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. Copyright © 2014 Elsevier B.V. All rights reserved.
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.
Study on Huber fractal image compression.
Jeng, Jyh-Horng; Tseng, Chun-Chieh; Hsieh, Jer-Guang
2009-05-01
In this paper, a new similarity measure for fractal image compression (FIC) is introduced. In the proposed Huber fractal image compression (HFIC), the linear Huber regression technique from robust statistics is embedded into the encoding procedure of the fractal image compression. When the original image is corrupted by noises, we argue that the fractal image compression scheme should be insensitive to those noises presented in the corrupted image. This leads to a new concept of robust fractal image compression. The proposed HFIC is one of our attempts toward the design of robust fractal image compression. The main disadvantage of HFIC is the high computational cost. To overcome this drawback, particle swarm optimization (PSO) technique is utilized to reduce the searching time. Simulation results show that the proposed HFIC is robust against outliers in the image. Also, the PSO method can effectively reduce the encoding time while retaining the quality of the retrieved image.
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-based image edge detection
NASA Astrophysics Data System (ADS)
Luo, Huiguo; Zhu, Yaoting; Zhu, Guang-Xi; Wan, Faguang; Zhang, Ping
1993-08-01
Image edge is an important feature of image. Usually, we use Laplacian or Sober operator to get an image edge. In this paper, we use fractal method to get the edge. After introducing Fractal Brownian Random (FBR) field, we give the definition of Discrete Fractal Brownian Increase Random (DFBIR) field and discuss its properties, then we apply the DFBIR field to detect the edge of an image. According to the parameters H and D of DFBIR, we give a measure M equals (alpha) H + (beta) D. From the M value of each pixel, we can detect the edge of 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
Fractal Image Informatics: from SEM to DEM
NASA Astrophysics Data System (ADS)
Oleschko, K.; Parrot, J.-F.; Korvin, G.; Esteves, M.; Vauclin, M.; Torres-Argüelles, V.; Salado, C. Gaona; Cherkasov, S.
2008-05-01
In this paper, we introduce a new branch of Fractal Geometry: Fractal Image Informatics, devoted to the systematic and standardized fractal analysis of images of natural systems. The methods of this discipline are based on the properties of multiscale images of selfaffine fractal surfaces. As proved in the paper, the image inherits the scaling and lacunarity of the surface and of its reflectance distribution [Korvin, 2005]. We claim that the fractal analysis of these images must be done without any smoothing, thresholding or binarization. Two new tools of Fractal Image Informatics, firmagram analysis (FA) and generalized lacunarity (GL), are presented and discussed in details. These techniques are applicable to any kind of image or to any observed positive-valued physical field, and can be used to correlate between images. It will be shown, by a modified Grassberger-Hentschel-Procaccia approach [Phys. Lett. 97A, 227 (1983); Physica 8D, 435 (1983)] that GL obeys the same scaling law as the Allain-Cloitre lacunarity [Phys. Rev. A 44, 3552 (1991)] but is free of the problems associated with gliding boxes. Several applications are shown from Soil Physics, Surface Science, and other fields.
Pre-Service Teachers' Concept Images on Fractal Dimension
ERIC Educational Resources Information Center
Karakus, Fatih
2016-01-01
The analysis of pre-service teachers' concept images can provide information about their mental schema of fractal dimension. There is limited research on students' understanding of fractal and fractal dimension. Therefore, this study aimed to investigate the pre-service teachers' understandings of fractal dimension based on concept image. The…
Pre-Service Teachers' Concept Images on Fractal Dimension
ERIC Educational Resources Information Center
Karakus, Fatih
2016-01-01
The analysis of pre-service teachers' concept images can provide information about their mental schema of fractal dimension. There is limited research on students' understanding of fractal and fractal dimension. Therefore, this study aimed to investigate the pre-service teachers' understandings of fractal dimension based on concept image. The…
MRI Image Processing Based on Fractal Analysis
Marusina, Mariya Y; Mochalina, Alexandra P; Frolova, Ekaterina P; Satikov, Valentin I; Barchuk, Anton A; Kuznetcov, Vladimir I; Gaidukov, Vadim S; Tarakanov, Segrey A
2017-01-01
Background: Cancer is one of the most common causes of human mortality, with about 14 million new cases and 8.2 million deaths reported in in 2012. Early diagnosis of cancer through screening allows interventions to reduce mortality. Fractal analysis of medical images may be useful for this purpose. Materials and Methods: In this study, we examined magnetic resonance (MR) images of healthy livers and livers containing metastases from colorectal cancer. The fractal dimension and the Hurst exponent were chosen as diagnostic features for tomographic imaging using Image J software package for image processings FracLac for applied for fractal analysis with a 120x150 pixel area. Calculations of the fractal dimensions of pathological and healthy tissue samples were performed using the box-counting method. Results: In pathological cases (foci formation), the Hurst exponent was less than 0.5 (the region of unstable statistical characteristics). For healthy tissue, the Hurst index is greater than 0.5 (the zone of stable characteristics). Conclusions: The study indicated the possibility of employing fractal rapid analysis for the detection of focal lesions of the liver. The Hurst exponent can be used as an important diagnostic characteristic for analysis of medical images.
Image Segmentation via Fractal Dimension
1987-12-01
statistical expectation K = a proportionality constant H = the Hurst exponent , in interval [0,1] (14:249) Eq (4) is a mathematical generalization of...ease, negatively correlated (24:16). The Hurst exponent is directly related to the fractal diment.ion of the process being modelled by the relation (24...24) DzE.I -H (5) where D = the fractal dimension E m the Euclidean dimension H = the Hurst exponent The effect of N1 on a typical trace can be seen
BOX DIMENSIONS OF α-FRACTAL FUNCTIONS
NASA Astrophysics Data System (ADS)
Akhtar, Md. Nasim; Prasad, M. Guru Prem; Navascués, M. A.
2016-08-01
The box dimension of the graph of non-affine, continuous, nowhere differentiable function fα which is a fractal analogue of a continuous function f corresponding to a certain iterated function system (IFS), is investigated in the present paper. The estimates for box dimension of the graph of α-fractal function fα for equally spaced as well as arbitrary data sets are found.
Three-dimensional tumor perfusion reconstruction using fractal interpolation functions.
Craciunescu, O I; Das, S K; Poulson, J M; Samulski, T V
2001-04-01
It has been shown that the perfusion of blood in tumor tissue can be approximated using the relative perfusion index determined from dynamic contrast-enhanced magnetic resonance imaging (DE-MRI) of the tumor blood pool. Also, it was concluded in a previous report that the blood perfusion in a two-dimensional (2-D) tumor vessel network has a fractal structure and that the evolution of the perfusion front can be characterized using invasion percolation. In this paper, the three-dimensional (3-D) tumor perfusion is reconstructed from the 2-D slices using the method of fractal interpolation functions (FIF), i.e., the piecewise self-affine fractal interpolation model (PSAFIM) and the piecewise hidden variable fractal interpolation model (PHVFIM). The fractal models are compared to classical interpolation techniques (linear, spline, polynomial) by means of determining the 2-D fractal dimension of the reconstructed slices. Using FIFs instead of classical interpolation techniques better conserves the fractal-like structure of the perfusion data. Among the two FIF methods, PHVFIM conserves the 3-D fractality better due to the cross correlation that exists between the data in the 2-D slices and the data along the reconstructed direction. The 3-D structures resulting from PHVFIM have a fractal dimension within 3%-5% of the one reported in literature for 3-D percolation. It is, thus, concluded that the reconstructed 3-D perfusion has a percolation-like scaling. As the perfusion term from bio-heat equation is possibly better described by reconstruction via fractal interpolation, a more suitable computation of the temperature field induced during hyperthermia treatments is expected.
Generalized fragmentation functions for fractal jet observables
NASA Astrophysics Data System (ADS)
Elder, Benjamin T.; Procura, Massimiliano; Thaler, Jesse; Waalewijn, Wouter J.; Zhou, Kevin
2017-06-01
We introduce a broad class of fractal jet observables that recursively probe the collective properties of hadrons produced in jet fragmentation. To describe these collinear-unsafe observables, we generalize the formalism of fragmentation functions, which are important objects in QCD for calculating cross sections involving identified final-state hadrons. Fragmentation functions are fundamentally nonperturbative, but have a calculable renormalization group evolution. Unlike ordinary fragmentation functions, generalized fragmentation functions exhibit nonlinear evolution, since fractal observables involve correlated subsets of hadrons within a jet. Some special cases of generalized fragmentation functions are reviewed, including jet charge and track functions. We then consider fractal jet observables that are based on hierarchical clustering trees, where the nonlinear evolution equations also exhibit tree-like structure at leading order. We develop a numeric code for performing this evolution and study its phenomenological implications. As an application, we present examples of fractal jet observables that are useful in discriminating quark jets from gluon jets.
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.
Fresnel diffraction of fractal grating and self-imaging effect.
Wang, Junhong; Zhang, Wei; Cui, Yuwei; Teng, Shuyun
2014-04-01
Based on the self-similarity property of fractal, two types of fractal gratings are produced according to the production and addition operations of multiple periodic gratings. Fresnel diffractions of fractal grating are analyzed theoretically, and the general mathematic expressions of the diffraction intensity distributions of fractal grating are deduced. The gray-scale patterns of the 2D diffraction distributions of fractal grating are provided through numerical calculations. The diffraction patterns take on the periodicity along the longitude and transverse directions. The 1D diffraction distribution at some certain distances shows the same structure as the fractal grating. This indicates that the self-image of fractal grating is really formed in the Fresnel diffraction region. The experimental measurement of the diffraction intensity distribution of fractal grating with different fractal dimensions and different fractal levels is performed, and the self-images of fractal grating are obtained successfully in experiments. The conclusions of this paper are helpful for the development of the application of fractal grating.
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 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.
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 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.
Smitha, K A; Gupta, A K; Jayasree, R S
2015-09-07
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.
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 analysis of palmar electronographic images. Medical anthropological perspectives.
Guja, Cornelia; Voinea, V; Baciu, Adina; Ciuhuţa, M; Crişan, Daniela A
2008-01-01
The present paper brings to the medical specialists' attention a possibility of multivalent imagistic investigation--the palmar electrographic method submitted to a totally new analysis by the fractal method. Its support for information recording is the radiosensitive film. This makes it resemble the radiological investigation, which opened the way of correlating the shape of certain structures of the organism with their function. By the specific electromagnetic impressing of the ultra photosensitive film, palmar electrography has the advantage of catching the shape of certain radiative phenomena, generated by certain structures in their functional dynamics--at the level of the human palmar tegument. This makes it resemble the EEG, EKG and EMG investigations. The purpose of this presentation is to highlight a new modality of studying the states of the human organism in its permanent adaptation to the living environment, using a new anthropological, informational vision--by fractal processing and by the couple of concepts system / interface--much closer to reality than the present systemic thinking. The human palm, which has a special medial-anthropological relevance, is analysed as a complex adaptive biological and socio-cultural interface between the internal and external environment. The fractal phenomena recorded on the image are ubicuitary in nature and especially in the living world and their shapes may he described mathematically and used for decoding their informational laws. They may have very useful implications in the medical act. The paper presents a few introductory elements to the fractal theory, and, in the final part, the pursued objectives are concretely shown by grouping the EG images according to certain more important medical-anthropological themes.
Fractal image coding based on replaced domain pools
NASA Astrophysics Data System (ADS)
Harada, Masaki; Fujii, Toshiaki; Kimoto, Tadahiko; Tanimoto, Masayuki
1998-01-01
Fractal image coding based on iterated function system has been attracting much interest because of the possibilities of drastic data compression. It performs compression by using the self-similarity included in an image. In the conventional schemes, under the assumption of the self- similarity in the image, each block is mapped from that larger block which is considered as the most suitable block to approximate the range block. However, even if the exact self-similarity of an image is found at the encoder, it hardly holds at the decoder because a domain pool of the encoder is different from that of the decoder. In this paper, we prose a fractal image coding scheme by using domain pools replaced with decoded or transformed values to reduce the difference between the domain pools of the encoder and that of the decoder. The proposed scheme performs two-stage encoding. The domain pool is replaced with decoded non-contractive blocks first and then with transformed values for contractive blocks. It is expected that the proposed scheme reduces errors of contractive blocks in the reconstructed image while those of non- contractive blocks are kept unchanged. The experimental result show the effectiveness of the proposed scheme.
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.
Fractal structures and fractal functions as disease indicators
Escos, J.M; Alados, C.L.; Emlen, J.M.
1995-01-01
Developmental instability is an early indicator of stress, and has been used to monitor the impacts of human disturbance on natural ecosystems. Here we investigate the use of different measures of developmental instability on two species, green peppers (Capsicum annuum), a plant, and Spanish ibex (Capra pyrenaica), an animal. For green peppers we compared the variance in allometric relationship between control plants, and a treatment group infected with the tomato spotted wilt virus. The results show that infected plants have a greater variance about the allometric regression line than the control plants. We also observed a reduction in complexity of branch structure in green pepper with a viral infection. Box-counting fractal dimension of branch architecture declined under stress infection. We also tested the reduction in complexity of behavioral patterns under stress situations in Spanish ibex (Capra pyrenaica). Fractal dimension of head-lift frequency distribution measures predator detection efficiency. This dimension decreased under stressful conditions, such as advanced pregnancy and parasitic infection. Feeding distribution activities reflect food searching efficiency. Power spectral analysis proves to be the most powerful tool for character- izing fractal behavior, revealing a reduction in complexity of time distribution activity under parasitic infection.
MR imaging and osteoporosis: fractal lacunarity analysis of trabecular bone.
Zaia, Annamaria; Eleonori, Roberta; Maponi, Pierluigi; Rossi, Roberto; Murri, Roberto
2006-07-01
We develop a method of magnetic resonance (MR) image analysis able to provide parameter(s) sensitive to bone microarchitecture changes in aging, and to osteoporosis onset and progression. The method has been built taking into account fractal properties of many anatomic and physiologic structures. Fractal lacunarity analysis has been used to determine relevant parameter(s) to differentiate among three types of trabecular bone structure (healthy young, healthy perimenopausal, and osteoporotic patients) from lumbar vertebra MR images. In particular, we propose to approximate the lacunarity function by a hyperbola model function that depends on three coefficients, alpha, beta, and gamma, and to compute these coefficients as the solution of a least squares problem. This triplet of coefficients provides a model function that better represents the variation of mass density of pixels in the image considered. Clinical application of this preliminary version of our method suggests that one of the three coefficients, beta, may represent a standard for the evaluation of trabecular bone architecture and a potentially useful parametric index for the early diagnosis of osteoporosis.
Dougherty, G; Henebry, G M
2001-07-01
Fractal analysis is a method of characterizing complex shapes such as the trabecular structure of bone. Numerous algorithms for estimating fractal dimension have been described, but the Fourier power spectrum method is particularly applicable to self-affine fractals, and facilitates corrections for the effects of noise and blurring in an image. We found that it provided accurate estimates of fractal dimension for synthesized fractal images. For natural texture images fractality is limited to a range of scales, and the fractal dimension as a function of spatial frequency presents as a fractal signature. We found that the fractal signature was more successful at discriminating between these textures than either the global fractal dimension or other metrics such as the mean width and root-mean-square width of the spectral density plots. Different natural textures were also readily distinguishable using lacunarity plots, which explicitly characterize the average size and spatial organization of structural sub-units within an image. The fractal signatures of small regions of interest (32x32 pixels), computed in the frequency domain after corrections for imaging system noise and MTF, were able to characterize the texture of vertebral trabecular bone in CT images. Even small differences in texture due to acquisition slice thickness resulted in measurably different fractal signatures. These differences were also readily apparent in lacunarity plots, which indicated that a slice thickness of 1 mm or less is necessary if essential architectural information is not to be lost. Since lacunarity measures gap size and is not predicated on fractality, it may be particularly useful for characterizing the texture of trabecular bone.
Laser image denoising technique based on multi-fractal theory
NASA Astrophysics Data System (ADS)
Du, Lin; Sun, Huayan; Tian, Weiqing; Wang, Shuai
2014-02-01
The noise of laser images is complex, which includes additive noise and multiplicative noise. Considering the features of laser images, the basic processing capacity and defects of the common algorithm, this paper introduces the fractal theory into the research of laser image denoising. The research of laser image denoising is implemented mainly through the analysis of the singularity exponent of each pixel in fractal space and the feature of multi-fractal spectrum. According to the quantitative and qualitative evaluation of the processed image, the laser image processing technique based on fractal theory not only effectively removes the complicated noise of the laser images obtained by range-gated laser active imaging system, but can also maintains the detail information when implementing the image denoising processing. For different laser images, multi-fractal denoising technique can increase SNR of the laser image at least 1~2dB compared with other denoising techniques, which basically meet the needs of the laser image denoising technique.
Fractal digital image synthesis and application in security holograms
NASA Astrophysics Data System (ADS)
Cao, Hanqiang; Zhu, Guang-Xi; Zhu, Yaoting; Zhang, Zhaoqun; Cao, Yulin; Ge, Hongwei; Li, Xuan
2000-10-01
Conventional method to generate a view angle combining rainbow hologram used a camera to record the sequence of pictures of an object. The object could be a model or a real object. It cost time and money. In recent years, computer-generated holograms have been investigated intensively because of their wide application range and their advantages in term of flexibility, accuracy, light weight and cost. In this paper, a new kind of fractal digital hologram is introduced. The fractal digital holograms are produced with the hyper-complex number model, the fractal hyper-texture model and the self-similar image model based on multi-scale Hurst parameters. The fractal digital holograms have been used in security holograms. In a security hologram, the more complex the model is, the more security the hologram has. The results indicate that fractal digital holograms have a good prospect for application in security holograms.
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.
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.
Imai, K; Ikeda, M; Enchi, Y; Niimi, T
2009-12-01
The purposes of our studies are to examine whether or not fractal-feature distance deduced from virtual volume method can simulate observer performance indices and to investigate the physical meaning of pseudo fractal dimension and complexity. Contrast-detail (C-D) phantom radiographs were obtained at various mAs values (0.5 - 4.0 mAs) and 140 kVp with a computed radiography system, and the reference image was acquired at 13 mAs. For all C-D images, fractal analysis was conducted using the virtual volume method that was devised with a fractional Brownian motion model. The fractal-feature distances between the considered and reference images were calculated using pseudo fractal dimension and complexity. Further, we have performed the C-D analysis in which ten radiologists participated, and compared the fractal-feature distances with the image quality figures (IQF). To clarify the physical meaning of the pseudo fractal dimension and complexity, contrast-to-noise ratio (CNR) and standard deviation (SD) of images noise were calculated for each mAs and compared with the pseudo fractal dimension and complexity, respectively. A strong linear correlation was found between the fractal-feature distance and IQF. The pseudo fractal dimensions became large as CNR increased. Further, a linear correlation was found between the exponential complexity and image noise SD.
Complex Flow Image Velocimetry in Shock Instabilities with Fractal Boundaries
NASA Astrophysics Data System (ADS)
Tellez Alvarez, Jackson David; Vila, Teresa
2017-04-01
laboratory experiments [8] in different types (2D-3D) of the turbulence cascade, using models of relative scaling exponents which are estimated as functions of the fractal dimension, D and the spectral slope b. Numerical simulations of Multi-Fractal grids are performed through OpenFoam or incompact3d software; using either direct numerical simulation (DNS) or Large Eddy Simulation (LES)[9]. REFERENCES [1] Tellez, J., M. Gomez, B. Russo, J.M. Redondo Surface Flow Image Velocimetry (SFIV) for hydraulics applications, 18th International Sym- posium on the Application of
Person identification using fractal analysis of retina images
NASA Astrophysics Data System (ADS)
Ungureanu, Constantin; Corniencu, Felicia
2004-10-01
Biometric is automated method of recognizing a person based on physiological or behavior characteristics. Among the features measured are retina scan, voice, and fingerprint. A retina-based biometric involves the analysis of the blood vessels situated at the back of the eye. In this paper we present a method, which uses the fractal analysis to characterize the retina images. The Fractal Dimension (FD) of retina vessels was measured for a number of 20 images and have been obtained different values of FD for each image. This algorithm provides a good accuracy is cheap and easy to implement.
Fractal-based image texture analysis of trabecular bone architecture.
Jiang, C; Pitt, R E; Bertram, J E; Aneshansley, D J
1999-07-01
Fractal-based image analysis methods are investigated to extract textural features related to the anisotropic structure of trabecular bone from the X-ray images of cubic bone specimens. Three methods are used to quantify image textural features: power spectrum, Minkowski dimension and mean intercept length. The global fractal dimension is used to describe the overall roughness of the image texture. The anisotropic features formed by the trabeculae are characterised by a fabric ellipse, whose orientation and eccentricity reflect the textural anisotropy of the image. Tests of these methods with synthetic images of known fractal dimension show that the Minkowski dimension provides a more accurate and consistent estimation of global fractal dimension. Tests on bone x-ray (eccentricity range 0.25-0.80) images indicate that the Minkowski dimension is more sensitive to the changes in textural orientation. The results suggest that the Minkowski dimension is a better measure for characterising trabecular bone anisotropy in the x-ray images of thick specimens.
Trabecular architecture analysis in femur radiographic images using fractals.
Udhayakumar, G; Sujatha, C M; Ramakrishnan, S
2013-04-01
Trabecular bone is a highly complex anisotropic material that exhibits varying magnitudes of strength in compression and tension. Analysis of the trabecular architectural alteration that manifest as loss of trabecular plates and connection has been shown to yield better estimation of bone strength. In this work, an attempt has been made toward the development of an automated system for investigation of trabecular femur bone architecture using fractal analysis. Conventional radiographic femur bone images recorded using standard protocols are used in this study. The compressive and tensile regions in the images are delineated using preprocessing procedures. The delineated images are analyzed using Higuchi's fractal method to quantify pattern heterogeneity and anisotropy of trabecular bone structure. The results show that the extracted fractal features are distinct for compressive and tensile regions of normal and abnormal human femur bone. As the strength of the bone depends on architectural variation in addition to bone mass, this study seems to be clinically useful.
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.
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. Copyright © 2014 Elsevier Inc. All rights reserved.
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.
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 Filters for Specialized Image Recognition Tasks
2010-02-11
The Fractal Geometry of Nature, [24], Mandelbrot argues that random frac- tals provide geometrical models for naturally occurring shapes and forms...Fractal Properties of Number Systems, Period. Math. Hungar 42 (2001) 51-68. [24] Benoit Mandelbrot , The Fractal Geometry of Nature, W. H. Freeman, San
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 for reduced reference image quality assessment.
Xu, Yong; Liu, Delei; Quan, Yuhui; Le Callet, Patrick
2015-07-01
In this paper, multifractal analysis is adapted to reduced-reference image quality assessment (RR-IQA). A novel RR-QA approach is proposed, which measures the difference of spatial arrangement between the reference image and the distorted image in terms of spatial regularity measured by fractal dimension. An image is first expressed in Log-Gabor domain. Then, fractal dimensions are computed on each Log-Gabor subband and concatenated as a feature vector. Finally, the extracted features are pooled as the quality score of the distorted image using l1 distance. Compared with existing approaches, the proposed method measures image quality from the perspective of the spatial distribution of image patterns. The proposed method was evaluated on seven public benchmark data sets. Experimental results have demonstrated the excellent performance of the proposed method in comparison with state-of-the-art approaches.
Fractal Dimension of Certain Continuous Functions of Unbounded Variation
NASA Astrophysics Data System (ADS)
Liang, Y. S.; Su, W. Y.
Continuous functions on closed intervals are composed of bounded variation functions and unbounded variation functions. Fractal dimension of continuous functions with bounded variation must be one-dimensional (1D). While fractal dimension of continuous functions with unbounded variation may be 1 or not. Certain continuous functions of unbounded variation whose fractal dimensions are 1 have been mainly investigated in the paper. A continuous function on a closed interval with finite unbounded variation points has been proved to be 1D. Furthermore, we deal with continuous functions which have infinite unbounded variation points and part of them have been proved to be 1D. Certain examples of 1D continuous functions which have uncountable unbounded variation points have been given in the present paper.
Do-It-Yourself Fractal Functions
ERIC Educational Resources Information Center
Shriver, Janet; Willard, Teri; McDaniel, Mandy
2017-01-01
In the set of fractal activities described in this article, students will accomplish much more than just creating a fun set of cards that simply resemble an art project. Goals of this activity, designed for an algebra 1 class, are to encourage students to generate data, look for and analyze patterns, and create their own models--all from a set of…
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)
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.
Characterization of nanostructured material images using fractal descriptors
NASA Astrophysics Data System (ADS)
Florindo, João B.; Sikora, Mariana S.; Pereira, Ernesto C.; Bruno, Odemir M.
2013-04-01
This work presents a methodology to the morphology analysis and characterization of nanostructured material images acquired from FEG-SEM (Field Emission Gun-Scanning Electron Microscopy) technique. The metrics were extracted from the image texture (mathematical surface) by the volumetric fractal descriptors, a methodology based on the Bouligand-Minkowski fractal dimension, which considers the properties of the Minkowski dilation of the surface points. An experiment with galvanostatic anodic titanium oxide samples prepared in oxalyc acid solution using different conditions of applied current, oxalyc acid concentration and solution temperature was performed. The results demonstrate that the approach is capable of characterizing complex morphology characteristics such as those present in the anodic titanium oxide.
Segmentation of magnetic resonance image using fractal dimension
NASA Astrophysics Data System (ADS)
Yau, Joseph K. K.; Wong, Sau-hoi; Chan, Kwok-Leung
1997-04-01
In recent years, much research has been conducted in the three-dimensional visualization of medical image. This requires a good segmentation technique. Many early works use first-order and second-order statistics. First-order statistical parameters can be calculated quickly but their effectiveness is influenced by many factors such as illumination, contrast and random noise of the image. Second-order statistical parameters, such as spatial gray level co-occurrence matrices statistics, take longer time to compute but can extract the textural information. In this investigating, two different parameters, namely the entropy and the fractal dimension, are employed to perform segmentation of the magnetic resonance images of the head of a male cadaver. The entropy is calculated from the spatial gray level co-occurrence matrices. The fractal dimension is calculated by the reticular cell counting method. Several regions of the human head are chosen for analysis. They are the bone, gyrus and lobe. Results show that the parameters are able to segment different types of tissue. The entropy gives very good result but it requires very long computation time and large amount of memory. The performance of the fractal dimension is comparable with the entropy. It is simple to estimate and demands lesser memory space.
Fractal analysis in radiological and nuclear medicine perfusion imaging: a systematic review.
Michallek, Florian; Dewey, Marc
2014-01-01
To provide an overview of recent research in fractal analysis of tissue perfusion imaging, using standard radiological and nuclear medicine imaging techniques including computed tomography (CT), magnetic resonance imaging (MRI), ultrasound, positron emission tomography (PET) and single-photon emission computed tomography (SPECT) and to discuss implications for different fields of application. A systematic review of fractal analysis for tissue perfusion imaging was performed by searching the databases MEDLINE (via PubMed), EMBASE (via Ovid) and ISI Web of Science. Thirty-seven eligible studies were identified. Fractal analysis was performed on perfusion imaging of tumours, lung, myocardium, kidney, skeletal muscle and cerebral diseases. Clinically, different aspects of tumour perfusion and cerebral diseases were successfully evaluated including detection and classification. In physiological settings, it was shown that perfusion under different conditions and in various organs can be properly described using fractal analysis. Fractal analysis is a suitable method for quantifying heterogeneity from radiological and nuclear medicine perfusion images under a variety of conditions and in different organs. Further research is required to exploit physiologically proven fractal behaviour in the clinical setting. • Fractal analysis of perfusion images can be successfully performed. • Tumour, pulmonary, myocardial, renal, skeletal muscle and cerebral perfusion have already been examined. • Clinical applications of fractal analysis include tumour and brain perfusion assessment. • Fractal analysis is a suitable method for quantifying perfusion heterogeneity. • Fractal analysis requires further research concerning the development of clinical applications.
Fractal analysis of high-resolution CT images as a tool for quantification of lung diseases
Uppaluri, R.; Mitsa, T.; Galvin, J.R.
1995-12-31
Fractal geometry is increasingly being used to model complex naturally occurring phenomena. There are two types of fractals in nature-geometric fractals and stochastic fractals. The pulmonary branching structure is a geometric fractal and the intensity of its grey scale image is a stochastic fractal. In this paper, the authors attempt to quantify the texture of CT lung images using properties of both types of fractals. A simple algorithm for detecting of abnormality in human lungs, based on 2-D and 3-D fractal dimensions, is presented. This method involves calculating the local fractal dimensions, based on intensities, in the 2-D slice to air edge enhancement. Following this, grey level thresholding is performed and a global fractal dimension, based on structure, for the entire data is estimated in 2-D and 3-D. High Resolution CT images of normal and abnormal lungs were analyzed. Preliminary results showed that classification of normal and abnormal images could be obtained based on the differences between their global fractal dimensions.
A Digital Image Steganography using Sierpinski Gasket Fractal and PLSB
NASA Astrophysics Data System (ADS)
Rupa, Ch.
2013-09-01
Information attacks are caused due to the weaknesses in the information security. These attacks affect the non-repudiation and integrity of the security services. In this paper, a novel security approach that can defend the message from information attacks is proposed. In this new approach the original message is encrypted by Fractal Sierpinski Gasket (FSG) cryptographic algorithm, that result is hidden into an image using penultimate and least significant bit (PLSB) embedding method. This method makes the security more robust than conventional approach. Important properties of fractals are sensitivity and self similarity. These can be exploited to produce avalanche effect. Stegoanalysis of the proposed method shows that it is resistant to various attacks and stronger than the existed steganographic approaches.
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.
Comparison of the segmentation of ultrasonic image utilizing different fractal parameters
NASA Astrophysics Data System (ADS)
Chan, Kwok-Leung
1995-04-01
Statistical texture analysis has been commonly applied in the quantitative characterization of ultrasonic image. Recently, another approach begins to emerge, which uses fractal dimension. In this investigation, fractal dimension is estimated from histologically confirmed ultrasonic images using three different approaches: intensity- based, spectrum-based and reticular cell counting. The parameters are then used in image segmentation. The fractal model has the advantages that the parameter generated is stable over transformations of scale and linear transforms of intensity. From the results obtained, the performance of fractal dimension obtained by the reticular cell counting method is better than the other two approaches and comparable to the spatial grey level co-occurrence matrices statistic.
