuber, H. J.
1991-12-01
A nontrivial tight-binding model for electron dynamics on the fractal Koch curve is investigated within the framework of the Green's-function formalism. The key result is the construction of a multiple exact renormalization group that allows one to derive all the rather unusual properties of the model. This group is generated by four nonequivalent decimation operations, which define distinct transformation rules for the 48 relevant parameters to be renormalized. The calculation of the density of states confirms the crucial results that were obtained recently using transfer-matrix methods: local self-affinity, dense gap structure, and singular electronic levels with infinite degeneracy. This demonstrates that the Green's-function approach is not inferior to other techniques even in topologically one-dimensional situations.
Functional Magnetic Resonance Imaging
ERIC Educational Resources Information Center
Voos, Avery; Pelphrey, Kevin
2013-01-01
Functional magnetic resonance imaging (fMRI), with its excellent spatial resolution and ability to visualize networks of neuroanatomical structures involved in complex information processing, has become the dominant technique for the study of brain function and its development. The accessibility of in-vivo pediatric brain-imaging techniques…
Functional imaging and endoscopy
Zhang, Jian-Guo; Liu, Hai-Feng
2011-01-01
The emergence of endoscopy for the diagnosis of gastrointestinal diseases and the treatment of gastrointestinal diseases has brought great changes. The mere observation of anatomy with the imaging mode using modern endoscopy has played a significant role in this regard. However, increasing numbers of endoscopies have exposed additional deficiencies and defects such as anatomically similar diseases. Endoscopy can be used to examine lesions that are difficult to identify and diagnose. Early disease detection requires that substantive changes in biological function should be observed, but in the absence of marked morphological changes, endoscopic detection and diagnosis are difficult. Disease detection requires not only anatomic but also functional imaging to achieve a comprehensive interpretation and understanding. Therefore, we must ask if endoscopic examination can be integrated with both anatomic imaging and functional imaging. In recent years, as molecular biology and medical imaging technology have further developed, more functional imaging methods have emerged. This paper is a review of the literature related to endoscopic optical imaging methods in the hopes of initiating integration of functional imaging and anatomical imaging to yield a new and more effective type of endoscopy. PMID:22090783
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.
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 DIMENSION OF GALAXY ISOPHOTES
Thanki, Sandip; Rhee, George; Lepp, Stephen E-mail: grhee@physics.unlv.edu
2009-09-15
In this paper we investigate the use of the fractal dimension of galaxy isophotes in galaxy classification. We have applied two different methods for determining fractal dimensions to the isophotes of elliptical and spiral galaxies derived from CCD images. We conclude that fractal dimension alone is not a reliable tool but that combined with other parameters in a neural net algorithm the fractal dimension could be of use. In particular, we have used three parameters to segregate the ellipticals and lenticulars from the spiral galaxies in our sample. These three parameters are the correlation fractal dimension D {sub corr}, the difference between the correlation fractal dimension and the capacity fractal dimension D {sub corr} - D {sub cap}, and, thirdly, the B - V color of the galaxy.
NASA Astrophysics Data System (ADS)
Shahi Ferdows, Mohammad; Ramazi, Hamidreza
2015-12-01
The selection of a suitable membership function and its parameters plays a critical role in the integration of layer information by the fuzzy method. In this paper, parameters of membership function for induced polarization (IP) and resistivity (RS) data (in the Hamyj copper deposit) have been determined by the threshold parameter of IP and resistivity data, already determined by expert opinion or drilling data. The Hamyj deposit is located about 80 km west of Birjand city, South Khorasan province, Iran. In this area, resistivity and induced polarization data have been surveyed by dipole-dipole array. In this paper, outlier-induced polarization data have been corrected by the Doerffel method and then IP and resistivity data have been inversed by the Newton and Gauss-Newton methods. The threshold of the IP data is recognized by statistical (gap statistic) and fractal (concentration-area) methods. The determined threshold by the fractal method is higher than the gap statistic. These two thresholds have been used to determine the S-shape function for the IP data. The thresholds of the RS data are recognized by the fractal method. These two thresholds have been used to determine the Z-shape function for the RS data. The integration of geoelectrical layer information has been carried out by the Gama method. Finally, the best drilling points were proposed based on fuzzy modelling for the area. The results show that the optimum exploration borehole is located at a depth of 25 m.
Fractal funcitons and multiwavelets
Massopust, P.R.
1997-04-01
This paper reviews how elements from the theory of fractal functions are employed to construct scaling vectors and multiwavelets. Emphasis is placed on the one-dimensional case, however extensions to IR{sup m} are indicated.
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.)
Image analysis of human corneal endothelial cells based on fractal theory
NASA Astrophysics Data System (ADS)
Zhang, Zhi; Luo, Qingming; Zeng, Shaoqun; Zhang, Xinyu; Huang, Dexiu; Chen, Weiguo
1999-09-01
A fast method is developed to quantitatively characterize the shape of human corneal endothelial cells with fractal theory and applied to analyze microscopic photographs of human corneal endothelial cells. The results show that human corneal endothelial cells possess the third characterization parameter-- fractal dimension, besides another two characterization parameter (its size and shape). Compared with tradition method, this method has many advantages, such as automatism, speediness, parallel processing and can be used to analyze large numbers of endothelial cells, the obtained values are statistically significant, it offers a new approach for clinic diagnosis of endothelial cells.
Characterization of branch complexity by fractal analyses and detect plant functional adaptations
Alados, C.L.; Escos, J.; Emlen, J.M.; Freeman, D.C.
1999-01-01
The comparison between complexity in the sense of space occupancy (box-counting fractal dimension Dc and information dimension DI ) and heterogeneity in the sense of space distribution (average evenness index and evenness variation coefficient JCV) were investigated in mathematical fractal objects and natural branch ¯ J structures. In general, increased fractal dimension was paired with low heterogeneity. Comparisons between branch architecture in Anthyllis cytisoides under different slope exposure and grazing impact revealed that branches were more complex and more homogeneously distributed for plants on northern exposures than southern, while grazing had no impact during a wet year. Developmental instability was also investigated by the statistical noise of the allometric relation between internode length and node order. In conclusion, our study demonstrated that fractal dimension of branch structure can be used to analyze the structural organization of plants, especially if we consider not only fractal dimension but also shoot distribution within the canopy (lacunarity). These indexes together with developmental instability analyses are good indicators of growth responses to the environment.
Fractal Feature Analysis Of Beef Marblingpatterns
NASA Astrophysics Data System (ADS)
Chen, Kunjie; Qin, Chunfang
The purpose of this study is to investigate fractal behavior of beef marbling patterns and to explore relationships between fractal dimensions and marbling scores. Authors firstly extracted marbling images from beef rib-eye crosssection images using computer image processing technologies and then implemented the fractal analysis on these marbling images based on the pixel covering method. Finally box-counting fractal dimension (BFD) and informational fractal dimension (IFD) of one hundred and thirty-five beef marbling images were calculated and plotted against the beef marbling scores. The results showed that all beef marbling images exhibit fractal behavior over the limited range of scales accessible to analysis. Furthermore, their BFD and IFD are closely related to the score of beef marbling, suggesting that fractal analyses can provide us a potential tool to calibrate the score of beef marbling.
Garrison, J.R., Jr.; Pearn, W.C.; von Rosenberg, D. W. )
1992-01-01
In this paper reservoir rock/pore systems are considered natural fractal objects and modeled as and compared to the regular fractal Menger Sponge and Sierpinski Carpet. The physical properties of a porous rock are, in part, controlled by the geometry of the pore system. The rate at which a fluid or electrical current can travel through the pore system of a rock is controlled by the path along which it must travel. This path is a subset of the overall geometry of the pore system. Reservoir rocks exhibit self-similarity over a range of length scales suggesting that fractal geometry offers a means of characterizing these complex objects. The overall geometry of a rock/pore system can be described, conveniently and concisely, in terms of effective fractal dimensions. The rock/pore system is modeled as the fractal Menger Sponge. A cross section through the rock/pore system, such as an image of a thin-section of a rock, is modeled as the fractal Sierpinski Carpet, which is equivalent to the face of the Menger Sponge.
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.
2006-01-01
Executive Summary Objective The objective of this analysis is to review a spectrum of functional brain imaging technologies to identify whether there are any imaging modalities that are more effective than others for various brain pathology conditions. This evidence-based analysis reviews magnetoencephalography (MEG), magnetic resonance spectroscopy (MRS), positron emission tomography (PET), and functional magnetic resonance imaging (fMRI) for the diagnosis or surgical management of the following conditions: Alzheimer’s disease (AD), brain tumours, epilepsy, multiple sclerosis (MS), and Parkinson’s disease (PD). Clinical Need: Target Population and Condition Alzheimer’s disease is a progressive, degenerative, neurologic condition characterized by cognitive impairment and memory loss. The Canadian Study on Health and Aging estimated that there will be 97,000 incident cases (about 60,000 women) of dementia (including AD) in Canada in 2006. In Ontario, there will be an estimated 950 new cases and 580 deaths due to brain cancer in 2006. Treatments for brain tumours include surgery and radiation therapy. However, one of the limitations of radiation therapy is that it damages tissue though necrosis and scarring. Computed tomography (CT) and magnetic resonance imaging (MRI) may not distinguish between radiation effects and resistant tissue, creating a potential role for functional brain imaging. Epilepsy is a chronic disorder that provokes repetitive seizures. In Ontario, the rate of epilepsy is estimated to be 5 cases per 1,000 people. Most people with epilepsy are effectively managed with drug therapy; but about 50% do not respond to drug therapy. Surgical resection of the seizure foci may be considered in these patients, and functional brain imaging may play a role in localizing the seizure foci. Multiple sclerosis is a progressive, inflammatory, demyelinating disease of the central nervous system (CNS). The cause of MS is unknown; however, it is thought to be
Fractal characterization of wear-erosion surfaces
Rawers, J.; Tylczak, J.
1999-12-01
Wear erosion is a complex phenomenon resulting in highly distorted and deformed surface morphologies. Most wear surface features have been described only qualitatively. In this study wear surfaces features were quantified using fractal analysis. The ability to assign numerical values to wear-erosion surfaces makes possible mathematical expressions that will enable wear mechanisms to be predicted and understood. Surface characterization came from wear-erosion experiments that included varying the erosive materials, the impact velocity, and the impact angle. Seven fractal analytical techniques were applied to micrograph images of wear-erosion surfaces. Fourier analysis was the most promising. Fractal values obtained were consistent with visual observations and provided a unique wear-erosion parameter unrelated to wear rate. In this study stainless steel was evaluated as a function of wear erosion conditions.
The Use of Fractals for the Study of the Psychology of Perception:
NASA Astrophysics Data System (ADS)
Mitina, Olga V.; Abraham, Frederick David
The present article deals with perception of time (subjective assessment of temporal intervals), complexity and aesthetic attractiveness of visual objects. The experimental research for construction of functional relations between objective parameters of fractals' complexity (fractal dimension and Lyapunov exponent) and subjective perception of their complexity was conducted. As stimulus material we used the program based on Sprott's algorithms for the generation of fractals and the calculation of their mathematical characteristics. For the research 20 fractals were selected which had different fractal dimensions that varied from 0.52 to 2.36, and the Lyapunov exponent from 0.01 to 0.22. We conducted two experiments: (1) A total of 20 fractals were shown to 93 participants. The fractals were displayed on the screen of a computer for randomly chosen time intervals ranging from 5 to 20 s. For each fractal displayed, the participant responded with a rating of the complexity and attractiveness of the fractal using ten-point scale with an estimate of the duration of the presentation of the stimulus. Each participant also answered the questions of some personality tests (Cattell and others). The main purpose of this experiment was the analysis of the correlation between personal characteristics and subjective perception of complexity, attractiveness, and duration of fractal's presentation. (2) The same 20 fractals were shown to 47 participants as they were forming on the screen of the computer for a fixed interval. Participants also estimated subjective complexity and attractiveness of fractals. The hypothesis on the applicability of the Weber-Fechner law for the perception of time, complexity and subjective attractiveness was confirmed for measures of dynamical properties of fractal images.
Target Detection Using Fractal Geometry
NASA Technical Reports Server (NTRS)
Fuller, J. Joseph
1991-01-01
The concepts and theory of fractal geometry were applied to the problem of segmenting a 256 x 256 pixel image so that manmade objects could be extracted from natural backgrounds. The two most important measurements necessary to extract these manmade objects were fractal dimension and lacunarity. Provision was made to pass the manmade portion to a lookup table for subsequent identification. A computer program was written to construct cloud backgrounds of fractal dimensions which were allowed to vary between 2.2 and 2.8. Images of three model space targets were combined with these backgrounds to provide a data set for testing the validity of the approach. Once the data set was constructed, computer programs were written to extract estimates of the fractal dimension and lacunarity on 4 x 4 pixel subsets of the image. It was shown that for clouds of fractal dimension 2.7 or less, appropriate thresholding on fractal dimension and lacunarity yielded a 64 x 64 edge-detected image with all or most of the cloud background removed. These images were enhanced by an erosion and dilation to provide the final image passed to the lookup table. While the ultimate goal was to pass the final image to a neural network for identification, this work shows the applicability of fractal geometry to the problems of image segmentation, edge detection and separating a target of interest from a natural background.
Fractal metrology for biogeosystems analysis
NASA Astrophysics Data System (ADS)
Torres-Argüelles, V.; Oleschko, K.; Tarquis, A. M.; Korvin, G.; Gaona, C.; Parrot, J.-F.; Ventura-Ramos, E.
2010-06-01
The solid-pore distribution pattern plays an important role in soil functioning being related with the main physical, chemical and biological multiscale and multitemporal processes. In the present research, this pattern is extracted from the digital images of three soils (Chernozem, Solonetz and "Chocolate'' Clay) and compared in terms of roughness of the gray-intensity distribution (the measurand) quantified by several measurement techniques. Special attention was paid to the uncertainty of each of them and to the measurement function which best fits to the experimental results. Some of the applied techniques are known as classical in the fractal context (box-counting, rescaling-range and wavelets analyses, etc.) while the others have been recently developed by our Group. The combination of all these techniques, coming from Fractal Geometry, Metrology, Informatics, Probability Theory and Statistics is termed in this paper Fractal Metrology (FM). We show the usefulness of FM through a case study of soil physical and chemical degradation applying the selected toolbox to describe and compare the main structural attributes of three porous media with contrasting structure but similar clay mineralogy dominated by montmorillonites.
Fractal electronic devices: simulation and implementation.
Fairbanks, M S; McCarthy, D N; Scott, S A; Brown, S A; Taylor, R P
2011-09-01
Many natural structures have fractal geometries that exhibit useful functional properties. These properties, which exploit the recurrence of patterns at increasingly small scales, are often desirable in applications and, consequently, fractal geometry is increasingly employed in diverse technologies ranging from radio antennae to storm barriers. In this paper, we explore the application of fractal geometry to electrical devices. First, we lay the foundations for the implementation of fractal devices by considering diffusion-limited aggregation (DLA) of atomic clusters. Under appropriate growth conditions, atomic clusters of various elements form fractal patterns driven by DLA. We perform a fractal analysis of both simulated and physical devices to determine their spatial scaling properties and demonstrate their potential as fractal circuit elements. Finally, we simulate conduction through idealized and DLA fractal devices and show that their fractal scaling properties generate novel, nonlinear conduction properties in response to depletion by electrostatic gates. PMID:21841218
Fractal electronic devices: simulation and implementation
NASA Astrophysics Data System (ADS)
Fairbanks, M. S.; McCarthy, D. N.; Scott, S. A.; Brown, S. A.; Taylor, R. P.