Fractal dimension metric for quantifying noise texture of computed tomography images
NASA Astrophysics Data System (ADS)
Khobragade, P.; Fan, Jiahua; Rupcich, Franco; Crotty, Dominic J.; Gilat Schmidt, Taly
2017-03-01
This study investigated a fractal dimension algorithm for noise texture quantification in CT images. Quantifying noise in CT images is important for assessing image quality. Noise is typically quantified by calculating noise standard deviation and noise power spectrum (NPS). Different reconstruction kernels and iterative reconstruction approaches affect both the noise magnitude and noise texture. The shape of the NPS can be used as a noise texture descriptor. However, the NPS requires numerous images for calculation and is a vector quantity. This study proposes the metric of fractal dimension to quantify noise texture, because fractal dimension is a single scalar metric calculated from a small number of images. Fractal dimension measures the complexity of a pattern. In this study, the ACR CT phantom was scanned and images were reconstructed using filtered back-projection with three reconstruction kernels: bone, soft and standard. Regions of interest were extracted from the uniform section of the phantom for NPS and fractal dimension calculation. The results demonstrated a mean fractal dimension of 1.86 for soft kernel, 1.92 for standard kernel, and 2.16 for bone kernel. Increasing fractal dimension corresponded to shift in the NPS towards higher spatial frequencies and grainier noise appearance. Stable fractal dimension was calculated from two ROI's compared to more than 250 ROI's used for NPS calculation. The scalar fractal dimension metric may be a useful noise texture descriptor for evaluating or optimizing reconstruction algorithms.
SAR image post-processing for the estimation of fractal parameters
NASA Astrophysics Data System (ADS)
Di Martino, Gerardo; Riccio, Daniele; Ruello, Giuseppe; Zinno, Ivana
2011-11-01
In this paper a fractal based processing for the analysis of SAR images of natural surfaces is presented. Its definition is based on a complete direct imaging model developed by the authors. The application of this innovative algorithm to SAR images makes possible to obtain complete maps of the two key parameters of a fractal scene: the fractal dimension and the increment standard deviation. The fractal parameters extraction is based on the estimation of the power spectral density of the SAR amplitude image. From a theoretic point of view, the attention is focused on the retrieving procedure of the increment standard deviation, here presented for the first time. In the last section of the paper, the application of the introduced processing to high resolution SAR images is presented, with the relevant maps of the fractal dimension and of the increment standard deviation.
Wavelets, Fractals, and Radial Basis Functions
2007-11-02
of Signal Processing. San Diego, CA: Aca- demic, 1998. [13] G. Strang and T. Q. Nguyen, Wavelets and Filter Banks . Cambridge, MA: Wellesley-Cambridge...localization, multiresolution, radial basis functions, re- finement filter , scaling functions, self-similarity, splines, tempered distributions, two-scale...one linear constraint per basis function, and the corresponding linear system of equations is invertible under relatively mild conditions [11]. The
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.
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.…
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.…
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.
Fractal analysis of AFM images of the surface of Bowman's membrane of the human cornea.
Ţălu, Ştefan; Stach, Sebastian; Sueiras, Vivian; Ziebarth, Noël Marysa
2015-04-01
The objective of this study is to further investigate the ultrastructural details of the surface of Bowman's membrane of the human cornea, using atomic force microscopy (AFM) images. One representative image acquired of Bowman's membrane of a human cornea was investigated. The three-dimensional (3-D) surface of the sample was imaged using AFM in contact mode, while the sample was completely submerged in optisol solution. Height and deflection images were acquired at multiple scan lengths using the MFP-3D AFM system software (Asylum Research, Santa Barbara, CA), based in IGOR Pro (WaveMetrics, Lake Oswego, OR). A novel approach, based on computational algorithms for fractal analysis of surfaces applied for AFM data, was utilized to analyze the surface structure. The surfaces revealed a fractal structure at the nanometer scale. The fractal dimension, D, provided quantitative values that characterize the scale properties of surface geometry. Detailed characterization of the surface topography was obtained using statistical parameters, in accordance with ISO 25178-2: 2012. Results obtained by fractal analysis confirm the relationship between the value of the fractal dimension and the statistical surface roughness parameters. The surface structure of Bowman's membrane of the human cornea is complex. The analyzed AFM images confirm a fractal nature of the surface, which is not taken into account by classical surface statistical parameters. Surface fractal dimension could be useful in ophthalmology to quantify corneal architectural changes associated with different disease states to further our understanding of disease evolution.
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.
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.
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
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.
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
Zaia, Annamaria
2015-03-18
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
Potts model partition functions on two families of fractal lattices
NASA Astrophysics Data System (ADS)
Gong, Helin; Jin, Xian'an
2014-11-01
The partition function of q-state Potts model, or equivalently the Tutte polynomial, is computationally intractable for regular lattices. The purpose of this paper is to compute partition functions of q-state Potts model on two families of fractal lattices. Based on their self-similar structures and by applying the subgraph-decomposition method, we divide their Tutte polynomials into two summands, and for each summand we obtain a recursive formula involving the other summand. As a result, the number of spanning trees and their asymptotic growth constants, and a lower bound of the number of connected spanning subgraphs or acyclic root-connected orientations for each of such two lattices are obtained.
Border extrapolation using fractal attributes in remote sensing images
NASA Astrophysics Data System (ADS)
Cipolletti, M. P.; Delrieux, C. A.; Perillo, G. M. E.; Piccolo, M. C.
2014-01-01
In management, monitoring and rational use of natural resources the knowledge of precise and updated information is essential. Satellite images have become an attractive option for quantitative data extraction and morphologic studies, assuring a wide coverage without exerting negative environmental influence over the study area. However, the precision of such practice is limited by the spatial resolution of the sensors and the additional processing algorithms. The use of high resolution imagery (i.e., Ikonos) is very expensive for studies involving large geographic areas or requiring long term monitoring, while the use of less expensive or freely available imagery poses a limit in the geographic accuracy and physical precision that may be obtained. We developed a methodology for accurate border estimation that can be used for establishing high quality measurements with low resolution imagery. The method is based on the original theory by Richardson, taking advantage of the fractal nature of geographic features. The area of interest is downsampled at different scales and, at each scale, the border is segmented and measured. Finally, a regression of the dependence of the measured length with respect to scale is computed, which then allows for a precise extrapolation of the expected length at scales much finer than the originally available. The method is tested with both synthetic and satellite imagery, producing accurate results in both cases.
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)
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.
Local fuzzy fractal dimension and its application in medical image processing.
Zhuang, Xiaodong; Meng, Qingchun
2004-09-01
The local fuzzy fractal dimension (LFFD) is proposed to extract local fractal feature of medical images. The definition of LFFD is an extension of the pixel-covering method by incorporating the fuzzy set. Multi-feature edge detection is implemented with the LFFD and the Sobel operator. The LFFD can also serve as a characteristic of motion in medical image sequences. The experimental results show that the LFFD is an important feature of edge areas in medical images and can provide information for segmentation of echocardiogram image sequences.
Simple fractal method of assessment of histological images for application in medical diagnostics
2010-01-01
We propose new method of assessment of histological images for medical diagnostics. 2-D image is preprocessed to form 1-D landscapes or 1-D signature of the image contour and then their complexity is analyzed using Higuchi's fractal dimension method. The method may have broad medical application, from choosing implant materials to differentiation between benign masses and malignant breast tumors. PMID:21134258
On the fractal distribution of primes and prime-indexed primes by the binary image analysis
NASA Astrophysics Data System (ADS)
Cattani, Carlo; Ciancio, Armando
2016-10-01
In this paper, the distribution of primes and prime-indexed primes (PIPs) is studied by mapping primes into a binary image which visualizes the distribution of primes. These images show that the distribution of primes (and PIPs) is similar to a Cantor dust, moreover the self-similarity with respect to the order of PIPs (already proven in Batchko (2014)) can be seen as an invariance of the binary images. The index of primes plays the same role of the scale for fractals, so that with respect to the index the distribution of prime-indexed primes is characterized by the self-similarity alike any other fractal. In particular, in order to single out the scale dependence, the PIPs fractal distribution will be evaluated by limiting to two parameters, fractal dimension (δ) and lacunarity (λ), that are usually used to measure the fractal nature. Because of the invariance of the corresponding binary plots, the fractal dimension and lacunarity of primes distribution are invariant with respect to the index of PIPs.
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.
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.
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.
Fast Basins and Branched Fractal Manifolds of Attractors of Iterated Function Systems
NASA Astrophysics Data System (ADS)
Barnsley, Michael F.; Vince, Andrew
2015-10-01
The fast basin of an attractor of an iterated function system (IFS) is the set of points in the domain of the IFS whose orbits under the associated semigroup intersect the attractor. Fast basins can have non-integer dimension and comprise a class of deterministic fractal sets. The relationship between the basin and the fast basin of a point-fibred attractor is analyzed. To better understand the topology and geometry of fast basins, and because of analogies with analytic continuation, branched fractal manifolds are introduced. A branched fractal manifold is a metric space constructed from the extended code space of a point-fibred attractor, by identifying some addresses. Typically, a branched fractal manifold is a union of a nondenumerable collection of nonhomeomorphic objects, isometric copies of generalized fractal blowups of the attractor.
Image fractal coding algorithm based on complex exponent moments and minimum variance
NASA Astrophysics Data System (ADS)
Yang, Feixia; Ping, Ziliang; Zhou, Suhua
2017-02-01
Image fractal coding possesses very high compression ratio, the main problem is low speed of coding. The algorithm based on Complex Exponent Moments(CEM) and minimum variance is proposed to speed up the fractal coding compression. The definition of CEM and its FFT algorithm are presented, and the multi-distorted invariance of CEM are discussed. The multi-distorted invariance of CEM is fit to the fractal property of an image. The optimal matching pair of range blocks and domain blocks in an image is determined by minimizing the variance of their CEM. Theory analysis and experimental results have proved that the algorithm can dramatically reduce the iteration time and speed up image encoding and decoding process.
Obert, Martin; Seyfried, Maren; Schumacher, Falk; Krombach, Gabriele A; Verhoff, Marcel A
2014-09-01
Aging human remains is a critical issue in anthropology and forensic medicine, and the search for accurate, new age-estimation methods is ongoing. In our study, we, therefore, explored a new approach to investigate a possible correlation between age-at-death (aad) and geometric irregularities in the bone structure of human skull caps. We applied the concept of fractal geometry and fractal dimension D analysis to describe heterogeneity within the bone structure. A high-resolution flat-panel computed tomography scanner (eXplore Locus Ultra) was used to obtain 229,500 images from 221 male and 120 female (total 341) European human skulls. Automated image analysis software was developed to evaluate the fractal dimension D, using the mass radius method. The frontal and the occipital portions of the skull caps of adult females and males were investigated separately. The age dependence of the fractal dimension D was studied by correlation analysis, and the prediction accuracy of age-at-death (aad) estimates for individual observations was calculated. D values for human skull caps scatter strongly as a function of age. We found sex-dependent correlation coefficients (CC) between D and age for adults (females CC=-0.67; males CC=-0.05). Prediction errors for aad estimates for individual observations were in the range of ±18 years at a 75% confidence interval. The detailed quantitative description of age-dependent irregularities in the bone microarchitecture of skull vaults through fractal dimension analysis does not, as we had hoped, enable a new aging method. Severe scattering of the data leads to an estimation error that is too great for this method to be of practical relevance in aad estimates. Thus, we disclosed an interesting sex difference. Copyright © 2014 Elsevier Ireland Ltd. All rights reserved.
Fractal Dimension Estimation of RGB Color Images Using Maximum Color Distance
NASA Astrophysics Data System (ADS)
Zhao, Xin; Wang, Xingyuan
2016-08-01
Natural images exhibit a high degree of complexity, randomness and irregularity in color and texture, however fractal can be an effective tool to describe various irregular phenomena in nature. Fractal dimensions are important because they can be defined in connection with real-world data, and they can be measured approximately by means of experiments. In this paper, we proposed a fractal dimension estimation method for RGB color images. In the proposed method, we present a hyper-surface partition method which considers the hyper-surface as continuous and divide the image into nonoverlapped blocks. We also defined a counting method in color domain. To validate the proposed method, experiments were carried on two types of color images: synthesized fractal images and natural RGB color images. The experimental results demonstrate that the proposed method is effective and efficient. The behaviors of the proposed method on the rescale images are also shown in the paper. And it can be performed as a reliable FD estimation approach for the RGB color images.
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 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.
Morphology and functions of astrocytes cultured on water-repellent fractal tripalmitin surfaces.
Hu, Wei-wei; Wang, Zhe; Zhang, Shan-shan; Jiang, Lei; Zhang, Jing; Zhang, Xiangnan; Lei, Qun-fang; Park, Hyun-Joo; Fang, Wen-jun; Chen, Zhong
2014-08-01
In the brain, astrocytes play an essential role with their multiple functions and sophisticated structure, as surrounded by a fractal environment which has not been available in our traditional cell culture. Water-repellent fractal tripalmitin (PPP) surfaces can imitate the fractal environment in vivo, so the morphology and biochemical characterization of astrocytes on these surfaces are examined. Water-repellent fractal PPP surface can induce astrocytes to display sophisticated morphology with smaller size of cell area, longer and finer filopodium-like processes, and higher morphological complexity. The super water-repellent fractal PPP surface with water contact angle of 150°∼160° produces the maximal effects compared with other surfaces at lower water contact angles. The trends of characteristic protein expression, including that of nestin, vimentin, GFAP and glutamine synthetase, for astrocytes cultured on super water-repellent fractal PPP surfaces approximate more to in vivo pattern. The super water-repellent PPP surface also render astrocytes to perform more pronounced promotion of neurogenesis by increasing the release of nerve growth factor in a co-culture system. Altogether, our results suggest that the super water-repellent fractal PPP surface facilitates the astrocytes to mimic their in vivo performance, thus provides a closer-to-natural culture environment for experimental assessment of glial structure and functions. Copyright © 2014 Elsevier Ltd. All rights reserved.
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.
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.
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)
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)
Buried mine detection using fractal geometry analysis to the LWIR successive line scan data image
NASA Astrophysics Data System (ADS)
Araki, Kan
2012-06-01
We have engaged in research on buried mine/IED detection by remote sensing method using LWIR camera. A IR image of a ground, containing buried objects can be assumed as a superimposed pattern including thermal scattering which may depend on the ground surface roughness, vegetation canopy, and effect of the sun light, and radiation due to various heat interaction caused by differences in specific heat, size, and buried depth of the objects and local temperature of their surrounding environment. In this cumbersome environment, we introduce fractal geometry for analyzing from an IR image. Clutter patterns due to these complex elements have oftentimes low ordered fractal dimension of Hausdorff Dimension. On the other hand, the target patterns have its tendency of obtaining higher ordered fractal dimension in terms of Information Dimension. Random Shuffle Surrogate method or Fourier Transform Surrogate method is used to evaluate fractional statistics by applying shuffle of time sequence data or phase of spectrum. Fractal interpolation to each line scan was also applied to improve the signal processing performance in order to evade zero division and enhance information of data. Some results of target extraction by using relationship between low and high ordered fractal dimension are to be presented.
ERIC Educational Resources Information Center
Dewdney, A. K.
1991-01-01
Explores the subject of fractal geometry focusing on the occurrence of fractal-like shapes in the natural world. Topics include iterated functions, chaos theory, the Lorenz attractor, logistic maps, the Mandelbrot set, and mini-Mandelbrot sets. Provides appropriate computer algorithms, as well as further sources of information. (JJK)
ERIC Educational Resources Information Center
Dewdney, A. K.
1991-01-01
Explores the subject of fractal geometry focusing on the occurrence of fractal-like shapes in the natural world. Topics include iterated functions, chaos theory, the Lorenz attractor, logistic maps, the Mandelbrot set, and mini-Mandelbrot sets. Provides appropriate computer algorithms, as well as further sources of information. (JJK)
Li, Hui-Ying; Du, Xiao-Ming; Yang, Bin; Wu, Bin; Xu, Zhu; Shi, Yi; Fang, Ji-Dun; Li, Fa-Sheng
2013-11-01
Dyes are frequently used to visualize fingering flow pathways, where the image process has an important role in the result analysis. The theory of fractal geometry is applied to give quantitative description of the stain patterns via image analysis, which is helpful for finger characterization and prediction. This description typically involves two parameters, a mass fractal dimension (D(m)) relative to the area, and a surface fractal dimension (D(s)) relative to the perimeter. This work detailed analyzes the influence of various choices during the thresholding step that transformed the origin color images to binary ones which are needed in the fractal analysis. One hundred and thirty images were obtained from laboratory two-dimension sand box infiltration experiments of four dyed non-aqueous phase liquids. Detailed comparisons of D(m) and D(s) were made respectively, considering a set of threshold algorithms and the filling of lakes. Results indicate that adjustments of the saturation threshold influence are less on both D(m) and D(s) in the laboratory experiments. The brightness threshold adjustments decrease the D(m) by 0.02 and increase the D(s) by 0.05. Filling lakes influence the D(m) less while the D(s) decrease by 0.10. Therefore the D(m) was recommended for further analysis to avoid subjective choices' influence in the image process.
On the fractal geometry of DNA by the binary image analysis.
Cattani, Carlo; Pierro, Gaetano
2013-09-01
The multifractal analysis of binary images of DNA is studied in order to define a methodological approach to the classification of DNA sequences. This method is based on the computation of some multifractality parameters on a suitable binary image of DNA, which takes into account the nucleotide distribution. The binary image of DNA is obtained by a dot-plot (recurrence plot) of the indicator matrix. The fractal geometry of these images is characterized by fractal dimension (FD), lacunarity, and succolarity. These parameters are compared with some other coefficients such as complexity and Shannon information entropy. It will be shown that the complexity parameters are more or less equivalent to FD, while the parameters of multifractality have different values in the sense that sequences with higher FD might have lower lacunarity and/or succolarity. In particular, the genome of Drosophila melanogaster has been considered by focusing on the chromosome 3r, which shows the highest fractality with a corresponding higher level of complexity. We will single out some results on the nucleotide distribution in 3r with respect to complexity and fractality. In particular, we will show that sequences with higher FD also have a higher frequency distribution of guanine, while low FD is characterized by the higher presence of adenine.
Klein, Katharina; Maier, Timo; Hirschfeld-Warneken, Vera C; Spatz, Joachim P
2013-01-01
Phenotyping of tumor cells by marker-free quantification is important for cancer diagnostics. For the first time, fractal analysis of reflection interference contrast microscopy images of single living cells was employed as a new method to distinguish between different nanoscopic membrane features of tumor cells. Since tumor progression correlates with a higher degree of chaos within the cell, it can be quantified mathematically by fractality. Our results show a high accuracy in identifying malignant cells with a failure chance of 3%, which is far better than today's applied methods.
NASA Astrophysics Data System (ADS)
Sau Fa, Kwok
2017-03-01
Recently, fractal and generalized Fokker–Planck equations have been the subject of considerable interest. In this work, the fractal and generalized Fokker–Planck equations connected with the Langevin equation and continuous time random walk model are considered. Descriptions and applications of these models to the fixed samples of the mouse brain using magnetic resonance imaging (MRI) are discussed.
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.
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
Stadnitski, Tatjana
2012-01-01
When investigating fractal phenomena, the following questions are fundamental for the applied researcher: (1) What are essential statistical properties of 1/f noise? (2) Which estimators are available for measuring fractality? (3) Which measurement instruments are appropriate and how are they applied? The purpose of this article is to give clear and comprehensible answers to these questions. First, theoretical characteristics of a fractal pattern (self-similarity, long memory, power law) and the related fractal parameters (the Hurst coefficient, the scaling exponent α, the fractional differencing parameter d of the autoregressive fractionally integrated moving average methodology, the power exponent β of the spectral analysis) are discussed. Then, estimators of fractal parameters from different software packages commonly used by applied researchers (R, SAS, SPSS) are introduced and evaluated. Advantages, disadvantages, and constrains of the popular estimators (d^ML, power spectral density, detrended fluctuation analysis, signal summation conversion) are illustrated by elaborate examples. Finally, crucial steps of fractal analysis (plotting time series data, autocorrelation, and spectral functions; performing stationarity tests; choosing an adequate estimator; estimating fractal parameters; distinguishing fractal processes from short-memory patterns) are demonstrated with empirical time series. PMID:22586408
Stadnitski, Tatjana
2012-01-01
WHEN INVESTIGATING FRACTAL PHENOMENA, THE FOLLOWING QUESTIONS ARE FUNDAMENTAL FOR THE APPLIED RESEARCHER: (1) What are essential statistical properties of 1/f noise? (2) Which estimators are available for measuring fractality? (3) Which measurement instruments are appropriate and how are they applied? The purpose of this article is to give clear and comprehensible answers to these questions. First, theoretical characteristics of a fractal pattern (self-similarity, long memory, power law) and the related fractal parameters (the Hurst coefficient, the scaling exponent α, the fractional differencing parameter d of the autoregressive fractionally integrated moving average methodology, the power exponent β of the spectral analysis) are discussed. Then, estimators of fractal parameters from different software packages commonly used by applied researchers (R, SAS, SPSS) are introduced and evaluated. Advantages, disadvantages, and constrains of the popular estimators ([Formula: see text] power spectral density, detrended fluctuation analysis, signal summation conversion) are illustrated by elaborate examples. Finally, crucial steps of fractal analysis (plotting time series data, autocorrelation, and spectral functions; performing stationarity tests; choosing an adequate estimator; estimating fractal parameters; distinguishing fractal processes from short-memory patterns) are demonstrated with empirical time series.
Detecting abrupt dynamic change based on changes in the fractal properties of spatial images
NASA Astrophysics Data System (ADS)
Liu, Qunqun; He, Wenping; Gu, Bin; Jiang, Yundi
2016-08-01
Many abrupt climate change events often cannot be detected timely by conventional abrupt detection methods until a few years after these events have occurred. The reason for this lag in detection is that abundant and long-term observational data are required for accurate abrupt change detection by these methods, especially for the detection of a regime shift. So, these methods cannot help us understand and forecast the evolution of the climate system in a timely manner. Obviously, spatial images, generated by a coupled spatiotemporal dynamical model, contain more information about a dynamic system than a single time series, and we find that spatial images show the fractal properties. The fractal properties of spatial images can be quantitatively characterized by the Hurst exponent, which can be estimated by two-dimensional detrended fluctuation analysis (TD-DFA). Based on this, TD-DFA is used to detect an abrupt dynamic change of a coupled spatiotemporal model. The results show that the TD-DFA method can effectively detect abrupt parameter changes in the coupled model by monitoring the changing in the fractal properties of spatial images. The present method provides a new way for abrupt dynamic change detection, which can achieve timely and efficient abrupt change detection results.
Zheng, Xiuqing; Liao, Zhiwu; Hu, Shaoxiang; Li, Ming; Zhou, Jiliu
2013-01-01
NLMs is a state-of-art image denoising method; however, it sometimes oversmoothes anatomical features in low-dose CT (LDCT) imaging. In this paper, we propose a simple way to improve the spatial adaptivity (SA) of NLMs using pointwise fractal dimension (PWFD). Unlike existing fractal image dimensions that are computed on the whole images or blocks of images, the new PWFD, named pointwise box-counting dimension (PWBCD), is computed for each image pixel. PWBCD uses a fixed size local window centered at the considered image pixel to fit the different local structures of images. Then based on PWBCD, a new method that uses PWBCD to improve SA of NLMs directly is proposed. That is, PWBCD is combined with the weight of the difference between local comparison windows for NLMs. Smoothing results for test images and real sinograms show that PWBCD-NLMs with well-chosen parameters can preserve anatomical features better while suppressing the noises efficiently. In addition, PWBCD-NLMs also has better performance both in visual quality and peak signal to noise ratio (PSNR) than NLMs in LDCT imaging.
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
Foulsham, Tom; Kingstone, Alan
2010-04-07
The direction in which people tend to move their eyes when inspecting images can reveal the different influences on eye guidance in scene perception, and their time course. We investigated biases in saccade direction during a memory-encoding task with natural scenes and computer-generated fractals. Images were rotated to disentangle egocentric and image-based guidance. Saccades in fractals were more likely to be horizontal, regardless of orientation. In scenes, the first saccade often moved down and subsequent eye movements were predominantly vertical, relative to the scene. These biases were modulated by the distribution of visual features (saliency and clutter) in the scene. The results suggest that image orientation, visual features and the scene frame-of-reference have a rapid effect on eye guidance. Copyright 2010 Elsevier Ltd. All rights reserved.
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.
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.
A novel fractal monocular and stereo video codec with object-based functionality
NASA Astrophysics Data System (ADS)
Zhu, Shiping; Li, Liyun; Wang, Zaikuo
2012-12-01
Based on the classical fractal video compression method, an improved monocular fractal compression method is proposed which includes using more effective macroblock partition scheme instead of classical quadtree partition scheme; using improved fast motion estimation to increase the calculation speed; using homo-I-frame like in H.264, etc. The monocular codec uses the motion compensated prediction (MCP) structure. And stereo fractal video coding is proposed which matches the macroblock with two reference frames in left and right views, and it results in increasing compression ratio and reducing bit rate/bandwidth when transmitting compressed video data. The stereo codec combines MCP and disparity compensated prediction. And a new method of object-based fractal video coding is proposed in which each object can be encoded and decoded independently with higher compression ratio and speed and less bit rate/bandwidth when transmitting compressed stereo video data greatly. Experimental results indicate that the proposed monocular method can raise compression ratio 3.6 to 7.5 times, speed up compression time 5.3 to 22.3 times, and improve the image quality 3.81 to 9.24 dB in comparison with circular prediction mapping and non-contractive interframe mapping. The PSNR of the proposed stereo video coding is about 0.17 dB higher than that of the proposed monocular video coding, and 0.69 dB higher than that of JMVC 4.0 on average. Comparing with the bit rate resulted by the proposed monocular video coding and JMVC 4.0, the proposed stereo video coding achieves, on average, 2.53 and 21.14 Kbps bit rate saving, respectively. The proposed object-based fractal monocular and stereo video coding methods are simple and effective, and they make the applications of fractal monocular and stereo video coding more flexible and practicable.
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)
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
Classification of diabetic retinopathy using fractal dimension analysis of eye fundus image
NASA Astrophysics Data System (ADS)
Safitri, Diah Wahyu; Juniati, Dwi
2017-08-01
Diabetes Mellitus (DM) is a metabolic disorder when pancreas produce inadequate insulin or a condition when body resist insulin action, so the blood glucose level is high. One of the most common complications of diabetes mellitus is diabetic retinopathy which can lead to a vision problem. Diabetic retinopathy can be recognized by an abnormality in eye fundus. Those abnormalities are characterized by microaneurysms, hemorrhage, hard exudate, cotton wool spots, and venous's changes. The diabetic retinopathy is classified depends on the conditions of abnormality in eye fundus, that is grade 1 if there is a microaneurysm only in the eye fundus; grade 2, if there are a microaneurysm and a hemorrhage in eye fundus; and grade 3: if there are microaneurysm, hemorrhage, and neovascularization in the eye fundus. This study proposed a method and a process of eye fundus image to classify of diabetic retinopathy using fractal analysis and K-Nearest Neighbor (KNN). The first phase was image segmentation process using green channel, CLAHE, morphological opening, matched filter, masking, and morphological opening binary image. After segmentation process, its fractal dimension was calculated using box-counting method and the values of fractal dimension were analyzed to make a classification of diabetic retinopathy. Tests carried out by used k-fold cross validation method with k=5. In each test used 10 different grade K of KNN. The accuracy of the result of this method is 89,17% with K=3 or K=4, it was the best results than others K value. Based on this results, it can be concluded that the classification of diabetic retinopathy using fractal analysis and KNN had a good performance.
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.
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.
Fractal coding of wavelet image based on human vision contrast-masking effect
NASA Astrophysics Data System (ADS)
Wei, Hai; Shen, Lansun
2000-06-01
In this paper, a fractal-based compression approach of wavelet image is presented. The scheme tries to make full use of the sensitivity features of the human visual system. With the wavelet-based multi-resolution representation of image, detail vectors of each high frequency sub-image are constructed in accordance with its spatial orientation in order to grasp the edge information to which human observer is sensitive. Then a multi-level selection algorithm based on human vision's contrast masking effect is proposed to make the decision whether a detail vector is coded or not. Those vectors below the contrast threshold are discarded without introducing visual artifacts because of the ignorance of human vision. As for the redundancy of the retained vectors, different fractal- based methods are employed to decrease the correlation in single sub-image and between the different resolution sub- images with the same orientation. Experimental results suggest the efficiency of the proposed scheme. With the standard test image, our approach outperforms the EZW algorithm and the JPEG method.
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.
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
Fractal and digital image processing to determine the degree of dispersion of carbon nanotubes
NASA Astrophysics Data System (ADS)
Liang, Xiao-ning; Li, Wei
2016-05-01
The degree of dispersion is an important parameter to quantitatively study properties of carbon nanotube composites. Among the many methods for studying dispersion, scanning electron microscopy, transmission electron microscopy, and atomic force microscopy are the most commonly used, intuitive, and convincing methods. However, they have the disadvantage of not being quantitative. To overcome this disadvantage, the fractal theory and digital image processing method can be used to provide a quantitative analysis of the morphology and properties of carbon nanotube composites. In this paper, the dispersion degree of carbon nanotubes was investigated using two fractal methods, namely, the box-counting method and the differential box-counting method. On the basis of the results, we propose a new method for the quantitative characterization of the degree of dispersion of carbon nanotubes. This hierarchical grid method can be used as a supplementary method, and can be combined with the fractal calculation method. Thus, the accuracy and effectiveness of the quantitative characterization of the dispersion degree of carbon nanotubes can be improved. (The outer diameter of the carbon nanotubes is about 50 nm; the length of the carbon nanotubes is 10-20 μm.)
Tomomitsu, Tatsushi; Mimura, Hiroaki; Murase, Kenya; Tamada, Tsutomu; Sone, Teruki; Fukunaga, Masao
2005-06-20
Many analyses of bone microarchitecture using three-dimensional images of micro CT (microCT) have been reported recently. However, as extirpated bone is the subject of measurement on microCT, various kinds of information are not available clinically. Our aim is to evaluate usefulness of fractal dimension as an index of bone strength different from bone mineral density in in-vivo, to which microCT could not be applied. In this fundamental study, the relation between pixel size and the slice thickness of images was examined when fractal analysis was applied to clinical images. We examined 40 lumbar spine specimens extirpated from 16 male cadavers (30-88 years; mean age, 60.8 years). Three-dimensional images of the trabeculae of 150 slices were obtained by a microCT system under the following conditions: matrix size, 512 x 512; slice thickness, 23.2 em; and pixel size, 18.6 em. Based on images of 150 slices, images of four different matrix sizes and nine different slice thicknesses were made using public domain software (NIH Image). The threshold value for image binarization, and the relation between pixel size and the slice thickness of an image used for two-dimensional and three-dimensional fractal analyses were studied. In addition, the box counting method was used for fractal analysis. One hundred forty-five in box counting was most suitable as the threshold value for image binarization on the 256 gray levels. The correlation coefficients between two-dimensional fractal dimensions of processed images and three-dimensional fractal dimensions of original images were more than 0.9 for pixel sizes < or =148.8 microm at a slice thickness of 1 mm, and < or =74.4 microm at one of 2 mm. In terms of the relation between the three-dimensional fractal dimension of processed images and three-dimensional fractal dimension of original images, when pixel size was less than 74.4 microm, a correlation coefficient of more than 0.9 was obtained even for the maximal slice thickness
After notes on self-similarity exponent for fractal structures
NASA Astrophysics Data System (ADS)
Fernández-Martínez, Manuel; Caravaca Garratón, Manuel
2017-06-01
Previous works have highlighted the suitability of the concept of fractal structure, which derives from asymmetric topology, to propound generalized definitions of fractal dimension. The aim of the present article is to collect some results and approaches allowing to connect the self-similarity index and the fractal dimension of a broad spectrum of random processes. To tackle with, we shall use the concept of induced fractal structure on the image set of a sample curve. The main result in this paper states that given a sample function of a random process endowed with the induced fractal structure on its image, it holds that the self-similarity index of that function equals the inverse of its fractal dimension.
NASA Astrophysics Data System (ADS)
Wang, Heming; Liu, Yu; Song, Yongchen; Zhao, Yuechao; Zhao, Jiafei; Wang, Dayong
2012-11-01
Pore structure is one of important factors affecting the properties of porous media, but it is difficult to describe the complexity of pore structure exactly. Fractal theory is an effective and available method for quantifying the complex and irregular pore structure. In this paper, the fractal dimension calculated by box-counting method based on fractal theory was applied to characterize the pore structure of artificial cores. The microstructure or pore distribution in the porous material was obtained using the nuclear magnetic resonance imaging (MRI). Three classical fractals and one sand packed bed model were selected as the experimental material to investigate the influence of box sizes, threshold value, and the image resolution when performing fractal analysis. To avoid the influence of box sizes, a sequence of divisors of the image was proposed and compared with other two algorithms (geometric sequence and arithmetic sequence) with its performance of partitioning the image completely and bringing the least fitted error. Threshold value selected manually and automatically showed that it plays an important role during the image binary processing and the minimum-error method can be used to obtain an appropriate or reasonable one. Images obtained under different pixel matrices in MRI were used to analyze the influence of image resolution. Higher image resolution can detect more quantity of pore structure and increase its irregularity. With benefits of those influence factors, fractal analysis on four kinds of artificial cores showed the fractal dimension can be used to distinguish the different kinds of artificial cores and the relationship between fractal dimension and porosity or permeability can be expressed by the model of D = a - bln(x + c).
Vlad, Marcel O.; Morán, Federico; Popa, Vlad T.; Szedlacsek, Stefan E.; Ross, John
2007-01-01
We give a functional generalization of fractal scaling laws applied to response problems as well as to probability distributions. We consider excitations and responses, which are functions of a given state vector. Based on scaling arguments, we derive a general nonlinear response functional scaling law, which expresses the logarithm of a response at a given state as a superposition of the values of the logarithms of the excitations at different states. Such a functional response law may result from the balance of different growth processes, characterized by variable growth rates, and it is the first order approximation of a perturbation expansion similar to the phase expansion. Our response law is a generalization of the static fractal scaling law and can be applied to the study of various problems from physics, chemistry, and biology. We consider some applications to heterogeneous and disordered kinetics, organ growth (allometry), and population genetics. Kinetics on inhomogeneous reconstructing surfaces leads to rate equations described by our nonlinear scaling law. For systems with dynamic disorder with random energy barriers, the probability density functional of the rate coefficient is also given by our scaling law. The relative growth rates of different biological organs (allometry) can be described by a similar approach. Our scaling law also emerges by studying the variation of macroscopic phenotypic variables in terms of genotypic growth rates. We study the implications of the causality principle for our theory and derive a set of generalized Kramers–Kronig relationships for the fractal scaling exponents. PMID:17360340
Michallek, Florian; Dewey, Marc
2017-04-01
To introduce a novel hypothesis and method to characterise pathomechanisms underlying myocardial ischemia in chronic ischemic heart disease by local fractal analysis (FA) of the ischemic myocardial transition region in perfusion imaging. Vascular mechanisms to compensate ischemia are regulated at various vascular scales with their superimposed perfusion pattern being hypothetically self-similar. Dedicated FA software ("FraktalWandler") has been developed. Fractal dimensions during first-pass (FDfirst-pass) and recirculation (FDrecirculation) are hypothesised to indicate the predominating pathomechanism and ischemic severity, respectively. Twenty-six patients with evidence of myocardial ischemia in 108 ischemic myocardial segments on magnetic resonance imaging (MRI) were analysed. The 40th and 60th percentiles of FDfirst-pass were used for pathomechanical classification, assigning lesions with FDfirst-pass ≤ 2.335 to predominating coronary microvascular dysfunction (CMD) and ≥2.387 to predominating coronary artery disease (CAD). Optimal classification point in ROC analysis was FDfirst-pass = 2.358. FDrecirculation correlated moderately with per cent diameter stenosis in invasive coronary angiography in lesions classified CAD (r = 0.472, p = 0.001) but not CMD (r = 0.082, p = 0.600). The ischemic transition region may provide information on pathomechanical composition and severity of myocardial ischemia. FA of this region is feasible and may improve diagnosis compared to traditional noninvasive myocardial perfusion analysis. • A novel hypothesis and method is introduced to pathophysiologically characterise myocardial ischemia. • The ischemic transition region appears a meaningful diagnostic target in perfusion imaging. • Fractal analysis may characterise pathomechanical composition and severity of myocardial ischemia.
Image compression for functional imaging
NASA Astrophysics Data System (ADS)
Feng, Dagan D.; Li, Xianjin; Siu, Wan-Chi
1997-04-01
Function imaging has been playing an important role in modern biomedical research and clinical diagnosis, which provides human internal biochemical information previously not available. However, for a routine dynamic study with a typical medical function imaging system, such as positron emission tomography (PET), it is easily to acquire nearly 1000 images for just one patient in one study. Such a large number of images has given a considerable burden for computer image storage space, data processing and transmission time. In this paper, we present the theory and principles for the minimization of image frames in dynamic biomedical function imaging. We show that the minimum number of image frames required is just equal to the model identifiable parameters and that the quality of the physiological parameter estimation, based on these minimum number of image frames, can be controlled at a comparable level. As a result of our study, the image storage space required can be reduced by more than 80 percent.
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.
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.
Fractal dimension of sparkles in automotive metallic coatings by multispectral imaging measurements.
Medina, José M; Díaz, José A; Vignolo, Carlos
2014-07-23
Sparkle in surface coatings is a property of mirror-like pigment particles that consists of remarkable bright spots over a darker surround under unidirectional illumination. We developed a novel nondestructive method to characterize sparkles based on the multispectral imaging technique, and we focused on automotive metallic coatings containing aluminum flake pigments. Multispectral imaging was done in the visible spectrum at different illumination angles around the test sample. Reflectance spectra at different spatial positions were mapped to color coordinates and visualized in different color spaces. Spectral analysis shows that sparkles exhibit higher reflectance spectra and narrower bandwidths. Colorimetric analysis indicates that sparkles present higher lightness values and are far apart from the bulk of color coordinates spanned by the surround. A box-counting procedure was applied to examine the fractal organization of color coordinates in the CIE 1976 L*a*b* color space. A characteristic noninteger exponent was found at each illumination position. The exponent was independent of the illuminant spectra. Together, these results demonstrate that sparkles are extreme deviations relative to the surround and that their spectral properties can be described as fractal patterns within the color space. Multispectral reflectance imaging provides a powerful, noninvasive method for spectral identification and classification of sparkles from metal flake pigments on the micron scale.
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.
Angle closure glaucoma detection using fractal dimension index on SS-OCT images.
Ni, Soe Ni; Marzilianol, Pina; Wong, Hon-Tym
2014-01-01
Optical coherence tomography (OCT) is a high resolution, rapid and non-invasive screening tool for angle closure glaucoma. In this paper, we propose a new strategy for automatic and landmark invariant quantification of the anterior chamber angle of the eye using swept source optical coherence tomography (SS-OCT) images. Seven hundred and eight swept source optical coherence tomography SS-OCT images from 148 patients with average age of (59.48 ± 8.97) were analyzed in this study. The angle structure is measured by fractal dimension (FD) analysis to quantify the complexity or changes of angle recess. We evaluated the FD index with biometric parameters for classification of open angle and angle closure glaucoma. The proposed fractal dimension index gives a better representation of the angle configuration for capturing the nature of the angle dynamics involved in different forms of open and closed angle glaucoma (average FD (standard deviation): 1.944 (0.045) for open and 1.894 (0.043) for closed angle). It showed that the proposed approach has promising potential to become a computer aided diagnostic tool for angle closure glaucoma (ACG) disease.
NASA Astrophysics Data System (ADS)
Zhang, Changjiang; Chen, Yuan; Lu, Juan
2014-11-01
An efficient algorithm for typhoon center location is proposed using fractal feature and gradient of infrared satellite cloud image. The centers are generally located in this region for a typhoon except the latter disappearing typhoon. The characteristics of dense cloud region are smoother texture and higher gray values than those of marginal clouds. So the window analysis method is used to select an appropriate cloud region. The window whose difference value between the sum of the gray-gradient co-occurrence matrix and fractal dimension is the biggest is chosen as the dense cloud region. The temperature gradient of the region, which is near typhoon center except typhoon eye, is small. Thus the gradient information is strengthened and is calculated by canny operator. Then we use a window to traverse the dense cloud region. If there is a closed curve, the region of curve is considered as the typhoon center region. Otherwise, the region in which there is the most texture intersection and the biggest density is considered as the typhoon center region. Finally, the geometric center of the center region is determined as the typhoon center location. The effectiveness is test by Chinese FY-2C stationary satellite cloud image. And the result is compared with the typhoon center location in the "tropical cyclone yearbook" which was compiled by Shanghai typhoon institute of China meteorological administration. Experimental results show that the high location accuracy can be obtained.
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 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.
Wang, Jianji; Zheng, Nanning
2013-09-01
Fractal image compression (FIC) is an image coding technology based on the local similarity of image structure. It is widely used in many fields such as image retrieval, image denoising, image authentication, and encryption. FIC, however, suffers from the high computational complexity in encoding. Although many schemes are published to speed up encoding, they do not easily satisfy the encoding time or the reconstructed image quality requirements. In this paper, a new FIC scheme is proposed based on the fact that the affine similarity between two blocks in FIC is equivalent to the absolute value of Pearson's correlation coefficient (APCC) between them. First, all blocks in the range and domain pools are chosen and classified using an APCC-based block classification method to increase the matching probability. Second, by sorting the domain blocks with respect to APCCs between these domain blocks and a preset block in each class, the matching domain block for a range block can be searched in the selected domain set in which these APCCs are closer to APCC between the range block and the preset block. Experimental results show that the proposed scheme can significantly speed up the encoding process in FIC while preserving the reconstructed image quality well.
Dim target detection in IR image sequences based on fractal and rough set theory
NASA Astrophysics Data System (ADS)
Yan, Xiaoke; Shi, Caicheng; He, Peikun
2005-11-01
This paper addresses the problem of detecting small, moving, low amplitude in image sequences that also contain moving nuisance objects and background noise. Rough sets (RS) theory is applied in similarity relation instead of equivalence relation to solve clustering issue. We propose fractal-based texture analysis to describe texture coarseness and locally adaptive threshold technique to seek latent object point. Finally, according to temporal and spatial correlations between different frames, the singular points can be filtered. We demonstrate the effectiveness of the technique by applying it to real infrared image sequences containing targets of opportunity and evolving cloud clutter. The experimental results show that the algorithm can effectively increase detection probability and has robustness.
NASA Astrophysics Data System (ADS)
Alonso, Carmelo; Tarquis, Ana M.; Zúñiga, Ignacio; Benito, Rosa M.
2017-03-01
Several studies have shown that vegetation indexes can be used to estimate root zone soil moisture. Earth surface images, obtained by high-resolution satellites, presently give a lot of information on these indexes, based on the data of several wavelengths. Because of the potential capacity for systematic observations at various scales, remote sensing technology extends the possible data archives from the present time to several decades back. Because of this advantage, enormous efforts have been made by researchers and application specialists to delineate vegetation indexes from local scale to global scale by applying remote sensing imagery. In this work, four band images have been considered, which are involved in these vegetation indexes, and were taken by satellites Ikonos-2 and Landsat-7 of the same geographic location, to study the effect of both spatial (pixel size) and radiometric (number of bits coding the image) resolution on these wavelength bands as well as two vegetation indexes: the Normalized Difference Vegetation Index (NDVI) and the Enhanced Vegetation Index (EVI). In order to do so, a multi-fractal analysis of these multi-spectral images was applied in each of these bands and the two indexes derived. The results showed that spatial resolution has a similar scaling effect in the four bands, but radiometric resolution has a larger influence in blue and green bands than in red and near-infrared bands. The NDVI showed a higher sensitivity to the radiometric resolution than EVI. Both were equally affected by the spatial resolution. From both factors, the spatial resolution has a major impact in the multi-fractal spectrum for all the bands and the vegetation indexes. This information should be taken in to account when vegetation indexes based on different satellite sensors are obtained.
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.
N'Diaye, Mambaye; Degeratu, Cristinel; Bouler, Jean-Michel; Chappard, Daniel
2013-05-01
Porous structures are becoming more and more important in biology and material science because they help in reducing the density of the grafted material. For biomaterials, porosity also increases the accessibility of cells and vessels inside the grafted area. However, descriptors of porosity are scanty. We have used a series of biomaterials with different types of porosity (created by various porogens: fibers, beads …). Blocks were studied by microcomputed tomography for the measurement of 3D porosity. 2D sections were re-sliced to analyze the microarchitecture of the pores and were transferred to image analysis programs: star volumes, interconnectivity index, Minkowski-Bouligand and Kolmogorov fractal dimensions were determined. Lacunarity and succolarity, two recently described fractal dimensions, were also computed. These parameters provided a precise description of porosity and pores' characteristics. Non-linear relationships were found between several descriptors e.g. succolarity and star volume of the material. A linear correlation was found between lacunarity and succolarity. These techniques appear suitable in the study of biomaterials usable as bone substitutes. Copyright © 2013 Elsevier B.V. All rights reserved.
LETTER TO THE EDITOR: Fractal diffusion coefficient from dynamical zeta functions
NASA Astrophysics Data System (ADS)
Cristadoro, Giampaolo
2006-03-01
Dynamical zeta functions provide a powerful method to analyse low-dimensional dynamical systems when the underlying symbolic dynamics is under control. On the other hand, even simple one-dimensional maps can show an intricate structure of the grammar rules that may lead to a non-smooth dependence of global observables on parameters changes. A paradigmatic example is the fractal diffusion coefficient arising in a simple piecewise linear one-dimensional map of the real line. Using the Baladi-Ruelle generalization of the Milnor-Thurnston kneading determinant, we provide the exact dynamical zeta function for such a map and compute the diffusion coefficient from its smallest zero.
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.
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)
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)
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.
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.
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.
Jitaree, Sirinapa; Phinyomark, Angkoon; Boonyaphiphat, Pleumjit; Phukpattaranont, Pornchai
2015-01-01
Having a classifier of cell types in a breast cancer microscopic image (BCMI), obtained with immunohistochemical staining, is required as part of a computer-aided system that counts the cancer cells in such BCMI. Such quantitation by cell counting is very useful in supporting decisions and planning of the medical treatment of breast cancer. This study proposes and evaluates features based on texture analysis by fractal dimension (FD), for the classification of histological structures in a BCMI into either cancer cells or non-cancer cells. The cancer cells include positive cells (PC) and negative cells (NC), while the normal cells comprise stromal cells (SC) and lymphocyte cells (LC). The FD feature values were calculated with the box-counting method from binarized images, obtained by automatic thresholding with Otsu's method of the grayscale images for various color channels. A total of 12 color channels from four color spaces (RGB, CIE-L*a*b*, HSV, and YCbCr) were investigated, and the FD feature values from them were used with decision tree classifiers. The BCMI data consisted of 1,400, 1,200, and 800 images with pixel resolutions 128 × 128, 192 × 192, and 256 × 256, respectively. The best cross-validated classification accuracy was 93.87%, for distinguishing between cancer and non-cancer cells, obtained using the Cr color channel with window size 256. The results indicate that the proposed algorithm, based on fractal dimension features extracted from a color channel, performs well in the automatic classification of the histology in a BCMI. This might support accurate automatic cell counting in a computer-assisted system for breast cancer diagnosis.
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
Zhang, Luduan; Butler, Andrew J.; Sun, Chang-Kai; Sahgal, Vinod; Wittenberg, George F.; Yue, Guang H.
2008-01-01
Little is known about the association between brain white matter (WM) structure and motor function in humans. This study investigated complexity of brain WM interior shape as determined by magnetic resonance imaging (MRI) and its relationship with upper-extremity (UE) motor function in patients post stroke. We hypothesized that (1) the WM complexity would decrease following stroke, and (2) higher WM complexity in non-affected cortical areas would be related to greater UE motor function. Thirty-eight stroke patients (16 with left-hemisphere lesions) underwent MRI anatomical brain scans. Fractal dimension (FD), a quantitative shape metric, was applied onto skeletonized brain WM images to evaluate WM internal structural complexity. Wolf Motor Function Test (WMFT) and Fugl-Meyer Motor Assessment (FM) scores were measured to assess motor function of the affected limb. The WM complexity was lower in the stroke-affected hemisphere. The FD was associated with better motor function in two subgroups: with left-subcortical lesions, FD values of the lesion-free areas of the left hemisphere were associated with better FM scores; with right-cortical lesions, FD values of lesion-free regions were robustly associated with better WMFT scores. These findings suggest that greater residual WM complexity is associated with less impaired UE motor function, which is more robust in patients with right-hemisphere lesions. No correlations were found between lesion volume and WMFT or FM scores. This study addressed WM complexity in stroke patients and its relationship with UE motor function. Measurement of brain WM reorganization may be a sensitive correlate of UE function in people recovering from stroke. PMID:18590710
NASA Astrophysics Data System (ADS)
Wang, Qiang; Bi, Sheng
2017-01-01
To predict the peak signal-to-noise ratio (PSNR) quality of decoded images in fractal image coding more efficiently and accurately, an improved method is proposed. After some derivations and analyses, we find that the linear correlation coefficients between coded range blocks and their respective best-matched domain blocks can determine the dynamic range of their collage errors, which can also provide the minimum and the maximum of the accumulated collage error (ACE) of uncoded range blocks. Moreover, the dynamic range of the actual percentage of accumulated collage error (APACE), APACEmin to APACEmax, can be determined as well. When APACEmin reaches a large value, such as 90%, APACEmin to APACEmax will be limited in a small range and APACE can be computed approximately. Furthermore, with ACE and the approximate APACE, the ACE of all range blocks and the average collage error (ACER) can be obtained. Finally, with the logarithmic relationship between ACER and the PSNR quality of decoded images, the PSNR quality of decoded images can be predicted directly. Experiments show that compared with the previous similar method, the proposed method can predict the PSNR quality of decoded images more accurately and needs less computation time simultaneously.
Extreme value laws for fractal intensity functions in dynamical systems: Minkowski analysis
NASA Astrophysics Data System (ADS)
Mantica, Giorgio; Perotti, Luca
2016-09-01
Typically, in the dynamical theory of extremal events, the function that gauges the intensity of a phenomenon is assumed to be convex and maximal, or singular, at a single, or at most a finite collection of points in phase-space. In this paper we generalize this situation to fractal landscapes, i.e. intensity functions characterized by an uncountable set of singularities, located on a Cantor set. This reveals the dynamical rôle of classical quantities like the Minkowski dimension and content, whose definition we extend to account for singular continuous invariant measures. We also introduce the concept of extremely rare event, quantified by non-standard Minkowski constants and we study its consequences to extreme value statistics. Limit laws are derived from formal calculations and are verified by numerical experiments. Dedicated to the memory of Joseph Ford, on the twentieth anniversary of his departure.
NASA Astrophysics Data System (ADS)
Jaroniec, Mietek; Kruk, Michal; Olivier, James
1995-11-01
Methods of calculating the fractal dimension (D) on the basis of single adsorption isotherms were critically tested by using argon composite adsorption isotherms for fractally porous solids. These isotherms were obtained from adsorption data for homogeneous slit-like pores calculated by employing the density functional theory (DFT). The composite adsorption isotherms were used to test the validity of the method based on the Frenkel-Halsey-Hill equation and so called "thermodynamic method" proposed by Neimark. The applicability of these methods was confirmed. However, our studies reveal new aspects of practical usage of both approaches, which need to be taken into consideration in analysis of experimental data.
Adaptive reconfiguration of fractal small-world human brain functional networks.
Bassett, Danielle S; Meyer-Lindenberg, Andreas; Achard, Sophie; Duke, Thomas; Bullmore, Edward
2006-12-19
Brain function depends on adaptive self-organization of large-scale neural assemblies, but little is known about quantitative network parameters governing these processes in humans. Here, we describe the topology and synchronizability of frequency-specific brain functional networks using wavelet decomposition of magnetoencephalographic time series, followed by construction and analysis of undirected graphs. Magnetoencephalographic data were acquired from 22 subjects, half of whom performed a finger-tapping task, whereas the other half were studied at rest. We found that brain functional networks were characterized by small-world properties at all six wavelet scales considered, corresponding approximately to classical delta (low and high), , alpha, beta, and gamma frequency bands. Global topological parameters (path length, clustering) were conserved across scales, most consistently in the frequency range 2-37 Hz, implying a scale-invariant or fractal small-world organization. Dynamical analysis showed that networks were located close to the threshold of order/disorder transition in all frequency bands. The highest-frequency gamma network had greater synchronizability, greater clustering of connections, and shorter path length than networks in the scaling regime of (lower) frequencies. Behavioral state did not strongly influence global topology or synchronizability; however, motor task performance was associated with emergence of long-range connections in both beta and gamma networks. Long-range connectivity, e.g., between frontal and parietal cortex, at high frequencies during a motor task may facilitate sensorimotor binding. Human brain functional networks demonstrate a fractal small-world architecture that supports critical dynamics and task-related spatial reconfiguration while preserving global topological parameters.
Physiological Heterogeneity: Fractals Link Determinism and Randomness in Structures and Functions
Bassingthwaighte, James B.
2010-01-01
Spatial variation in concentrations or flows within an organ and temporal variation in reaction rates or flows appear to broaden as one refines the scale of observation. How can we characterize heterogeneity independently of scale? Fractals come to our rescue! A system is fractal if its features adhere to the same rules through a succession of different scales. Fractals efficiently describe many types of observations, geometric and kinetic, and help to integrate physiological knowledge. PMID:20871797
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.
Fractal morphology, imaging and mass spectrometry of single aerosol particles in flight.
Loh, N D; Hampton, C Y; Martin, A V; Starodub, D; Sierra, R G; Barty, A; Aquila, A; Schulz, J; Lomb, L; Steinbrener, J; Shoeman, R L; Kassemeyer, S; Bostedt, C; Bozek, J; Epp, S W; Erk, B; Hartmann, R; Rolles, D; Rudenko, A; Rudek, B; Foucar, L; Kimmel, N; Weidenspointner, G; Hauser, G; Holl, P; Pedersoli, E; Liang, M; Hunter, M S; Hunter, M M; Gumprecht, L; Coppola, N; Wunderer, C; Graafsma, H; Maia, F R N C; Ekeberg, T; Hantke, M; Fleckenstein, H; Hirsemann, H; Nass, K; White, T A; Tobias, H J; Farquar, G R; Benner, W H; Hau-Riege, S P; Reich, C; Hartmann, A; Soltau, H; Marchesini, S; Bajt, S; Barthelmess, M; Bucksbaum, P; Hodgson, K O; Strüder, L; Ullrich, J; Frank, M; Schlichting, I; Chapman, H N; Bogan, M J
2012-06-27
The morphology of micrometre-size particulate matter is of critical importance in fields ranging from toxicology to climate science, yet these properties are surprisingly difficult to measure in the particles' native environment. Electron microscopy requires collection of particles on a substrate; visible light scattering provides insufficient resolution; and X-ray synchrotron studies have been limited to ensembles of particles. Here we demonstrate an in situ method for imaging individual sub-micrometre particles to nanometre resolution in their native environment, using intense, coherent X-ray pulses from the Linac Coherent Light Source free-electron laser. We introduced individual aerosol particles into the pulsed X-ray beam, which is sufficiently intense that diffraction from individual particles can be measured for morphological analysis. At the same time, ion fragments ejected from the beam were analysed using mass spectrometry, to determine the composition of single aerosol particles. Our results show the extent of internal dilation symmetry of individual soot particles subject to non-equilibrium aggregation, and the surprisingly large variability in their fractal dimensions. More broadly, our methods can be extended to resolve both static and dynamic morphology of general ensembles of disordered particles. Such general morphology has implications in topics such as solvent accessibilities in proteins, vibrational energy transfer by the hydrodynamic interaction of amino acids, and large-scale production of nanoscale structures by flame synthesis.
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 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…
NASA Astrophysics Data System (ADS)
Pepe, S.; Di Martino, G.; Iodice, A.; Manzo, M.; Pepe, A.; Riccio, D.; Ruello, G.; Sansosti, E.; Tizzani, P.; Zinno, I.
2012-04-01
In the last two decades several aspects relevant to volcanic activity have been analyzed in terms of fractal parameters that effectively describe natural objects geometry. More specifically, these researches have been aimed at the identification of (1) the power laws that governed the magma fragmentation processes, (2) the energy of explosive eruptions, and (3) the distribution of the associated earthquakes. In this paper, the study of volcano morphology via satellite images is dealt with; in particular, we use the complete forward model developed by some of the authors (Di Martino et al., 2012) that links the stochastic characterization of amplitude Synthetic Aperture Radar (SAR) images to the fractal dimension of the imaged surfaces, modelled via fractional Brownian motion (fBm) processes. Based on the inversion of such a model, a SAR image post-processing has been implemented (Di Martino et al., 2010), that allows retrieving the fractal dimension of the observed surfaces, dictating the distribution of the roughness over different spatial scales. The fractal dimension of volcanic structures has been related to the specific nature of materials and to the effects of active geodynamic processes. Hence, the possibility to estimate the fractal dimension from a single amplitude-only SAR image is of fundamental importance for the characterization of volcano structures and, moreover, can be very helpful for monitoring and crisis management activities in case of eruptions and other similar natural hazards. The implemented SAR image processing performs the extraction of the point-by-point fractal dimension of the scene observed by the sensor, providing - as an output product - the map of the fractal dimension of the area of interest. In this work, such an analysis is performed on Cosmo-SkyMed, ERS-1/2 and ENVISAT images relevant to active stratovolcanoes in different geodynamic contexts, such as Mt. Somma-Vesuvio, Mt. Etna, Vulcano and Stromboli in Southern Italy, Shinmoe
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.
Liu, Shuai; Wang, Yinyan; Xu, Kaibin; Wang, Zheng; Fan, Xing; Zhang, Chuanbao; Li, Shaowu; Qiu, Xiaoguang; Jiang, Tao
2017-08-16
Necrosis is a hallmark feature of glioblastoma (GBM). This study investigated the prognostic role of necrotic patterns in GBM using fractal dimension (FD) and lacunarity analyses of magnetic resonance imaging (MRI) data and evaluated the role of lacunarity in the biological processes leading to necrosis. We retrospectively reviewed clinical and MRI data of 95 patients with GBM. FD and lacunarity of the necrosis on MRI were calculated by fractal analysis and subjected to survival analysis. We also performed gene ontology analysis in 32 patients with available RNA-seq data. Univariate analysis revealed that FD < 1.56 and lacunarity > 0.46 significantly correlated with poor progression-free survival (p = 0.006 and p = 0.012, respectively) and overall survival (p = 0.008 and p = 0.005, respectively). Multivariate analysis revealed that both parameters were independent factors for unfavorable progression-free survival (p = 0.001 and p = 0.015, respectively) and overall survival (p = 0.002 and p = 0.007, respectively). Gene ontology analysis revealed that genes positively correlated with lacunarity were involved in the suppression of apoptosis and necrosis-associated biological processes. We demonstrate that the fractal parameters of necrosis in GBM can predict patient survival and are associated with the biological processes of tumor necrosis.
Radlinski, A.P.; Radlinska, E.Z.; Agamalian, M.; Wignall, G.D.; Lindner, P.; Randl, O.G.
1999-04-01
The analysis of small- and ultra-small-angle neutron scattering data for sedimentary rocks shows that the pore-rock fabric interface is a surface fractal (D{sub s}=2.82) over 3 orders of magnitude of the length scale and 10 orders of magnitude in intensity. The fractal dimension and scatterer size obtained from scanning electron microscopy image processing are consistent with neutron scattering data. {copyright} {ital 1999} {ital The American Physical Society}
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.)
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.)