2011-09-01
Many natural structures have fractal geometries that exhibit useful functional properties. These properties, which exploit the recurrence of patterns at increasingly small scales, are often desirable in applications and, consequently, fractal geometry is increasingly employed in diverse technologies ranging from radio antennae to storm barriers. In this paper, we explore the application of fractal geometry to electrical devices. First, we lay the foundations for the implementation of fractal devices by considering diffusion-limited aggregation (DLA) of atomic clusters. Under appropriate growth conditions, atomic clusters of various elements form fractal patterns driven by DLA. We perform a fractal analysis of both simulated and physical devices to determine their spatial scaling properties and demonstrate their potential as fractal circuit elements. Finally, we simulate conduction through idealized and DLA fractal devices and show that their fractal scaling properties generate novel, nonlinear conduction properties in response to depletion by electrostatic gates.
Texture Analysis In Cytology Using Fractals
NASA Astrophysics Data System (ADS)
Basu, Santanu; Barba, Joseph; Chan, K. S.
1990-01-01
We present some preliminary results of a study aimed to assess the actual effectiveness of fractal theory in the area of medical image analysis for texture description. The specific goal of this research is to utilize "fractal dimension" to discriminate between normal and cancerous human cells. In particular, we have considered four types of cells namely, breast, bronchial, ovarian and uterine. A method based on fractal Brownian motion theory is employed to compute the "fractal dimension" of cells. Experiments with real images reveal that the range of scales over which the cells exhibit fractal property can be used as the discriminatory feature to identify cancerous cells.
Functional magnetic resonance imaging.
Buchbinder, Bradley R
2016-01-01
Functional magnetic resonance imaging (fMRI) maps the spatiotemporal distribution of neural activity in the brain under varying cognitive conditions. Since its inception in 1991, blood oxygen level-dependent (BOLD) fMRI has rapidly become a vital methodology in basic and applied neuroscience research. In the clinical realm, it has become an established tool for presurgical functional brain mapping. This chapter has three principal aims. First, we review key physiologic, biophysical, and methodologic principles that underlie BOLD fMRI, regardless of its particular area of application. These principles inform a nuanced interpretation of the BOLD fMRI signal, along with its neurophysiologic significance and pitfalls. Second, we illustrate the clinical application of task-based fMRI to presurgical motor, language, and memory mapping in patients with lesions near eloquent brain areas. Integration of BOLD fMRI and diffusion tensor white-matter tractography provides a road map for presurgical planning and intraoperative navigation that helps to maximize the extent of lesion resection while minimizing the risk of postoperative neurologic deficits. Finally, we highlight several basic principles of resting-state fMRI and its emerging translational clinical applications. Resting-state fMRI represents an important paradigm shift, focusing attention on functional connectivity within intrinsic cognitive networks. PMID:27432660
Matsueda, Hiroaki; Lee, Ching Hua
2015-03-10
We examine singular value spectrum of a class of two-dimensional fractal images. We find that the spectra can be mapped onto entanglement spectra of free fermions in one dimension. This exact mapping tells us that the singular value decomposition is a way of detecting a holographic relation between classical and quantum systems.
Fractal Metrology for biogeosystems analysis
NASA Astrophysics Data System (ADS)
Torres-Argüelles, V.; Oleschko, K.; Tarquis, A. M.; Korvin, G.; Gaona, C.; Parrot, J.-F.; Ventura-Ramos, E.
2010-11-01
The solid-pore distribution pattern plays an important role in soil functioning being related with the main physical, chemical and biological multiscale and multitemporal processes of this complex system. In the present research, we studied the aggregation process as self-organizing and operating near a critical point. The structural pattern is extracted from the digital images of three soils (Chernozem, Solonetz and "Chocolate" Clay) and compared in terms of roughness of the gray-intensity distribution quantified by several measurement techniques. Special attention was paid to the uncertainty of each of them measured in terms of standard deviation. Some of the applied methods are known as classical in the fractal context (box-counting, rescaling-range and wavelets analyses, etc.) while the others have been recently developed by our Group. The combination of these techniques, coming from Fractal Geometry, Metrology, Informatics, Probability Theory and Statistics is termed in this paper Fractal Metrology (FM). We show the usefulness of FM for complex systems analysis through a case study of the soil's physical and chemical degradation applying the selected toolbox to describe and compare the structural attributes of three porous media with contrasting structure but similar clay mineralogy dominated by montmorillonites.
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.
NASA Technical Reports Server (NTRS)
Bruno, B. C.; Taylor, G. J.; Rowland, S. K.; Lucey, P. G.; Self, S.
1992-01-01
Results are presented of a preliminary investigation of the fractal nature of the plan-view shapes of lava flows in Hawaii (based on field measurements and aerial photographs), as well as in Idaho and the Galapagos Islands (using aerial photographs only). The shapes of the lava flow margins are found to be fractals: lava flow shape is scale-invariant. This observation suggests that nonlinear forces are operating in them because nonlinear systems frequently produce fractals. A'a and pahoehoe flows can be distinguished by their fractal dimensions (D). The majority of the a'a flows measured have D between 1.05 and 1.09, whereas the pahoehoe flows generally have higher D (1.14-1.23). The analysis is extended to other planetary bodies by measuring flows from orbital images of Venus, Mars, and the moon. All are fractal and have D consistent with the range of terrestrial a'a and have D consistent with the range of terrestrial a'a and pahoehoe values.
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.
NASA Astrophysics Data System (ADS)
Mukhopadhyay, Sabyasachi; Das, Nandan K.; Pradhan, Asima; Ghosh, Nirmalya; Panigrahi, Prasanta K.
2014-05-01
DIC (Differential Interference Contrast Image) images of cervical pre-cancer tissues are taken from epithelium region, on which wavelet transform and multi-fractal analysis are applied. Discrete wavelet transform (DWT) through Daubechies basis are done for identifying fluctuations over polynomial trends for clear characterization and differentiation of tissues. A systematic investigation of denoised images is carried out through the continuous Morlet wavelet. The scalogram reveals the changes in coefficient peak values from grade-I to grade-III. Wavelet normalized energy plots are computed in order to show the difference of periodicity among different grades of cancerous tissues. Using the multi-fractal de-trended fluctuation analysis (MFDFA), it is observed that the values of Hurst exponent and width of singularity spectrum decrease as cancer progresses from grade-I to grade-III tissue.
Brain imaging and brain function
Sokoloff, L.
1985-01-01
This book is a survey of the applications of imaging studies of regional cerebral blood flow and metabolism to the investigation of neurological and psychiatric disorders. Contributors review imaging techniques and strategies for measuring regional cerebral blood flow and metabolism, for mapping functional neural systems, and for imaging normal brain functions. They then examine the applications of brain imaging techniques to the study of such neurological and psychiatric disorders as: cerebral ischemia; convulsive disorders; cerebral tumors; Huntington's disease; Alzheimer's disease; depression and other mood disorders. A state-of-the-art report on magnetic resonance imaging of the brain and central nervous system rounds out the book's coverage.
Entanglement entropy on fractals
NASA Astrophysics Data System (ADS)
Faraji Astaneh, Amin
2016-03-01
We use the heat kernel method to calculate the entanglement entropy for a given entangling region on a fractal. The leading divergent term of the entropy is obtained as a function of the fractal dimension as well as the walk dimension. The power of the UV cutoff parameter is (generally) a fractional number, which, indeed, is a certain combination of these two indices. This exponent is known as the spectral dimension. We show that there is a novel log-periodic oscillatory behavior in the expression of entropy which has root in the complex dimension of the fractal. We finally indicate that the holographic calculation in a certain hyperscaling-violating bulk geometry yields the same leading term for the entanglement entropy, if one identifies the effective dimension of the hyperscaling-violating theory with the spectral dimension of the fractal. We provide additional support by comparing the behavior of the thermal entropy in terms of the temperature, computed for two geometries, the fractal geometry and the hyperscaling-violating background.
Fractal dynamics of earthquakes
Bak, P.; Chen, K.
1995-05-01
Many objects in nature, from mountain landscapes to electrical breakdown and turbulence, have a self-similar fractal spatial structure. It seems obvious that to understand the origin of self-similar structures, one must understand the nature of the dynamical processes that created them: temporal and spatial properties must necessarily be completely interwoven. This is particularly true for earthquakes, which have a variety of fractal aspects. The distribution of energy released during earthquakes is given by the Gutenberg-Richter power law. The distribution of epicenters appears to be fractal with dimension D {approx} 1--1.3. The number of after shocks decay as a function of time according to the Omori power law. There have been several attempts to explain the Gutenberg-Richter law by starting from a fractal distribution of faults or stresses. But this is a hen-and-egg approach: to explain the Gutenberg-Richter law, one assumes the existence of another power-law--the fractal distribution. The authors present results of a simple stick slip model of earthquakes, which evolves to a self-organized critical state. Emphasis is on demonstrating that empirical power laws for earthquakes indicate that the Earth`s crust is at the critical state, with no typical time, space, or energy scale. Of course the model is tremendously oversimplified; however in analogy with equilibrium phenomena they do not expect criticality to depend on details of the model (universality).
Mesh generation/refinement using fractal concepts and iterated function systems
NASA Technical Reports Server (NTRS)
Bova, S. W.; Carey, G. F.
1992-01-01
A novel method of mesh generation is proposed which is based on the use of fractal concepts to derive contractive, affine transformations. The transformations are constructed in such a manner that the attractors of the resulting maps are a union of the points, lines and surfaces in the domain. In particular, the mesh nodes may be generated recursively as a sequence of points which are obtained by applying the transformations to a coarse background mesh constructed from the given boundary data. A Delaunay triangulation or similar edge connection approach can then be performed on the resulting set of nodes in order to generate the mesh. Local refinement of an existing mesh can also be performed using the procedure. The method is easily extended to three dimensions, in which case the Delaunay triangulation is replaced by an analogous 3D tesselation.
Waliszewski, Przemyslaw
2016-01-01
The subjective evaluation of tumor aggressiveness is a cornerstone of the contemporary tumor pathology. A large intra- and interobserver variability is a known limiting factor of this approach. This fundamental weakness influences the statistical deterministic models of progression risk assessment. It is unlikely that the recent modification of tumor grading according to Gleason criteria for prostate carcinoma will cause a qualitative change and improve significantly the accuracy. The Gleason system does not allow the identification of low aggressive carcinomas by some precise criteria. The ontological dichotomy implies the application of an objective, quantitative approach for the evaluation of tumor aggressiveness as an alternative. That novel approach must be developed and validated in a manner that is independent of the results of any subjective evaluation. For example, computer-aided image analysis can provide information about geometry of the spatial distribution of cancer cell nuclei. A series of the interrelated complexity measures characterizes unequivocally the complex tumor images. Using those measures, carcinomas can be classified into the classes of equivalence and compared with each other. Furthermore, those measures define the quantitative criteria for the identification of low- and high-aggressive prostate carcinomas, the information that the subjective approach is not able to provide. The co-application of those complexity measures in cluster analysis leads to the conclusion that either the subjective or objective classification of tumor aggressiveness for prostate carcinomas should comprise maximal three grades (or classes). Finally, this set of the global fractal dimensions enables a look into dynamics of the underlying cellular system of interacting cells and the reconstruction of the temporal-spatial attractor based on the Taken’s embedding theorem. Both computer-aided image analysis and the subsequent fractal synthesis could be performed
Waliszewski, Przemyslaw
2016-01-01
The subjective evaluation of tumor aggressiveness is a cornerstone of the contemporary tumor pathology. A large intra- and interobserver variability is a known limiting factor of this approach. This fundamental weakness influences the statistical deterministic models of progression risk assessment. It is unlikely that the recent modification of tumor grading according to Gleason criteria for prostate carcinoma will cause a qualitative change and improve significantly the accuracy. The Gleason system does not allow the identification of low aggressive carcinomas by some precise criteria. The ontological dichotomy implies the application of an objective, quantitative approach for the evaluation of tumor aggressiveness as an alternative. That novel approach must be developed and validated in a manner that is independent of the results of any subjective evaluation. For example, computer-aided image analysis can provide information about geometry of the spatial distribution of cancer cell nuclei. A series of the interrelated complexity measures characterizes unequivocally the complex tumor images. Using those measures, carcinomas can be classified into the classes of equivalence and compared with each other. Furthermore, those measures define the quantitative criteria for the identification of low- and high-aggressive prostate carcinomas, the information that the subjective approach is not able to provide. The co-application of those complexity measures in cluster analysis leads to the conclusion that either the subjective or objective classification of tumor aggressiveness for prostate carcinomas should comprise maximal three grades (or classes). Finally, this set of the global fractal dimensions enables a look into dynamics of the underlying cellular system of interacting cells and the reconstruction of the temporal-spatial attractor based on the Taken's embedding theorem. Both computer-aided image analysis and the subsequent fractal synthesis could be performed
Lung cancer-a fractal viewpoint.
Lennon, Frances E; Cianci, Gianguido C; Cipriani, Nicole A; Hensing, Thomas A; Zhang, Hannah J; Chen, Chin-Tu; Murgu, Septimiu D; Vokes, Everett E; Vannier, Michael W; Salgia, Ravi
2015-11-01
Fractals are mathematical constructs that show self-similarity over a range of scales and non-integer (fractal) dimensions. Owing to these properties, fractal geometry can be used to efficiently estimate the geometrical complexity, and the irregularity of shapes and patterns observed in lung tumour growth (over space or time), whereas the use of traditional Euclidean geometry in such calculations is more challenging. The application of fractal analysis in biomedical imaging and time series has shown considerable promise for measuring processes as varied as heart and respiratory rates, neuronal cell characterization, and vascular development. Despite the advantages of fractal mathematics and numerous studies demonstrating its applicability to lung cancer research, many researchers and clinicians remain unaware of its potential. Therefore, this Review aims to introduce the fundamental basis of fractals and to illustrate how analysis of fractal dimension (FD) and associated measurements, such as lacunarity (texture) can be performed. We describe the fractal nature of the lung and explain why this organ is particularly suited to fractal analysis. Studies that have used fractal analyses to quantify changes in nuclear and chromatin FD in primary and metastatic tumour cells, and clinical imaging studies that correlated changes in the FD of tumours on CT and/or PET images with tumour growth and treatment responses are reviewed. Moreover, the potential use of these techniques in the diagnosis and therapeutic management of lung cancer are discussed. PMID:26169924
Lung cancer—a fractal viewpoint
Lennon, Frances E.; Cianci, Gianguido C.; Cipriani, Nicole A.; Hensing, Thomas A.; Zhang, Hannah J.; Chen, Chin-Tu; Murgu, Septimiu D.; Vokes, Everett E.; W. Vannier, Michael; Salgia, Ravi
2016-01-01
Fractals are mathematical constructs that show self-similarity over a range of scales and non-integer (fractal) dimensions. Owing to these properties, fractal geometry can be used to efficiently estimate the geometrical complexity, and the irregularity of shapes and patterns observed in lung tumour growth (over space or time), whereas the use of traditional Euclidean geometry in such calculations is more challenging. The application of fractal analysis in biomedical imaging and time series has shown considerable promise for measuring processes as varied as heart and respiratory rates, neuronal cell characterization, and vascular development. Despite the advantages of fractal mathematics and numerous studies demonstrating its applicability to lung cancer research, many researchers and clinicians remain unaware of its potential. Therefore, this Review aims to introduce the fundamental basis of fractals and to illustrate how analysis of fractal dimension (FD) and associated measurements, such as lacunarity (texture) can be performed. We describe the fractal nature of the lung and explain why this organ is particularly suited to fractal analysis. Studies that have used fractal analyses to quantify changes in nuclear and chromatin FD in primary and metastatic tumour cells, and clinical imaging studies that correlated changes in the FD of tumours on CT and/or PET images with tumour growth and treatment responses are reviewed. Moreover, the potential use of these techniques in the diagnosis and therapeutic management of lung cancer are discussed. PMID:26169924
Fractal Trigonometric Polynomials for Restricted Range Approximation
NASA Astrophysics Data System (ADS)
Chand, A. K. B.; Navascués, M. A.; Viswanathan, P.; Katiyar, S. K.