NASA Astrophysics Data System (ADS)
Strichartz, Robert S.; Usher, Michael
2000-09-01
A general theory of piecewise multiharmonic splines is constructed for a class of fractals (post-critically finite) that includes the familiar Sierpinski gasket, based on Kigami's theory of Laplacians on these fractals. The spline spaces are the analogues of the spaces of piecewise Cj polynomials of degree 2j + 1 on an interval, with nodes at dyadic rational points. We give explicit algorithms for effectively computing multiharmonic functions (solutions of [Delta]j+1u = 0) and for constructing bases for the spline spaces (for general fractals we need to assume that j is odd), and also for computing inner products of these functions. This enables us to give a finite element method for the approximate solution of fractal differential equations. We give the analogue of Simpson's method for numerical integration on the Sierpinski gasket. We use splines to approximate functions vanishing on the boundary by functions vanishing in a neighbourhood of the boundary.
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.
NASA Astrophysics Data System (ADS)
West, Bruce J.
The proper methodology for describing the dynamics of certain complex phenomena and fractal time series is the fractional calculus through the fractional Langevin equation discussed herein and applied in a biomedical context. We show that a fractional operator (derivative or integral) acting on a fractal function, yields another fractal function, allowing us to construct a fractional Langevin equation to describe the evolution of a fractal statistical process, for example, human gait and cerebral blood flow. The goal of this talk is to make clear how certain complex phenomena, such as those that are abundantly present in human physiology, can be faithfully described using dynamical models involving fractional differential stochastic equations. These models are tested against existing data sets and shown to describe time series from complex physiologic phenomena quite well.
NASA Astrophysics Data System (ADS)
Beech, M.
1989-02-01
The author discusses some of the more recent research on fractal astronomy and results presented in several astronomical studies. First, the large-scale structure of the universe is considered, while in another section one drops in scale to examine some of the smallest bodies in our solar system; the comets and meteoroids. The final section presents some thoughts on what influence the fractal ideology might have on astronomy, focusing particularly on the question recently raised by Kadanoff, "Fractals: where's the physics?"
[Power-law species richness accumulation as manifestation of the fractal community structure].
Gelashvili, D B; Iudin, D I; Rozenberg, G S; Iakimov, N V
2007-01-01
Applications of the fractal to describing the species structure of communities are discussed. Fundamental notions of fractal geometry are explained in the first part. The problem of applying the concept of fractal to describe the spatial allocation of particular species and of community as a whole is reviewed in the second part. In the final part, the usage of the selfsimirity principle for analyzing community organization is substantiated, and evidence of the fractal structure of biocenoses is presented according to Whittaker's concept of alpha diversity. It is shown that community is characterized, as a fractal object, by scale invariance, by power function relationship between the number of structural elements of the community (individuals, populations, species) and the scale (sampling effort), and, finally, by fractional value of the power (fractal dimension). Power function is the formula the takes into account the share of rare species, or species represented by a single individual. providing for no saturation of the function f(x). This formula also does not contradict the A.P. Levich's "rule of ecological non-additivity" and, lastly, allows the application of fractal formalism to characterize the species structure of a community. It is concluded that the mathematical image of species richness is a monofractal, i.e., a set characterised by only one parameter, fractal dimension. Thus, the species structure of a community (as well as the pattern of its spatial allocation) displays self-similarity and is a fractal.
Modeling Fractal Structure of City-Size Distributions Using Correlation Functions
Chen, Yanguang
2011-01-01
Zipf's law is one the most conspicuous empirical facts for cities, however, there is no convincing explanation for the scaling relation between rank and size and its scaling exponent. Using the idea from general fractals and scaling, I propose a dual competition hypothesis of city development to explain the value intervals and the special value, 1, of the power exponent. Zipf's law and Pareto's law can be mathematically transformed into one another, but represent different processes of urban evolution, respectively. Based on the Pareto distribution, a frequency correlation function can be constructed. By scaling analysis and multifractals spectrum, the parameter interval of Pareto exponent is derived as (0.5, 1]; Based on the Zipf distribution, a size correlation function can be built, and it is opposite to the first one. By the second correlation function and multifractals notion, the Pareto exponent interval is derived as [1, 2). Thus the process of urban evolution falls into two effects: one is the Pareto effect indicating city number increase (external complexity), and the other the Zipf effect indicating city size growth (internal complexity). Because of struggle of the two effects, the scaling exponent varies from 0.5 to 2; but if the two effects reach equilibrium with each other, the scaling exponent approaches 1. A series of mathematical experiments on hierarchical correlation are employed to verify the models and a conclusion can be drawn that if cities in a given region follow Zipf's law, the frequency and size correlations will follow the scaling law. This theory can be generalized to interpret the inverse power-law distributions in various fields of physical and social sciences. PMID:21949753
Modeling fractal structure of city-size distributions using correlation functions.
Chen, Yanguang
2011-01-01
Zipf's law is one the most conspicuous empirical facts for cities, however, there is no convincing explanation for the scaling relation between rank and size and its scaling exponent. Using the idea from general fractals and scaling, I propose a dual competition hypothesis of city development to explain the value intervals and the special value, 1, of the power exponent. Zipf's law and Pareto's law can be mathematically transformed into one another, but represent different processes of urban evolution, respectively. Based on the Pareto distribution, a frequency correlation function can be constructed. By scaling analysis and multifractals spectrum, the parameter interval of Pareto exponent is derived as (0.5, 1]; Based on the Zipf distribution, a size correlation function can be built, and it is opposite to the first one. By the second correlation function and multifractals notion, the Pareto exponent interval is derived as [1, 2). Thus the process of urban evolution falls into two effects: one is the Pareto effect indicating city number increase (external complexity), and the other the Zipf effect indicating city size growth (internal complexity). Because of struggle of the two effects, the scaling exponent varies from 0.5 to 2; but if the two effects reach equilibrium with each other, the scaling exponent approaches 1. A series of mathematical experiments on hierarchical correlation are employed to verify the models and a conclusion can be drawn that if cities in a given region follow Zipf's law, the frequency and size correlations will follow the scaling law. This theory can be generalized to interpret the inverse power-law distributions in various fields of physical and social sciences.
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.
Fractal design concepts for stretchable electronics
NASA Astrophysics Data System (ADS)
Fan, Jonathan A.; Yeo, Woon-Hong; Su, Yewang; Hattori, Yoshiaki; Lee, Woosik; Jung, Sung-Young; Zhang, Yihui; Liu, Zhuangjian; Cheng, Huanyu; Falgout, Leo; Bajema, Mike; Coleman, Todd; Gregoire, Dan; Larsen, Ryan J.; Huang, Yonggang; Rogers, John A.
2014-02-01
Stretchable electronics provide a foundation for applications that exceed the scope of conventional wafer and circuit board technologies due to their unique capacity to integrate with soft materials and curvilinear surfaces. The range of possibilities is predicated on the development of device architectures that simultaneously offer advanced electronic function and compliant mechanics. Here we report that thin films of hard electronic materials patterned in deterministic fractal motifs and bonded to elastomers enable unusual mechanics with important implications in stretchable device design. In particular, we demonstrate the utility of Peano, Greek cross, Vicsek and other fractal constructs to yield space-filling structures of electronic materials, including monocrystalline silicon, for electrophysiological sensors, precision monitors and actuators, and radio frequency antennas. These devices support conformal mounting on the skin and have unique properties such as invisibility under magnetic resonance imaging. The results suggest that fractal-based layouts represent important strategies for hard-soft materials integration.
Fractal design concepts for stretchable electronics.
Fan, Jonathan A; Yeo, Woon-Hong; Su, Yewang; Hattori, Yoshiaki; Lee, Woosik; Jung, Sung-Young; Zhang, Yihui; Liu, Zhuangjian; Cheng, Huanyu; Falgout, Leo; Bajema, Mike; Coleman, Todd; Gregoire, Dan; Larsen, Ryan J; Huang, Yonggang; Rogers, John A
2014-01-01
Stretchable electronics provide a foundation for applications that exceed the scope of conventional wafer and circuit board technologies due to their unique capacity to integrate with soft materials and curvilinear surfaces. The range of possibilities is predicated on the development of device architectures that simultaneously offer advanced electronic function and compliant mechanics. Here we report that thin films of hard electronic materials patterned in deterministic fractal motifs and bonded to elastomers enable unusual mechanics with important implications in stretchable device design. In particular, we demonstrate the utility of Peano, Greek cross, Vicsek and other fractal constructs to yield space-filling structures of electronic materials, including monocrystalline silicon, for electrophysiological sensors, precision monitors and actuators, and radio frequency antennas. These devices support conformal mounting on the skin and have unique properties such as invisibility under magnetic resonance imaging. The results suggest that fractal-based layouts represent important strategies for hard-soft materials integration.
Fractal characterization and wettability of ion treated silicon surfaces
NASA Astrophysics Data System (ADS)
Yadav, R. P.; Kumar, Tanuj; Baranwal, V.; Vandana, Kumar, Manvendra; Priya, P. K.; Pandey, S. N.; Mittal, A. K.
2017-02-01
Fractal characterization of surface morphology can be useful as a tool for tailoring the wetting properties of solid surfaces. In this work, rippled surfaces of Si (100) are grown using 200 keV Ar+ ion beam irradiation at different ion doses. Relationship between fractal and wetting properties of these surfaces are explored. The height-height correlation function extracted from atomic force microscopic images, demonstrates an increase in roughness exponent with an increase in ion doses. A steep variation in contact angle values is found for low fractal dimensions. Roughness exponent and fractal dimensions are found correlated with the static water contact angle measurement. It is observed that after a crossover of the roughness exponent, the surface morphology has a rippled structure. Larger values of interface width indicate the larger ripples on the surface. The contact angle of water drops on such surfaces is observed to be lowest. Autocorrelation function is used for the measurement of ripple wavelength.
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.
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.
Imaging basal ganglia function
BROOKS, DAVID J.
2000-01-01
In this review, the value of functional imaging for providing insight into the role of the basal ganglia in motor control is reviewed. Brain activation findings in normal subjects and Parkinson's disease patients are examined and evidence supporting the existence for functionally independent distributed basal ganglia-frontal loops is presented. It is argued that the basal ganglia probably act to focus and filter cortical output, optimising the running of motor programs. PMID:10923986
The transience of virtual fractals.
Taylor, R P
2012-01-01
Artists have a long and fruitful tradition of exploiting electronic media to convert static images into dynamic images that evolve with time. Fractal patterns serve as an example: computers allow the observer to zoom in on virtual images and so experience the endless repetition of patterns in a matter that cannot be matched using static images. This year's featured cover artist, Susan Lowedermilk, instead plans to employ persistence of human vision to bring virtual fractals to life. This will be done by incorporating her prints of fractal patterns into zoetropes and phenakistoscopes.
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.
ERIC Educational Resources Information Center
Gray, Shirley B.
1992-01-01
This article traces the historical development of fractal geometry from early in the twentieth century and offers an explanation of the mathematics behind the recursion formulas and their representations within computer graphics. Also included are the fundamentals behind programing for fractal graphics in the C Language with appropriate…
The fractal heart — embracing mathematics in the cardiology clinic
Captur, Gabriella; Karperien, Audrey L.; Hughes, Alun D.; Francis, Darrel P.; Moon, James C.
2017-01-01
For clinicians grappling with quantifying the complex spatial and temporal patterns of cardiac structure and function (such as myocardial trabeculae, coronary microvascular anatomy, tissue perfusion, myocyte histology, electrical conduction, heart rate, and blood-pressure variability), fractal analysis is a powerful, but still underused, mathematical tool. In this Perspectives article, we explain some fundamental principles of fractal geometry and place it in a familiar medical setting. We summarize studies in the cardiovascular sciences in which fractal methods have successfully been used to investigate disease mechanisms, and suggest potential future clinical roles in cardiac imaging and time series measurements. We believe that clinical researchers can deploy innovative fractal solutions to common cardiac problems that might ultimately translate into advancements for patient care. PMID:27708281
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.
NASA Astrophysics Data System (ADS)
Wong, V. C.
2004-05-01
Fractal is a ubiquitous phenomenon. It can be classified as deterministic or stochastic. Deterministic fractals have been commonly generated by iterative function systems (e.g., Cantor set, Sierpinski carpet and Koch snowflake) or recurrence relation (e.g., Lyapunov fractal). Stochastic fractals involve random processes and they have been used to describe some highly irregular real-world phenomena (e.g., clouds and turbulence). Stochastic fractals have been investigated with local models (e.g., Diffusion Limited Aggregation, and Percolation), as well as non-local models (e.g., Dielectric Breakdown Model and Self Organization). The objective of this study is to construct a universal non-local model to provide a plausible explanation of the origination of fractal characteristic in a wide variety of natural phenomena, without taking into account the underlying microscopic physics on a detailed level. The natural phenomena under consideration include turbulence, river networks, soil hydrology, lightning, avalanches, earthquakes, volcanic activities and distribution of leaves, updrafts/downdrafts, rain areas, clouds, interstellar clouds, sunspots or galaxies.
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.
Ingvar, M
1999-01-01
Functional neuroimaging has fundamentally changed our knowledge about the cerebral representation of pain. For the first time it has been possible to delineate the functional anatomy of different aspects of pain in the medial and lateral pain systems in the brain. The rapid developments in imaging methods over the past years have led to a consensus in the description of the central pain responses between different studies and also to a definition of a central pain matrix with specialized subfunctions in man. In the near future we will see studies where a systems perspective allows for a better understanding of the regulatory mechanisms in the higher-order frontal and parietal cortices. Also, pending the development of experimental paradigms, the functional anatomy of the emotional aspects of pain will become better known. PMID:10466155
Li, Heheng; Luo, Liangping; Huang, Li
2011-02-01
The present paper is aimed to study the fractal spectrum of the cerebral computerized tomography in 158 normal infants of different age groups, based on the calculation of chaotic theory. The distribution range of neonatal period was 1.88-1.90 (mean = 1.8913 +/- 0.0064); It reached a stable condition at the level of 1.89-1.90 during 1-12 months old (mean = 1.8927 +/- 0.0045); The normal range of 1-2 years old infants was 1.86-1.90 (mean = 1.8863 +/- 4 0.0085); It kept the invariance of the quantitative value among 1.88-1.91(mean = 1.8958 +/- 0.0083) during 2-3 years of age. ANOVA indicated there's no significant difference between boys and girls (F = 0.243, P > 0.05), but the difference of age groups was significant (F = 8.947, P < 0.001). The fractal dimension of cerebral computerized tomography in normal infants computed by box methods was maintained at an efficient stability from 1.86 to 1.91. It indicated that there exit some attractor modes in pediatric brain development.
Fractal processes in soil water retention
Tyler, S.W.; Wheatcraft, S.W. )
1990-05-01
The authors propose a physical conceptual model for soil texture and pore structure that is based on the concept of fractal geometry. The motivation for a fractal model of soil texture is that some particle size distributions in granular soils have already been shown to display self-similar scaling that is typical of fractal objects. Hence it is reasonable to expect that pore size distributions may also display fractal scaling properties. The paradigm that they used for the soil pore size distribution is the Sierpinski carpet, which is a fractal that contains self similar holes (or pores) over a wide range of scales. The authors evaluate the water retention properties of regular and random Sierpinski carpets and relate these properties directly to the Brooks and Corey (or Campbell) empirical water retention model. They relate the water retention curves directly to the fractal dimension of the Sierpinski carpet and show that the fractal dimension strongly controls the water retention properties of the Sierpinski carpet soil. Higher fractal dimensions are shown to mimic clay-type soils, with very slow dewatering characteristics and relatively low fractal dimensions are shown to mimic a sandy soil with relatively rapid dewatering characteristics. Their fractal model of soil water retention removes the empirical fitting parameters from the soil water retention models and provides paramters which are intrinsic to the nature of the fractal porous structure. The relative permeability functions of Burdine and Mualem are also shown to be fractal directly from fractal water retention results.
Contour fractal analysis of grains
NASA Astrophysics Data System (ADS)
Guida, Giulia; Casini, Francesca; Viggiani, Giulia MB
2017-06-01
Fractal analysis has been shown to be useful in image processing to characterise the shape and the grey-scale complexity in different applications spanning from electronic to medical engineering (e.g. [1]). Fractal analysis consists of several methods to assign a dimension and other fractal characteristics to a dataset describing geometric objects. Limited studies have been conducted on the application of fractal analysis to the classification of the shape characteristics of soil grains. The main objective of the work described in this paper is to obtain, from the results of systematic fractal analysis of artificial simple shapes, the characterization of the particle morphology at different scales. The long term objective of the research is to link the microscopic features of granular media with the mechanical behaviour observed in the laboratory and in situ.
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 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.
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.
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).
Terahertz spectroscopy of plasmonic fractals.
Agrawal, A; Matsui, T; Zhu, W; Nahata, A; Vardeny, Z V
2009-03-20
We use terahertz time-domain spectroscopy to study the transmission properties of metallic films perforated with aperture arrays having deterministic or stochastic fractal morphologies ("plasmonic fractals"), and compare them with random aperture arrays. All of the measured plasmonic fractals show transmission resonances and antiresonances at frequencies that correspond to prominent features in their structure factors in k space. However, in sharp contrast to periodic aperture arrays, the resonant transmission enhancement decreases with increasing array size. This property is explained using a density-density correlation function, and is utilized for determining the underlying fractal dimensionality, D(<2). Furthermore, a sum rule for the transmission resonances and antiresonances in plasmonic fractals relative to the transmission of the corresponding random aperture arrays is obtained, and is shown to be universal.
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.
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.
Applications of fractals in ecology.
Sugihara, G; M May, R
1990-03-01
Fractal models describe the geometry of a wide variety of natural objects such as coastlines, island chains, coral reefs, satellite ocean-color images and patches of vegetation. Cast in the form of modified diffusion models, they can mimic natural and artificial landscapes having different types of complexity of shape. This article provides a brief introduction to fractals and reports on how they can be used by ecologists to answer a variety of basic questions, about scale, measurement and hierarchy in, ecological systems.
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…
Fractal structure of asphaltene aggregates.
Rahmani, Nazmul H G; Dabros, Tadeusz; Masliyah, Jacob H
2005-05-15
A photographic technique coupled with image analysis was used to measure the size and fractal dimension of asphaltene aggregates formed in toluene-heptane solvent mixtures. First, asphaltene aggregates were examined in a Couette device and the fractal-like aggregate structures were quantified using boundary fractal dimension. The evolution of the floc structure with time was monitored. The relative rates of shear-induced aggregation and fragmentation/restructuring determine the steady-state floc structure. The average floc structure became more compact or more organized as the floc size distribution attained steady state. Moreover, the higher the shear rate is, the more compact the floc structure is at steady state. Second, the fractal dimensions of asphaltene aggregates were also determined in a free-settling test. The experimentally determined terminal settling velocities and characteristic lengths of the aggregates were utilized to estimate the 2D and 3D fractal dimensions. The size-density fractal dimension (D(3)) of the asphaltene aggregates was estimated to be in the range from 1.06 to 1.41. This relatively low fractal dimension suggests that the asphaltene aggregates are highly porous and very tenuous. The aggregates have a structure with extremely low space-filling capacity.
Dougherty, G
2001-06-01
The structural integrity of trabecular bone is an important factor characterizing the biomechanical strength of the vertebra, and is determined by the connectivity of the bone network and the trabeculation pattern. These can be assessed using texture measures such as the fractal signature and lacunarity from a high resolution projection radiograph. Using central sections of lumbar vertebrae we compared the results obtained from high-resolution transverse projection images with those obtained from spatially registered low-resolution images from a conventional clinical CT scanner to determine whether clinical CT data can provide useful structural information. Provided the power spectra of the CT images are corrected for image system blurring, the resulting fractal signature is similar for both modalities. Although the CT images are blurred relative to the projection images, with a consequent reduction in lacunarity, the estimated trabecular separation obtained from the lacunarity plots is similar for both modalities. This suggests that these texture measures contain essential information on trabecular microarchitecture, which is present even in low resolution CT images. Such quantitative texture measurements from CT or MRI images are potentially useful in monitoring bone strength and predicting future fracture risk.
Losa, Gabriele A
2009-01-01
The extension of the concepts of Fractal Geometry (Mandelbrot [1983]) toward the life sciences has led to significant progress in understanding complex functional properties and architectural / morphological / structural features characterising cells and tissues during ontogenesis and both normal and pathological development processes. It has even been argued that fractal geometry could provide a coherent description of the design principles underlying living organisms (Weibel [1991]). Fractals fulfil a certain number of theoretical and methodological criteria including a high level of organization, shape irregularity, functional and morphological self-similarity, scale invariance, iterative pathways and a peculiar non-integer fractal dimension [FD]. Whereas mathematical objects are deterministic invariant or self-similar over an unlimited range of scales, biological components are statistically self-similar only within a fractal domain defined by upper and lower limits, called scaling window, in which the relationship between the scale of observation and the measured size or length of the object can be established (Losa and Nonnenmacher [1996]). Selected examples will contribute to depict complex biological shapes and structures as fractal entities, and also to show why the application of the fractal principle is valuable for measuring dimensional, geometrical and functional parameters of cells, tissues and organs occurring within the vegetal and animal realms. If the criteria for a strict description of natural fractals are met, then it follows that a Fractal Geometry of Life may be envisaged and all natural objects and biological systems exhibiting self-similar patterns and scaling properties may be considered as belonging to the new subdiscipline of "fractalomics".
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…
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…
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.
[Therapeutic function of images].
Aisenson Kogan, A
1986-03-01
The aim here searched is to explore the reasons why some systems of psychotherapy choose images as a means for attaining the cure. In one case at least (Roger Desoille's "awake dream"--the production and interpretation of images constitutes the basic procedure. The question arises: which sort of images? It is not dealt here with the oniric ones, but with the consciously created and must be called symbolic images. Almost every image that appears during a therapy session reveals a symbolic nature, but the very concept of symbol is not free from ambiguity some positions originated in different areas of investigation are mentioned, ending with a description of the traits that, according to the writer, bestow a symbolic character to images. These can be sensible ones or linguistic, as they appear in literary productions. Their importance as a factor of the psychotherapeutic change resides in the fact that symbolic images thus created are felt as not real events and at the same time containing subjective meaning. These two traits combine to lessen the anxiety before the confrontation with one's own impulses or feelings and at same time to stimulate towards new ways of behavior, until then desired -perhaps unconsciously- but too frightening to materialize in the real world.
Fractal features of seismic noise
NASA Astrophysics Data System (ADS)
Caserta, A.; Consolini, G.; Michelis, P. De
2003-04-01
We present experimental observations and data analysis concerning the fractal features of seismic noise in the frequency range from 1 Hz to 40 Hz. In detail, we investigate the 3D average squared soil displacement and the distribution function of its fluctuations for different near-surface geological structures. We found that the seismic noise is consistent with a persistent fractal brownian motion characterized by a Hurst exponent grather than 1/2. Moreover, a clear dependence of the fractal nature of the seismic noise on the near-surface local geology has been found.
NASA Astrophysics Data System (ADS)
Aushev, A. A.; Barinov, S. P.; Vasin, M. G.; Drozdov, Yu M.; Ignat'ev, Yu V.; Izgorodin, V. M.; Kovshov, D. K.; Lakhtikov, A. E.; Lukovkina, D. D.; Markelov, V. V.; Morovov, A. P.; Shishlov, V. V.
2015-06-01
We present the results of employing the alpha-spectrometry method to determine the characteristics of porous materials used in targets for laser plasma experiments. It is shown that the energy spectrum of alpha-particles, after their passage through porous samples, allows one to determine the distribution of their path length in the foam skeleton. We describe the procedure of deriving such a distribution, excluding both the distribution broadening due to statistical nature of the alpha-particle interaction with an atomic structure (straggling) and hardware effects. The fractal analysis of micro-images is applied to the same porous surface samples that have been studied by alpha-spectrometry. The fractal dimension and size distribution of the number of the foam skeleton grains are obtained. Using the data obtained, a distribution of the total foam skeleton thickness along a chosen direction is constructed. It roughly coincides with the path length distribution of alpha-particles within a range of larger path lengths. It is concluded that the combined use of the alpha-spectrometry method and fractal analysis of images will make it possible to determine the size distribution of foam skeleton grains (or pores). The results can be used as initial data in theoretical studies on propagation of the laser and X-ray radiation in specific porous samples.
Aushev, A A; Barinov, S P; Vasin, M G; Drozdov, Yu M; Ignat'ev, Yu V; Izgorodin, V M; Kovshov, D K; Lakhtikov, A E; Lukovkina, D D; Markelov, V V; Morovov, A P; Shishlov, V V
2015-06-30
We present the results of employing the alpha-spectrometry method to determine the characteristics of porous materials used in targets for laser plasma experiments. It is shown that the energy spectrum of alpha-particles, after their passage through porous samples, allows one to determine the distribution of their path length in the foam skeleton. We describe the procedure of deriving such a distribution, excluding both the distribution broadening due to statistical nature of the alpha-particle interaction with an atomic structure (straggling) and hardware effects. The fractal analysis of micro-images is applied to the same porous surface samples that have been studied by alpha-spectrometry. The fractal dimension and size distribution of the number of the foam skeleton grains are obtained. Using the data obtained, a distribution of the total foam skeleton thickness along a chosen direction is constructed. It roughly coincides with the path length distribution of alpha-particles within a range of larger path lengths. It is concluded that the combined use of the alpha-spectrometry method and fractal analysis of images will make it possible to determine the size distribution of foam skeleton grains (or pores). The results can be used as initial data in theoretical studies on propagation of the laser and X-ray radiation in specific porous samples. (laser plasma)
Pippa, Natassa; Pispas, Stergios; Demetzos, Costas
2014-09-01
The major advance of mixed liposomes (the so-called chimeric systems) is to control the size, structure, and morphology of these nanoassemblies, and therefore, system colloidal properties, with the aid of a large variety of parameters, such as chemical architecture and composition. The goal of this study is to investigate the alterations of the physicochemical and morphological characteristics of chimeric dipalmitoylphosphatidylcholine (DPPC) liposomes, caused by the incorporation of block and gradient copolymers (different macromolecular architecture) with different chemical compositions (different amounts of hydrophobic component). Light scattering techniques were utilized in order to characterize physicochemically and to delineate the fractal morphology of chimeric liposomes. In this study, we also investigated the structural differences between the prepared chimeric liposomes as are visualized by scanning electron microscopy (SEM). It could be concluded that all the chimeric liposomes have regular structure, as SEM images revealed, while their fractal dimensionality was found to be dependent on the macromolecular architecture of the polymeric guest.
Region-based fractal video coding
NASA Astrophysics Data System (ADS)
Zhu, Shiping; Belloulata, Kamel
2008-10-01
A novel video sequence compression scheme is proposed in order to realize the efficient and economical transmission of video sequence, and also the region-based functionality of MPEG-4. The CPM and NCIM fractal coding scheme is applied on each region independently by a prior image segmentation map (alpha plane) which is exactly the same as defined in MPEG-4. The first n frames of video sequence are encoded as a "set" using the Circular Prediction Mapping (CPM) and encode the remaining frames using the Non Contractive Interframe Mapping (NCIM). The CPM and NCIM accomplish the motion estimation and compensation, which can exploit the high temporal correlations between the adjacent frames of video sequence. The experimental results with the monocular video sequences provide promising performances at low bit rate coding, such as the application in video conference. We believe the proposed fractal video codec will be a powerful and efficient technique for the region-based video sequence coding.
Takeshita, Toshiki; Morita, Keishin; Tsutsui, Yuji; Kidera, Daisuke; Mikasa, Shohei; Maebatake, Akira; Akamatsu, Go; Miwa, Kenta; Baba, Shingo; Sasaki, Masayuki
2016-07-01
The purpose of this study was to investigate the influence of respiratory motion on the evaluation of the intratumoral heterogeneity of FDG uptake using cumulative SUV-volume histogram (CSH) and fractal analyses. We used an NEMA IEC body phantom with a homogeneous hot sphere phantom (HO) and two heterogeneous hot sphere phantoms (HE1 and HE2). The background radioactivity of (18)F in the NEMA phantom was 5.3 kBq/mL. The ratio of radioactivity was 4:2:1 for the HO and the outer rims of the HE1 and HE2 phantoms, the inner cores of the HE1 and HE2 phantoms, and background, respectively. Respiratory motion was simulated using a motion table with an amplitude of 2 cm. PET/CT data were acquired using Biograph mCT in motionless and moving conditions. The PET images were analyzed by both CSH and fractal analyses. The area under the CSH (AUC-CSH) and the fractal dimension (FD) was used as quantitative metrics. In motionless conditions, the AUC-CSHs of the HO (0.80), HE1 (0.75) and HE2 (0.65) phantoms were different. They did not differ in moving conditions (HO, 0.63; HE1, 0.65; HE2, 0.60). The FD of the HO phantom (0.77) was smaller than the FDs of the HE1 (1.71) and HE2 (1.98) phantoms in motionless conditions; however, the FDs of the HO (1.99) and HE1 (2.19) phantoms were not different from each other and were smaller than that of the HE2 (3.73) phantom in moving conditions. Respiratory motion affected the results of the CSH and fractal analyses for the evaluation of the heterogeneity of the PET/CT images. The influence of respiratory motion was considered to vary depending on the object size.
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.
Functional neurological disorders: imaging.
Voon, V
2014-10-01
Functional neurological disorders, also known as conversion disorder, are unexplained neurological symptoms. These symptoms are common and can be associated with significant consequences. This review covers the neuroimaging literature focusing on functional motor symptoms including motor functioning and upstream influences including self-monitoring and internal representations, voluntariness and arousal and trauma. Copyright © 2014. Published by Elsevier SAS.
Functional imaging in the fetus.
Schöpf, Veronika; Kasprian, Gregor; Prayer, Daniela
2011-06-01
This review focuses on the application of magnetic resonance imaging methods in utero studying functional brain development of spontaneous brain activity generated under resting conditions and of task-evoked activity using stimulation. These imaging approaches have been useful to explore the brain's functional organization during development, as already shown in different substantial resting-state studies in preterms. We also discuss emerging future directions regarding analyzing methods and combination of functional and structural connectivity approaches.
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...
Functional Imaging: CT and MRI
van Beek, Edwin JR; Hoffman, Eric A
2008-01-01
Synopsis Numerous imaging techniques permit evaluation of regional pulmonary function. Contrast-enhanced CT methods now allow assessment of vasculature and lung perfusion. Techniques using spirometric controlled MDCT allow for quantification of presence and distribution of parenchymal and airway pathology, Xenon gas can be employed to assess regional ventilation of the lungs and rapid bolus injections of iodinated contrast agent can provide quantitative measure of regional parenchymal perfusion. Advances in magnetic resonance imaging (MRI) of the lung include gadolinium-enhanced perfusion imaging and hyperpolarized helium imaging, which can allow imaging of pulmonary ventilation and .measurement of the size of emphysematous spaces. PMID:18267192
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.