2016-05-01
One-sided approximation tackles the problem of approximation of a prescribed function by simple traditional functions such as polynomials or trigonometric functions that lie completely above or below it. In this paper, we use the concept of fractal interpolation function (FIF), precisely of fractal trigonometric polynomials, to construct one-sided uniform approximants for some classes of continuous functions.
Investigation into How 8th Grade Students Define Fractals
ERIC Educational Resources Information Center
Karakus, Fatih
2015-01-01
The analysis of 8th grade students' concept definitions and concept images can provide information about their mental schema of fractals. There is limited research on students' understanding and definitions of fractals. Therefore, this study aimed to investigate the elementary students' definitions of fractals based on concept image and concept…
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…
NASA Technical Reports Server (NTRS)
Huikuri, H. V.; Makikallio, T. H.; Peng, C. K.; Goldberger, A. L.; Hintze, U.; Moller, M.
2000-01-01
BACKGROUND: Preliminary data suggest that the analysis of R-R interval variability by fractal analysis methods may provide clinically useful information on patients with heart failure. The purpose of this study was to compare the prognostic power of new fractal and traditional measures of R-R interval variability as predictors of death after acute myocardial infarction. METHODS AND RESULTS: Time and frequency domain heart rate (HR) variability measures, along with short- and long-term correlation (fractal) properties of R-R intervals (exponents alpha(1) and alpha(2)) and power-law scaling of the power spectra (exponent beta), were assessed from 24-hour Holter recordings in 446 survivors of acute myocardial infarction with a depressed left ventricular function (ejection fraction fractal measures of R-R interval variability were significant univariate predictors of all-cause mortality. Reduced short-term scaling exponent alpha(1) was the most powerful R-R interval variability measure as a predictor of all-cause mortality (alpha(1) <0.75, relative risk 3.0, 95% confidence interval 2.5 to 4.2, P<0.001). It remained an independent predictor of death (P<0.001) after adjustment for other postinfarction risk markers, such as age, ejection fraction, NYHA class, and medication. Reduced alpha(1) predicted both arrhythmic death (P<0.001) and nonarrhythmic cardiac death (P<0.001). CONCLUSIONS: Analysis of the fractal characteristics of short-term R-R interval dynamics yields more powerful prognostic information than the traditional measures of HR variability among patients with depressed left ventricular function after an acute myocardial infarction.
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
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.
NASA Astrophysics Data System (ADS)
Muto, Jun; Nakatani, Tsurugi; Nishikawa, Osamu; Nagahama, Hiroyuki
2015-05-01
The size distributions of particle in pulverized rocks from the San Andreas fault and the Arima-Takatsuki Tectonic Line were measured. The rocks are characterized by the development of opening mode fractures with an apparent lack of shear. Fragments in the rocks in both fault zones show a fractal size distribution down to the micron scale. Fractal dimensions, dependent on mineral type, decrease from 2.92 to 1.97 with increasing distance normal to the fault core. The fractal dimensions of the rocks are higher than those of both natural and experimentally created fault gouges measured in previous studies. Moreover, the dimensions are higher than the theoretically estimated upper fractal limit under confined comminution. Dimensions close to 3.0 have been reported in impact loading experiments. The observed characteristics indicate that pulverization is likely to have occurred by a dynamic stress pulse with instantaneous volumetric expansion, possibly during seismic rupture propagation similar to impact loading.
NASA Astrophysics Data System (ADS)
Muzy, J. F.; Bacry, E.; Arneodo, A.
1993-02-01
Several attempts have been made recently to generalize the multifractal formalism, originally introduced for singular measures, to fractal signals. We report on a systematic comparison between the structure-function approach, pioneered by Parisi and Frisch [in 2 Proceedings of the International School on Turbulence and Predictability in Geophysical Fluid Dynamics and Climate Dynamics, edited by M. Ghil, R. Benzi, and G. Parisi (North-Holland, Amsterdam, 1985), p. 84] to account for the multifractal nature of fully developed turbulent signals, and an alternative method we have developed within the framework of the wavelet-transform analysis. We comment on the intrinsic limitations of the structure-function approach; this technique has fundamental drawbacks and does not provide a full characterization of the singularities of a signal in many cases. We demonstrate that our method, based on the wavelet-transform modulus-maxima representation, works in most situations and is likely to be the ground of a unified multifractal description of self-affine distributions. Our theoretical considerations are both illustrated on pedagogical examples and supported by numerical simulations.
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...
Fractal analysis: A new remote sensing tool for lava flows
NASA Technical Reports Server (NTRS)
Bruno, B. C.; Taylor, G. J.; Rowland, S. K.; Lucey, P. G.; Self, S.
1992-01-01
Many important quantitative parameters have been developed that relate to the rheology and eruption and emplacement mechanics of lavas. This research centers on developing additional, unique parameters, namely the fractal properties of lava flows, to add to this matrix of properties. There are several methods of calculating the fractal dimension of a lava flow margin. We use the 'structured walk' or 'divider' method. In this method, we measure the length of a given lava flow margin by walking rods of different lengths along the margin. Since smaller rod lengths transverse more smaller-scaled features in the flow margin, the apparent length of the flow outline will increase as the length of the measuring rod decreases. By plotting the apparent length of the flow outline as a function of the length of the measuring rod on a log-log plot, fractal behavior can be determined. A linear trend on a log-log plot indicates that the data are fractal. The fractal dimension can then be calculated from the slope of the linear least squares fit line to the data. We use this 'structured walk' method to calculate the fractal dimension of many lava flows using a wide range of rod lengths, from 1/8 to 16 meters, in field studies of the Hawaiian islands. We also use this method to calculate fractal dimensions from aerial photographs of lava flows, using lengths ranging from 20 meters to over 2 kilometers. Finally, we applied this method to orbital images of extraterrestrial lava flows on Venus, Mars, and the Moon, using rod lengths up to 60 kilometers.
Functional imaging in lung cancer
Harders, S W; Balyasnikowa, S; Fischer, B M
2014-01-01
Lung cancer represents an increasingly frequent cancer diagnosis worldwide. An increasing awareness on smoking cessation as an important mean to reduce lung cancer incidence and mortality, an increasing number of therapy options and a steady focus on early diagnosis and adequate staging have resulted in a modestly improved survival. For early diagnosis and precise staging, imaging, especially positron emission tomography combined with CT (PET/CT), plays an important role. Other functional imaging modalities such as dynamic contrast-enhanced CT (DCE-CT) and diffusion-weighted MR imaging (DW-MRI) have demonstrated promising results within this field. The purpose of this review is to provide the reader with a brief and balanced introduction to these three functional imaging modalities and their current or potential application in the care of patients with lung cancer. PMID:24289258
Fractal signatures in the aperiodic Fibonacci grating.
Verma, Rupesh; Banerjee, Varsha; Senthilkumaran, Paramasivam
2014-05-01
The Fibonacci grating (FbG) is an archetypal example of aperiodicity and self-similarity. While aperiodicity distinguishes it from a fractal, self-similarity identifies it with a fractal. Our paper investigates the outcome of these complementary features on the FbG diffraction profile (FbGDP). We find that the FbGDP has unique characteristics (e.g., no reduction in intensity with increasing generations), in addition to fractal signatures (e.g., a non-integer fractal dimension). These make the Fibonacci architecture potentially useful in image forming devices and other emerging technologies. PMID:24784044
NASA Technical Reports Server (NTRS)
Makikallio, T. H.; Hoiber, S.; Kober, L.; Torp-Pedersen, C.; Peng, C. K.; Goldberger, A. L.; Huikuri, H. V.
1999-01-01
A number of new methods have been recently developed to quantify complex heart rate (HR) dynamics based on nonlinear and fractal analysis, but their value in risk stratification has not been evaluated. This study was designed to determine whether selected new dynamic analysis methods of HR variability predict mortality in patients with depressed left ventricular (LV) function after acute myocardial infarction (AMI). Traditional time- and frequency-domain HR variability indexes along with short-term fractal-like correlation properties of RR intervals (exponent alpha) and power-law scaling (exponent beta) were studied in 159 patients with depressed LV function (ejection fraction <35%) after an AMI. By the end of 4-year follow-up, 72 patients (45%) had died and 87 (55%) were still alive. Short-term scaling exponent alpha (1.07 +/- 0.26 vs 0.90 +/- 0.26, p <0.001) and power-law slope beta (-1.35 +/- 0.23 vs -1.44 +/- 0.25, p <0.05) differed between survivors and those who died, but none of the traditional HR variability measures differed between these groups. Among all analyzed variables, reduced scaling exponent alpha (<0.85) was the best univariable predictor of mortality (relative risk 3.17, 95% confidence interval 1.96 to 5.15, p <0.0001), with positive and negative predictive accuracies of 65% and 86%, respectively. In the multivariable Cox proportional hazards analysis, mortality was independently predicted by the reduced exponent alpha (p <0.001) after adjustment for several clinical variables and LV function. A short-term fractal-like scaling exponent was the most powerful HR variability index in predicting mortality in patients with depressed LV function. Reduction in fractal correlation properties implies more random short-term HR dynamics in patients with increased risk of death after AMI.
Fractal analysis of Mesoamerican pyramids.
Burkle-Elizondo, Gerardo; Valdez-Cepeda, Ricardo David
2006-01-01
A myth of ancient cultural roots was integrated into Mesoamerican cult, and the reference to architecture denoted a depth religious symbolism. The pyramids form a functional part of this cosmovision that is centered on sacralization. The space architecture works was an expression of the ideological necessities into their conception of harmony. The symbolism of the temple structures seems to reflect the mathematical order of the Universe. We contemplate two models of fractal analysis. The first one includes 16 pyramids. We studied a data set that was treated as a fractal profile to estimate the Df through variography (Dv). The estimated Fractal Dimension Dv = 1.383 +/- 0.211. In the second one we studied a data set to estimate the Dv of 19 pyramids and the estimated Fractal Dimension Dv = 1.229 +/- 0.165. PMID:16393505
Functional imaging for regenerative medicine.
Leahy, Martin; Thompson, Kerry; Zafar, Haroon; Alexandrov, Sergey; Foley, Mark; O'Flatharta, Cathal; Dockery, Peter
2016-01-01
In vivo imaging is a platform technology with the power to put function in its natural structural context. With the drive to translate stem cell therapies into pre-clinical and clinical trials, early selection of the right imaging techniques is paramount to success. There are many instances in regenerative medicine where the biological, biochemical, and biomechanical mechanisms behind the proposed function of stem cell therapies can be elucidated by appropriate imaging. Imaging techniques can be divided according to whether labels are used and as to whether the imaging can be done in vivo. In vivo human imaging places additional restrictions on the imaging tools that can be used. Microscopies and nanoscopies, especially those requiring fluorescent markers, have made an extraordinary impact on discovery at the molecular and cellular level, but due to their very limited ability to focus in the scattering tissues encountered for in vivo applications they are largely confined to superficial imaging applications in research laboratories. Nanoscopy, which has tremendous benefits in resolution, is limited to the near-field (e.g. near-field scanning optical microscope (NSNOM)) or to very high light intensity (e.g. stimulated emission depletion (STED)) or to slow stochastic events (photo-activated localization microscopy (PALM) and stochastic optical reconstruction microscopy (STORM)). In all cases, nanoscopy is limited to very superficial applications. Imaging depth may be increased using multiphoton or coherence gating tricks. Scattering dominates the limitation on imaging depth in most tissues and this can be mitigated by the application of optical clearing techniques that can impose mild (e.g. topical application of glycerol) or severe (e.g. CLARITY) changes to the tissue to be imaged. Progression of therapies through to clinical trials requires some thought as to the imaging and sensing modalities that should be used. Smoother progression is facilitated by the use of
Microbialites on Mars: a fractal analysis of the Athena's microscopic images
NASA Astrophysics Data System (ADS)
Bianciardi, G.; Rizzo, V.; Cantasano, N.
2015-10-01
The Mars Exploration Rovers investigated Martian plains where laminated sedimentary rocks are present. The Athena morphological investigation [1] showed microstructures organized in intertwined filaments of microspherules: a texture we have also found on samples of terrestrial (biogenic) stromatolites and other microbialites and not on pseudo-abiogenicstromatolites. We performed a quantitative image analysis in order to compare 50 microbialites images with 50 rovers (Opportunity and Spirit) ones (approximately 30,000/30,000 microstructures). Contours were extracted and morphometric indexes obtained: geometric and algorithmic complexities, entropy, tortuosity, minimum and maximum diameters. Terrestrial and Martian textures resulted multifractals. Mean values and confidence intervals from the Martian images overlapped perfectly with those from terrestrial samples. The probability of this occurring by chance was less than 1/28, p<0.004. Our work show the evidence of a widespread presence of microbialites in the Martian outcroppings: i.e., the presence of unicellular life on the ancient Mars, when without any doubt, liquid water flowed on the Red Planet.
Fractal Characterization of Hyperspectral Imagery
NASA Technical Reports Server (NTRS)
Qiu, Hon-Iie; Lam, Nina Siu-Ngan; Quattrochi, Dale A.; Gamon, John A.
1999-01-01
Two Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) hyperspectral images selected from the Los Angeles area, one representing urban and the other, rural, were used to examine their spatial complexity across their entire spectrum of the remote sensing data. Using the ICAMS (Image Characterization And Modeling System) software, we computed the fractal dimension values via the isarithm and triangular prism methods for all 224 bands in the two AVIRIS scenes. The resultant fractal dimensions reflect changes in image complexity across the spectral range of the hyperspectral images. Both the isarithm and triangular prism methods detect unusually high D values on the spectral bands that fall within the atmospheric absorption and scattering zones where signature to noise ratios are low. Fractal dimensions for the urban area resulted in higher values than for the rural landscape, and the differences between the resulting D values are more distinct in the visible bands. The triangular prism method is sensitive to a few random speckles in the images, leading to a lower dimensionality. On the contrary, the isarithm method will ignore the speckles and focus on the major variation dominating the surface, thus resulting in a higher dimension. It is seen where the fractal curves plotted for the entire bandwidth range of the hyperspectral images could be used to distinguish landscape types as well as for screening noisy bands.
Print protection using high-frequency fractal noise
NASA Astrophysics Data System (ADS)
Mahmoud, Khaled W.; Blackledge, Jonathon M.; Datta, Sekharjit; Flint, James A.
2004-06-01
All digital images are band-limited to a degree that is determined by a spatial extent of the point spread function; the bandwidth of the image being determined by the optical transfer function. In the printing industry, the limit is determined by the resolution of the printed material. By band limiting the digital image in such away that the printed document maintains its fidelity, it is possible to use the out-of-band frequency space to introduce low amplitude coded data that remains hidden in the image. In this way, a covert signature can be embedded into an image to provide a digital watermark, which is sensitive to reproduction. In this paper a high frequency fractal noise is used as a low amplitude signal. A statistically robust solution to the authentication of printed material using high-fractal noise is proposed here which is based on cross-entropy metrics to provide a statistical confidence test. The fractal watermark is based on application of self-affine fields, which is suitable for documents containing high degree of texture. In principle, this new approach will allow batch tracking to be performed using coded data that has been embedded into the high frequency components of the image whose statistical characteristics are dependent on the printer/scanner technology. The details of this method as well as experimental results are presented.
Multiscale differential fractal feature with application to target detection
NASA Astrophysics Data System (ADS)
Shi, Zelin; Wei, Ying; Huang, Shabai
2004-07-01
A multiscale differential fractal feature of an image is proposed and a small target detection method from complex nature clutter is presented. Considering the speciality that the fractal features of man-made objects change much more violently than that of nature's when the scale is varied, fractal features at multiple scales used for distinguishing man-made target from nature clutter should have more advantages over standard fractal dimensions. Multiscale differential fractal dimensions are deduced from typical fractal model and standard covering-blanket method is improved and used to estimate multiscale fractal dimensions. A multiscale differential fractal feature is defined as the variation of fractal dimensions between two scales at a rational scale range. It can stand out the fractal feature of man-made object from natural clutters much better than the fractal dimension by standard covering-blanket method. Meanwhile, the calculation and the storage amount are reduced greatly, they are 4/M and 2/M that of the standard covering-blanket method respectively (M is scale). In the image of multiscale differential fractal feature, local gray histogram statistical method is used for target detection. Experiment results indicate that this method is suitable for both kinds background of land and sea. It also can be appropriate in both kinds of infrared and TV images, and can detect small targets from a single frame correctly. This method is with high speed and is easy to be implemented.
Dynamic imaging of brain function
Hyder, Fahmeed
2013-01-01
In recent years, there have been unprecedented methodological advances in the dynamic imaging of brain activities. Electrophysiological, optical, and magnetic resonance methods now allow mapping of functional activation (or deactivation) by measurement of neuronal activity (e.g., membrane potential, ion flux, neurotransmitter flux), energy metabolism (e.g., glucose consumption, oxygen consumption, creatine kinase flux), and functional hyperemia (e.g., blood oxygenation, blood flow, blood volume). Properties of the glutamatergic synapse are used as a model to reveal activities at the nerve terminal and their associated changes in energy demand and blood flow. This approach reveals that each method measures different tissue- and/or cell-specific components with specified spatiotemporal resolution. While advantages and disadvantages of different methods are apparent and often used to supersede one another in terms of specificity and/or sensitivity, no particular technique is the optimal dynamic brain imaging method because each method is unique in some respect. Because the demand for energy substrates is a fundamental requirement for function, energy-based methods may allow quantitative dynamic imaging in vivo. However there are exclusive neurobiological insights gained by combining some of these different dynamic imaging techniques. PMID:18839085
Magnetohydrodynamics of fractal media
Tarasov, Vasily E.
2006-05-15
The fractal distribution of charged particles is considered. An example of this distribution is the charged particles that are distributed over the fractal. The fractional integrals are used to describe fractal distribution. These integrals are considered as approximations of integrals on fractals. Typical turbulent media could be of a fractal structure and the corresponding equations should be changed to include the fractal features of the media. The magnetohydrodynamics equations for fractal media are derived from the fractional generalization of integral Maxwell equations and integral hydrodynamics (balance) equations. Possible equilibrium states for these equations are considered.
Fractal vector optical fields.
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. PMID:27420485
Fractal Structure in Human Cerebellum Measured by MRI
NASA Astrophysics Data System (ADS)
Zhang, Luduan; Yue, Guang; Brown, Robert; Liu, Jingzhi
2003-10-01
Fractal dimension has been used to quantify the structures of a wide range of objects in biology and medicine. We measured fractal dimension of human cerebellum (CB) in magnetic resonance images of 24 healthy young subjects (12 men, 12 women). CB images were resampled to a series of image sets with different three-dimensional resolutions. At each resolution, the skeleton of the CB white matter was obtained and the number of pixels belonging to the skeleton was determined. Fractal dimension of the CB skeleton was calculated using the box-counting method. The results indicated that the CB skeleton is a highly fractal structure, with a fractal dimension of 2.57+/-0.01. No significant difference in the CB fractal dimension was observed between men and women. Fractal dimension may serve as a quantitative index for structural complexity of the CB at its developmental, degenerative, or evolutionary stages.
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.
Diffraction from fractal grating Cantor sets
NASA Astrophysics Data System (ADS)
Golmankhaneh, Alireza K.; Baleanu, D.
2016-08-01
In this paper, we have generalized the Fα-calculus by suggesting Fourier and Laplace transformations of the function with support of the fractals set which are the subset of the real line. Using this generalization, we have found the diffraction fringes from the fractal grating Cantor sets.
a New Construction of the Fractal Interpolation Surface
NASA Astrophysics Data System (ADS)
Ri, Songil
2015-10-01
In this paper, we introduce a new construction of the fractal interpolation surface (FIS) using an even more general iterated function systems (IFS) which can generate self-affine and non self-affine fractal surfaces. Here we present the general types of fractal surfaces that are based on nonlinear IFSs.
Estimation of Surface Soil Moisture Using Fractal
NASA Astrophysics Data System (ADS)
Chen, Yen Chang; He, Chun Hsuan
2016-04-01
This study establishes the relationship between surface soil moisture and fractal dimension. The surface soil moisture is one of important factors in the hydrological cycle of surface evaporation. It could be used in many fields, such as reservoir management, early drought warning systems, irrigation scheduling and management, and crop yield estimations. Soil surface cracks due to dryness can be used to describe drought conditions. Soil cracking phenomenon and moisture have a certain relationship, thus this study makes used the fractal theory to interpret the soil moisture represented by soil cracks. The fractal dimension of surface soil cracking is a measure of the surface soil moisture. Therefore fractal dimensions can also be used to indicate how dry of the surface soil is. This study used the sediment in the Shimen Reservoir to establish the fractal dimension and soil moisture relation. The soil cracking is created under the control of temperature and thickness of surface soil layers. The results show the increase in fractal dimensions is accompanied by a decreases in surface soil moisture. However the fractal dimensions will approach a constant even the soil moisture continually decreases. The sigmoid function is used to fit the relation of fractal dimensions and surface soil moistures. The proposed method can be successfully applied to estimate surface soil moisture. Only a photo taken from the field is needed and is sufficient to provide the fractal dimension. Consequently, the surface soil moisture can be estimated quickly and accurately.
Fractals in art and nature: why do we like them?
NASA Astrophysics Data System (ADS)
Spehar, Branka; Taylor, Richard P.
2013-03-01
Fractals have experienced considerable success in quantifying the visual complexity exhibited by many natural patterns, and continue to capture the imagination of scientists and artists alike. Fractal patterns have also been noted for their aesthetic appeal, a suggestion further reinforced by the discovery that the poured patterns of the American abstract painter Jackson Pollock are also fractal, together with the findings that many forms of art resemble natural scenes in showing scale-invariant, fractal-like properties. While some have suggested that fractal-like patterns are inherently pleasing because they resemble natural patterns and scenes, the relation between the visual characteristics of fractals and their aesthetic appeal remains unclear. Motivated by our previous findings that humans display a consistent preference for a certain range of fractal dimension across fractal images of various types we turn to scale-specific processing of visual information to understand this relationship. Whereas our previous preference studies focused on fractal images consisting of black shapes on white backgrounds, here we extend our investigations to include grayscale images in which the intensity variations exhibit scale invariance. This scale-invariance is generated using a 1/f frequency distribution and can be tuned by varying the slope of the rotationally averaged Fourier amplitude spectrum. Thresholding the intensity of these images generates black and white fractals with equivalent scaling properties to the original grayscale images, allowing a direct comparison of preferences for grayscale and black and white fractals. We found no significant differences in preferences between the two groups of fractals. For both set of images, the visual preference peaked for images with the amplitude spectrum slopes from 1.25 to 1.5, thus confirming and extending the previously observed relationship between fractal characteristics of images and visual preference.
Surface topography characterization of automotive cylinder liner surfaces using fractal methods
NASA Astrophysics Data System (ADS)
Lawrence K, Deepak; Ramamoorthy, B.
2013-09-01
This paper explores the use of fractal approaches for the possible characterization of automotive cylinder bore surface topography by employing methods such as differential box counting method, power spectral method and structure function method. Three stage plateau honing experiments were conducted to manufacture sixteen cylinder liner surfaces with different surface topographies, for the study. The three fractal methods are applied on the image data obtained using a computer vision system and 3-D profile data obtained using vertical scanning white light interferometer from the cylinder liner surfaces. The computed fractal parameters (fractal dimension and topothesy) are compared and correlated with the measured 3-D Abbott-Firestone curve parameters (Sk, Spk, Svk, Sr1 and Sr2) that are currently used for the surface topography characterization cylinder liner surfaces. The analyses of the results indicated that the fractal dimension (D) computed using the vision data as well as 3-D profile data by employing three different fractal methods consistantly showed a negative correlation with the functional surface topographical parameters that represents roughness at peak (Spk),core (Sk) and valley (Svk) regions and positive correlation with the upper bearing area (Sr1) and lower bearing area (Sr2) of the automotive of cylinder bore surface.
Fractal kinetics in drug release from finite fractal matrices
NASA Astrophysics Data System (ADS)
Kosmidis, Kosmas; Argyrakis, Panos; Macheras, Panos
2003-09-01
We have re-examined the random release of particles from fractal polymer matrices using Monte Carlo simulations, a problem originally studied by Bunde et al. [J. Chem. Phys. 83, 5909 (1985)]. A certain population of particles diffuses on a fractal structure, and as particles reach the boundaries of the structure they are removed from the system. We find that the number of particles that escape from the matrix as a function of time can be approximated by a Weibull (stretched exponential) function, similar to the case of release from Euclidean matrices. The earlier result that fractal release rates are described by power laws is correct only at the initial stage of the release, but it has to be modified if one is to describe in one picture the entire process for a finite system. These results pertain to the release of drugs, chemicals, agrochemicals, etc., from delivery systems.
Quantitating the subtleties of microglial morphology with fractal analysis
Karperien, Audrey; Ahammer, Helmut; Jelinek, Herbert F.
2013-01-01
It is well established that microglial form and function are inextricably linked. In recent years, the traditional view that microglial form ranges between “ramified resting” and “activated amoeboid” has been emphasized through advancing imaging techniques that point to microglial form being highly dynamic even within the currently accepted morphological categories. Moreover, microglia adopt meaningful intermediate forms between categories, with considerable crossover in function and varying morphologies as they cycle, migrate, wave, phagocytose, and extend and retract fine and gross processes. From a quantitative perspective, it is problematic to measure such variability using traditional methods, but one way of quantitating such detail is through fractal analysis. The techniques of fractal analysis have been used for quantitating microglial morphology, to categorize gross differences but also to differentiate subtle differences (e.g., amongst ramified cells). Multifractal analysis in particular is one technique of fractal analysis that may be useful for identifying intermediate forms. Here we review current trends and methods of fractal analysis, focusing on box counting analysis, including lacunarity and multifractal analysis, as applied to microglial morphology. PMID:23386810
Fractality in the neuron axonal topography of the human brain based on 3-D diffusion MRI
NASA Astrophysics Data System (ADS)
Katsaloulis, P.; Ghosh, A.; Philippe, A. C.; Provata, A.; Deriche, R.
2012-05-01
In this work the fractal architecture of the neuron axonal topography of the human brain is evaluated, as derived from 3-D diffusion MRI (dMRI) acquisitions. This is a 3D extension of work performed previously in 2D regions of interest (ROIs), where the fractal dimension of the neuron axonal topography was computed from dMRI data. A group study with 18 subjects is here conducted and the fractal dimensions D f of the entire 3-D volume of the brains is estimated via the box counting, the correlation dimension and the fractal mass dimension methods. The neuron axon data is obtained using tractography algorithms on diffusion tensor imaging of the brain. We find that all three calculations of D f give consistent results across subjects, namely, they demonstrate fractal characteristics in the short and medium length scales: different fractal exponents prevail at different length scales, an indication of multifractality. We surmise that this complexity stems as a collective property emerging when many local brain units, performing different functional tasks and having different local topologies, are recorded together.
NASA Astrophysics Data System (ADS)
Chacón-Cardona, C. A.; Casas-Miranda, R. A.
2014-10-01
Recent works about large structure in the universe put in doubt the homogeneity transition almost universally accepted, (Joyce et al.2005), (Gaite 2007), (Chacón-Cardona & Casas-Miranda 2012). In the present work we develop theoretically the density contrast for the spherical collapse of an over-density of dark matter which evolve in a inhomogeneous universe inside a fractal cosmology presented by (Bondi 1947).
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)
Multiresolution processing for fractal analysis of airborne remotely sensed data
NASA Technical Reports Server (NTRS)
Jaggi, S.; Quattrochi, D.; Lam, N.
1992-01-01
Images acquired by NASA's Calibrated Airborne Multispectral Scanner are used to compute the fractal dimension as a function of spatial resolution. Three methods are used to determine the fractal dimension: Shelberg's (1982, 1983) line-divider method, the variogram method, and the triangular prism method. A description of these methods and the result of applying these methods to a remotely-sensed image is also presented. The scanner data was acquired over western Puerto Rico in January, 1990 over land and water. The aim is to study impacts of man-induced changes on land that affect sedimentation into the near-shore environment. The data were obtained over the same area at three different pixel sizes: 10 m, 20 m, and 30 m.
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
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
Routes to fractality and entropy in Liesegang systems.
Kalash, Leen; Sultan, Rabih
2014-06-01
Liesegang bands are formed when solutions of co-precipitate ions interdiffuse in a 1D gel matrix. In a recent study [R. F. Sultan, Acta. Mech. Sin. 27, 119 (2011)], Liesegang patterns have been characterized as fractal structures. In addition to experimentally obtained patterns, geometric Liesegang patterns were constructed in conformity with the well-known empirical laws. Both mathematical fractal dimensions and box count dimensions for images of PbF2 and PbI2 Liesegang patterns have been calculated. Liesegang patterns can also be described by the entropy state function, and categorized as more or less ordered structures. We revisit the relation between entropy and fractal dimension, and apply it to simulated geometrical Liesegang patterns. We have resort to three different routes for the estimation of the entropy of a Liesegang pattern. The HarFA software enabled the calculation of the Hausdorff dimension and the topological entropy, then the information dimension and the Shannon entropy. In a third pathway, analytical calculations were carried out by estimating the probability of occurrence of a fractal element or coverage. The product of Shannon entropy and Boltzmann constant yields the thermodynamic entropy. The values for PbF2 and PbI2 Liesegang patterns attained the order of magnitude of the reported Third Law entropies, but yet remained lower, in conformity with the more ordered Liesegang structures. PMID:24985435
Routes to fractality and entropy in Liesegang systems
Kalash, Leen; Sultan, Rabih
2014-06-01
Liesegang bands are formed when solutions of co-precipitate ions interdiffuse in a 1D gel matrix. In a recent study [R. F. Sultan, Acta. Mech. Sin. 27, 119 (2011)], Liesegang patterns have been characterized as fractal structures. In addition to experimentally obtained patterns, geometric Liesegang patterns were constructed in conformity with the well-known empirical laws. Both mathematical fractal dimensions and box count dimensions for images of PbF{sub 2} and PbI{sub 2} Liesegang patterns have been calculated. Liesegang patterns can also be described by the entropy state function, and categorized as more or less ordered structures. We revisit the relation between entropy and fractal dimension, and apply it to simulated geometrical Liesegang patterns. We have resort to three different routes for the estimation of the entropy of a Liesegang pattern. The HarFA software enabled the calculation of the Hausdorff dimension and the topological entropy, then the information dimension and the Shannon entropy. In a third pathway, analytical calculations were carried out by estimating the probability of occurrence of a fractal element or coverage. The product of Shannon entropy and Boltzmann constant yields the thermodynamic entropy. The values for PbF{sub 2} and PbI{sub 2} Liesegang patterns attained the order of magnitude of the reported Third Law entropies, but yet remained lower, in conformity with the more ordered Liesegang structures.
Routes to fractality and entropy in Liesegang systems
NASA Astrophysics Data System (ADS)
Kalash, Leen; Sultan, Rabih
2014-06-01
Liesegang bands are formed when solutions of co-precipitate ions interdiffuse in a 1D gel matrix. In a recent study [R. F. Sultan, Acta. Mech. Sin. 27, 119 (2011)], Liesegang patterns have been characterized as fractal structures. In addition to experimentally obtained patterns, geometric Liesegang patterns were constructed in conformity with the well-known empirical laws. Both mathematical fractal dimensions and box count dimensions for images of PbF2 and PbI2 Liesegang patterns have been calculated. Liesegang patterns can also be described by the entropy state function, and categorized as more or less ordered structures. We revisit the relation between entropy and fractal dimension, and apply it to simulated geometrical Liesegang patterns. We have resort to three different routes for the estimation of the entropy of a Liesegang pattern. The HarFA software enabled the calculation of the Hausdorff dimension and the topological entropy, then the information dimension and the Shannon entropy. In a third pathway, analytical calculations were carried out by estimating the probability of occurrence of a fractal element or coverage. The product of Shannon entropy and Boltzmann constant yields the thermodynamic entropy. The values for PbF2 and PbI2 Liesegang patterns attained the order of magnitude of the reported Third Law entropies, but yet remained lower, in conformity with the more ordered Liesegang structures.