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.
Fractal analysis of complex microstructure in castings
Lu, S.Z.; Lipp, D.C.; Hellawell, A.
1995-12-31
Complex microstructures in castings are usually characterized descriptively which often raises ambiguity and makes it difficult to relate the microstructure to the growth kinetics or mechanical properties in processing modeling. Combining the principle of fractal geometry and computer image processing techniques, it is feasible to characterize the complex microstructures numerically by the parameters of fractal dimension, D, and shape factor, a, without ambiguity. Procedures of fractal measurement and analysis are described, and a test case of its application to cast irons is provided. The results show that the irregular cast structures may all be characterized numerically by fractal analysis.
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.
Chappard, Daniel; Stancu, Izabela-Cristina
2015-04-01
Porosity is an important factor to consider in a large variety of materials. Porosity can be visualized in bone or 3D synthetic biomaterials by microcomputed tomography (microCT). Blocks of porous poly(2-hydroxyethyl methacrylate) were prepared with polystyrene beads of different diameter (500, 850, 1160 and 1560 μm) and analysed by microCT. On each 2D binarized microCT section, pixels of the pores which belong to the same image column received the same pseudo-colour according to a look up table. The same colour was applied on the same column of a frontal plane image which was constructed line by line from all images of the microCT stack. The fractal dimension Df of the frontal plane image was measured as well as the descriptors of the 3D models (porosity, 3D fractal dimension D3D, thickness, density and separation of material walls. Porosity, thickness Df and D3D increased with the size of the porogen beads. A linear correlation was observed between Df and D3D. This method provides quantitative and qualitative analysis of porosity on a single frontal plane image of a porous object. © 2014 The Authors Journal of Microscopy © 2014 Royal Microscopical Society.
Comparison of two fractal interpolation methods
NASA Astrophysics Data System (ADS)
Fu, Yang; Zheng, Zeyu; Xiao, Rui; Shi, Haibo
2017-03-01
As a tool for studying complex shapes and structures in nature, fractal theory plays a critical role in revealing the organizational structure of the complex phenomenon. Numerous fractal interpolation methods have been proposed over the past few decades, but they differ substantially in the form features and statistical properties. In this study, we simulated one- and two-dimensional fractal surfaces by using the midpoint displacement method and the Weierstrass-Mandelbrot fractal function method, and observed great differences between the two methods in the statistical characteristics and autocorrelation features. From the aspect of form features, the simulations of the midpoint displacement method showed a relatively flat surface which appears to have peaks with different height as the fractal dimension increases. While the simulations of the Weierstrass-Mandelbrot fractal function method showed a rough surface which appears to have dense and highly similar peaks as the fractal dimension increases. From the aspect of statistical properties, the peak heights from the Weierstrass-Mandelbrot simulations are greater than those of the middle point displacement method with the same fractal dimension, and the variances are approximately two times larger. When the fractal dimension equals to 1.2, 1.4, 1.6, and 1.8, the skewness is positive with the midpoint displacement method and the peaks are all convex, but for the Weierstrass-Mandelbrot fractal function method the skewness is both positive and negative with values fluctuating in the vicinity of zero. The kurtosis is less than one with the midpoint displacement method, and generally less than that of the Weierstrass-Mandelbrot fractal function method. The autocorrelation analysis indicated that the simulation of the midpoint displacement method is not periodic with prominent randomness, which is suitable for simulating aperiodic surface. While the simulation of the Weierstrass-Mandelbrot fractal function method has
Fractal pattern of canine trichoblastoma.
De Vico, Gionata; Cataldi, Marielda; Maiolino, Paola; Carella, Francesca; Beltraminelli, Stefano; Losa, Gabriele A
2011-06-01
To assess by fractal analysis the specific architecture, growth pattern, and tissue distribution that characterize subtypes of canine trichoblastoma, a benign tumor derived from or reduplicating the primitive hair germ of embryonic follicular development. Tumor masks and outlines obtained from immunohistologic images by gray threshold segmentation of epithelial components were analyzed by fractal and conventional morphometry. The fractal dimension [FD] of each investigated case was determined from the slope of the regression line describing the fractal region within a bi-asymptotic curve experimentally established. All tumor masks and outlines obtained by gray threshold segmentation of epithelial components showed fractal self-similar properties that were evaluated by peculiar FDs. However, only masks revealed significantly different FD values, ranging from 1.75 to 1.85, enabling the discrimination of canine trichoblastoma subtypes. The FD data suggest that an iterative morphogenetic process, involving both the air germ and associated dermal papilla, may be responsible of the peculiar tissue architecture of trichoblastoma. The present study emphasized the reliability of fractal analysis in achieving the objective characterization of canine trichoblastoma.
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.
Quantitative imaging of lymph function.
Sharma, Ruchi; Wang, Wei; Rasmussen, John C; Joshi, Amit; Houston, Jessica P; Adams, Kristen E; Cameron, Arlin; Ke, Shi; Kwon, Sunkuk; Mawad, Michel E; Sevick-Muraca, Eva M
2007-06-01
Functional lymphatic imaging was demonstrated in the abdomen and anterior hindlimb of anesthetized, intact Yorkshire swine by using near-infrared (NIR) fluorescence imaging following intradermal administration of 100-200 microl of 32 microM indocyanine green (ICG) and 64 microM hyaluronan NIR imaging conjugate to target the lymph vascular endothelial receptor (LYVE)-1 on the lymph endothelium. NIR fluorescence imaging employed illumination of 780 nm excitation light ( approximately 2 mW/cm(2)) and collection of 830 nm fluorescence generated from the imaging agents. Our results show the ability to image the immediate trafficking of ICG from the plexus, through the vessels and lymphangions, and to the superficial mammary, subiliac, and middle iliac lymph nodes, which were located as deep as 3 cm beneath the tissue surface. "Packets" of ICG-transited lymph vessels of 2-16 cm length propelled at frequencies of 0.5-3.3 pulses/min and velocities of 0.23-0.75 cm/s. Lymph propulsion was independent of respiration rate. In the case of the hyaluronan imaging agent, lymph propulsion was absent as the dye progressed immediately through the plexus and stained the lymph vessels and nodes. Lymph imaging required 5.0 and 11.9 microg of ICG and hyaluronan conjugate, respectively. Our results suggest that microgram quantities of NIR optical imaging agents and their conjugates have a potential to image lymph function in patients suffering from lymph-related disorders.
NASA Astrophysics Data System (ADS)
Banerjee, Amit; Banerjee, S. S.
2016-10-01
We investigate the formation of fractal like nano-structures on free standing gold films grown via surfactant mediated thin film growth process. We determine these structures to be confined within the first few monolayers of the thin film. Their chemical composition is identical to that of the Au film, although their density is different from the surrounding film. We observe changes in the morphology of these fractal structures by controlling the film growth rate, which spans across three orders of magnitude. From our study, we quantify the morphological changes in the fractal structure via a roundness parameter and we suggest an empirical relation between the roundness parameter and the growth rate. The study shows an inverse relationship between the roundness parameter and the growth rate and also that the fractal to compact morphological transition is continuous.
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.
Pribic, Jelena; Vasiljevic, Jelena; Kanjer, Ksenija; Konstantinovic, Zora Neskovic; Milosevic, Nebojsa T; Vukosavljevic, Dragica Nikolic; Radulovic, Marko
2015-01-01
Research in the field of breast cancer outcome prognosis has been focused on molecular biomarkers, while neglecting the discovery of novel tumor histology structural clues. We thus aimed to improve breast cancer prognosis by fractal analysis of tumor histomorphology. This retrospective study included 92 breast cancer patients without systemic treatment. Fractal dimension and lacunarity of the breast tumor microscopic histology possess prognostic value comparable to the major clinicopathological prognostic parameters. Fractal analysis was performed for the first time on routinely produced archived pan-tissue stained primary breast tumor sections, indicating its potential for clinical use as a simple and cost-effective prognostic indicator of distant metastasis risk to complement the molecular approaches for cancer risk prognosis.
Dynamics of fractals in Euclidean and measure spaces
NASA Astrophysics Data System (ADS)
Shahidul Islam, Md.; Jahurul Islam, Md.
2017-09-01
In this paper, we formulate iterated function system of the square fractal and three dimensional fractals such as the Mensger sponge and the Sierpinski tetrahedron using affine transformation method and fixed points method of Devaney [1]. We show that these functions are asymptotically stable and also the Lebesgue measures of these fractals are zero.
NASA Technical Reports Server (NTRS)
Harper, David William (Inventor)
2017-01-01
A structural support having fractal-stiffening and method of fabricating the support is presented where an optimized location of at least three nodes is predetermined prior to fabricating the structural support where a first set of webs is formed on one side of the support and joined to the nodes to form a first pocket region. A second set of webs is formed within the first pocket region forming a second pocket region where the height of the first set of webs extending orthogonally from the side of the support is greater than the second set of webs extending orthogonally from the support.
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.
Segmentation of histological structures for fractal analysis
NASA Astrophysics Data System (ADS)
Dixon, Vanessa; Kouznetsov, Alexei; Tambasco, Mauro
2009-02-01
Pathologists examine histology sections to make diagnostic and prognostic assessments regarding cancer based on deviations in cellular and/or glandular structures. However, these assessments are subjective and exhibit some degree of observer variability. Recent studies have shown that fractal dimension (a quantitative measure of structural complexity) has proven useful for characterizing structural deviations and exhibits great potential for automated cancer diagnosis and prognosis. Computing fractal dimension relies on accurate image segmentation to capture the architectural complexity of the histology specimen. For this purpose, previous studies have used techniques such as intensity histogram analysis and edge detection algorithms. However, care must be taken when segmenting pathologically relevant structures since improper edge detection can result in an inaccurate estimation of fractal dimension. In this study, we established a reliable method for segmenting edges from grayscale images. We used a Koch snowflake, an object of known fractal dimension, to investigate the accuracy of various edge detection algorithms and selected the most appropriate algorithm to extract the outline structures. Next, we created validation objects ranging in fractal dimension from 1.3 to 1.9 imitating the size, structural complexity, and spatial pixel intensity distribution of stained histology section images. We applied increasing intensity thresholds to the validation objects to extract the outline structures and observe the effects on the corresponding segmentation and fractal dimension. The intensity threshold yielding the maximum fractal dimension provided the most accurate fractal dimension and segmentation, indicating that this quantitative method could be used in an automated classification system for histology specimens.
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.
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.
Speckle interferometry from fiber-reinforced materials:A fractal geometry approach
NASA Astrophysics Data System (ADS)
Horta, J. M.; Castano, V. M.
Speckle field studies were performed on fiber-modified Portland cement-based microconcrete beam models subjected to flexural loading. The resulting speckle fields were analyzed in terms of their associated mass fractal dimension by using digital image processing techniques. The experiments showed a change in the fractal dimension of the speckle fields as a function both of the loading and the structure of the microconcrete beams. A study was also conducted on the free-damped frequencies of the beams, which allowed to draw a fractal dimension vs. frequency plot on each loading cycle. These results allow to foresee the use of fractal geometry as a promising tool for better understanding the mechanical behavior of structures.
Texture analysis of diagnostic x-ray images by use of fractals
NASA Astrophysics Data System (ADS)
Lundahl, T.; Ohley, W. J.; Kay, S. M.; White, H.; Williams, D. O.; Most, A. S.
1986-11-01
In this work a discrete fractional Brownian motion (FBM) model is applied to xray images as a measure of the regional texture. FBM is a generalization of ordinary Wiener-Levy Brownian motion. A Parameter H is introduced which describes the roughness of the realizations. Using generated realizations, a Cramer-Rao bound for the variance of an estimate of Hwas evaluated using asymptotic statistics. The results show that the accuracy of the estimate is independent of the true H. A maximum likelihood estimator is derived for H and applied to the data sets The results were close to the C-R bound. The MLE is then applied to sequences of digital coronary angiograms. The results show that the H parameter is a useful index by which to segment vessels from background noise.
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.
Church, E.L.
1988-04-15
Surface finish measurements are usually fitted to models of the finish correlation function which are parametrized in terms of root-mean-square roughnesses, sigma, and correlation lengths, l. Highly finished optical surfaces, however, are frequently better described by fractal models, which involve inverse power-law spectra and are parametrized by spectral strengths, K/sub n/, and spectral indices, n. Analyzing measurements of fractal surfaces in terms of sigma and l gives results which are not intrinsic surface parameters but which depend on the bandwidth parameters of the measurement process used. This paper derives expressions for these pseudoparameters and discusses the errors involved in using them for the characterization and specification of surface finish.
Church, E.L.
1988-01-01
Surface finish measurements are usually fitted to models of the finish correlation function which are parameterized in terms of root-mean-square roughness, sigma, and correlation lengths, l. Highly-finished optical surfaces, however, are frequently better described by fractal models, which involve inverse-power-law spectra and are parameterized by spectral strengths, K/sub n/, and spectral indices, n. Analyzing measurements of fractal surfaces in terms of sigma and l gives results which are not intrinsic surface parameters but which depend on the bandwidth parameters of the measurement process used. This paper derives expressions for these pseudo parameters and discusses the errors involved in using them for the characterization and specification of surface finish. 30 refs., 5 figs., 1 tab.
Retinal vascular fractals and cognitive impairment.
Ong, Yi-Ting; Hilal, Saima; Cheung, Carol Yim-Lui; Xu, Xin; Chen, Christopher; Venketasubramanian, Narayanaswamy; Wong, Tien Yin; Ikram, Mohammad Kamran
2014-05-01
Retinal microvascular network changes have been found in patients with age-related brain diseases such as stroke and dementia including Alzheimer's disease. We examine whether retinal microvascular network changes are also present in preclinical stages of dementia. This is a cross-sectional study of 300 Chinese participants (age: ≥60 years) from the ongoing Epidemiology of Dementia in Singapore study who underwent detailed clinical examinations including retinal photography, brain imaging and neuropsychological testing. Retinal vascular parameters were assessed from optic disc-centered photographs using a semiautomated program. A comprehensive neuropsychological battery was administered, and cognitive function was summarized as composite and domain-specific Z-scores. Cognitive impairment no dementia (CIND) and dementia were diagnosed according to standard diagnostic criteria. Among 268 eligible nondemented participants, 78 subjects were categorized as CIND-mild and 69 as CIND-moderate. In multivariable adjusted models, reduced retinal arteriolar and venular fractal dimensions were associated with an increased risk of CIND-mild and CIND-moderate. Reduced fractal dimensions were associated with poorer cognitive performance globally and in the specific domains of verbal memory, visuoconstruction and visuomotor speed. A sparser retinal microvascular network, represented by reduced arteriolar and venular fractal dimensions, was associated with cognitive impairment, suggesting that early microvascular damage may be present in preclinical stages of dementia.
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
NASA Astrophysics Data System (ADS)
Kunze, Herb; La Torre, Davide; Lin, Jianyi
2017-01-01
We consider the inverse problem associated with IFSM: Given a target function f , find an IFSM, such that its fixed point f ¯ is sufficiently close to f in the Lp distance. Forte and Vrscay [1] showed how to reduce this problem to a quadratic optimization model. In this paper, we extend the collage-based method developed by Kunze, La Torre and Vrscay ([2][3][4]), by proposing the minimization of the 1-norm instead of the 0-norm. In fact, optimization problems involving the 0-norm are combinatorial in nature, and hence in general NP-hard. To overcome these difficulties, we introduce the 1-norm and propose a Sequential Quadratic Programming algorithm to solve the corresponding inverse problem. As in Kunze, La Torre and Vrscay [3] in our formulation, the minimization of collage error is treated as a multi-criteria problem that includes three different and conflicting criteria i.e., collage error, entropy and sparsity. This multi-criteria program is solved by means of a scalarization technique which reduces the model to a single-criterion program by combining all objective functions with different trade-off weights. The results of some numerical computations are presented.
[Morphological and functional cartilage imaging].
Rehnitz, C; Weber, M-A
2014-06-01
Excellent morphological imaging of cartilage is now possible and allows the detection of subtle cartilage pathologies. Besides the standard 2D sequences, a multitude of 3D sequences are available for high-resolution cartilage imaging. The first part therefore deals with modern possibilities of morphological imaging. The second part deals with functional cartilage imaging with which it is possible to detect changes in cartilage composition and thus early osteoarthritis as well as to monitor biochemical changes after therapeutic interventions. Validated techniques such as delayed gadolinium-enhanced magnetic resonance imaging of cartilage (dGEMRIC) and T2 mapping as well the latest techniques, such as the glycosaminoglycan chemical exchange-dependent saturation transfer (gagCEST) technique will be discussed.
[Morphological and functional cartilage imaging].
Rehnitz, C; Weber, M-A
2015-04-01
Excellent morphological imaging of cartilage is now possible and allows the detection of subtle cartilage pathologies. Besides the standard 2D sequences, a multitude of 3D sequences are available for high-resolution cartilage imaging. The first part therefore deals with modern possibilities of morphological imaging. The second part deals with functional cartilage imaging with which it is possible to detect changes in cartilage composition and thus early osteoarthritis as well as to monitor biochemical changes after therapeutic interventions. Validated techniques such as delayed gadolinium-enhanced magnetic resonance imaging of cartilage (dGEMRIC) and T2 mapping as well the latest techniques, such as the glycosaminoglycan chemical exchange-dependent saturation transfer (gagCEST) technique will be discussed.
Isherwood, Zoey J; Schira, Mark M; Spehar, Branka
2017-02-01
Natural scenes share a consistent distribution of energy across spatial frequencies (SF) known as the 1/f(α) amplitude spectrum (α≈0.8-1.5, mean 1.2). This distribution is scale-invariant, which is a fractal characteristic of natural scenes with statistically similar structure at different spatial scales. While the sensitivity of the visual system to the 1/f properties of natural scenes has been studied extensively using psychophysics, relatively little is known about the tuning of cortical responses to these properties. Here, we use fMRI and retinotopic mapping techniques to measure and analyze BOLD responses in early visual cortex (V1, V2, and V3) to synthetic noise images that vary in their 1/f(α) amplitude spectra (α=0.25 to 2.25, step size: 0.50) and contrast levels (10% and 30%) (Experiment 1). To compare the dependence of the BOLD response between the photometric (intensity based) and geometric (fractal) properties of our stimuli, in Experiment 2 we compared grayscale noise images to their binary (thresholded) counterparts, which contain only black and white regions. In both experiments, early visual cortex responded maximally to stimuli generated to have an input 1/f slope corresponding to natural 1/f(α) amplitude spectra, and lower BOLD responses were found for steeper or shallower 1/f slopes (peak modulation: 0.59% for 1.25 vs. 0.31% for 2.25). To control for changing receptive field sizes, responses were also analyzed across multiple eccentricity bands in cortical surface space. For most eccentricity bands, BOLD responses were maximal for natural 1/f(α) amplitude spectra, but importantly there was no difference in the BOLD response to grayscale stimuli and their corresponding thresholded counterparts. Since the thresholding of an image changes its measured 1/f slope (α) but not its fractal characteristics, this suggests that neuronal responses in early visual cortex are not strictly driven by spectral slope values (photometric properties) but
Application of Fractal Dimension on Palsar Data
NASA Astrophysics Data System (ADS)
Singh, Dharmendra; Pant, Triloki
Study of land cover is the primal task of remote sensing where microwave imaging plays an important role. As an alternate of optical imaging, microwave, in particular, Synthetic Aperture Radar (SAR) imaging is very popular. With the advancement of technology, multi-polarized images are now available, e.g., ALOS-PALSAR (Phased Array type L-band SAR), which are beneficial because each of the polarization channel shows different sensitivity to various land features. Further, using the textural features, various land classes can be classified on the basis of the textural measures. One of the textural measure is fractal dimension. It is noteworthy that fractal dimension is a measure of roughness and thus various land classes can be distinguished on the basis of their roughness. The value of fractal dimension for the surfaces lies between 2.0 and 3.0 where 2.0 represents a smooth surface while 3.0 represents drastically rough surface. The study area covers subset images lying between 2956'53"N, 7750'32"E and 2950'40"N, 7757'19"E. The PALSAR images of the year 2007 and 2009 are considered for the study. In present paper a fractal based classification of PALSAR images has been performed for identification of Water, Urban and Agricultural Area. Since fractals represent the image texture, hence the present study attempts to find the fractal properties of land covers to distinguish them from one another. For the purpose a context has been defined on the basis of a moving window, which is used to estimate the local fractal dimension and then moved over the whole image. The size of the window is an important issue for estimation of textural measures which is considered to be 55 in present study. This procedure, in response, produces a textural map called fractal map. The fractal map is constituted with the help of local fractal dimension values and can be used for contextual classification. In order to study the fractal properties of PALSAR images, the three polarization images
2017-08-10
See Jupiter's Great Red Spot as you've never seen it before in this new Jovian work of art. Artist Mik Petter created this unique, digital artwork using data from the JunoCam imager on NASA's Juno spacecraft. The art form, known as fractals, uses mathematical formulas to create art with an infinite variety of form, detail, color and light. The tumultuous atmospheric zones in and around the Great Red Spot are highlighted by the author's use of colorful fractals. Vibrant colors of various tints and hues, combined with the almost organic-seeming shapes, make this image seem to be a colorized and crowded petri dish of microorganisms, or a close-up view of microscopic and wildly-painted seashells. The original JunoCam image was taken on July 10, 2017 at 7:10 p.m. PDT (10:10 p.m. EDT), as the Juno spacecraft performed its seventh close flyby of Jupiter. The spacecraft captured the image from about 8,648 miles (13,917 kilometers) above the tops of the clouds of the planet at a latitude of -32.6 degrees. https://photojournal.jpl.nasa.gov/catalog/PIA21777
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.
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.
Functional imaging for regenerative medicine.
Leahy, Martin; Thompson, Kerry; Zafar, Haroon; Alexandrov, Sergey; Foley, Mark; O'Flatharta, Cathal; Dockery, Peter
2016-04-19
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
Functional near-infrared imager
NASA Astrophysics Data System (ADS)
Luo, Qingming; Nioka, Shoko; Chance, Britton
1997-08-01
We developed a continuous wave (cw) light imaging probe which includes 9 light sources and four pairs detectors (each pair has one 850 nm filtered detector and one 760 nm filtered detector). The light sources are controlled by a computer and the signals from the detectors are converted and processed in the computer. There are 16 measurement sections and total detection area is 9 cm multiplied by 4 cm which can be scanned every 8 seconds. The detector-source uses 2.5 cm spacing. In this study, we present the noise, drift, detectivity and spatial resolution test results of the imager. Changes of oxygenation and blood volume in about 2 cm depth from the surface of brain model can be detected. The temporal resolution is 8 seconds and spatial resolution is about 2 cm. The detectivity of OD changes can reach 0.008. With this cw imaging probe, we measured motor function in motor cortex area, visual function in occipital area, and cognitive activity in frontal forehead area of the human brian when the subjects are stimulated by moving fingers, viewing a flashing light and doing an analogy test, respectively. The experimental results show that the cw imaging probe can be used for functional images of brain activity, base upon changes of oxygenation and blood volume due to the stimulus.
NASA Astrophysics Data System (ADS)
Orbach, R.
1986-02-01
Random structures often exhibit fractal geometry, defined in terms of the mass scaling exponent, D, the fractal dimension. The vibrational dynamics of fractal networks are expressed in terms of the exponent d double bar, the fracton dimensionality. The eigenstates on a fractal network are spatially localized for d double bar less than or equal to 2. The implications of fractal geometry are discussed for thermal transport on fractal networks. The electron-fracton interaction is developed, with a brief outline given for the time dependence of the electronic relaxation on fractal networks. It is suggested that amorphous or glassy materials may exhibit fractal properties at short length scales or, equivalently, at high energies. The calculations of physical properties can be used to test the fractal character of the vibrational excitations in these materials.
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.
Feltrin, Gian Pietro; Stramare, Roberto; Miotto, Diego; Giacomini, Dario; Saccavini, Claudio
2004-06-01
Fractal analysis is a quantitative method used to evaluate complex anatomic findings in their elementary component. Its application to biologic images, particularly to cancellous bones, has been well practiced within the past few years. The aims of these applications are to assess changes in bone and the loss of spongious architecture, indicate bone fragility, and to show the increased risk for fracture in primary or secondary osteoporosis. The applications are very promising to help complete the studies that can define bone density (bone mineral density by dual energy x-ray absorptiometry or quantitative computed tomography), and also have the capacity to distinguish the patients with a high or low risk for fracture. Their extension to the clinical fields, to define a test for fracture risk, is still limited by difficult application to the medical quantitative imaging of bones, between correct application at superficial bones and unreliable application to deep bones. The future evolution and validity do not depend upon fractal methods but upon well-detailed imaging of the bones in clinical conditions.
[Presurgical functional magnetic resonance imaging].
Stippich, C
2010-02-01
Functional magnetic resonance imaging (fMRI) is an important and novel neuroimaging modality for patients with brain tumors. By non-invasive measurement, localization and lateralization of brain activiation, most importantly of motor and speech function, fMRI facilitates the selection of the most appropriate and sparing treatment and function-preserving surgery. Prerequisites for the diagnostic use of fMRI are the application of dedicated clinical imaging protocols and standardization of the respective imaging procedures. The combination with diffusion tensor imaging (DTI) also enables tracking and visualization of important fiber bundles such as the pyramidal tract and the arcuate fascicle. These multimodal MR data can be implemented in computer systems for functional neuronavigation or radiation treatment. The practicability, accuracy and reliability of presurgical fMRI have been validated by large numbers of published data. However, fMRI cannot be considered as a fully established modality of diagnostic neuroimaging due to the lack of guidelines of the responsible medical associations as well as the lack of medical certification of important hardware and software components. This article reviews the current research in the field and provides practical information relevant for presurgical fMRI.
Experiments in the use of fractal in computer pattern recognition
NASA Astrophysics Data System (ADS)
Sadjadi, Firooz A.
1993-10-01
The results of a study in the uses of fractal for the automatic detection of man made objects in infrared (IR) and millimeter wave (MMW) radar imagery are discussed in this paper. The fractal technique that is used is based on the estimation of the fractal dimensions of sequential blocks of an image of a scene and then by slicing the histogram of the computed fractal dimensions. The fractal dimension is computed by a Fourier regression approach. The technique is shown to be effective for the detection of tactical military vehicles in IR, and for the detection of airport attributes in MMW radar imagery.
Observing the Twinkling Fractal Nature of the Glass Transition
NASA Astrophysics Data System (ADS)
Stanzione, Joseph, III; Wool, Richard; Strawhecker, Kenneth
2010-03-01
The main idea underlying the Twinkling Fractal Theory (TFT) of the glass transition is the development of dynamic percolating solid fractal structures near Tg, which are in dynamic equilibrium with the surrounding liquid. Solid and liquid clusters interchange at a frequency φTF, which is controlled by the population of intermolecular oscillators in excited energy levels in accord with the Orbach vibrational density of states for a particular fractal cluster g(φ) ˜ φ^df-1, where the fracton dimension df = 4/3. To an observer, these clusters would appear to be ``twinkling.'' A time-lapse tapping-mode atomic force microscopy (AFM) technique has been developed in order to experimentally confirm such phenomena. The twinkling behavior of amorphous, atactic polystyrene with MW = 194,000 g/mol, PDI = 1.07 (GPC) and Tg = 375 K (DSC-heating rate of 3 K/min) has been captured above (383 K), below (358 K), and well below (298 K) its Tg. Two-dimensional space images reveal fractal dimensions consistent with the TFT. The twinkling behavior was analyzed using a statistical autocorrelation function in conjunction with the apparent stretched exponential Kohlrausch-Williams-Watts relaxation function.
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
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.
Dik, O E; Sviatogor, I A; Ishinova, V A; Nozdrachev, A D
2012-01-01
The task of estimation of the functional state of the human brain during psychotherapeutic treatment of psychogenic pain in patients with anxious phobic disorders is examined. For solving the task the methods of spectral and multifractal analyses of EEG fragments are applied during the perception of psychogenic pain and its removal by the psychorelaxation technique. Contrary to power spectra singularity spectra allow to distinguish EEGs quanitatively in the examined functional states of the human brain. The pain suppression in patients with anxious phobic disorders during psychorelaxation is accompanied by changing the width of the singularity spectrum and approximation of this multifractal partameter to the value corresponding to a healthy subject.
Fractal antenna and fractal resonator primer
NASA Astrophysics Data System (ADS)
Cohen, Nathan
2015-03-01
Self-similarity and fractals have opened new and important avenues for antenna and electronic solutions over the last 25 years. This primer provides an introduction to the benefits provided by fractal geometry in antennas, resonators, and related structures. Such benefits include, among many, wider bandwidths, smaller sizes, part-less electronic components, and better performance. Fractals also provide a new generation of optimized design tools, first used successfully in antennas but applicable in a general fashion.
NASA Astrophysics Data System (ADS)
Raupov, Dmitry S.; Myakinin, Oleg O.; Bratchenko, Ivan A.; Zakharov, Valery P.; Khramov, Alexander G.
2016-10-01
In this paper, we propose a report about our examining of the validity of OCT in identifying changes using a skin cancer texture analysis compiled from Haralick texture features, fractal dimension, Markov random field method and the complex directional features from different tissues. Described features have been used to detect specific spatial characteristics, which can differentiate healthy tissue from diverse skin cancers in cross-section OCT images (B- and/or C-scans). In this work, we used an interval type-II fuzzy anisotropic diffusion algorithm for speckle noise reduction in OCT images. The Haralick texture features as contrast, correlation, energy, and homogeneity have been calculated in various directions. A box-counting method is performed to evaluate fractal dimension of skin probes. Markov random field have been used for the quality enhancing of the classifying. Additionally, we used the complex directional field calculated by the local gradient methodology to increase of the assessment quality of the diagnosis method. Our results demonstrate that these texture features may present helpful information to discriminate tumor from healthy tissue. The experimental data set contains 488 OCT-images with normal skin and tumors as Basal Cell Carcinoma (BCC), Malignant Melanoma (MM) and Nevus. All images were acquired from our laboratory SD-OCT setup based on broadband light source, delivering an output power of 20 mW at the central wavelength of 840 nm with a bandwidth of 25 nm. We obtained sensitivity about 97% and specificity about 73% for a task of discrimination between MM and Nevus.