Is a chaotic multi-fractal approach for rainfall possible?
NASA Astrophysics Data System (ADS)
Sivakumar, Bellie
2001-04-01
Applications of the ideas gained from fractal theory to characterize rainfall have been one of the most exciting areas of research in recent times. The studies conducted thus far have nearly unanimously yielded positive evidence regarding the existence of fractal behaviour in rainfall. The studies also revealed the insufficiency of the mono-fractal approaches to characterizing the rainfall process in time and space and, hence, the necessity for multi-fractal approaches. The assumption behind multi-fractal approaches for rainfall is that the variability of the rainfall process could be directly modelled as a stochastic (or random) turbulent cascade process, since such stochastic cascade processes were found to generically yield multi-fractals. However, it has been observed recently that multi-fractal approaches might provide positive evidence of a multi-fractal nature not only in stochastic processes but also in, for example, chaotic processes. The purpose of the present study is to investigate the presence of both chaotic and fractal behaviours in the rainfall process to consider the possibility of using a chaotic multi-fractal approach for rainfall characterization. For this purpose, daily rainfall data observed at the Leaf River basin in Mississippi are studied, and only temporal analysis is carried out. The autocorrelation function, the power spectrum, the empirical probability distribution function, and the statistical moment scaling function are used as indicators to investigate the presence of fractal, whereas the presence of chaos is investigated by employing the correlation dimension method. The results from the fractal identification methods indicate that the rainfall data exhibit multi-fractal behaviour. The correlation dimension method yields a low dimension, suggesting the presence of chaotic behaviour. The existence of both multi-fractal and chaotic behaviours in the rainfall data suggests the possibility of a chaotic multi-fractal approach for
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.…
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.
Functional Magnetic Resonance Imaging Methods
Chen, Jingyuan E.; Glover, Gary H.
2015-01-01
Since its inception in 1992, Functional Magnetic Resonance Imaging (fMRI) has become an indispensible tool for studying cognition in both the healthy and dysfunctional brain. FMRI monitors changes in the oxygenation of brain tissue resulting from altered metabolism consequent to a task-based evoked neural response or from spontaneous fluctuations in neural activity in the absence of conscious mentation (the “resting state”). Task-based studies have revealed neural correlates of a large number of important cognitive processes, while fMRI studies performed in the resting state have demonstrated brain-wide networks that result from brain regions with synchronized, apparently spontaneous activity. In this article, we review the methods used to acquire and analyze fMRI signals. PMID:26248581
ERIC Educational Resources Information Center
Marks-Tarlow, Terry
2010-01-01
In this article, the author draws on contemporary science to illuminate the relationship between early play experiences, processes of self-development, and the later emergence of the fractal self. She argues that orientation within social space is a primary function of early play and developmentally a two-step process. With other people and with…
Multiplexing of encrypted data using fractal masks.
Barrera, John F; Tebaldi, Myrian; Amaya, Dafne; Furlan, Walter D; Monsoriu, Juan A; Bolognini, Néstor; Torroba, Roberto
2012-07-15
In this Letter, we present to the best of our knowledge a new all-optical technique for multiple-image encryption and multiplexing, based on fractal encrypting masks. The optical architecture is a joint transform correlator. The multiplexed encrypted data are stored in a photorefractive crystal. The fractal parameters of the key can be easily tuned to lead to a multiplexing operation without cross talk effects. Experimental results that support the potential of the method are presented. PMID:22825170
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.
Foucher, F.; Mounaim-Rousselle, C.
2005-11-01
The burning rate in the vicinity of a piston is estimated from a fractal analysis. The fractal parameters are determined from laser sheet tomography flame images for methane-air mixtures with three equivalence ratios (1, 0.9, 0.8) in a transparent spark-ignition engine. Two imaging configurations were used: five horizontal planes placed at different distances from the piston (0, 1, 2, 3, and 5 mm) and a vertical one passed through the center of the combustion chamber. The methodology proposed by Foucher et al. [F. Foucher, S. Burnel, C. Mounaim-Rousselle, Proc. Combust. Inst. 29 (2002) 751-757] allows the effect of cyclic variations to be avoided. The fractal formulation is modified to take into account the flame-piston distance and flame quenching. Far from the piston, evolution of the fractal dimension versus q{sup '}/S{sub L}{sup 0} is found to be in good agreement with literature results. Near the piston, the fractal dimension evolves significantly when the distance is about twice the integral length scale and tends toward 2, the fractal dimension of a laminar flame front. The quenching ratio parameter Q{sub R} is introduced to consider the quenching of the flame by the piston. Finally, the burning rate is determined as a function of the distance between the wall and the mean flame contour and compared to a flame density approach, and similar results are found.
Novel optical password security technique based on optical fractal synthesizer
NASA Astrophysics Data System (ADS)
Wu, Kenan; Hu, Jiasheng; Wu, Xu
2009-06-01
A novel optical security technique for safeguarding user passwords based on an optical fractal synthesizer is proposed. A validating experiment has been carried out. In the proposed technique, a user password is protected by being converted to a fractal image. When a user sets up a new password, the password is transformed into a fractal pattern, and the fractal pattern is stored in authority. If the user is online-validated, his or her password is converted to a fractal pattern again to compare with the previous stored fractal pattern. The converting process is called the fractal encoding procedure, which consists of two steps. First, the password is nonlinearly transformed to get the parameters for the optical fractal synthesizer. Then the optical fractal synthesizer is operated to generate the output fractal image. The experimental result proves the validity of our method. The proposed technique bridges the gap between digital security systems and optical security systems and has many advantages, such as high security level, convenience, flexibility, hyper extensibility, etc. This provides an interesting optical security technique for the protection of digital passwords.
Hexagonal and Pentagonal Fractal Multiband Antennas
NASA Technical Reports Server (NTRS)
Tang, Philip W.; Wahid, Parveen
2005-01-01
Multiband dipole antennas based on hexagonal and pentagonal fractals have been analyzed by computational simulations and functionally demonstrated in experiments on prototypes. These antennas are capable of multiband or wide-band operation because they are subdivided into progressively smaller substructures that resonate at progressively higher frequencies by virtue of their smaller dimensions. The novelty of the present antennas lies in their specific hexagonal and pentagonal fractal configurations and the resonant frequencies associated with them. These antennas are potentially applicable to a variety of multiband and wide-band commercial wireless-communication products operating at different frequencies, including personal digital assistants, cellular telephones, pagers, satellite radios, Global Positioning System receivers, and products that combine two or more of the aforementioned functions. Perhaps the best-known prior multiband antenna based on fractal geometry is the Sierpinski triangle antenna (also known as the Sierpinski gasket), shown in the top part of the figure. In this antenna, the scale length at each iteration of the fractal is half the scale length of the preceding iteration, yielding successive resonant frequencies related by a ratio of about 2. The middle and bottom parts of the figure depict the first three iterations of the hexagonal and pentagonal fractals along with typical dipole-antenna configuration based on the second iteration. Successive resonant frequencies of the hexagonal fractal antenna have been found to be related by a ratio of about 3, and those of the pentagonal fractal antenna by a ratio of about 2.59.
New Horizons for Imaging Lymphatic Function
Sharma, Ruchi; Wendt, Juliet A.; Rasmussen, John C.; Adams, Kristen E.; Marshall, Milton V.; Sevick-Muraca, Eva M.
2011-01-01
In this review, we provide a comprehensive summary of noninvasive imaging modalities used clinically for the diagnosis of lymphatic diseases, new imaging agents for assessing lymphatic architecture and cancer status of lymph nodes, and emerging near-infrared (NIR) fluorescent optical imaging technologies and agents for functional lymphatic imaging. Given the promise of NIR optical imaging, we provide example results of functional lymphatic imaging in mice, swine, and humans, showing the ability of this technology to quantify lymph velocity and frequencies of propulsion resulting from the contractility of lymphatic structures. PMID:18519956
Sporadically Fractal Basin Boundaries of Chaotic Systems
Hunt, B.R.; Ott, E.; Rosa, E. Jr.
1999-05-01
We demonstrate a new type of basin boundary for typical chaotic dynamical systems. For the case of a two dimensional map, this boundary has the character of the graph of a function that is smooth and differentiable except on a set of fractal dimensions less than one. In spite of the basin boundary being smooth {open_quotes}almost everywhere,{close_quotes} its fractal dimension exceeds one (implying degradation of one{close_quote}s ability to predict the attractor an orbit approaches in the presence of small initial condition uncertainty). We call such a boundary {ital sporadically fractal}. {copyright} {ital 1999} {ital The American Physical Society}
Multi-resolution processing for fractal analysis of airborne remotely sensed data
NASA Technical Reports Server (NTRS)
Jaggi, S.; Quattrochi, D.; Lam, N.
1992-01-01
Fractal geometry is increasingly becoming a useful tool for modeling natural phenomenon. As an alternative to Euclidean concepts, fractals allow for a more accurate representation of the nature of complexity in natural boundaries and surfaces. Since they are characterized by self-similarity, an ideal fractal surface is scale-independent; i.e. at different scales a fractal surface looks the same. This is not exactly true for natural surfaces. When viewed at different spatial resolutions parts of natural surfaces look alike in a statistical manner and only for a limited range of scales. Images acquired by NASA's Thermal Infrared Multispectral Scanner are used to compute the fractal dimension as a function of spatial resolution. Three methods are used to determine the fractal dimension - Schelberg's line-divider method, the variogram method, and the triangular prism method. A description of these methods and the results of applying these methods to a remotely-sensed image is also presented. Five flights were flown in succession at altitudes of 2 km (low), 6 km (mid), 12 km (high), and then back again at 6 km and 2 km. The area selected was the Ross Barnett reservoir near Jackson, Mississippi. The mission was flown during the predawn hours of 1 Feb. 1992. Radiosonde data was collected for that duration to profile the characteristics of the atmosphere. This corresponds to 3 different pixel sizes - 5m, 15m, and 30m. After, simulating different spatial sampling intervals within the same image for each of the 3 image sets, the results are cross-correlated to compare the extent of detail and complexity that is obtained when data is taken at lower spatial intervals.
Edges of Saturn's rings are fractal.
Li, Jun; Ostoja-Starzewski, Martin
2015-01-01
The images recently sent by the Cassini spacecraft mission (on the NASA website http://saturn.jpl.nasa.gov/photos/halloffame/) show the complex and beautiful rings of Saturn. Over the past few decades, various conjectures were advanced that Saturn's rings are Cantor-like sets, although no convincing fractal analysis of actual images has ever appeared. Here we focus on four images sent by the Cassini spacecraft mission (slide #42 "Mapping Clumps in Saturn's Rings", slide #54 "Scattered Sunshine", slide #66 taken two weeks before the planet's Augus't 200'9 equinox, and slide #68 showing edge waves raised by Daphnis on the Keeler Gap) and one image from the Voyager 2' mission in 1981. Using three box-counting methods, we determine the fractal dimension of edges of rings seen here to be consistently about 1.63 ~ 1.78. This clarifies in what sense Saturn's rings are fractal. PMID:25883885
Functional Imaging for Prostate Cancer: Therapeutic Implications
Aparici, Carina Mari; Seo, Youngho
2012-01-01
Functional radionuclide imaging modalities, now commonly combined with anatomical imaging modalities CT or MRI (SPECT/CT, PET/CT, and PET/MRI) are promising tools for the management of prostate cancer particularly for therapeutic implications. Sensitive detection capability of prostate cancer using these imaging modalities is one issue; however, the treatment of prostate cancer using the information that can be obtained from functional radionuclide imaging techniques is another challenging area. There are not many SPECT or PET radiotracers that can cover the full spectrum of the management of prostate cancer from initial detection, to staging, prognosis predictor, and all the way to treatment response assessment. However, when used appropriately, the information from functional radionuclide imaging improves, and sometimes significantly changes, the whole course of the cancer management. The limitations of using SPECT and PET radiotracers with regards to therapeutic implications are not so much different from their limitations solely for the task of detecting prostate cancer; however, the specific imaging target and how this target is reliably imaged by SPECT and PET can potentially make significant impact in the treatment of prostate cancer. Finally, while the localized prostate cancer is considered manageable, there is still significant need for improvement in noninvasive imaging of metastatic prostate cancer, in treatment guidance, and in response assessment from functional imaging including radionuclide-based techniques. In this review article, we present the rationale of using functional radionuclide imaging and the therapeutic implications for each of radionuclide imaging agent that have been studied in human subjects. PMID:22840598
Exploring Fractals in the Classroom.
ERIC Educational Resources Information Center
Naylor, Michael
1999-01-01
Describes an activity involving six investigations. Introduces students to fractals, allows them to study the properties of some famous fractals, and encourages them to create their own fractal artwork. Contains 14 references. (ASK)
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)
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.
Functional Magnetic Resonance Imaging and Pediatric Anxiety
ERIC Educational Resources Information Center
Pine, Daniel S.; Guyer, Amanda E.; Leibenluft, Ellen; Peterson, Bradley S.; Gerber, Andrew
2008-01-01
The use of functional magnetic resonance imaging in investigating pediatric anxiety disorders is studied. Functional magnetic resonance imaging can be utilized in demonstrating parallels between the neural architecture of difference in anxiety of humans and the neural architecture of attention-orienting behavior in nonhuman primates or rodents.…
Fractal Geometry of Architecture
NASA Astrophysics Data System (ADS)
Lorenz, Wolfgang E.
In Fractals smaller parts and the whole are linked together. Fractals are self-similar, as those parts are, at least approximately, scaled-down copies of the rough whole. In architecture, such a concept has also been known for a long time. Not only architects of the twentieth century called for an overall idea that is mirrored in every single detail, but also Gothic cathedrals and Indian temples offer self-similarity. This study mainly focuses upon the question whether this concept of self-similarity makes architecture with fractal properties more diverse and interesting than Euclidean Modern architecture. The first part gives an introduction and explains Fractal properties in various natural and architectural objects, presenting the underlying structure by computer programmed renderings. In this connection, differences between the fractal, architectural concept and true, mathematical Fractals are worked out to become aware of limits. This is the basis for dealing with the problem whether fractal-like architecture, particularly facades, can be measured so that different designs can be compared with each other under the aspect of fractal properties. Finally the usability of the Box-Counting Method, an easy-to-use measurement method of Fractal Dimension is analyzed with regard to architecture.
Fractal dimension analyses of lava surfaces and flow boundaries
NASA Technical Reports Server (NTRS)
Cleghorn, Timothy F.
1993-01-01
An improved method of estimating fractal surface dimensions has been developed. The accuracy of this method is illustrated using artificially generated fractal surfaces. A slightly different from usual concept of linear dimension is developed, allowing a direct link between that and the corresponding surface dimension estimate. These methods are applied to a series of images of lava flows, representing a variety of physical and chemical conditions. These include lavas from California, Idaho, and Hawaii, as well as some extraterrestrial flows. The fractal surface dimension estimations are presented, as well as the fractal line dimensions where appropriate.
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.
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.
The use of fractal dimension for texture classification
Dixon, K.E.
1989-04-01
This paper addresses the idea of using fractal dimension as a measure of image texture. The computation of the fractal dimension of a grey-scale image and also of the ''fractal signature'' of the image is presented. Two methods of scanning the image for these calculations are introduced: a line scan and a window scan. Several subsets of features extracted from the calculations are investigated as features for classification of the texture. Results from various classification experiments are presented. 5 refs., 8 tabs.
The topology of fractal universes
NASA Technical Reports Server (NTRS)
Hamilton, A. J. S.
1988-01-01
It is shown how the genus per unit volume of isodensity surfaces in general nonlinear universes is related to the entire hierarchy of correlation functions. The general relation between the correlation function, the probability distribution of densities at several points, and the probability distributions of density and its derivatives at a point are given. Formulas for the area and genus per unit volume of isodensity surfaces are presented. As an application, after first reviewing the case of Gaussian fields, analytic results are reported for one particular example of a thoroughly nonlinear universe, Mandelbrot's Rayleigh-Levy random-walk fractal. While this fractal bears little resemblance to the real universe of galaxies, it possesses the singular and theoretically interesting property that in it cluster-cluster correlations are identically equal to galaxy-galaxy correlations to all orders.
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.
Fractal analysis of yeast cell optical speckle
NASA Astrophysics Data System (ADS)
Flamholz, A.; Schneider, P. S.; Subramaniam, R.; Wong, P. K.; Lieberman, D. H.; Cheung, T. D.; Burgos, J.; Leon, K.; Romero, J.
2006-02-01
Steady state laser light propagation in diffuse media such as biological cells generally provide bulk parameter information, such as the mean free path and absorption, via the transmission profile. The accompanying optical speckle can be analyzed as a random spatial data series and its fractal dimension can be used to further classify biological media that show similar mean free path and absorption properties, such as those obtained from a single population. A population of yeast cells can be separated into different portions by centrifuge, and microscope analysis can be used to provide the population statistics. Fractal analysis of the speckle suggests that lower fractal dimension is associated with higher cell packing density. The spatial intensity correlation revealed that the higher cell packing gives rise to higher refractive index. A calibration sample system that behaves similar as the yeast samples in fractal dimension, spatial intensity correlation and diffusion was selected. Porous silicate slabs with different refractive index values controlled by water content were used for system calibration. The porous glass as well as the yeast random spatial data series fractal dimension was found to depend on the imaging resolution. The fractal method was also applied to fission yeast single cell fluorescent data as well as aging yeast optical data; and consistency was demonstrated. It is concluded that fractal analysis can be a high sensitivity tool for relative comparison of cell structure but that additional diffusion measurements are necessary for determining the optimal image resolution. Practical application to dental plaque bio-film and cam-pill endoscope images was also demonstrated.
Taxonomy of Individual Variations in Aesthetic Responses to Fractal Patterns.
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
Clinical applications of functional MR imaging.
Belyaev, Artem S; Peck, Kyung K; Brennan, Nicole M Petrovich; Holodny, Andrei I
2013-05-01
Functional magnetic resonance (fMR) imaging for neurosurgical planning has become the standard of care in centers where it is available. Although paradigms to measure eloquent cortices are not yet standardized, simple tasks elicit reliable maps for planning neurosurgical procedures. A patient-specific paradigm design will refine the usability of fMR imaging for prognostication and recovery of function. Certain pathologic conditions and technical issues limit the interpretation of fMR imaging maps in clinical use and should be considered carefully. However, fMR imaging for neurosurgical planning continues to provide insights into how the brain works and how it responds to pathologic insults. PMID:23642553
Namazi, Hamidreza; Kulish, Vladimir V; Akrami, Amin
2016-01-01
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. PMID:27217194
Namazi, Hamidreza; Kulish, Vladimir V.; Akrami, Amin
2016-01-01
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. PMID:27217194
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.
Functional imaging in tumor-associated lymphatics
NASA Astrophysics Data System (ADS)
Kwon, Sunkuk; Sevick-Muraca, Eva M.
2011-03-01
The lymphatic system plays an important role in cancer cell dissemination; however whether lymphatic drainage pathways and function change during tumor progression and metastasis remains to be elucidated. In this report, we employed a non-invasive, dynamic near-infrared (NIR) fluorescence imaging technique for functional lymphatic imaging. Indocyanine green (ICG) was intradermally injected into tumor-free mice and mice bearing C6/LacZ rat glioma tumors in the tail or hindlimb. Our imaging data showed abnormal lymphatic drainage pathways and reduction/loss of lymphatic contractile function in mice with lymph node (LN) metastasis, indicating that cancer metastasis to the draining LNs is accompanied by transient changes of the lymphatic architectural network and its function. Therefore, functional lymphatic imaging may provide a role in the clinical staging of cancer.
Fractal Analysis of Cervical Intraepithelial Neoplasia
Fabrizii, Markus; Moinfar, Farid; Jelinek, Herbert F.; Karperien, Audrey; Ahammer, Helmut
2014-01-01
Introduction Cervical intraepithelial neoplasias (CIN) represent precursor lesions of cervical cancer. These neoplastic lesions are traditionally subdivided into three categories CIN 1, CIN 2, and CIN 3, using microscopical criteria. The relation between grades of cervical intraepithelial neoplasia (CIN) and its fractal dimension was investigated to establish a basis for an objective diagnosis using the method proposed. Methods Classical evaluation of the tissue samples was performed by an experienced gynecologic pathologist. Tissue samples were scanned and saved as digital images using Aperio scanner and software. After image segmentation the box counting method as well as multifractal methods were applied to determine the relation between fractal dimension and grades of CIN. A total of 46 images were used to compare the pathologist's neoplasia grades with the predicted groups obtained by fractal methods. Results Significant or highly significant differences between all grades of CIN could be found. The confusion matrix, comparing between pathologist's grading and predicted group by fractal methods showed a match of 87.1%. Multifractal spectra were able to differentiate between normal epithelium and low grade as well as high grade neoplasia. Conclusion Fractal dimension can be considered to be an objective parameter to grade cervical intraepithelial neoplasia. PMID:25302712
Fractal structures and processes
Bassingthwaighte, J.B.; Beard, D.A.; Percival, D.B.; Raymond, G.M.
1996-06-01
Fractals and chaos are closely related. Many chaotic systems have fractal features. Fractals are self-similar or self-affine structures, which means that they look much of the same when magnified or reduced in scale over a reasonably large range of scales, at least two orders of magnitude and preferably more (Mandelbrot, 1983). The methods for estimating their fractal dimensions or their Hurst coefficients, which summarize the scaling relationships and their correlation structures, are going through a rapid evolutionary phase. Fractal measures can be regarded as providing a useful statistical measure of correlated random processes. They also provide a basis for analyzing recursive processes in biology such as the growth of arborizing networks in the circulatory system, airways, or glandular ducts. {copyright} {ital 1996 American Institute of Physics.}
Molecular and Functional Imaging of Internet Addiction
Zhu, Yunqi; Zhang, Hong; Tian, Mei
2015-01-01
Maladaptive use of the Internet results in Internet addiction (IA), which is associated with various negative consequences. Molecular and functional imaging techniques have been increasingly used for analysis of neurobiological changes and neurochemical correlates of IA. This review summarizes molecular and functional imaging findings on neurobiological mechanisms of IA, focusing on magnetic resonance imaging (MRI) and nuclear imaging modalities including positron emission tomography (PET) and single photon emission computed tomography (SPECT). MRI studies demonstrate that structural changes in frontal cortex are associated with functional abnormalities in Internet addicted subjects. Nuclear imaging findings indicate that IA is associated with dysfunction of the brain dopaminergic systems. Abnormal dopamine regulation of the prefrontal cortex (PFC) could underlie the enhanced motivational value and uncontrolled behavior over Internet overuse in addicted subjects. Further investigations are needed to determine specific changes in the Internet addictive brain, as well as their implications for behavior and cognition. PMID:25879023
Functional imaging of the musculoskeletal system
2015-01-01
Functional imaging, which provides information of how tissues function rather than structural information, is well established in neuro- and cardiac imaging. Many musculoskeletal structures, such as ligaments, fascia and mineralized bone, have by definition a mainly structural role and clearly don’t have the same functional capacity as the brain, heart, liver or kidney. The main functionally responsive musculoskeletal tissues are the bone marrow, muscle and nerve and, as such, magnetic resonance (MR) functional imaging has primarily addressed these areas. Proton or phosphorus spectroscopy, other fat quantification techniques, perfusion imaging, BOLD imaging, diffusion and diffusion tensor imaging (DTI) are the main functional techniques applied. The application of these techniques in the musculoskeletal system has mainly been research orientated where they have already greatly enhanced our understanding of marrow physiology, muscle physiology and neural function. Going forwards, they will have a greater clinical impact helping to bridge the disconnect often seen between structural appearances and clinical symptoms, allowing a greater understanding of disease processes and earlier recognition of disease, improving prognostic prediction and optimizing the monitoring of treatment effect. PMID:26029633
Tutte polynomial in functional magnetic resonance imaging
NASA Astrophysics Data System (ADS)
García-Castillón, Marlly V.
2015-09-01
Methods of graph theory are applied to the processing of functional magnetic resonance images. Specifically the Tutte polynomial is used to analyze such kind of images. Functional Magnetic Resonance Imaging provide us connectivity networks in the brain which are represented by graphs and the Tutte polynomial will be applied. The problem of computing the Tutte polynomial for a given graph is #P-hard even for planar graphs. For a practical application the maple packages "GraphTheory" and "SpecialGraphs" will be used. We will consider certain diagram which is depicting functional connectivity, specifically between frontal and posterior areas, in autism during an inferential text comprehension task. The Tutte polynomial for the resulting neural networks will be computed and some numerical invariants for such network will be obtained. Our results show that the Tutte polynomial is a powerful tool to analyze and characterize the networks obtained from functional magnetic resonance imaging.
SPECT functional brain imaging. Technical considerations.
Devous, M D
1995-07-01
The technical aspects of functional brain single-photon emission computed tomography (SPECT) imaging, referring primarily to the most common SPECT brain function measure--regional cerebral blood flow--are reviewed. SPECT images of regional cerebral blood flow are influenced by a number of factors unrelated to pathology, including tomographic quality, radiopharmaceuticals, environmental conditions at the time of radiotracer administration, characteristics of the subject (e.g., age, sex), image presentation, and image processing techniques. Modern SPECT scans yield excellent image quality, and instrumentation continues to improve. The armamentarium of regional cerebral blood flow and receptor radiopharmaceuticals is rapidly expanding. Standards regarding the environment for patient imaging and image presentation are emerging. However, there is still much to learn about the circumstances for performances and evaluation of SPECT functional brain imaging. Challenge tests, primarily established in cerebrovascular disease (i.e., the acetazolamide test), offer great promise in defining the extent and nature of disease, as well as predicting therapeutic responses. Clearly, SPECT brain imaging is a powerful clinical and research tool. However, SPECT will only achieve its full potential in the management of patients with cerebral pathology through close cooperation among members of the nuclear medicine, neurology, psychiatry, neurosurgery, and internal medicine specialties. PMID:7626833
NASA Astrophysics Data System (ADS)
Mandal, Prantik; Rodkin, Mikhail V.
2011-11-01
We use precisely located aftershocks of the 2001 Mw7.7 Bhuj earthquake (2001-2009) to explore the structure of the Kachchh seismic zone by mapping the 3-D distributions of b-value, fractal dimension (D) and seismic velocities. From frequency-magnitude analysis, we find that the catalog is complete above Mw = 3.0. Thus, we analyze 2159 aftershocks with Mw ≥ 3.0 to estimate the 3-D distribution of b-value and fractal dimensions using maximum-likelihood and spatial correlation dimension approaches, respectively. Our results show an area of high b-, D- and Vp/Vs ratio values at 15-35 km depth in the main rupture zone (MRZ), while relatively low b- and D values characterize the surrounding rigid regions and Gedi fault (GF) zone. We propose that higher material heterogeneities in the vicinity of the MRZ and/or circulation of deep aqueous fluid/volatile CO 2 is the main cause of the increased b-, D- and Vp/Vs ratio values at 15-35 km depth. Seismic velocity images also show some low velocity zones continuing in to the deep lower crust, supporting the existence of circulation of deep aqueous fluid / volatile CO 2 in the region (probably released from the eclogitasation of olivine rich lower crustal rocks). The presence of number of high and low velocity patches further reveals the heterogeneous and fractured nature of the MRZ. Interestingly, we observe that Aki (1981)'s relation (D = 2b) is not valid for the spatial b-D correlation of the events in the GF (D 2 = 1.2b) zone. However, the events in the MRZ (D 2 = 1.7b) show a fair agreement with the D = 2b relationship while the earthquakes associated with the remaining parts of the aftershock zone (D 2 = 1.95b) show a strong correlation with the Aki (1981)'s relationship. Thus, we infer that the remaining parts of the aftershock zone are probably behaving like locked un-ruptured zones, where larger stresses accumulate. We also propose that deep fluid involvement may play a key role in generating seismic activity in the
Fractal analysis of DNA sequence data
Berthelsen, C.L.
1993-01-01
DNA sequence databases are growing at an almost exponential rate. New analysis methods are needed to extract knowledge about the organization of nucleotides from this vast amount of data. Fractal analysis is a new scientific paradigm that has been used successfully in many domains including the biological and physical sciences. Biological growth is a nonlinear dynamic process and some have suggested that to consider fractal geometry as a biological design principle may be most productive. This research is an exploratory study of the application of fractal analysis to DNA sequence data. A simple random fractal, the random walk, is used to represent DNA sequences. The fractal dimension of these walks is then estimated using the [open quote]sandbox method[close quote]. Analysis of 164 human DNA sequences compared to three types of control sequences (random, base-content matched, and dimer-content matched) reveals that long-range correlations are present in DNA that are not explained by base or dimer frequencies. The study also revealed that the fractal dimension of coding sequences was significantly lower than sequences that were primarily noncoding, indicating the presence of longer-range correlations in functional sequences. The multifractal spectrum is used to analyze fractals that are heterogeneous and have a different fractal dimension for subsets with different scalings. The multifractal spectrum of the random walks of twelve mitochondrial genome sequences was estimated. Eight vertebrate mtDNA sequences had uniformly lower spectra values than did four invertebrate mtDNA sequences. Thus, vertebrate mitochondria show significantly longer-range correlations than to invertebrate mitochondria. The higher multifractal spectra values for invertebrate mitochondria suggest a more random organization of the sequences. This research also includes considerable theoretical work on the effects of finite size, embedding dimension, and scaling ranges.
Fractal Analysis of DNA Sequence Data
NASA Astrophysics Data System (ADS)
Berthelsen, Cheryl Lynn
DNA sequence databases are growing at an almost exponential rate. New analysis methods are needed to extract knowledge about the organization of nucleotides from this vast amount of data. Fractal analysis is a new scientific paradigm that has been used successfully in many domains including the biological and physical sciences. Biological growth is a nonlinear dynamic process and some have suggested that to consider fractal geometry as a biological design principle may be most productive. This research is an exploratory study of the application of fractal analysis to DNA sequence data. A simple random fractal, the random walk, is used to represent DNA sequences. The fractal dimension of these walks is then estimated using the "sandbox method." Analysis of 164 human DNA sequences compared to three types of control sequences (random, base -content matched, and dimer-content matched) reveals that long-range correlations are present in DNA that are not explained by base or dimer frequencies. The study also revealed that the fractal dimension of coding sequences was significantly lower than sequences that were primarily noncoding, indicating the presence of longer-range correlations in functional sequences. The multifractal spectrum is used to analyze fractals that are heterogeneous and have a different fractal dimension for subsets with different scalings. The multifractal spectrum of the random walks of twelve mitochondrial genome sequences was estimated. Eight vertebrate mtDNA sequences had uniformly lower spectra values than did four invertebrate mtDNA sequences. Thus, vertebrate mitochondria show significantly longer-range correlations than do invertebrate mitochondria. The higher multifractal spectra values for invertebrate mitochondria suggest a more random organization of the sequences. This research also includes considerable theoretical work on the effects of finite size, embedding dimension, and scaling ranges.