Fractal Analysis Of Colors And Shapes For Natural And Urbanscapes URBANSCAPES
NASA Astrophysics Data System (ADS)
Wang, J.; Ogawa, S.
2015-04-01
Fractal analysis has been applied in many fields since it was proposed by Mandelbrot in 1967. Fractal dimension is a basic parameter of fractal analysis. According to the difference of fractal dimensions for images, natural landscapes and urbanscapes could be differentiated, which is of great significance. In this paper, two methods were used for two types of landscape images to discuss the difference between natural landscapes and urbanscapes. Traditionally, a box-counting method was adopted to evaluate the shape of grayscale images. On the other way, for the spatial distributions of RGB values in images, the fractal Brownian motion (fBm) model was employed to calculate the fractal dimensions of colour images for two types of landscape images. From the results, the fractal dimensions of natural landscape images were lower than that of urbanscapes for both grayscale images and colour images with two types of methods. Moreover, the spatial distributions of RGB values in images were clearly related with the fractal dimensions. The results indicated that there was obvious difference (about 0.09) between the fractal dimensions for two kinds of landscapes. It was worthy to mention that when the correlation coefficient is 0 in the semivariogram, the fractal dimension is 2, which means that when the RGB values are completely random for their locations in the colour image, the fractal dimension becomes 3. Two kinds of fractal dimensions could evaluate the shape and the color distributions of landscapes and discriminate the natural landscapes from urbanscapes clearly.
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.
Hashemi, S. M.; Jagodič, U.; Mozaffari, M. R.; Ejtehadi, M. R.; Muševič, I.; Ravnik, M.
2017-01-01
Fractals are remarkable examples of self-similarity where a structure or dynamic pattern is repeated over multiple spatial or time scales. However, little is known about how fractal stimuli such as fractal surfaces interact with their local environment if it exhibits order. Here we show geometry-induced formation of fractal defect states in Koch nematic colloids, exhibiting fractal self-similarity better than 90% over three orders of magnitude in the length scales, from micrometers to nanometres. We produce polymer Koch-shaped hollow colloidal prisms of three successive fractal iterations by direct laser writing, and characterize their coupling with the nematic by polarization microscopy and numerical modelling. Explicit generation of topological defect pairs is found, with the number of defects following exponential-law dependence and reaching few 100 already at fractal iteration four. This work demonstrates a route for generation of fractal topological defect states in responsive soft matter. PMID:28117325
Thamrin, Cindy; Stern, Georgette; Frey, Urs
2010-06-01
There is increasing interest in the study of fractals in medicine. In this review, we provide an overview of fractals, of techniques available to describe fractals in physiological data, and we propose some reasons why a physician might benefit from an understanding of fractals and fractal analysis, with an emphasis on paediatric respiratory medicine where possible. Among these reasons are the ubiquity of fractal organisation in nature and in the body, and how changes in this organisation over the lifespan provide insight into development and senescence. Fractal properties have also been shown to be altered in disease and even to predict the risk of worsening of disease. Finally, implications of a fractal organisation include robustness to errors during development, ability to adapt to surroundings, and the restoration of such organisation as targets for intervention and treatment. Copyright 2010 Elsevier Ltd. All rights reserved.
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)
Hashemi, S M; Jagodič, U; Mozaffari, M R; Ejtehadi, M R; Muševič, I; Ravnik, M
2017-01-24
Fractals are remarkable examples of self-similarity where a structure or dynamic pattern is repeated over multiple spatial or time scales. However, little is known about how fractal stimuli such as fractal surfaces interact with their local environment if it exhibits order. Here we show geometry-induced formation of fractal defect states in Koch nematic colloids, exhibiting fractal self-similarity better than 90% over three orders of magnitude in the length scales, from micrometers to nanometres. We produce polymer Koch-shaped hollow colloidal prisms of three successive fractal iterations by direct laser writing, and characterize their coupling with the nematic by polarization microscopy and numerical modelling. Explicit generation of topological defect pairs is found, with the number of defects following exponential-law dependence and reaching few 100 already at fractal iteration four. This work demonstrates a route for generation of fractal topological defect states in responsive soft matter.
NASA Astrophysics Data System (ADS)
Hashemi, S. M.; Jagodič, U.; Mozaffari, M. R.; Ejtehadi, M. R.; Muševič, I.; Ravnik, M.
2017-01-01
Fractals are remarkable examples of self-similarity where a structure or dynamic pattern is repeated over multiple spatial or time scales. However, little is known about how fractal stimuli such as fractal surfaces interact with their local environment if it exhibits order. Here we show geometry-induced formation of fractal defect states in Koch nematic colloids, exhibiting fractal self-similarity better than 90% over three orders of magnitude in the length scales, from micrometers to nanometres. We produce polymer Koch-shaped hollow colloidal prisms of three successive fractal iterations by direct laser writing, and characterize their coupling with the nematic by polarization microscopy and numerical modelling. Explicit generation of topological defect pairs is found, with the number of defects following exponential-law dependence and reaching few 100 already at fractal iteration four. This work demonstrates a route for generation of fractal topological defect states in responsive soft matter.
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.
Fractal aggregates in Titan's atmosphere
NASA Astrophysics Data System (ADS)
Cabane, M.; Rannou, P.; Chassefiere, E.; Israel, G.
1993-04-01
The cluster structure of Titan's atmosphere was modeled by using an Eulerian microphysical model with the specific formulation of microphysical laws applying to fractal particles. The growth of aggregates in the settling phase was treated by introducing the fractal dimension as a parameter of the model. The model was used to obtain a vertical distribution of size and number density of the aggregates for different production altitudes. Results confirm previous estimates of the formation altitude of photochemical aerosols. The vertical profile of the effective radius of aggregates was calculated as a function of the visible optical depth.
Hydrodynamic behavior of fractal aggregates
NASA Astrophysics Data System (ADS)
Wiltzius, Pierre
1987-02-01
Measurements of the radius of gyration RG and the hydrodynamic radius RH of colloidal silica aggregates are reported. These aggregates have fractal geometry and RH is proportional to RG for 500 Å<=RH<=7000 Å, with a ratio RH/RG=0.72+/-0.02. The results are compared with predictions for macromolecules of various shapes. The proportionality of the two radii can be understood with use of the pair correlation function of fractal objects and hydrodynamic interactions on the Oseen level. The value of the ratio remains to be explained.
Fractal interpretation of intermittency
Hwa, R.C.
1991-12-01
Implication of intermittency in high-energy collisions is first discussed. Then follows a description of the fractal interpretation of intermittency. A basic quantity with asymptotic fractal behavior is introduced. It is then shown how the factorial moments and the G moments can be expressed in terms of it. The relationship between the intermittency indices and the fractal indices is made explicit.
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.…
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.…
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.
[Molecular structure and fractal analysis of oligosaccharide].
Liu, Wen-long; Wang, Lu-man; He, Dong-qi; Zhang, Tian-lan; Gou, Bao-di; Li, Qing
2014-10-18
To propose a calculation method of oligosaccharides' fractal dimension, and to provide a new approach to studying the drug molecular design and activity. By using the principle of energy optimization and computer simulation technology, the steady structures of oligosaccharides were found, and an effective way of oligosaccharides fractal dimension's calculation was further established by applying the theory of box dimension to the chemical compounds. By using the proposed method, 22 oligosaccharides' fractal dimensions were calculated, with the mean 1.518 8 ± 0.107 2; in addition, the fractal dimensions of the two activity multivalent oligosaccharides which were confirmed by experiments, An-2 and Gu-4, were about 1.478 8 and 1.516 0 respectively, while C-type lectin-like receptor Dectin-1's fractal dimension was about 1.541 2. The experimental and computational results were expected to help to find a class of glycoside drugs whose target receptor was Dectin-1. Fractal dimension, differing from other known macro parameters, is a useful tool to characterize the compound molecules' microscopic structure and function, which may play an important role in the molecular design and biological activity study. In the process of oligosaccharides drug screening, the fractal dimension of receptor and designed oligosaccharides or glycoclusters can be calculated respectively. The oligosaccharides with fractal dimension close to that of target receptor should then take priority compared with others, to get the drug molecules with latent activity.
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.
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…
Chamot, Stéphane; Migacheva, Elena; Seydoux, Olivier; Marquet, Pierre; Depeursinge, Christian
2010-11-08
The optical properties within limited volumes of diffusive media can be probed by carrying spatially-resolved measurements of diffused light at short source-detector separation (typically one scattering mean free path). At such distance, analytical models only relying on the absorption and reduced scattering coefficients fail at correctly predicting reflectance and it was demonstrated that adding a third optical coefficient γ improves the description of light propagation conditions near the source. In an attempt to relate the γ coefficient to physical properties of turbid media, this paper uses a fractal distribution law for modeling scatterers' sizes distributions and investigates numerically and experimentally how γ is related to the fractal power α. The results indicate that within the range of γ typically encountered in biological samples, this coefficient is approximately linearly correlated with α.
Exploring fractal behaviour of blood oxygen saturation in preterm babies
NASA Astrophysics Data System (ADS)
Zahari, Marina; Hui, Tan Xin; Zainuri, Nuryazmin Ahmat; Darlow, Brian A.
2017-04-01
Recent evidence has been emerging that oxygenation instability in preterm babies could lead to an increased risk of retinal injury such as retinopathy of prematurity. There is a potential that disease severity could be better understood using nonlinear methods for time series data such as fractal theories [1]. Theories on fractal behaviours have been employed by researchers in various disciplines who were motivated to look into the behaviour or structure of irregular fluctuations in temporal data. In this study, an investigation was carried out to examine whether fractal behaviour could be detected in blood oxygen time series. Detection for the presence of fractals in oxygen data of preterm infants was performed using the methods of power spectrum, empirical probability distribution function and autocorrelation function. The results from these fractal identification methods indicate the possibility that these data exhibit fractal nature. Subsequently, a fractal framework for future research was suggested for oxygen time series.
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.
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.
Functional imaging in chronic migraine.
Maniyar, Farooq H; Goadsby, Peter J
2013-05-01
Chronic migraine is a relatively common disorder in neurological terms that causes very significant disability at a high cost. The precise mechanisms behind the progression of episodic migraine to chronic migraine are not well understood. Functional neuro-imaging works on the basis that neuronal activations are associated with changes in regional cerebral blood flow, and it can help us answer some of these questions. In this review, we discuss important recent studies in chronic migraine or studies relating to increasing frequency of migraine attacks. The findings show that increasing frequency of migraine attacks is associated with changes in key brainstem areas, basal ganglia and various cortical areas involved in pain.
Quantitative evaluation of midpalatal suture maturation via fractal analysis
Kwak, Kyoung Ho; Kim, Yong-Il; Kim, Yong-Deok
2016-01-01
Objective The purpose of this study was to determine whether the results of fractal analysis can be used as criteria for midpalatal suture maturation evaluation. Methods The study included 131 subjects aged over 18 years of age (range 18.1–53.4 years) who underwent cone-beam computed tomography. Skeletonized images of the midpalatal suture were obtained via image processing software and used to calculate fractal dimensions. Correlations between maturation stage and fractal dimensions were calculated using Spearman's correlation coefficient. Optimal fractal dimension cut-off values were determined using a receiver operating characteristic curve. Results The distribution of maturation stages of the midpalatal suture according to the cervical vertebrae maturation index was highly variable, and there was a strong negative correlation between maturation stage and fractal dimension (−0.623, p < 0.001). Fractal dimension was a statistically significant indicator of dichotomous results with regard to maturation stage (area under curve = 0.794, p < 0.001). A test in which fractal dimension was used to predict the resulting variable that splits maturation stages into ABC and D or E yielded an optimal fractal dimension cut-off value of 1.0235. Conclusions There was a strong negative correlation between fractal dimension and midpalatal suture maturation. Fractal analysis is an objective quantitative method, and therefore we suggest that it may be useful for the evaluation of midpalatal suture maturation. PMID:27668195
Functional brain imaging across development.
Rubia, Katya
2013-12-01
The developmental cognitive neuroscience literature has grown exponentially over the last decade. This paper reviews the functional magnetic resonance imaging (fMRI) literature on brain function development of typically late developing functions of cognitive and motivation control, timing and attention as well as of resting state neural networks. Evidence shows that between childhood and adulthood, concomitant with cognitive maturation, there is progressively increased functional activation in task-relevant lateral and medial frontal, striatal and parieto-temporal brain regions that mediate these higher level control functions. This is accompanied by progressively stronger functional inter-regional connectivity within task-relevant fronto-striatal and fronto-parieto-temporal networks. Negative age associations are observed in earlier developing posterior and limbic regions, suggesting a shift with age from the recruitment of "bottom-up" processing regions towards "top-down" fronto-cortical and fronto-subcortical connections, leading to a more mature, supervised cognition. The resting state fMRI literature further complements this evidence by showing progressively stronger deactivation with age in anti-correlated task-negative resting state networks, which is associated with better task performance. Furthermore, connectivity analyses during the resting state show that with development increasingly stronger long-range connections are being formed, for example, between fronto-parietal and fronto-cerebellar connections, in both task-positive networks and in task-negative default mode networks, together with progressively lesser short-range connections, suggesting progressive functional integration and segregation with age. Overall, evidence suggests that throughout development between childhood and adulthood, there is progressive refinement and integration of both task-positive fronto-cortical and fronto-subcortical activation and task-negative deactivation, leading to
[Fractal analysis in the diagnosis of breast tumors].
Crişan, D A; Lesaru, M; Dobrescu, R; Vasilescu, C
2007-01-01
Last years studies made by researchers from over the world show that fractal geometry is a viable alternative for image analysis. Fractal features of natural forms give to fractal analysis new valences in various fields, medical imaging being a very important one. This paper intend to prove that fractal dimension, as a way to characterize the complexity of a form, can be used for diagnosis of mammographic lesions classified BI-RADS 4, further investigations being not necessary. The experiments made on 30 cases classified BI-RADS 4 confirmed that 89% of benign lesions have an average fractal dimension under the threshold 1.4, meanwhile malign lesions are characterized, in a similar percentage, by an average fractal dimension over that threshold.
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.
[Functional imaging in mental disorders].
Borbély, Katalin
2004-02-08
Considerable progress has been achieved by functional brain imaging over the past 20 years in uncovering the biological basis of major psychiatric disorders and to more effectively target therapeutics. Radioligand techniques, especially the PET (positron emission tomography) method, are specific and sensitive tools for quantitative in vivo imaging of molecular pathways and molecular interactions within brain tissues. Since 1980s, advances in neuroimaging and neurophysiological techniques have provided tremendous merits for investigations into different psychiatric disorders. PET and SPECT (single photon emission computer tomography) neuroreceptor imaging, especially in schizophrenia has been an extremely fruitful area of research. Evidences from these studies suggest that schizophrenia affects various cortical and subcortical regions involved in cognitive, emotional, and motivational aspects of human behavior. PET and SPECT provide useful data in studying the fundamental neurobiology of mood disorders. Both techniques are playing a central role in studying patients with new methods and ligands for specific receptor subtypes, and are likely to increase the application of PET/SPECT in the development of new pharmacotherapies. Nuclear medicine plays an important role in studying patients with other psychiatric disorders such as obsessive-compulsive disorder (OCD), attention deficit hyperactivity disorder (ADHD), anxiety, etc. Some forms of OCD seem to share a common genetic etiology with Tourette-syndrome (TS) and to be a facultative part of the TS phenotypic spectrum. In conclusion, PET and SPECT methods seem to be helpful in the diagnosis and management of patients with different psychiatric disorders and may provide a better understanding of clinical symptomatology or the relationship of these physiological parameters to the patient's prognosis. Additionally, radionuclide techniques may improve medical therapy by demonstrating individual biochemical abnormalities
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.
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.
Anatomical and functional imaging in endocrine hypertension
Chaudhary, Vikas; Bano, Shahina
2012-01-01
In endocrine hypertension, hormonal excess results in clinically significant hypertension. The functional imaging (such as radionuclide imaging) complements anatomy-based imaging (such as ultrasound, computed tomography, and magnetic resonance imaging) to facilitate diagnostic localization of a lesion causing endocrine hypertension. The aim of this review article is to familiarize general radiologists, endocrinologists, and clinicians with various anatomical and functional imaging techniques used in patients with endocrine hypertension. PMID:23087854
Oliveira, Naiara C; Silva, João H; Barros, Olga A; Pinheiro, Allysson P; Santana, William; Saraiva, Antônio A F; Ferreira, Odair P; Freire, Paulo T C; Paula, Amauri J
2015-10-06
We used here a scanning electron microscopy approach that detected backscattered electrons (BSEs) and X-rays (from ionization processes) along a large-field (LF) scan, applied on a Cretaceous fossil of a shrimp (area ∼280 mm(2)) from the Araripe Sedimentary Basin. High-definition LF images from BSEs and X-rays were essentially generated by assembling thousands of magnified images that covered the whole area of the fossil, thus unveiling morphological and compositional aspects at length scales from micrometers to centimeters. Morphological features of the shrimp such as pleopods, pereopods, and antennae located at near-surface layers (undetected by photography techniques) were unveiled in detail by LF BSE images and in calcium and phosphorus elemental maps (mineralized as hydroxyapatite). LF elemental maps for zinc and sulfur indicated a rare fossilization event observed for the first time in fossils from the Araripe Sedimentary Basin: the mineralization of zinc sulfide interfacing to hydroxyapatite in the fossil. Finally, a dimensional analysis of the phosphorus map led to an important finding: the existence of a fractal characteristic (D = 1.63) for the hydroxyapatite-matrix interface, a result of physical-geological events occurring with spatial scale invariance on the specimen, over millions of years.
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.
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
Functional imaging of decision conflict.
Pochon, Jean-Baptiste; Riis, Jason; Sanfey, Alan G; Nystrom, Leigh E; Cohen, Jonathan D
2008-03-26
Decision conflict occurs when people feel uncertain as to which option to choose from a set of similarly attractive (or unattractive) options, with many studies demonstrating that this conflict can lead to suboptimal decision making. In this article, we investigate the neurobiological underpinnings of decision conflict, in particular, the involvement of the anterior cingulate cortex (ACC). Previous studies have implicated the ACC in conflict monitoring during perceptual tasks, but there is considerable controversy as to whether the ACC actually indexes conflict related to choice, or merely conflict related to selection of competing motor responses. In a functional magnetic resonance imaging study, we dissociate the decision and response phases of a decision task, and show that the ACC does indeed index conflict at the decision stage. Furthermore, we show that it does so for a complex decision task, one that requires the integration of beliefs and preferences and not just perceptual judgments.
Molecular dynamics simulation of fractal aggregate diffusion
NASA Astrophysics Data System (ADS)
Pranami, Gaurav; Lamm, Monica H.; Vigil, R. Dennis
2010-11-01
The diffusion of fractal aggregates constructed with the method by Thouy and Jullien [J. Phys. A 27, 2953 (1994)10.1088/0305-4470/27/9/012] comprised of Np spherical primary particles was studied as a function of the aggregate mass and fractal dimension using molecular dynamics simulations. It is shown that finite-size effects have a strong impact on the apparent value of the diffusion coefficient (D) , but these can be corrected by carrying out simulations using different simulation box sizes. Specifically, the diffusion coefficient is inversely proportional to the length of a cubic simulation box, and the constant of proportionality appears to be independent of the aggregate mass and fractal dimension. Using this result, it is possible to compute infinite dilution diffusion coefficients (Do) for aggregates of arbitrary size and fractal dimension, and it was found that Do∝Np-1/df , as is often assumed by investigators simulating Brownian aggregation of fractal aggregates. The ratio of hydrodynamic radius to radius of gyration is computed and shown to be independent of mass for aggregates of fixed fractal dimension, thus enabling an estimate of the diffusion coefficient for a fractal aggregate based on its radius of gyration.
Fractal morphometry of cell complexity.
Losa, Gabriele A
2002-01-01
Irregularity and self-similarity under scale changes are the main attributes of the morphological complexity of both normal and abnormal cells and tissues. In other words, the shape of a self-similar object does not change when the scale of measurement changes, because each part of it looks similar to the original object. However, the size and geometrical parameters of an irregular object do differ when it is examined at increasing resolution, which reveals more details. Significant progress has been made over the past three decades in understanding how irregular shapes and structures in the physical and biological sciences can be analysed. Dominant influences have been the discovery of a new practical geometry of Nature, now known as fractal geometry, and the continuous improvements in computation capabilities. Unlike conventional Euclidean geometry, which was developed to describe regular and ideal geometrical shapes which are practically unknown in nature, fractal geometry can be used to measure the fractal dimension, contour length, surface area and other dimension parameters of almost all irregular and complex biological tissues. We have used selected examples to illustrate the application of the fractal principle to measuring irregular and complex membrane ultrastructures of cells at specific functional and pathological stage.
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)
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)
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)
NASA Astrophysics Data System (ADS)
Knutson, Paul; Dahlberg, E. Dan
2003-10-01
In examples of fractals such as moon craters, rivers,2 cauliflower,3 and bread,4 the actual growth process of the fractal object is missed. In the simple experiment described here, one can observe and record the growth of calcium carbonate crystals — a ubiquitous material found in marble and seashells — in real time. The video frames can be digitized and analyzed to determine the fractal dimension.
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.
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.
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.
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.
Automatic detection of microcalcifications with multi-fractal spectrum.
Ding, Yong; Dai, Hang; Zhang, Hang
2014-01-01
For improving the detection of micro-calcifications (MCs), this paper proposes an automatic detection of MC system making use of multi-fractal spectrum in digitized mammograms. The approach of automatic detection system is based on the principle that normal tissues possess certain fractal properties which change along with the presence of MCs. In this system, multi-fractal spectrum is applied to reveal such fractal properties. By quantifying the deviations of multi-fractal spectrums between normal tissues and MCs, the system can identify MCs altering the fractal properties and finally locate the position of MCs. The performance of the proposed system is compared with the leading automatic detection systems in a mammographic image database. Experimental results demonstrate that the proposed system is statistically superior to most of the compared systems and delivers a superior performance.
Investigations of human EEG response to viewing fractal patterns.
Hagerhall, Caroline M; Laike, Thorbjörn; Taylor, Richard P; Küller, Marianne; Küller, Rikard; Martin, Theodore P
2008-01-01
Owing to the prevalence of fractal patterns in natural scenery and their growing impact on cultures around the world, fractals constitute a common feature of our daily visual experiences, raising an important question: what responses do fractals induce in the observer? We monitored subjects' EEG while they were viewing fractals with different fractal dimensions, and the results show that significant effects could be found in the EEG even by employing relatively simple silhouette images. Patterns with a fractal dimension of 1.3 elicited the most interesting EEG, with the highest alpha in the frontal lobes but also the highest beta in the parietal area, pointing to a complicated interplay between different parts of the brain when experiencing this pattern.
Paradigms of Complexity: Fractals and Structures in the Sciences
NASA Astrophysics Data System (ADS)
Novak, Miroslav M.
The Table of Contents for the book is as follows: * Preface * The Origin of Complexity (invited talk) * On the Existence of Spatially Uniform Scaling Laws in the Climate System * Multispectral Backscattering: A Fractal-Structure Probe * Small-Angle Multiple Scattering on a Fractal System of Point Scatterers * Symmetric Fractals Generated by Cellular Automata * Bispectra and Phase Correlations for Chaotic Dynamical Systems * Self-Organized Criticality Models of Neural Development * Altered Fractal and Irregular Heart Rate Behavior in Sick Fetuses * Extract Multiple Scaling in Long-Term Heart Rate Variability * A Semi-Continous Box Counting Method for Fractal Dimension Measurement of Short Single Dimension Temporal Signals - Preliminary Study * A Fractional Brownian Motion Model of Cracking * Self-Affine Scaling Studies on Fractography * Coarsening of Fractal Interfaces * A Fractal Model of Ocean Surface Superdiffusion * Stochastic Subsurface Flow and Transport in Fractal Fractal Conductivity Fields * Rendering Through Iterated Function Systems * The σ-Hull - The Hull Where Fractals Live - Calculating a Hull Bounded by Log Spirals to Solve the Inverse IFS-Problem by the Detected Orbits * On the Multifractal Properties of Passively Convected Scalar Fields * New Statistical Textural Transforms for Non-Stationary Signals: Application to Generalized Mutlifractal Analysis * Laplacian Growth of Parallel Needles: Their Mullins-Sekerka Instability * Entropy Dynamics Associated with Self-Organization * Fractal Properties in Economics (invited talk) * Fractal Approach to the Regional Seismic Event Discrimination Problem * Fractal and Topological Complexity of Radioactive Contamination * Pattern Selection: Nonsingular Saffman-Taylor Finger and Its Dynamic Evolution with Zero Surface Tension * A Family of Complex Wavelets for the Characterization of Singularities * Stabilization of Chaotic Amplitude Fluctuations in Multimode, Intracavity-Doubled Solid-State Lasers * Chaotic
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
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.
Fractal dimension and architecture of trabecular bone.
Fazzalari, N L; Parkinson, I H
1996-01-01
The fractal dimension of trabecular bone was determined for biopsies from the proximal femur of 25 subjects undergoing hip arthroplasty. The average age was 67.7 years. A binary profile of the trabecular bone in the biopsy was obtained from a digitized image. A program written for the Quantimet 520 performed the fractal analysis. The fractal dimension was calculated for each specimen, using boxes whose sides ranged from 65 to 1000 microns in length. The mean fractal dimension for the 25 subjects was 1.195 +/- 0.064 and shows that in Euclidean terms the surface extent of trabecular bone is indeterminate. The Quantimet 520 was also used to perform bone histomorphometric measurements. These were bone volume/total volume (BV/TV) (per cent) = 11.05 +/- 4.38, bone surface/total volume (BS/TV) (mm2/mm3) = 1.90 +/- 0.51, trabecular thickness (Tb.Th) (mm) = 0.12 +/- 0.03, trabecular spacing (Tb.Sp) (mm) = 1.03 +/- 0.36, and trabecular number (Tb.N) (number/mm) = 0.95 +/- 0.25. Pearsons' correlation coefficients showed a statistically significant relationship between the fractal dimension and all the histomorphometric parameters, with BV/TV (r = 0.85, P < 0.0001), BS/TV (r = 0.74, P < 0.0001), Tb.Th (r = 0.50, P < 0.02), Tb.Sp (r = -0.81, P < 0.0001), and Tb.N (r = 0.76, P < 0.0001). This method for calculating fractal dimension shows that trabecular bone exhibits fractal properties over a defined box size, which is within the dimensions of a structural unit for trabecular bone. Therefore, the fractal dimension of trabecular bone provides a measure which does not rely on Euclidean descriptors in order to describe a complex geometry.
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 properties of financial markets
NASA Astrophysics Data System (ADS)
Budinski-Petković, Lj.; Lončarević, I.; Jakšić, Z. M.; Vrhovac, S. B.
2014-09-01
We present an analysis of the USA stock market using a simple fractal function. Financial bubbles preceding the 1987, 2000 and 2007 crashes are investigated using the Besicovitch-Ursell fractal function. Fits show a good agreement with the S&P 500 data when a complete financial growth is considered, starting at the threshold of the abrupt growth and ending at the peak. Moving the final time of the fitting interval towards earlier dates causes growing discrepancy between two curves. On the basis of a detailed analysis of the financial index behavior we propose a method for identifying the stage of the current financial growth and estimating the time in which the index value is going to reach the maximum.
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.
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.
Fractal analysis of cervical intraepithelial neoplasia.
Fabrizii, Markus; Moinfar, Farid; Jelinek, Herbert F; Karperien, Audrey; Ahammer, Helmut
2014-01-01
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. 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. 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. Fractal dimension can be considered to be an objective parameter to grade cervical intraepithelial neoplasia.
NASA Astrophysics Data System (ADS)
Warchalowski, Wiktor; Krawczyk, Malgorzata J.
2017-03-01
We found the Lindenmayer systems for line graphs built on selected fractals. We show that the fractal dimension of such obtained graphs in all analysed cases is the same as for their original graphs. Both for the original graphs and for their line graphs we identified classes of nodes which reflect symmetry of the graph.
NASA Astrophysics Data System (ADS)
Uzol, Oguz; Hazaveh, Hooman Amiri
2016-11-01
The 3D flow structure within the near wake of a four-iteration fractal square turbulence grid is obtained by combining data from closely-spaced horizontal and vertical two-dimensional PIV measurement planes. For this purpose, the grid is placed inside the entrance of the test section of a suction type wind tunnel. The experiments are conducted at a freestream velocity of 8 m/s, corresponding to a Reynolds number of 9000 based on effective mesh size. The freestream turbulence intensity is about 0.5%. The measurement volume extends about 7 effective mesh sizes downstream of the grid. Within the measurement volume, 1000 vector maps are obtained on each one of the 220 horizontal and 220 vertical 2D PIV planes that are separated from each other by 500 microns, which is close to the in-plane vector spacing of 600 microns. This dataset allowed us to calculate all components of mean velocity, velocity gradient tensor, and vorticity as well as the Reynolds stress tensor except for (v'w') component. Using the analyzed three-dimensional mean flow field data, we are able to observe the three dimensional structure of the wakes of the largest bars that dominate the flow field and the corresponding turbulence generation characteristics. We focus on how the wake geometry, decay characteristics and stress-strain relations get impacted by the presence of smaller wakes surrounding the largest wake regions. We also investigate how 3D mean flow non-uniformities get generated downstream of the grid such as lateral contraction and bulging of mean wake shapes.
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.}
Functional data analysis in brain imaging studies.
Tian, Tian Siva
2010-01-01
Functional data analysis (FDA) considers the continuity of the curves or functions, and is a topic of increasing interest in the statistics community. FDA is commonly applied to time-series and spatial-series studies. The development of functional brain imaging techniques in recent years made it possible to study the relationship between brain and mind over time. Consequently, an enormous amount of functional data is collected and needs to be analyzed. Functional techniques designed for these data are in strong demand. This paper discusses three statistically challenging problems utilizing FDA techniques in functional brain imaging analysis. These problems are dimension reduction (or feature extraction), spatial classification in functional magnetic resonance imaging studies, and the inverse problem in magneto-encephalography studies. The application of FDA to these issues is relatively new but has been shown to be considerably effective. Future efforts can further explore the potential of FDA in functional brain imaging studies.
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
Advances in noninvasive functional imaging of bone.
Lan, Sheng-Min; Wu, Ya-Na; Wu, Ping-Ching; Sun, Chi-Kuang; Shieh, Dar-Bin; Lin, Ruey-Mo
2014-02-01
The demand for functional imaging in clinical medicine is comprehensive. Although the gold standard for the functional imaging of human bones in clinical settings is still radionuclide-based imaging modalities, nonionizing noninvasive imaging technology in small animals has greatly advanced in recent decades, especially the diffuse optical imaging to which Britton Chance made tremendous contributions. The evolution of imaging probes, instruments, and computation has facilitated exploration in the complicated biomedical research field by allowing longitudinal observation of molecular events in live cells and animals. These research-imaging tools are being used for clinical applications in various specialties, such as oncology, neuroscience, and dermatology. The Bone, a deeply located mineralized tissue, presents a challenge for noninvasive functional imaging in humans. Using nanoparticles (NP) with multiple favorable properties as bioimaging probes has provided orthopedics an opportunity to benefit from these noninvasive bone-imaging techniques. This review highlights the historical evolution of radionuclide-based imaging, computed tomography, positron emission tomography, and magnetic resonance imaging, diffuse optics-enabled in vivo technologies, vibrational spectroscopic imaging, and a greater potential for using NPs for biomedical imaging.
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.
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.…
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.…
Thermodynamics of fractal universe
NASA Astrophysics Data System (ADS)
Sheykhi, Ahmad; Teimoori, Zeinab; Wang, Bin
2013-01-01
We investigate the thermodynamical properties of the apparent horizon in a fractal universe. We find that one can always rewrite the Friedmann equation of the fractal universe in the form of the entropy balance relation δQ=ThdSh, where δQ and Th are the energy flux and Unruh temperature seen by an accelerated observer just inside the apparent horizon. We find that the entropy Sh consists two terms, the first one which obeys the usual area law and the second part which is the entropy production term due to nonequilibrium thermodynamics of fractal universe. This shows that in a fractal universe, a treatment with nonequilibrium thermodynamics of spacetime may be needed. We also study the generalized second law of thermodynamics in the framework of fractal universe. When the temperature of the apparent horizon and the matter fields inside the horizon are equal, i.e. T=Th, the generalized second law of thermodynamics can be fulfilled provided the deceleration and the equation of state parameters ranges either as -1⩽q<0, -1⩽w<-1/3 or as q<-1, w<-1 which are consistent with recent observations. We also find that for Th=bT, with b<1, the GSL of thermodynamics can be secured in a fractal universe by suitably choosing the fractal parameter β.
NASA Astrophysics Data System (ADS)
McAteer, R. T. J.
2013-06-01
When Mandelbrot, the father of modern fractal geometry, made this seemingly obvious statement he was trying to show that we should move out of our comfortable Euclidean space and adopt a fractal approach to geometry. The concepts and mathematical tools of fractal geometry provides insight into natural physical systems that Euclidean tools cannot do. The benet from applying fractal geometry to studies of Self-Organized Criticality (SOC) are even greater. SOC and fractal geometry share concepts of dynamic n-body interactions, apparent non-predictability, self-similarity, and an approach to global statistics in space and time that make these two areas into naturally paired research techniques. Further, the iterative generation techniques used in both SOC models and in fractals mean they share common features and common problems. This chapter explores the strong historical connections between fractal geometry and SOC from both a mathematical and conceptual understanding, explores modern day interactions between these two topics, and discusses how this is likely to evolve into an even stronger link in the near future.
Improved Fourier-based characterization of intracellular fractal features
Xylas, Joanna; Quinn, Kyle P.; Hunter, Martin; Georgakoudi, Irene
2012-01-01
A novel Fourier-based image analysis method for measuring fractal features is presented which can significantly reduce artifacts due to non-fractal edge effects. The technique is broadly applicable to the quantitative characterization of internal morphology (texture) of image features with well-defined borders. In this study, we explore the capacity of this method for quantitative assessment of intracellular fractal morphology of mitochondrial networks in images of normal and diseased (precancerous) epithelial tissues. Using a combination of simulated fractal images and endogenous two-photon excited fluorescence (TPEF) microscopy, our method is shown to more accurately characterize the exponent of the high-frequency power spectral density (PSD) of these images in the presence of artifacts that arise due to cellular and nuclear borders. PMID:23188308
Magnetic resonance imaging based functional imaging in paediatric oncology.
Manias, Karen A; Gill, Simrandip K; MacPherson, Lesley; Foster, Katharine; Oates, Adam; Peet, Andrew C
2017-02-01
Imaging is central to management of solid tumours in children. Conventional magnetic resonance imaging (MRI) is the standard imaging modality for tumours of the central nervous system (CNS) and limbs and is increasingly used in the abdomen. It provides excellent structural detail, but imparts limited information about tumour type, aggressiveness, metastatic potential or early treatment response. MRI based functional imaging techniques, such as magnetic resonance spectroscopy, diffusion and perfusion weighted imaging, probe tissue properties to provide clinically important information about metabolites, structure and blood flow. This review describes the role of and evidence behind these functional imaging techniques in paediatric oncology and implications for integrating them into routine clinical practice. Copyright © 2016 Elsevier Ltd. All rights reserved.
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 imaging for prostate cancer: therapeutic implications.
Mari Aparici, Carina; Seo, Youngho
2012-09-01
Functional radionuclide imaging modalities, now commonly combined with anatomical imaging modalities computed tomography (CT) or magnetic resonance imaging (single photon emission computed tomography [SPECT]/CT, positron emission tomography [PET]/CT, and PET/magnetic resonance imaging), 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 regard 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, although 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.
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.
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
2015-09-07
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.
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
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
2013-11-01
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. © 2013 The Authors. Biological Reviews © 2013 Cambridge Philosophical Society.
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.
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.
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)
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)
Recognition of spatial weak targets based on fractal geometry
NASA Astrophysics Data System (ADS)
Zhu, Mengyu; Yang, Yuliang; Li, Dongxia
2005-11-01
Recognition of the interesting targets is the key techniques of precise guided weapon systems. Because fractal dimension is an interesting textual feature of an image, it has been used in many pattern recognition applications including classification and segmentation. According to the fractal feature of man-made objects in infrared images, a new algorithm is presented to detect the airplanes in this paper. And then we can partition and identify the potential targets using this fractal algorithm. Simulations illustrate that the airplane is successfully identified with the algorithm. The algorithm only requires moderate operations, so it is easy to be implemented for automatic target detection in real-time systems. The results of the experiments show that the fractal dimension can efficiently reflect the object surface complexity or irregularity in images. The algorithm is a powerful tool in identifying airplanes from infrared images.
Talbot effect of grating with fractal rough edges
NASA Astrophysics Data System (ADS)
Teng, Shuyun; Cui, Yuwei; Li, Zhong
2016-01-01
Since the random edges of practically manufactured grating can be described by the self-affine fractal model, this paper investigates theoretically Fresnel diffraction of grating with rough edges on the basis of the self-affine fractal theory and discusses the variation of the Talbot image of grating with the rough parameters of edges. The amplitude gratings with different rough edges are produced with the help of the correlation function of the random distribution. Then, simulations of the diffraction intensity distributions of rough gratings are performed, and the modulation effect of speckles on Talbot image are shown. In order to explain the variation of the Talbot image of grating with rough edges, the theoretical analysis of the Talbot effect of grating with rough edges is given according to the statistic optics theory. The presented approximate analytic expression of the average diffraction intensity indicates the relationship between the diffraction and rough parameters of grating edges. The conclusions of this paper are useful for evaluating the Talbot image of practical grating.
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.
NASA Astrophysics Data System (ADS)
Turcotte, Donald L.
Tectonic processes build landforms that are subsequently destroyed by erosional processes. Landforms exhibit fractal statistics in a variety of ways; examples include (1) lengths of coast lines; (2) number-size statistics of lakes and islands; (3) spectral behavior of topography and bathymetry both globally and locally; and (4) branching statistics of drainage networks. Erosional processes are dominant in the development of many landforms on this planet, but similar fractal statistics are also applicable to the surface of Venus where minimal erosion has occurred. A number of dynamical systems models for landforms have been proposed, including (1) cellular automata; (2) diffusion limited aggregation; (3) self-avoiding percolation; and (4) advective-diffusion equations. The fractal statistics and validity of these models will be discussed. Earthquakes also exhibit fractal statistics. The frequency-magnitude statistics of earthquakes satisfy the fractal Gutenberg-Richter relation both globally and locally. Earthquakes are believed to be a classic example of self-organized criticality. One model for earthquakes utilizes interacting slider-blocks. These slider block models have been shown to behave chaotically and to exhibit self-organized criticality. The applicability of these models will be discussed and alternative approaches will be presented. Fragmentation has been demonstrated to produce fractal statistics in many cases. Comminution is one model for fragmentation that yields fractal statistics. It has been proposed that comminution is also responsible for much of the deformation in the earth's crust. The brittle disruption of the crust and the resulting earthquakes present an integrated problem with many fractal aspects.
Baish, J W; Jain, R K
2000-07-15
Recent studies have shown that fractal geometry, a vocabulary of irregular shapes, can be useful for describing the pathological architecture of tumors and, perhaps more surprisingly, for yielding insights into the mechanisms of tumor growth and angiogenesis that complement those obtained by modern molecular methods. This article outlines the basic methods of fractal geometry and discusses the value and limitations of applying this new tool to cancer research.
Local connected fractal dimensions and lacunarity analyses of 60 degrees fluorescein angiograms.
Landini, G; Murray, P I; Misson, G P
1995-12-01
The retinal vascular tree exhibits fractal characteristics. These findings relate to the mechanisms involved in the vascularization process and to the objective morphologic characterization of retinal vessels using fractal analysis. Although normal retinas show uniform patterns of blood vessels, in pathologic retinas with central vein or artery occlusions, the patterns are irregular. Because the generalized box fractal dimension fails to differentiate successfully between normal and abnormal retinal vessels in 60 degrees fluorescein angiograms, the authors have further investigated this problem using the local connected fractal dimension (alpha). The authors studied 24 digitized 60 degrees fluorescein angiograms of patients with normal retinas and 5 angiograms of patients with central retinal vein or artery occlusion. The pointwise method estimated the local complexity of the angiogram within a finite window centered on those pixels that belong to the retinal vessels. Color-coded dimensional images of the angiograms were constructed by plotting the pixels forming the object with a color that corresponded to specific values of alpha +/- delta alpha. The color-coded representation allowed recognition of areas with increased or decreased local angiogram complexity. The alpha distributions showed differences between normal and pathologic retinas, which overcomes problems encountered when using the methods of calculating the generalized fractal dimensions. A multivariate linear discriminant function using parameters from the alpha distribution and a further fractal parameter--lacunarity--reclassified 23 of the 24 normal and 4 of the 5 pathologic angiograms in their original groups (total: 92.1% correct). This methodology may be used for automatic detection and objective characterization of local retinal vessel abnormalities.
Use of fractal zone plates for transmission X-ray microscopy.
Ge, Xin; Wang, Zhili; Gao, Kun; Wang, Dajiang; Wu, Zhao; Chen, Jian; Pan, Zhiyun; Zhang, Kai; Hong, Youli; Zhu, Peiping; Wu, Ziyu
2012-09-01
In this contribution we discuss the possibility of designing a modified transmission X-ray microscope by using fractal zone plates (Fzps) as diffractive optical elements. In the modified transmission X-ray microscope optical layout, we first introduced a fractal zone plate as the microscope objective. Indeed, a fractal zone plate cannot only be used as an image-forming component but also as a condenser element to achieve an extended depth of field. Numerical analysis reveals that fractal zone plates and conventional Fresnel zone plates have similar imaging capabilities under different coherent illumination. Using a fractal zone plate as a condenser we also simulated axial irradiance. Results confirm that fractal zone plates can improve focusing capability with an extended depth of field. Although preliminary, these simulations clearly reveal that fractal zone plates, when available, will be of great help in microscope layouts, in particular for foreseen high-resolution applications in the "water window" as strongly required in biological research.
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.
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.
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
Sánchez, Iván; Uzcátegui, Gladys
2011-04-01
To systematically review applications of fractal geometry in different aspects of dental practice. In this review, we present a short introduction to fractals and specifically address the following topics: treatment and healing monitoring, dental materials, dental tissue, caries, osteoporosis, periodontitis, cancer, Sjögren's syndrome, diagnosis of several other conditions and a discussion on the reliability of FD determinations from dental radiographs. Google Scholar, Ovid MEDLINE, ScienceDirect, etc. (up to August 2010). The review considered original studies, reviews and conference proceedings, published in English or Spanish. Abstracts and posters were not taken into account. Fractal geometry has found plenty of applications in several branches of dental practice. It provides a way to quantify the complexity of structures. Whereas one desires to study a radiograph, an histological section or the signal from a transducer, there are several methods available to determine the degree of complexity using fractal analysis. Several pathological conditions can alter the complexity of anatomical structures, and this change can be detectable with the help of fractal parameters. Although during the last two decades there have been plenty of works on the field, reported cases having enough reproducibility, with different groups showing similar results are not very common. Further replications are needed before we can establish statistically significant correlations amongst fractal parameters and pathological conditions. Copyright © 2011 Elsevier Ltd. All rights reserved.
Juergens, H.; Peitgen, H.O.; Saupe, D. )
1990-08-01
The pathological structures conjured up by 19th-century mathematicians have, in recent years, taken the form of fractals, mathematical figures that have fractional dimension rather than the integral dimensions of familiar geometric figures (such as one-dimensional lines or two-dimensional planes). Fractals are much more than a mathematical curiosity. They offer an extremely compact method for describing objects and formations. Many structures have an underlying geometric regularity, known as scale invariance or self-similarity. If one examines these objects at different size scales, one repeatedly encounters the same fundamental elements. The repetitive pattern defines the fractional, or fractal, dimension of the structure. Fractal geometry seems to describe natural shapes and forms more gracefully and succinctly than does Euclidean geometry. Scale invariance has a noteworthy parallel in contemporary chaos theory, which reveals that many phenomena, even though they follow strict deterministic rules, are in principle unpredictable. Chaotic events, such as turbulence in the atmosphere or the beating of a human heart, show similar patterns of variation on different time scales, much as scale-invariant objects show similar structural patterns on different spatial scales. The correspondence between fractals and chaos is no accident. Rather it is a symptom of a deep-rooted relation: fractal geometry is the geometry of chaos.
Trabecular Pattern Analysis Using Fractal Dimension
NASA Astrophysics Data System (ADS)
Ishida, Takayuki; Yamashita, Kazuya; Takigawa, Atsushi; Kariya, Komyo; Itoh, Hiroshi
1993-04-01
Feature extraction from a digitized image is advantageous for the detection of signs of disease. In this work, we attempted to evaluate bone trabecular pattern changes in osteoporosis using the fractal dimension and the root mean square (RMS) values. The relationship between the fractal dimension and the 1st moment of the power spectrum is explored, and we investigated the relationship between the results of this analysis and the bone mineral density (BMD) value which was measured using dual-energy X-ray absorptiometry (DEXA). As a result, we were able to extract useful information, using the fractal dimension and the RMS value of the radiographs (lateral view of the lumbar vertebrae), for the diagnosis of osteoporosis. Abnormal clinical cases were separated from normal cases based on the evaluation values. Negligible correlation between the BMD value and these indexes was observed.
Retinal fractals and acute lacunar stroke.
Cheung, Ning; Liew, Gerald; Lindley, Richard I; Liu, Erica Y; Wang, Jie Jin; Hand, Peter; Baker, Michelle; Mitchell, Paul; Wong, Tien Y
2010-07-01
This study aimed to determine whether retinal fractal dimension, a quantitative measure of microvascular branching complexity and density, is associated with lacunar stroke. A total of 392 patients presenting with acute ischemic stroke had retinal fractal dimension measured from digital photographs, and lacunar infarct ascertained from brain imaging. After adjusting for age, gender, and vascular risk factors, higher retinal fractal dimension (highest vs lowest quartile and per standard deviation increase) was independently and positively associated with lacunar stroke (odds ratio [OR], 4.27; 95% confidence interval [CI], 1.49-12.17 and OR, 1.85; 95% CI, 1.20-2.84, respectively). Increased retinal microvascular complexity and density is associated with lacunar stroke.
``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
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.
Towards new functional nanostructures for medical imaging
Matsuura, Naomi; Rowlands, J. A.
2008-10-15
Nanostructures represent a promising new type of contrast agent for clinical medical imaging modalities, including magnetic resonance imaging, x-ray computed tomography, ultrasound, and nuclear imaging. Currently, most nanostructures are simple, single-purpose imaging agents based on spherical constructs (e.g., liposomes, micelles, nanoemulsions, macromolecules, dendrimers, and solid nanoparticle structures). In the next decade, new clinical imaging nanostructures will be designed as multi-functional constructs, to both amplify imaging signals at disease sites and deliver localized therapy. Proposals for nanostructures to fulfill these new functions will be outlined. New functional nanostructures are expected to develop in five main directions: Modular nanostructures with additive functionality; cooperative nanostructures with synergistic functionality; nanostructures activated by their in vivo environment; nanostructures activated by sources outside the patient; and novel, nonspherical nanostructures and components. The development and clinical translation of next-generation nanostructures will be facilitated by a combination of improved clarity of the in vivo imaging and biological challenges and the requirements to successfully overcome them; development of standardized characterization and validation systems tailored for the preclinical assessment of nanostructure agents; and development of streamlined commercialization strategies and pipelines tailored for nanostructure-based agents for their efficient translation to the clinic.
Finite transformers for construction of fractal curves
Lisovik, L.P.
1995-01-01
In this paper we continue the study of infinite R{sup n}-transformers that can be used to define real functions and three-dimensional curves. An R{sup n}-transformer A generates an output n-tuple A(x) = (Y{sub 1},...,Y{sub n}), consisting of output binary representations. We have previously shown that finite R{sup n}-transformers with n = 1, 2 can be used to define a continuous, nowhere differentiable function and a Peano curve. Curves of this kind are objects of fractal geometry. Here we show that some other fractal curves, which are analogs of the Koch curve and the Sierpinski napkin, can be defined by finite R{sup 2}-transformers. R{sup n}-transformers (and also finite R{sup n}-transformers) thus provide a convenient tool for definition of fractal curves.
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.
On image analysis in fractography (Methodological Notes)
NASA Astrophysics Data System (ADS)
Shtremel', M. A.
2015-10-01
As other spheres of image analysis, fractography has no universal method for information convolution. An effective characteristic of an image is found by analyzing the essence and origin of every class of objects. As follows from the geometric definition of a fractal curve, its projection onto any straight line covers a certain segment many times; therefore, neither a time series (one-valued function of time) nor an image (one-valued function of plane) can be a fractal. For applications, multidimensional multiscale characteristics of an image are necessary. "Full" wavelet series break the law of conservation of information.
Functional Imaging and Migraine: New Connections?
Schwedt, Todd J.; Chong, Catherine D.
2015-01-01
Purpose of Review Over the last several years, a growing number of brain functional imaging studies have provided insights into mechanisms underlying migraine. This manuscript reviews the recent migraine functional neuroimaging literature and provides recommendations for future studies that will help fill knowledge gaps. Recent Findings Positron emission tomography (PET) and functional magnetic resonance imaging (fMRI) studies have identified brain regions that might be responsible for mediating the onset of a migraine attack and those associated with migraine symptoms. Enhanced activation of brain regions that facilitate processing of sensory stimuli suggests a mechanism by which migraineurs are hypersensitive to visual, olfactory, and cutaneous stimuli. Resting state functional connectivity MRI studies have identified numerous brain regions and functional networks with atypical functional connectivity in migraineurs, suggesting that migraine is associated with aberrant brain functional organization. Summary fMRI and PET studies that have identified brain regions and brain networks that are atypical in migraine have helped to describe the neurofunctional basis for migraine symptoms. Future studies should compare functional imaging findings in migraine to other headache and pain disorders and should explore the utility of functional imaging data as biomarkers for diagnostic and treatment purposes. PMID:25887764
Quantitative Amyloid Imaging Using Image-Derived Arterial Input Function
Su, Yi; Blazey, Tyler M.; Snyder, Abraham Z.; Raichle, Marcus E.; Hornbeck, Russ C.; Aldea, Patricia; Morris, John C.; Benzinger, Tammie L. S.
2015-01-01
Amyloid PET imaging is an indispensable tool widely used in the investigation, diagnosis and monitoring of Alzheimer’s disease (AD). Currently, a reference region based approach is used as the mainstream quantification technique for amyloid imaging. This approach assumes the reference region is amyloid free and has the same tracer influx and washout kinetics as the regions of interest. However, this assumption may not always be valid. The goal of this work is to evaluate an amyloid imaging quantification technique that uses arterial region of interest as the reference to avoid potential bias caused by specific binding in the reference region. 21 participants, age 58 and up, underwent Pittsburgh compound B (PiB) PET imaging and MR imaging including a time-of-flight (TOF) MR angiography (MRA) scan and a structural scan. FreeSurfer based regional analysis was performed to quantify PiB PET data. Arterial input function was estimated based on coregistered TOF MRA using a modeling based technique. Regional distribution volume (VT) was calculated using Logan graphical analysis with estimated arterial input function. Kinetic modeling was also performed using the estimated arterial input function as a way to evaluate PiB binding (DVRkinetic) without a reference region. As a comparison, Logan graphical analysis was also performed with cerebellar cortex as reference to obtain DVRREF. Excellent agreement was observed between the two distribution volume ratio measurements (r>0.89, ICC>0.80). The estimated cerebellum VT was in line with literature reported values and the variability of cerebellum VT in the control group was comparable to reported variability using arterial sampling data. This study suggests that image-based arterial input function is a viable approach to quantify amyloid imaging data, without the need of arterial sampling or a reference region. This technique can be a valuable tool for amyloid imaging, particularly in population where reference normalization
Quantitative amyloid imaging using image-derived arterial input function.
Su, Yi; Blazey, Tyler M; Snyder, Abraham Z; Raichle, Marcus E; Hornbeck, Russ C; Aldea, Patricia; Morris, John C; Benzinger, Tammie L S
2015-01-01
Amyloid PET imaging is an indispensable tool widely used in the investigation, diagnosis and monitoring of Alzheimer's disease (AD). Currently, a reference region based approach is used as the mainstream quantification technique for amyloid imaging. This approach assumes the reference region is amyloid free and has the same tracer influx and washout kinetics as the regions of interest. However, this assumption may not always be valid. The goal of this work is to evaluate an amyloid imaging quantification technique that uses arterial region of interest as the reference to avoid potential bias caused by specific binding in the reference region. 21 participants, age 58 and up, underwent Pittsburgh compound B (PiB) PET imaging and MR imaging including a time-of-flight (TOF) MR angiography (MRA) scan and a structural scan. FreeSurfer based regional analysis was performed to quantify PiB PET data. Arterial input function was estimated based on coregistered TOF MRA using a modeling based technique. Regional distribution volume (VT) was calculated using Logan graphical analysis with estimated arterial input function. Kinetic modeling was also performed using the estimated arterial input function as a way to evaluate PiB binding (DVRkinetic) without a reference region. As a comparison, Logan graphical analysis was also performed with cerebellar cortex as reference to obtain DVRREF. Excellent agreement was observed between the two distribution volume ratio measurements (r>0.89, ICC>0.80). The estimated cerebellum VT was in line with literature reported values and the variability of cerebellum VT in the control group was comparable to reported variability using arterial sampling data. This study suggests that image-based arterial input function is a viable approach to quantify amyloid imaging data, without the need of arterial sampling or a reference region. This technique can be a valuable tool for amyloid imaging, particularly in population where reference normalization may
Functional magnetic resonance imaging studies of language.
Small, Steven L; Burton, Martha W
2002-11-01
Functional neuroimaging of language builds on almost 150 years of study in neurology, psychology, linguistics, anatomy, and physiology. In recent years, there has been an explosion of research using functional imaging technology, especially positron emission tomography (PET) and functional magnetic resonance imaging (fMRI), to understand the relationship between brain mechanisms and language processing. These methods combine high-resolution anatomic images with measures of language-specific brain activity to reveal neural correlates of language processing. This article reviews some of what has been learned about the neuroanatomy of language from these imaging techniques. We first discuss the normal case, organizing the presentation according to the levels of language, encompassing words (lexicon), sound structure (phonemes), and sentences (syntax and semantics). Next, we delve into some unusual language processing circumstances, including second languages and sign languages. Finally, we discuss abnormal language processing, including developmental and acquired dyslexia and aphasia.
The fractal forest: fractal geometry and applications in forest science.
Nancy D. Lorimer; Robert G. Haight; Rolfe A. Leary
1994-01-01
Fractal geometry is a tool for describing and analyzing irregularity. Because most of what we measure in the forest is discontinuous, jagged, and fragmented, fractal geometry has potential for improving the precision of measurement and description. This study reviews the literature on fractal geometry and its applications to forest measurements.
Functional magnetic resonance imaging: imaging techniques and contrast mechanisms.
Howseman, A M; Bowtell, R W
1999-01-01
Functional magnetic resonance imaging (fMRI) is a widely used technique for generating images or maps of human brain activity. The applications of the technique are widespread in cognitive neuroscience and it is hoped they will eventually extend into clinical practice. The activation signal measured with fMRI is predicated on indirectly measuring changes in the concentration of deoxyhaemoglobin which arise from an increase in blood oxygenation in the vicinity of neuronal firing. The exact mechanisms of this blood oxygenation level dependent (BOLD) contrast are highly complex. The signal measured is dependent on both the underlying physiological events and the imaging physics. BOLD contrast, although sensitive, is not a quantifiable measure of neuronal activity. A number of different imaging techniques and parameters can be used for fMRI, the choice of which depends on the particular requirements of each functional imaging experiment. The high-speed MRI technique, echo-planar imaging provides the basis for most fMRI experiments. The problems inherent to this method and the ways in which these may be overcome are particularly important in the move towards performing functional studies on higher field MRI systems. Future developments in techniques and hardware are also likely to enhance the measurement of brain activity using MRI. PMID:10466145
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.
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.
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)
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
Functional minimization problems in image processing
NASA Astrophysics Data System (ADS)
Kim, Yunho; Vese, Luminita A.
2008-02-01
In this work we wish to recover an unknown image from a blurry version. We solve this inverse problem by energy minimization and regularization. We seek a solution of the form u + v, where u is a function of bounded variation (cartoon component), while v is an oscillatory component (texture), modeled by a Sobolev function with negative degree of differentiability. Experimental results show that this cartoon + texture model better recovers textured details in natural images, by comparison with the more standard models where the unknown is restricted only to the space of functions of bounded variation.
NASA Astrophysics Data System (ADS)
Marks-Tarlow, Terry
Linear concepts of time plus the modern capacity to track history emerged out of circular conceptions characteristic of ancient and traditional cultures. A fractal concept of time lies implicitly within the analog clock, where each moment is treated as unique. With fractal geometry the best descriptor of nature, qualities of self-similarity and scale invariance easily model her endless variety and recursive patterning, both in time and across space. To better manage temporal aspects of our lives, a fractal concept of time is non-reductive, based more on the fullness of being than on fragments of doing. By using a fractal concept of time, each activity or dimension of life is multiply and vertically nested. Each nested cycle remains simultaneously present, operating according to intrinsic dynamics and time scales. By adding the vertical axis of simultaneity to the horizontal axis of length, time is already full and never needs to be filled. To attend to time's vertical dimension is to tap into the imaginary potential for infinite depth. To switch from linear to fractal time allows us to relax into each moment while keeping in mind the whole.
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
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.
NASA Astrophysics Data System (ADS)
Lee, Bum Han; Lee, Sung Keun
2013-07-01
Despite the importance of understanding and quantifying the microstructure of porous networks in diverse geologic settings, the effects of the specific surface area and porosity on the key structural parameters of the networks have not been fully understood. We performed cube-counting fractal dimension (Dcc) and lacunarity analyses of 3D porous networks of model sands and configurational entropy analysis of 2D cross sections of model sands using random packing simulations and nuclear magnetic resonance (NMR) micro-imaging. We established relationships among porosity, specific surface area, structural parameters (Dcc and lacunarity), and the corresponding macroscopic properties (configurational entropy and permeability). The Dcc of the 3D porous networks increases with increasing specific surface area at a constant porosity and with increasing porosity at a constant specific surface area. Predictive relationships correlating Dcc, specific surface area, and porosity were also obtained. The lacunarity at the minimum box size decreases with increasing porosity, and that at the intermediate box size (∼0.469 mm in the current model sands) was reproduced well with specific surface area. The maximum configurational entropy increases with increasing porosity, and the entropy length of the pores decreases with increasing specific surface area and was used to calculate the average connectivity among the pores. The correlation among porosity, specific surface area, and permeability is consistent with the prediction from the Kozeny-Carman equation. From the relationship between the permeability and the Dcc of pores, the permeability can be expressed as a function of the Dcc of pores and porosity. The current methods and these newly identified correlations among structural parameters and properties provide improved insights into the nature of porous media and have useful geophysical and hydrological implications for elasticity and shear viscosity of complex composites of rock
Advantages in functional imaging of the brain
Mier, Walter; Mier, Daniela
2015-01-01
As neuronal pathologies cause only minor morphological alterations, molecular imaging techniques are a prerequisite for the study of diseases of the brain. The development of molecular probes that specifically bind biochemical markers and the advances of instrumentation have revolutionized the possibilities to gain insight into the human brain organization and beyond this—visualize structure-function and brain-behavior relationships. The review describes the development and current applications of functional brain imaging techniques with a focus on applications in psychiatry. A historical overview of the development of functional imaging is followed by the portrayal of the principles and applications of positron emission tomography (PET) and functional magnetic resonance imaging (fMRI), two key molecular imaging techniques that have revolutionized the ability to image molecular processes in the brain. We conclude that the juxtaposition of PET and fMRI in hybrid PET/MRI scanners enhances the significance of both modalities for research in neurology and psychiatry and might pave the way for a new area of personalized medicine. PMID:26042013
Fractal and Multifractal Analysis of Human Gait
NASA Astrophysics Data System (ADS)
Muñoz-Diosdado, A.; del Río Correa, J. L.; Angulo-Brown, F.