Electromagnetic fields in fractal continua
NASA Astrophysics Data System (ADS)
Balankin, Alexander S.; Mena, Baltasar; Patiño, Julián; Morales, Daniel
2013-04-01
Fractal continuum electrodynamics is developed on the basis of a model of three-dimensional continuum ΦD3⊂E3 with a fractal metric. The generalized forms of Maxwell equations are derived employing the local fractional vector calculus related to the Hausdorff derivative. The difference between the fractal continuum electrodynamics based on the fractal metric of continua with Euclidean topology and the electrodynamics in fractional space Fα accounting the fractal topology of continuum with the Euclidean metric is outlined. Some electromagnetic phenomena in fractal media associated with their fractal time and space metrics are discussed.
Subband/transform functions for image processing
NASA Technical Reports Server (NTRS)
Glover, Daniel
1993-01-01
Functions for image data processing written for use with the MATLAB(TM) software package are presented. These functions provide the capability to transform image data with block transformations (such as the Walsh Hadamard) and to produce spatial frequency subbands of the transformed data. Block transforms are equivalent to simple subband systems. The transform coefficients are reordered using a simple permutation to give subbands. The low frequency subband is a low resolution version of the original image, while the higher frequency subbands contain edge information. The transform functions can be cascaded to provide further decomposition into more subbands. If the cascade is applied to all four of the first stage subbands (in the case of a four band decomposition), then a uniform structure of sixteen bands is obtained. If the cascade is applied only to the low frequency subband, an octave structure of seven bands results. Functions for the inverse transforms are also given. These functions can be used for image data compression systems. The transforms do not in themselves produce data compression, but prepare the data for quantization and compression. Sample quantization functions for subbands are also given. A typical compression approach is to subband the image data, quantize it, then use statistical coding (e.g., run-length coding followed by Huffman coding) for compression. Contour plots of image data and subbanded data are shown.
NASA Astrophysics Data System (ADS)
Subramaniam, Raji; Sullivan, R.; Schneider, P. S.; Flamholz, A.; Cheung, E.; Tremberger, G., Jr.; Wong, P. K.; Lieberman, D. H.; Cheung, T. D.; Garcia, F.; Bewry, N.; Yee, A.
2006-10-01
Images of packaged raw chicken purchased in neighborhood supermarkets were captured via a digital camera in laboratory and home settings. Each image contained the surface reflectivity information of the chicken tissue. The camera's red, green and blue light signals fluctuated and each spectral signal exhibited a random series across the surface. The Higuchi method, where the length of each increment in time (or spatial) lag is plotted against the lag, was used to explore the fractal property of the random series. (Higuchi, T., "Approach to an irregular time series on the basis of fractal theory", Physica D, vol 31, 277-283, 1988). The fractal calculation algorithm was calibrated with the Weierstrass function. The standard deviation and fractal dimension were shown to correlate with the time duration that a package was left at room temperature within a 24-hour period. Comparison to packaged beef results suggested that the time dependence could be due microbial spoilage. The fractal dimension results in this study were consistent with those obtained from yeast cell, mammalian cell and bacterial cell studies. This analysis method can be used to detect the re-refrigeration of a "left-out" package of chicken. The extension to public health issues such as consumer shopping is also discussed.
Functional cardiac imaging: positron emission tomography
Mullani, N.A.; Gould, K.L.
1984-02-01
Dynamic cardiovascular imaging plays a vital role in the diagnosis and treatment of cardiac disease by providing information about the function of the heart. During the past 30 years, cardiovascular imaging has evolved from the simple chest x-ray and fluoroscopy to such sophisticated techniques as invasive cardiac angiography and cinearteriography and, more recently, to noninvasive cardiac CT scanning, nuclear magnetic resonance, and positron emission tomography, which reflect more complex physiologic functions. As research tools, CT, NMR, and PET provide quantitative information on global as well as regional ventricular function, coronary artery stenosis, myocardial perfusion, glucose and fatty acid metabolism, or oxygen utilization, with little discomfort or risk to the patient. As imaging modalities become more sophisticated and more oriented toward clinical application, the prospect of routinely obtaining such functional information about the heart is becoming realistic. However, these advances are double-edged in that the interpretation of functional data is more complex than that of the anatomic imaging familiar to most physicians. They will require an enhanced understanding of the physiologic and biochemical processes, as well as of the instrumentation and techniques for analyzing the data. Of the new imaging modalities that provide functional information about the heart, PET is the most useful because it quantitates the regional distribution of radionuclides in vivo. Clinical applications, interpretation of data, and the impact of PET on our understanding of cardiac pathophysiology are discussed. 5 figures.
Multimodal Imaging of Dynamic Functional Connectivity
Tagliazucchi, Enzo; Laufs, Helmut
2015-01-01
The study of large-scale functional interactions in the human brain with functional magnetic resonance imaging (fMRI) extends almost to the first applications of this technology. Due to historical reasons and preconceptions about the limitations of this brain imaging method, most studies have focused on assessing connectivity over extended periods of time. It is now clear that fMRI can resolve the temporal dynamics of functional connectivity, like other faster imaging techniques such as electroencephalography and magnetoencephalography (albeit on a different temporal scale). However, the indirect nature of fMRI measurements can hinder the interpretability of the results. After briefly summarizing recent advances in the field, we discuss how the simultaneous combination of fMRI with electrophysiological activity measurements can contribute to a better understanding of dynamic functional connectivity in humans both during rest and task, wakefulness, and other brain states. PMID:25762977
Modeling of functional brain imaging data
NASA Astrophysics Data System (ADS)
Horwitz, Barry
1999-03-01
The richness and complexity of data sets obtained from functional neuroimaging studies of human cognitive behavior, using techniques such as positron emission tomography and functional magnetic resonance imaging, have until recently not been exploited by computational neural modeling methods. In this article, following a brief introduction to functional neuroimaging methodology, two neural modeling approaches for use with functional brain imaging data are described. One, which uses structural equation modeling, examines the effective functional connections between various brain regions during specific cognitive tasks. The second employs large-scale neural modeling to relate functional neuroimaging signals in multiple, interconnected brain regions to the underlying neurobiological time-varying activities in each region. These two modeling procedures are illustrated using a visual processing paradigm.
Fractal Property in the Light Curve of BL Lac Object S5 0716 + 714
NASA Astrophysics Data System (ADS)
Ou, J. W.; Zheng, Y. G.
2014-09-01
In this paper, we compile the historical R-band data of S5 0716 + 714 from literature and obtain its fractal dimension by using a fractal method and then simulate the data with the Weierstrass-Mandelbrot (W-M) function. It is considered that the light curve has a fractal property.
The role of the circadian system in fractal neurophysiological control
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
Fractal frontiers in cardiovascular magnetic resonance: towards clinical implementation.
Captur, Gabriella; Karperien, Audrey L; Li, Chunming; Zemrak, Filip; Tobon-Gomez, Catalina; Gao, Xuexin; Bluemke, David A; Elliott, Perry M; Petersen, Steffen E; Moon, James C
2015-01-01
Many of the structures and parameters that are detected, measured and reported in cardiovascular magnetic resonance (CMR) have at least some properties that are fractal, meaning complex and self-similar at different scales. To date however, there has been little use of fractal geometry in CMR; by comparison, many more applications of fractal analysis have been published in MR imaging of the brain.This review explains the fundamental principles of fractal geometry, places the fractal dimension into a meaningful context within the realms of Euclidean and topological space, and defines its role in digital image processing. It summarises the basic mathematics, highlights strengths and potential limitations of its application to biomedical imaging, shows key current examples and suggests a simple route for its successful clinical implementation by the CMR community.By simplifying some of the more abstract concepts of deterministic fractals, this review invites CMR scientists (clinicians, technologists, physicists) to experiment with fractal analysis as a means of developing the next generation of intelligent quantitative cardiac imaging tools. PMID:26346700
Spatial Pattern of Biological Soil Crust with Fractal Geometry
NASA Astrophysics Data System (ADS)
Ospina, Abelardo; Florentino, Adriana; Tarquis, Ana M.
2015-04-01
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. This study focus on characterize the spatial arrangements of the BSC based on image analysis and fractal concepts. To this end, RGB images of different types of biological soil crust where taken, each image corresponding to an area of 3.6 cm2 with a resolution of 1024x1024 pixels. For each image and channel, mass dimension and entropy were calculated. Preliminary results indicate that fractal methods are useful to describe changes associated to different types of BSC. Further research is necessary to apply these methodologies to several situations.
ERIC Educational Resources Information Center
Clark, Garry
1999-01-01
Reports on a mathematical investigation of fractals and highlights the thinking involved, problem solving strategies used, generalizing skills required, the role of technology, and the role of mathematics. (ASK)
Persistence intervals of fractals
NASA Astrophysics Data System (ADS)
Máté, Gabriell; Heermann, Dieter W.
2014-07-01
Objects and structures presenting fractal like behavior are abundant in the world surrounding us. Fractal theory provides a great deal of tools for the analysis of the scaling properties of these objects. We would like to contribute to the field by analyzing and applying a particular case of the theory behind the P.H. dimension, a concept introduced by MacPherson and Schweinhart, to seek an intuitive explanation for the relation of this dimension and the fractality of certain objects. The approach is based on recently elaborated computational topology methods and it proves to be very useful for investigating scaling hidden in dimensions lower than the “native” dimension in which the investigated object is embedded. We demonstrate the applicability of the method with two examples: the Sierpinski gasket-a traditional fractal-and a two dimensional object composed of short segments arranged according to a circular structure.
ERIC Educational Resources Information Center
Bannon, Thomas J.
1991-01-01
Discussed are several different transformations based on the generation of fractals including self-similar designs, the chaos game, the koch curve, and the Sierpinski Triangle. Three computer programs which illustrate these concepts are provided. (CW)
Functional Imaging in Hereditary Dystonia
Carbon, Maren; Argyelan, Miklos; Eidelberg, David
2015-01-01
Background Impaired cortical inhibiton and maladaptive cortical plasticity are functional hallmarks of sporadic focal dystonias. Whether or not these mechanisms translate to generalized dystonias and whether these features reflect state or trait characteristics is a topic of research in hereditary dystonias. Methods We present a series of studies using a multitracer approach with positron emission tomography (PET) and diffusion tensor MRI (DTI) in the DYT1 and the DYT6 genotype. Results In these hereditary dystonias maladaptive motor cortical plasticity was present as a state characteristic. As a trait characteristic neuroplastic changes were also found in secondary motor cortices and in multimodal association regions. Consistent abnormalities of resting regional brain metabolism were additionally found in interconnected elements of cortico-striatal-pallido-thalamocortical (CSPTC) and related cerebellar-thalamo-cortical circuits. Changes in specific subsets of these regions have been found to relate to genotype, phenotype, or both. Thus, a penetrance-related metabolic network was characterized by increases in the pre-supplementary motor area (pre-SMA) and parietal association areas, associated with relative reductions in the cerebellum, brainstem, and ventral thalamus. By contrast, genotype-specific abnormalities were localized to the basal ganglia, SMA and cerebellum. In both genotypes, the striatal metabolic abnormalities were paralleled by genotype-specific reductions in D2 receptor availability. Moreover, DTI studies disclosed microstructural changes within CSPTC and related cerebellar pathways. These disruptions may represent the main intrinsic abnormality underlying cortical downstream effects, such as increased sensorimotor responsivity. Conclusions These studies are consistent with the view of primary torsion dystonia as a neurodevelopmental circuit disorder involving CSPTC and related cerebellar pathways. PMID:20590810
Image sharpness function based on edge feature
NASA Astrophysics Data System (ADS)
Jun, Ni
2009-11-01
Autofocus technique has been widely used in optical tracking and measure system, but it has problem that when the autofocus device should to work. So, no-reference image sharpness assessment has become an important issue. A new Sharpness Function that can estimate current frame image be in focus or not is proposed in this paper. According to current image whether in focus or not and choose the time of auto focus automatism. The algorithm measures object typical edge and edge direction, and then get image local kurtosis information to determine the degree of image sharpness. It firstly select several grads points cross the edge line, secondly calculates edge sharpness value and get the cure of the kurtosis, according the measure precision of optical-equipment, a threshold value will be set beforehand. If edge kurtosis value is more than threshold, it can conclude current frame image is in focus. Otherwise, it is out of focus. If image is out of focus, optics system then takes autofocus program. This algorithm test several thousands of digital images captured from optical tracking and measure system. The results show high correlation with subjective sharpness assessment for s images of sky object.
Fractal Dimension in Epileptic EEG Signal Analysis
NASA Astrophysics Data System (ADS)
Uthayakumar, R.
Fractal Analysis is the well developed theory in the data analysis of non-linear time series. Especially Fractal Dimension is a powerful mathematical tool for modeling many physical and biological time signals with high complexity and irregularity. Fractal dimension is a suitable tool for analyzing the nonlinear behaviour and state of the many chaotic systems. Particularly in analysis of chaotic time series such as electroencephalograms (EEG), this feature has been used to identify and distinguish specific states of physiological function.Epilepsy is the main fatal neurological disorder in our brain, which is analyzed by the biomedical signal called Electroencephalogram (EEG). The detection of Epileptic seizures in the EEG Signals is an important tool in the diagnosis of epilepsy. So we made an attempt to analyze the EEG in depth for knowing the mystery of human consciousness. EEG has more fluctuations recorded from the human brain due to the spontaneous electrical activity. Hence EEG Signals are represented as Fractal Time Series.The algorithms of fractal dimension methods have weak ability to the estimation of complexity in the irregular graphs. Divider method is widely used to obtain the fractal dimension of curves embedded into a 2-dimensional space. The major problem is choosing initial and final step length of dividers. We propose a new algorithm based on the size measure relationship (SMR) method, quantifying the dimensional behaviour of irregular rectifiable graphs with minimum time complexity. The evidence for the suitability (equality with the nature of dimension) of the algorithm is illustrated graphically.We would like to demonstrate the criterion for the selection of dividers (minimum and maximum value) in the calculation of fractal dimension of the irregular curves with minimum time complexity. For that we design a new method of computing fractal dimension (FD) of biomedical waveforms. Compared to Higuchi's algorithm, advantages of this method include
Functional MR Imaging in Chest Malignancies.
Broncano, Jordi; Luna, Antonio; Sánchez-González, Javier; Alvarez-Kindelan, Antonio; Bhalla, Sanjeev
2016-02-01
With recent advances in MR imaging, its application in the thorax has been feasible. The performance of both morphologic and functional techniques in the evaluation of thoracic malignances has improved not only differentiation from benign etiologies but also treatment monitoring based on a multiparametric approach. Several MR imaging-derived parameters have been described as potential biomarkers linked with prognosis and survival. Therefore, an integral approach with a nonradiating and noninvasive technique could be an optimal alternative for evaluating those patients. PMID:26613879
Rheological and fractal hydrodynamics of aerobic granules.
Tijani, H I; Abdullah, N; Yuzir, A; Ujang, Zaini
2015-06-01
The structural and hydrodynamic features for granules were characterized using settling experiments, predefined mathematical simulations and ImageJ-particle analyses. This study describes the rheological characterization of these biologically immobilized aggregates under non-Newtonian flows. The second order dimensional analysis defined as D2=1.795 for native clusters and D2=1.099 for dewatered clusters and a characteristic three-dimensional fractal dimension of 2.46 depicts that these relatively porous and differentially permeable fractals had a structural configuration in close proximity with that described for a compact sphere formed via cluster-cluster aggregation. The three-dimensional fractal dimension calculated via settling-fractal correlation, U∝l(D) to characterize immobilized granules validates the quantitative measurements used for describing its structural integrity and aggregate complexity. These results suggest that scaling relationships based on fractal geometry are vital for quantifying the effects of different laminar conditions on the aggregates' morphology and characteristics such as density, porosity, and projected surface area. PMID:25836036
Functionalized gold nanorods for molecular optoacoustic imaging
NASA Astrophysics Data System (ADS)
Eghtedari, Mohammad; Oraevsky, Alexander; Conjusteau, Andre; Copland, John A.; Kotov, Nicholas A.; Motamedi, Massoud
2007-02-01
The development of gold nanoparticles for molecular optoacoustic imaging is a very promising area of research and development. Enhancement of optoacoustic imaging for molecular detection of tumors requires the engineering of nanoparticles with geometrical and molecular features that can enhance selective targeting of malignant cells while optimizing the sensitivity of optoacoustic detection. In this article, cylindrical gold nanoparticles (i.e. gold nanorods) were fabricated with a plasmon resonance frequency in the near infra-red region of the spectrum, where deep irradiation of tissue is possible using an Alexandrite laser. Gold nanorods (Au-NRs) were functionalized by covalent attachment of Poly(ethylene glycol) to enhance their biocompatibility. These particles were further functionalized with the aim of targeting breast cancer cells using monoclonal antibodies that binds to Her2/neu receptors, which are over expressed on the surface of breast cancer cells. A custom Laser Optoacoustic Imaging System (LOIS) was designed and employed to image nanoparticle-targeted cancer cells in a phantom and PEGylated Au-NRs that were injected subcutaneously into a nude mouse. The results of our experiments show that functionalized Au-NRs with a plasmon resonance frequency at near infra-red region of the spectrum can be detected and imaged in vivo using laser optoacoustic imaging system.
``the Human BRAIN & Fractal quantum mechanics''
NASA Astrophysics Data System (ADS)
Rosary-Oyong, Se, Glory
In mtDNA ever retrieved from Iman Tuassoly, et.al:Multifractal analysis of chaos game representation images of mtDNA''.Enhances the price & valuetales of HE. Prof. Dr-Ing. B.J. HABIBIE's N-219, in J. Bacteriology, Nov 1973 sought:'' 219 exist as separate plasmidDNA species in E.coli & Salmonella panama'' related to ``the brain 2 distinct molecular forms of the (Na,K)-ATPase..'' & ``neuron maintains different concentration of ions(charged atoms'' thorough Rabi & Heisenber Hamiltonian. Further, after ``fractal space time are geometric analogue of relativistic quantum mechanics''[Ord], sought L.Marek Crnjac: ``Chaotic fractals at the root of relativistic quantum physics''& from famous Nottale: ``Scale relativity & fractal space-time:''Application to Quantum Physics , Cosmology & Chaotic systems'',1995. Acknowledgements to HE. Mr. H. TUK SETYOHADI, Jl. Sriwijaya Raya 3, South-Jakarta, INDONESIA.
Fractal characterization of wear-erosion surfaces
Rawers, James C.; Tylczak, Joseph H.
1999-12-01
Wear erosion is a complex phenomenon resulting in highly distorted and deformed surface morphologies. Most wear surface features have been described only qualitatively. In this study wear surfaces features were quantified using fractal analysis. The ability to assign numerical values to wear-erosion surfaces makes possible mathematical expressions that will enable wear mechanisms to be predicted and understood. Surface characterization came from wear-erosion experiments that included varying the erosive materials, the impact velocity, and the impact angle. Seven fractal analytical techniques were applied to micrograph images of wear-erosion surfaces. Fourier analysis was the most promising. Fractal values obtained were consistent with visual observations and provided a unique wear-erosion parameter unrelated to wear rate.
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
Adolescent body image and psychosocial functioning.
Davison, Tanya E; McCabe, Marita P
2006-02-01
Researchers have highlighted the significance of a poor body image in the development of dysfunctional eating but have systematically investigated few other outcomes. The authors examined the relationships between different aspects of body image and psychosocial functioning. Participants were 245 boys and 173 girls from Grades 8 and 9 (M age = 13.92 years, SD = 0.69 years). Respondents completed measures of physical attractiveness, body satisfaction, body image importance, body image behaviors, appearance comparison, social physique anxiety, self-esteem, depression, anxiety, and same-sex and opposite-sex relations. Whereas girls tended to report a more negative body image than did boys, the relevance of body image to self-esteem was similar for boys and girls. Concern about others' evaluation of their bodies was especially important in understanding low female self-esteem, whereas for boys, ratings of general attractiveness most strongly predicted self-esteem. The authors found a negative body image to be unrelated to symptoms of negative affect but to be strongly associated with poor opposite-sex peer relationships, especially among boys. A negative body image also affected same-sex relations among girls. PMID:16480119
Functional and Dysfunctional Sensorimotor Anatomy and Imaging.
Ulmer, John L; Klein, Andrew P; Mark, Leighton P; Tuna, Ibrahim; Agarwal, Mohit; DeYoe, Edgar
2015-06-01
The sensorimotor system of the human brain and body is fundamental only in its central role in our daily lives. On further examination, it is a system with intricate and complex anatomical, physiological, and functional relationships. Sensorimotor areas including primary sensorimotor, premotor, supplementary motor, and higher order somatosensory cortices are critical for function and can be localized at routine neuroimaging with a familiarity of sulcal and gyral landmarks. Likewise, a thorough understanding of the functions and dysfunctions of these areas can empower the neuroradiologist and lead to superior imaging search patterns, diagnostic considerations, and patient care recommendations in daily clinical practice. Presurgical functional brain mapping of the sensorimotor system may be necessary in scenarios with distortion of anatomical landmarks, multiplanar localization, homunculus localization, congenital brain anomalies, informing diffusion tensor imaging interpretations, and localizing nonvisible targets. PMID:26233857
Functional-metabolic imaging of neuroblastoma.
Sharp, S E; Parisi, M T; Gelfand, M J; Yanik, G A; Shulkin, B L
2013-03-01
Neuroblastoma is the third most common malignant solid tumor of childhood. It originates from primitive neural crest cells of the sympathetic nervous system. Many imaging procedures help guide therapy and predict outcomes. Anatomic imaging methods, such as CT and MRI, are most useful for evaluation of the primary tumor mass and nearby involved lymph nodes. Functional imaging tracers, such as [123I]MIBG, [18F]FDG, and [99mTc]MDP, are used to assess the extent of disease and to search for distant metastases. [123I]MIBG is the principal functional imaging tracer for the detection and monitoring of neuroblastoma. [18F]FDG PET/CT is an alternative that is valuable in tumors with poor or no MIBG-uptake. [99mTc]MDP bone scans may be useful to assess cortical bone metastases. This article will review the use of [123I]MIBG and other functional imaging agents for the management of patients with neuroblastoma. PMID:23474631
Functional lumen imaging of the gastrointestinal tract.
Lottrup, Christian; Gregersen, Hans; Liao, Donghua; Fynne, Lotte; Frøkjær, Jens Brøndum; Krogh, Klaus; Regan, Julie; Kunwald, Peter; McMahon, Barry P
2015-10-01
This nonsystematic review aims to describe recent developments in the use of functional lumen imaging in the gastrointestinal tract stimulated by the introduction of the functional lumen imaging probe. When ingested food in liquid and solid form is transported along the gastrointestinal tract, sphincters provide an important role in the flow and control of these contents. Inadequate function of sphincters is the basis of many gastrointestinal diseases. Despite this, traditional methods of sphincter diagnosis and measurement such as fluoroscopy, manometry, and the barostat are limited in what they can tell us. It has long been thought that measurement of sphincter function through resistance to distension is a better approach, now more commonly known as distensibility testing. The functional lumen imaging probe is the first medical measurement device that purports in a practical way to provide geometric profiling and measurement of distensibility in sphincters. With use of impedance planimetry, an axial series of cross-sectional areas and pressure in a catheter-mounted allantoid bag are used for the calculation of distensibility parameters. The technique has been trialed in many valvular areas of the gastrointestinal tract, including the upper esophageal sphincter, the esophagogastric junction, and the anorectal region. It has shown potential in the biomechanical assessment of sphincter function and characterization of swallowing disorders, gastroesophageal reflux disease, eosinophilic esophagitis, achalasia, and fecal incontinence. From this early work, the functional lumen imaging technique has the potential to contribute to a better and more physiological understanding of narrowing regions in the gastrointestinal tract in general and sphincters in particular. PMID:25980822
Building Fractal Models with Manipulatives.
ERIC Educational Resources Information Center
Coes, Loring
1993-01-01
Uses manipulative materials to build and examine geometric models that simulate the self-similarity properties of fractals. Examples are discussed in two dimensions, three dimensions, and the fractal dimension. Discusses how models can be misleading. (Contains 10 references.) (MDH)
Fractal Patterns and Chaos Games
ERIC Educational Resources Information Center
Devaney, Robert L.
2004-01-01
Teachers incorporate the chaos game and the concept of a fractal into various areas of the algebra and geometry curriculum. The chaos game approach to fractals provides teachers with an opportunity to help students comprehend the geometry of affine transformations.
NASA Astrophysics Data System (ADS)
Oleshko, Klaudia; de Jesús Correa López, María; Romero, Alejandro; Ramírez, Victor; Pérez, Olga
2016-04-01
The effectiveness of fractal toolbox to capture the scaling or fractal probability distribution, and simply fractal statistics of main hydrocarbon reservoir attributes, was highlighted by Mandelbrot (1995) and confirmed by several researchers (Zhao et al., 2015). Notwithstanding, after more than twenty years, it's still common the opinion that fractals are not useful for the petroleum engineers and especially for Geoengineering (Corbett, 2012). In spite of this negative background, we have successfully applied the fractal and multifractal techniques to our project entitled "Petroleum Reservoir as a Fractal Reactor" (2013 up to now). The distinguishable feature of Fractal Reservoir is the irregular shapes and rough pore/solid distributions (Siler, 2007), observed across a broad range of scales (from SEM to seismic). At the beginning, we have accomplished the detailed analysis of Nelson and Kibler (2003) Catalog of Porosity and Permeability, created for the core plugs of siliciclastic rocks (around ten thousand data were compared). We enriched this Catalog by more than two thousand data extracted from the last ten years publications on PoroPerm (Corbett, 2012) in carbonates deposits, as well as by our own data from one of the PEMEX, Mexico, oil fields. The strong power law scaling behavior was documented for the major part of these data from the geological deposits of contrasting genesis. Based on these results and taking into account the basic principles and models of the Physics of Fractals, introduced by Per Back and Kan Chen (1989), we have developed new software (Muukíl Kaab), useful to process the multiscale geological and geophysical information and to integrate the static geological and petrophysical reservoir models to dynamic ones. The new type of fractal numerical model with dynamical power law relations among the shapes and sizes of mesh' cells was designed and calibrated in the studied area. The statistically sound power law relations were established
NASA Astrophysics Data System (ADS)
Oleshko, Klaudia; de Jesús Correa López, María; Romero, Alejandro; Ramírez, Victor; Pérez, Olga
2016-04-01
The effectiveness of fractal toolbox to capture the scaling or fractal probability distribution, and simply fractal statistics of main hydrocarbon reservoir attributes, was highlighted by Mandelbrot (1995) and confirmed by several researchers (Zhao et al., 2015). Notwithstanding, after more than twenty years, i&tacute;s still common the opinion that fractals are not useful for the petroleum engineers and especially for Geoengineering (Corbett, 2012). In spite of this negative background, we have successfully applied the fractal and multifractal techniques to our project entitled "Petroleum Reservoir as a Fractal Reactor" (2013 up to now). The distinguishable feature of Fractal Reservoir is the irregular shapes and rough pore/solid distributions (Siler, 2007), observed across a broad range of scales (from SEM to seismic). At the beginning, we have accomplished the detailed analysis of Nelson and Kibler (2003) Catalog of Porosity and Permeability, created for the core plugs of siliciclastic rocks (around ten thousand data were compared). We enriched this Catalog by more than two thousand data extracted from the last ten years publications on PoroPerm (Corbett, 2012) in carbonates deposits, as well as by our own data from one of the PEMEX, Mexico, oil fields. The strong power law scaling behavior was documented for the major part of these data from the geological deposits of contrasting genesis. Based on these results and taking into account the basic principles and models of the Physics of Fractals, introduced by Per Back and Kan Chen (1989), we have developed new software (Muuḱil Kaab), useful to process the multiscale geological and geophysical information and to integrate the static geological and petrophysical reservoiŕ models to dynamic ones. The new type of fractal numerical model with dynamical power law relations among the shapes and sizes of mes&hacute; cells was designed and calibrated in the studied area. The statistically sound power law relations were
Izhaky, David; Nelson, Darin A; Burgansky-Eliash, Zvia; Grinvald, Amiram
2009-07-01
The Retinal Function Imager (RFI; Optical Imaging, Rehovot, Israel) is a unique, noninvasive multiparameter functional imaging instrument that directly measures hemodynamic parameters such as retinal blood-flow velocity, oximetric state, and metabolic responses to photic activation. In addition, it allows capillary perfusion mapping without any contrast agent. These parameters of retinal function are degraded by retinal abnormalities. This review delineates the development of these parameters and demonstrates their clinical applicability for noninvasive detection of retinal function in several modalities. The results suggest multiple clinical applications for early diagnosis of retinal diseases and possible critical guidance of their treatment. PMID:19763751
Random sequential adsorption on fractals
NASA Astrophysics Data System (ADS)
Ciesla, Michal; Barbasz, Jakub
2012-07-01
Irreversible adsorption of spheres on flat collectors having dimension d < 2 is studied. Molecules are adsorbed on Sierpinski's triangle and carpet-like fractals (1 < d < 2), and on general Cantor set (d < 1). Adsorption process is modeled numerically using random sequential adsorption (RSA) algorithm. The paper concentrates on measurement of fundamental properties of coverages, i.e., maximal random coverage ratio and density autocorrelation function, as well as RSA kinetics. Obtained results allow to improve phenomenological relation between maximal random coverage ratio and collector dimension. Moreover, simulations show that, in general, most of known dimensional properties of adsorbed monolayers are valid for non-integer dimensions.
Random sequential adsorption on fractals.
Ciesla, Michal; Barbasz, Jakub
2012-07-28
Irreversible adsorption of spheres on flat collectors having dimension d < 2 is studied. Molecules are adsorbed on Sierpinski's triangle and carpet-like fractals (1 < d < 2), and on general Cantor set (d < 1). Adsorption process is modeled numerically using random sequential adsorption (RSA) algorithm. The paper concentrates on measurement of fundamental properties of coverages, i.e., maximal random coverage ratio and density autocorrelation function, as well as RSA kinetics. Obtained results allow to improve phenomenological relation between maximal random coverage ratio and collector dimension. Moreover, simulations show that, in general, most of known dimensional properties of adsorbed monolayers are valid for non-integer dimensions. PMID:22852643
Edge extraction of optical subaperture based on fractal dimension method
NASA Astrophysics Data System (ADS)
Wang, Yunqi; Hui, Mei; Liu, Ming; Dong, Liquan; Liu, Xiaohua; Zhao, Yuejin
2015-09-01
Optical synthetic aperture imaging technology is an effective approach to increase the aperture diameter of optical system for purpose of improving resolution. In optical synthetic aperture imaging system, the edge is more complex than that of traditional optical imaging system, and the relatively large size of the gaps between the subapertures makes cophasing a difficult problem. So it is significant to extract edge phase of each subaperture for achieving phase stitching and avoiding the loss of effective frequency. Fractal dimension as a measure feature of image surface irregularities can statistically evaluate the complexity which is consistent with human visual image perception of rough surface texture. Therefore, fractal dimension provides a powerful tool to describe surface characteristics of image and can be applied to edge extraction. In our research, the box-counting dimension was used to calculate fractal dimension of the whole image. Then the calculated fractal dimension is mapped to grayscale image. The region with large fractal dimension represents a sharper change of the gray scale in original image, which was accurately extracted as the edge region. Subaperture region and interference fringe edge was extracted from interference pattern of optical subaperture, which has laid the foundation for the subaperture edge phase detection in the future work.