2003-09-01
We carried out a fractal and multifractal analysis of human gait time series of young and old individuals, and adults with three illnesses that affect the march: The Parkinson's and Huntington's diseases and the amyotrophic lateral sclerosis (ALS). We obtained cumulative plots of events, the correlation function, the Hurst exponent and the Higuchi's fractal dimension of these time series and found that these fractal markers could be a factor to characterize the march, since we obtained different values of these quantities for youths and adults and they are different also for healthy and ill persons and the most anomalous values belong to ill persons. In other physiological signals there is complexity lost related with the age and the illness, in the case of the march the opposite occurs. The multifractal analysis could be also a useful tool to understand the dynamics of these and other complex systems.
Pond fractals in a tidal flat.
Cael, B B; Lambert, Bennett; Bisson, Kelsey
2015-11-01
Studies over the past decade have reported power-law distributions for the areas of terrestrial lakes and Arctic melt ponds, as well as fractal relationships between their areas and coastlines. Here we report similar fractal structure of ponds in a tidal flat, thereby extending the spatial and temporal scales on which such phenomena have been observed in geophysical systems. Images taken during low tide of a tidal flat in Damariscotta, Maine, reveal a well-resolved power-law distribution of pond sizes over three orders of magnitude with a consistent fractal area-perimeter relationship. The data are consistent with the predictions of percolation theory for unscreened perimeters and scale-free cluster size distributions and are robust to alterations of the image processing procedure. The small spatial and temporal scales of these data suggest this easily observable system may serve as a useful model for investigating the evolution of pond geometries, while emphasizing the generality of fractal behavior in geophysical surfaces.
NASA Astrophysics Data System (ADS)
Cael, B. B.; Lambert, Bennett; Bisson, Kelsey
2015-11-01
Studies over the past decade have reported power-law distributions for the areas of terrestrial lakes and Arctic melt ponds, as well as fractal relationships between their areas and coastlines. Here we report similar fractal structure of ponds in a tidal flat, thereby extending the spatial and temporal scales on which such phenomena have been observed in geophysical systems. Images taken during low tide of a tidal flat in Damariscotta, Maine, reveal a well-resolved power-law distribution of pond sizes over three orders of magnitude with a consistent fractal area-perimeter relationship. The data are consistent with the predictions of percolation theory for unscreened perimeters and scale-free cluster size distributions and are robust to alterations of the image processing procedure. The small spatial and temporal scales of these data suggest this easily observable system may serve as a useful model for investigating the evolution of pond geometries, while emphasizing the generality of fractal behavior in geophysical surfaces.
Fractal radar scattering from soil.
Oleschko, Klaudia; Korvin, Gabor; Figueroa, Benjamin; Vuelvas, Marco Antonio; Balankin, Alexander S; Flores, Lourdes; Carreón, Dora
2003-04-01
A general technique is developed to retrieve the fractal dimension of self-similar soils through microwave (radar) scattering. The technique is based on a mathematical model relating the fractal dimensions of the georadargram to that of the scattering structure. Clear and different fractal signatures have been observed over four geosystems (soils and sediments) compared in this work.
A Tutorial Review on Fractal Spacetime and Fractional Calculus
NASA Astrophysics Data System (ADS)
He, Ji-Huan
2014-11-01
This tutorial review of fractal-Cantorian spacetime and fractional calculus begins with Leibniz's notation for derivative without limits which can be generalized to discontinuous media like fractal derivative and q-derivative of quantum calculus. Fractal spacetime is used to elucidate some basic properties of fractal which is the foundation of fractional calculus, and El Naschie's mass-energy equation for the dark energy. The variational iteration method is used to introduce the definition of fractional derivatives. Fractal derivative is explained geometrically and q-derivative is motivated by quantum mechanics. Some effective analytical approaches to fractional differential equations, e.g., the variational iteration method, the homotopy perturbation method, the exp-function method, the fractional complex transform, and Yang-Laplace transform, are outlined and the main solution processes are given.
Determining Effective Thermal Conductivity of Fabrics by Using Fractal Method
NASA Astrophysics Data System (ADS)
Zhu, Fanglong; Li, Kejing
2010-03-01
In this article, a fractal effective thermal conductivity model for woven fabrics with multiple layers is developed. Structural models of yarn and plain woven fabric are derived based on the fractal characteristics of macro-pores (gap or channel) between the yarns and micro-pores inside the yarns. The fractal effective thermal conductivity model can be expressed as a function of the pore structure (fractal dimension) and architectural parameters of the woven fabric. Good agreement is found between the fractal model and the thermal conductivity measurements in the general porosity ranges. It is expected that the model will be helpful in the evaluation of thermal comfort for woven fabric in the whole range of porosity.
[Physical and fractal properties of polyaluminum chloride-humic acid (PACl-HA) flocs].
Wang, Yi-Li; Liu, Jie; Du, Bai-Yu
2006-11-01
The powder of polyaluminum chloride-humic acid (PACl-HA) flocs was prepared by cryo-freezing-vacuum-drying method. These flocs were characterized by X-ray diffractometry, FTIR spectroscopy, elementary analysis and surface area determination. The results show that these flocs are amorphous, mainly composed by elements of C, O, Al, and reserve some characteristic functional groups from PACl, HA or Kaolin. The N2 absorption-desorption data determined the microstructure of PACl-HA flocs: 130 - 161 m2 x g(-1) of BET specific surface area, 0.38 - 0.52 cm3 x g(-1) of BJH cumulative absorbed volume and 7.7 - 9.6nm of BJH desorption average pore diameter. The peak values of pore size distribution (PSD) curves were found at 8.4 - 11.2nm of pore diameter. The self-similar and rough surface was observed in SEM images of PACl-HA flocs. The surface fractal dimensions D(s) of the flocs determined from both SEM images method and N2 absorption-desorption one were 2.03 - 2.26 and 2.24 - 2.37, respectively. The correspondent fractal scale for the former method was 23 - 390nm, mainly belonging to exterior surface scales, and the lowest limit of the fractal scale for the latter method was 0.2nm and fell in pore surface scales. This demonstrated that the flocs surface had multi-scale fractal properties. Furthermore, some difference was given between the pore surface fractal dimensions D(s) calculated from N2 absorption data and desorption data. The calculated pore surface D(s) values of much more than three through thermodynamic model had discrepancy from Sahouli et al's results.
[Recent progress of research and applications of fractal and its theories in medicine].
Cai, Congbo; Wang, Ping
2014-10-01
Fractal, a mathematics concept, is used to describe an image of self-similarity and scale invariance. Some organisms have been discovered with the fractal characteristics, such as cerebral cortex surface, retinal vessel structure, cardiovascular network, and trabecular bone, etc. It has been preliminarily confirmed that the three-dimensional structure of cells cultured in vitro could be significantly enhanced by bionic fractal surface. Moreover, fractal theory in clinical research will help early diagnosis and treatment of diseases, reducing the patient's pain and suffering. The development process of diseases in the human body can be expressed by the fractal theories parameter. It is of considerable significance to retrospectively review the preparation and application of fractal surface and its diagnostic value in medicine. This paper gives an application of fractal and its theories in the medical science, based on the research achievements in our laboratory.
A tale of two fractals: The Hofstadter butterfly and the integral Apollonian gaskets
NASA Astrophysics Data System (ADS)
Satija, Indubala I.
2016-11-01
This paper unveils a mapping between a quantum fractal that describes a physical phenomena, and an abstract geometrical fractal. The quantum fractal is the Hofstadter butterfly discovered in 1976 in an iconic condensed matter problem of electrons moving in a two-dimensional lattice in a transverse magnetic field. The geometric fractal is the integer Apollonian gasket characterized in terms of a 300 BC problem of mutually tangent circles. Both of these fractals are made up of integers. In the Hofstadter butterfly, these integers encode the topological quantum numbers of quantum Hall conductivity. In the Apollonian gaskets an infinite number of mutually tangent circles are nested inside each other, where each circle has integer curvature. The mapping between these two fractals reveals a hidden D3 symmetry embedded in the kaleidoscopic images that describe the asymptotic scaling properties of the butterfly. This paper also serves as a mini review of these fractals, emphasizing their hierarchical aspects in terms of Farey fractions.
Deterministic fractals: extracting additional information from small-angle scattering data.
Cherny, A Yu; Anitas, E M; Osipov, V A; Kuklin, A I
2011-09-01
The small-angle scattering curves of deterministic mass fractals are studied and analyzed in momentum space. In the fractal region, the curve I(q)q(D) is found to be log-periodic with good accuracy, and the period is equal to the scaling factor of the fractal. Here, D and I(q) are the fractal dimension and the scattering intensity, respectively. The number of periods of this curve coincides with the number of fractal iterations. We show that the log-periodicity of I(q)q(D) in the momentum space is related to the log-periodicity of the quantity g(r)r(3-D) in the real space, where g(r) is the pair distribution function. The minima and maxima positions of the scattering intensity are estimated explicitly by relating them to the pair distance distribution in real space. It is shown that the minima and maxima are damped with increasing polydispersity of the fractal sets; however, they remain quite pronounced even at sufficiently large values of polydispersity. A generalized self-similar Vicsek fractal with controllable fractal dimension is introduced, and its scattering properties are studied to illustrate the above findings. In contrast with the usual methods, the present analysis allows us to obtain not only the fractal dimension and the edges of the fractal region, but also the fractal iteration number, the scaling factor, and the number of structural units from which the fractal is composed.
Universal fractality of morphological transitions in stochastic growth processes.
Nicolás-Carlock, J R; Carrillo-Estrada, J L; Dossetti, V
2017-06-14
Stochastic growth processes give rise to diverse and intricate structures everywhere in nature, often referred to as fractals. In general, these complex structures reflect the non-trivial competition among the interactions that generate them. In particular, the paradigmatic Laplacian-growth model exhibits a characteristic fractal to non-fractal morphological transition as the non-linear effects of its growth dynamics increase. So far, a complete scaling theory for this type of transitions, as well as a general analytical description for their fractal dimensions have been lacking. In this work, we show that despite the enormous variety of shapes, these morphological transitions have clear universal scaling characteristics. Using a statistical approach to fundamental particle-cluster aggregation, we introduce two non-trivial fractal to non-fractal transitions that capture all the main features of fractal growth. By analyzing the respective clusters, in addition to constructing a dynamical model for their fractal dimension, we show that they are well described by a general dimensionality function regardless of their space symmetry-breaking mechanism, including the Laplacian case itself. Moreover, under the appropriate variable transformation this description is universal, i.e., independent of the transition dynamics, the initial cluster configuration, and the embedding Euclidean space.
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.
Backbone fractal dimension and fractal hybrid orbital of protein structure
NASA Astrophysics Data System (ADS)
Peng, Xin; Qi, Wei; Wang, Mengfan; Su, Rongxin; He, Zhimin
2013-12-01
Fractal geometry analysis provides a useful and desirable tool to characterize the configuration and structure of proteins. In this paper we examined the fractal properties of 750 folded proteins from four different structural classes, namely (1) the α-class (dominated by α-helices), (2) the β-class (dominated by β-pleated sheets), (3) the (α/β)-class (α-helices and β-sheets alternately mixed) and (4) the (α + β)-class (α-helices and β-sheets largely segregated) by using two fractal dimension methods, i.e. "the local fractal dimension" and "the backbone fractal dimension" (a new and useful quantitative parameter). The results showed that the protein molecules exhibit a fractal behavior in the range of 1 ⩽ N ⩽ 15 (N is the number of the interval between two adjacent amino acid residues), and the value of backbone fractal dimension is distinctly greater than that of local fractal dimension for the same protein. The average value of two fractal dimensions decreased in order of α > α/β > α + β > β. Moreover, the mathematical formula for the hybrid orbital model of protein based on the concept of backbone fractal dimension is in good coincidence with that of the similarity dimension. So it is a very accurate and simple method to analyze the hybrid orbital model of protein by using the backbone fractal dimension.
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.
Contrast sensitivity function and image discrimination.
Peli, E
2001-02-01
A previous study tested the validity of simulations of the appearance of a natural image (from different observation distances) generated by using a visual model and contrast sensitivity functions of the individual observers [J. Opt. Soc. Am. A 13, 1131 (1996)]. Deleting image spatial-frequency components that should be undetectable made the simulations indistinguishable from the original images at distances larger than the simulated distance. The simulated observation distance accurately predicted the distance at which the simulated image could be discriminated from the original image. Owing to the 1/f characteristic of natural images' spatial spectra, the individual contrast sensitivity functions (CSF's) used in the simulations of the previous study were actually tested only over a narrow range of retinal spatial frequencies. To test the CSF's over a wide range of frequencies, the same simulations and testing procedure were applied to five contrast versions of the images (10-300%). This provides a stronger test of the model, of the simulations, and specifically of the CSF's used. The relevant CSF for a discrimination task was found to be obtained by using 1-octave Gabor stimuli measured in a contrast detection task. The relevant CSF data had to be measured over a range of observation distances, owing to limitations of the displays.
NASA Astrophysics Data System (ADS)
Li, Jian-Hua; Yu, Bo-Ming; Zou, Ming-Qing
2009-11-01
We report a model for the fractal dimension Ds of rough surfaces based on the fractal distribution of roughness elements on surfaces and the fractal character of surface profiles. The proposed model for the fractal dimension Ds is expressed as a function of the fractal dimensions D for conic roughness diameter/height and Dp for surface profile, maximum roughness base diameter λmax, the ratio β of conic roughness height to its base radius as well as the ratio λminλmax of the minimum to the maximal base diameter.
The Classification of HEp-2 Cell Patterns Using Fractal Descriptor.
Xu, Rudan; Sun, Yuanyuan; Yang, Zhihao; Song, Bo; Hu, Xiaopeng
2015-07-01
Indirect immunofluorescence (IIF) with HEp-2 cells is considered as a powerful, sensitive and comprehensive technique for analyzing antinuclear autoantibodies (ANAs). The automatic classification of the HEp-2 cell images from IIF has played an important role in diagnosis. Fractal dimension can be used on the analysis of image representing and also on the property quantification like texture complexity and spatial occupation. In this study, we apply the fractal theory in the application of HEp-2 cell staining pattern classification, utilizing fractal descriptor firstly in the HEp-2 cell pattern classification with the help of morphological descriptor and pixel difference descriptor. The method is applied to the data set of MIVIA and uses the support vector machine (SVM) classifier. Experimental results show that the fractal descriptor combining with morphological descriptor and pixel difference descriptor makes the precisions of six patterns more stable, all above 50%, achieving 67.17% overall accuracy at best with relatively simple feature vectors.
NASA Astrophysics Data System (ADS)
Cheng, Qiuming
2016-04-01
Singularity theory states that extreme geo-processes result in anomalous amounts of energy release or material accumulation within a narrow spatial-temporal interval. The products (e.g. mass density and energy density) caused by extreme geo-processes depict singularity without the ordinary derivative and antiderivative (integration) properties. Based on the definition of fractal density, the density measured in fractal dimensional space, in the current paper the author is proposing several operations including fractal derivative and fractal integral to analyze singularity of fractal density. While the ordinary derivative including fractional derivatives as a fundamental tool measuring the sensitivity of change of function (quantity as dependent variable) with change of another quantity as independent variable, the changes are measured in the ordinary space with additive property, fractal derivative (antiderivative) measures the ratio of changes of two quantities measured in fractal space-fractal dimensional space. For example, if the limit of ratio of increment of quantity (Δf) over the associated increment of time (Δtα) measured in α - dimensional space approaches to a finite value, then the limit is referred a α-dimensional fractal derivative of function fand denoted as f' = lim Δf--= df- α Δt→0 Δtα dtα According to the definition of the fractal derivative the ordinary derivative becomes the special case if the space becomes non-fractal space with α value as an integer. In the rest of the paper we demonstrate that fractal density concept and fractal derivative can be applied in describing singularity property of products caused by extreme or avalanche events. The extreme earth-thermal processes such as hydrothermal mineralization occurred in the earth crust, heat flow over ocean ridges, igneous activities or juvenile crust grows, originated from cascade earth dynamics (mantle convection, plate tectonics, and continent crust grow etc.) were analyzed
Fractal Physiology and the Fractional Calculus: A Perspective
West, Bruce J.
2010-01-01
This paper presents a restricted overview of Fractal Physiology focusing on the complexity of the human body and the characterization of that complexity through fractal measures and their dynamics, with fractal dynamics being described by the fractional calculus. Not only are anatomical structures (Grizzi and Chiriva-Internati, 2005), such as the convoluted surface of the brain, the lining of the bowel, neural networks and placenta, fractal, but the output of dynamical physiologic networks are fractal as well (Bassingthwaighte et al., 1994). The time series for the inter-beat intervals of the heart, inter-breath intervals and inter-stride intervals have all been shown to be fractal and/or multifractal statistical phenomena. Consequently, the fractal dimension turns out to be a significantly better indicator of organismic functions in health and disease than the traditional average measures, such as heart rate, breathing rate, and stride rate. The observation that human physiology is primarily fractal was first made in the 1980s, based on the analysis of a limited number of datasets. We review some of these phenomena herein by applying an allometric aggregation approach to the processing of physiologic time series. This straight forward method establishes the scaling behavior of complex physiologic networks and some dynamic models capable of generating such scaling are reviewed. These models include simple and fractional random walks, which describe how the scaling of correlation functions and probability densities are related to time series data. Subsequently, it is suggested that a proper methodology for describing the dynamics of fractal time series may well be the fractional calculus, either through the fractional Langevin equation or the fractional diffusion equation. A fractional operator (derivative or integral) acting on a fractal function, yields another fractal function, allowing us to construct a fractional Langevin equation to describe the evolution of a
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.
Functional Spectral Domain Optical Coherence Tomography imaging
NASA Astrophysics Data System (ADS)
Bower, Bradley A.
Spectral Domain Optical Coherence Tomography (SDOCT) is a high-speed, high resolution imaging modality capable of structural and functional characterization of tissue microstructure. SDOCT fills a niche between histology and ultrasound imaging, providing non-contact, non-invasive backscattering amplitude and phase from a sample. Due to the translucent nature of the tissue, ophthalmic imaging is an ideal space for SDOCT imaging. Structural imaging of the retina has provided new insights into ophthalmic disease. The phase component of SDOCT images remains largely underexplored, though. While Doppler SDOCT has been explored in a research setting, it has yet to gain traction in the clinic. Other, functional exploitations of the phase are possible and necessary to expand the utility of SDOCT. Spectral Domain Phase Microscopy (SDPM) is an extension of SDOCT that is capable of resolving sub-wavelength displacements within a focal volume. Application of sub-wavelength displacement measurement imaging could provide a new method for non-invasive optophysiological measurement. This body of work encompasses both hardware and software design and development for implementation of SDOCT. Structural imaging was proven in both the lab and the clinic. Coarse phase changes associated with Doppler flow frequency shifts were recorded and a study was conducted to validate Doppler measurement. Fine phase changes were explored through SDPM applications. Preliminary optophysiology data was acquired to study the potential of sub-wavelength measurements in the retina. To remove the complexity associated with in-vivo human retinal imaging, a first principles approach using isolated nerve samples was applied using standard SDPM and a depthencoded technique for measuring conduction velocity. Results from amplitude as well as both coarse and fine phase processing are presented. In-vivo optophysiology using SDPM is a promising avenue for exploration, and projects furthering or extending this body
Right ventricular plasticity and functional imaging
Brittain, Evan L.; Hemnes, Anna R.; Keebler, Mary; Lawson, Mark; Byrd, Benjamin F.; DiSalvo, Tom
2012-01-01
Right ventricular (RV) function is a strong independent predictor of outcome in a number of distinct cardiopulmonary diseases. The RV has a remarkable ability to sustain damage and recover function which may be related to unique anatomic, physiologic, and genetic factors that differentiate it from the left ventricle. This capacity has been described in patients with RV myocardial infarction, pulmonary arterial hypertension, and chronic thromboembolic disease as well as post-lung transplant and post-left ventricular assist device implantation. Various echocardiographic and magnetic resonance imaging parameters of RV function contribute to the clinical assessment and predict outcomes in these patients; however, limitations remain with these techniques. Early diagnosis of RV function and better insight into the mechanisms of RV recovery could improve patient outcomes. Further refinement of established and emerging imaging techniques is necessary to aid subclinical diagnosis and inform treatment decisions. PMID:23130100
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
ERIC Educational Resources Information Center
Camp, Dane R.
1991-01-01
After introducing the two-dimensional Koch curve, which is generated by simple recursions on an equilateral triangle, the process is extended to three dimensions with simple recursions on a regular tetrahedron. Included, for both fractal sequences, are iterative formulae, illustrations of the first several iterations, and a sample PASCAL program.…
ERIC Educational Resources Information Center
Marks, Tim K.
1992-01-01
Presents a three-lesson unit that uses fractal geometry to measure the coastline of Massachusetts. Two lessons provide hands-on activities utilizing compass and grid methods to perform the measurements and the third lesson analyzes and explains the results of the activities. (MDH)
Hsü, K J; Hsü, A J
1990-01-01
Music critics have compared Bach's music to the precision of mathematics. What "mathematics" and what "precision" are the questions for a curious scientist. The purpose of this short note is to suggest that the mathematics is, at least in part, Mandelbrot's fractal geometry and the precision is the deviation from a log-log linear plot. PMID:11607061
Fractal branching pattern in the pial vasculature in the cat.
Hermán, P; Kocsis, L; Eke, A
2001-06-01
Arborization pattern was studied in pial vascular networks by treating them as fractals. Rather than applying elaborate taxonomy assembled from measures from individual vessel segments and bifurcations arranged in their branching order, the authors' approach captured the structural details at once in high-resolution digital images processed for the skeleton of the networks. The pial networks appear random and at the same time having structural elements similar to each other when viewed at different scales--a property known as self-similarity revealed by the geometry of fractals. Fractal (capacity) dimension, Dcap, was calculated to evaluate the network's spatial complexity by the box counting method (BCM) and its variant, the extended counting method (XCM). Box counting method and XCM were subject to numerical testing on ideal fractals of known D. The authors found that precision of these fractal methods depends on the fractal character (branching, nonbranching) of the structure they evaluate. Dcaps (group mean +/- SD) for the arterial and venous pial networks in the cat (n = 6) are 1.37 +/- 0.04, 1.37 +/- 0.02 by XCM, and 1.30 +/- 0.04, 1.31 +/- 0.03 by BCM, respectively. The arterial and venous systems thus appear to be developed according to the same fractal generation rule in the cat.
A Fractal Perspective on Scale in Geography
NASA Astrophysics Data System (ADS)
Jiang, Bin; Brandt, S.
2016-06-01
Scale is a fundamental concept that has attracted persistent attention in geography literature over the past several decades. However, it creates enormous confusion and frustration, particularly in the context of geographic information science, because of scale-related issues such as image resolution, and the modifiable areal unit problem (MAUP). This paper argues that the confusion and frustration mainly arise from Euclidean geometric thinking, with which locations, directions, and sizes are considered absolute, and it is time to reverse this conventional thinking. Hence, we review fractal geometry, together with its underlying way of thinking, and compare it to Euclidean geometry. Under the paradigm of Euclidean geometry, everything is measurable, no matter how big or small. However, geographic features, due to their fractal nature, are essentially unmeasurable or their sizes depend on scale. For example, the length of a coastline, the area of a lake, and the slope of a topographic surface are all scale-dependent. Seen from the perspective of fractal geometry, many scale issues, such as the MAUP, are inevitable. They appear unsolvable, but can be dealt with. To effectively deal with scale-related issues, we introduce topological and scaling analyses based on street-related concepts such as natural streets, street blocks, and natural cities. We further contend that spatial heterogeneity, or the fractal nature of geographic features, is the first and foremost effect of two spatial properties, because it is general and universal across all scales. Keywords: Scaling, spatial heterogeneity, conundrum of length, MAUP, topological analysis
Flames in fractal grid generated turbulence
NASA Astrophysics Data System (ADS)
Goh, K. H. H.; Geipel, P.; Hampp, F.; Lindstedt, R. P.
2013-12-01
Twin premixed turbulent opposed jet flames were stabilized for lean mixtures of air with methane and propane in fractal grid generated turbulence. A density segregation method was applied alongside particle image velocimetry to obtain velocity and scalar statistics. It is shown that the current fractal grids increase the turbulence levels by around a factor of 2. Proper orthogonal decomposition (POD) was applied to show that the fractal grids produce slightly larger turbulent structures that decay at a slower rate as compared to conventional perforated plates. Conditional POD (CPOD) was also implemented using the density segregation technique and the results show that CPOD is essential to segregate the relative structures and turbulent kinetic energy distributions in each stream. The Kolmogorov length scales were also estimated providing values ∼0.1 and ∼0.5 mm in the reactants and products, respectively. Resolved profiles of flame surface density indicate that a thin flame assumption leading to bimodal statistics is not perfectly valid under the current conditions and it is expected that the data obtained will be of significant value to the development of computational methods that can provide information on the conditional structure of turbulence. It is concluded that the increase in the turbulent Reynolds number is without any negative impact on other parameters and that fractal grids provide a route towards removing the classical problem of a relatively low ratio of turbulent to bulk strain associated with the opposed jet configuration.
Biophilic fractals and the visual journey of organic screen-savers.
Taylor, R P; Sprott, J C
2008-01-01
Computers have led to the remarkable popularity of mathematically-generated fractal patterns. Fractals have also assumed a rapidly expanding role as an art form. Due to their growing impact on cultures around the world and their prevalence in nature, fractals constitute a central feature of our daily visual experiences throughout our lives. This intimate association raises a crucial question - does exposure to fractals have a positive impact on our mental and physical condition? This question raises the opportunity for readers of this journal to have some visual fun. Each year a different nonlinear inspired artist is featured on the front cover of the journal. This year, Scott Draves's fractal art works continues this tradition. In May 2007, we selected twenty of Draves's artworks and invited readers to vote for their favorites from this selection. The most popular images will feature on the front covers this year. In this article, we discuss fractal aesthetics and Draves's remarkable images.
NASA Astrophysics Data System (ADS)
Maslovskaya, A. G.; Barabash, T. K.
2017-01-01
The article presents some results of fractal analysis of ferroelectric domain structure images visualized with scanning electron microscope (SEM) techniques. The fractal and multifractal characteristics were estimated to demonstrate self-similar organization of ferroelectric domain structure registered with static and dynamic contrast modes of SEM. Fractal methods as sensitive analytical tools were used to indicate degree of domain structure and domain boundary imperfections. The electron irradiation-induced erosion effect of ferroelectric domain boundaries in electron beam-stimulated polarization current mode of SEM is characterized by considerable raising of fractal dimension. For dynamic contrast mode of SEM there was revealed that complication of domain structure during its dynamics is specified by increase in fractal dimension of images and slight raising of boundary fractal dimension.
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.
Acoustic noise during functional magnetic resonance imaging.
Ravicz, M E; Melcher, J R; Kiang, N Y
2000-10-01
Functional magnetic resonance imaging (fMRI) enables sites of brain activation to be localized in human subjects. For studies of the auditory system, acoustic noise generated during fMRI can interfere with assessments of this activation by introducing uncontrolled extraneous sounds. As a first step toward reducing the noise during fMRI, this paper describes the temporal and spectral characteristics of the noise present under typical fMRI study conditions for two imagers with different static magnetic field strengths. Peak noise levels were 123 and 138 dB re 20 microPa in a 1.5-tesla (T) and a 3-T imager, respectively. The noise spectrum (calculated over a 10-ms window coinciding with the highest-amplitude noise) showed a prominent maximum at 1 kHz for the 1.5-T imager (115 dB SPL) and at 1.4 kHz for the 3-T imager (131 dB SPL). The frequency content and timing of the most intense noise components indicated that the noise was primarily attributable to the readout gradients in the imaging pulse sequence. The noise persisted above background levels for 300-500 ms after gradient activity ceased, indicating that resonating structures in the imager or noise reverberating in the imager room were also factors. The gradient noise waveform was highly repeatable. In addition, the coolant pump for the imager's permanent magnet and the room air-handling system were sources of ongoing noise lower in both level and frequency than gradient coil noise. Knowledge of the sources and characteristics of the noise enabled the examination of general approaches to noise control that could be applied to reduce the unwanted noise during fMRI sessions.
Fractal Images: Procedure and Theory.
1987-08-01
impossible to comprehend how anyone ever thought of them." -- Michael Spivak , A Comprehensive Introduction to Differential Geometry In the last few years, the...several results which gave relation- ships between set theory and calculus . In 1874, he produced his proof that there are only countably many algebraic
Optical imaging device of retinal function
NASA Astrophysics Data System (ADS)
Kardon, Randy H.; Kwon, Young; Truitt, Paul; Nemeth, Sheila C.; T'so, Dan; Soliz, Peter
2002-06-01
An optical imaging device of retina function (OID-RF) has been constructed to record changes in reflected 700-nm light from the fundus caused by retinal activation in response to a visual 535-nm stimulus. The resulting images reveal areas of the retina activated by visual stimulation. This device is a modified fundus camera designed to provide a patterned, moving visual stimulus over a 45-degree field of view to the subject in the green wavelength portion of the visual spectrum while simultaneously imaging the fundus in another, longer wavelength range. Data was collected from 3 normal subjects and recorded for 13 seconds at 4 Hz; 3 seconds were recorded during pre-stimulus baseline, 5 seconds during the stimulus, and 5 seconds post-stimulus. This procedure was repeated several times and, after image registration, the images were averaged to improve signal to noise. The change in reflected intensity from the retina due to the stimulus was then calculated by comparison to the pre-stimulus state. Reflected intensity from areas of stimulated retina began to increase steadily within 1 second after stimulus onset and decayed after stimulus offset. These results indicated that a functional optical signal can be recorded from the human eye.
Emergence of fractals in aggregation with stochastic self-replication.
Hassan, Md Kamrul; Hassan, Md Zahedul; Islam, Nabila
2013-10-01
We propose and investigate a simple model which describes the kinetics of aggregation of Brownian particles with stochastic self-replication. An exact solution and the scaling theory are presented alongside numerical simulation which fully support all theoretical findings. In particular, we show analytically that the particle size distribution function exhibits dynamic scaling and we verify it numerically using the idea of data collapse. Furthermore, the conditions under which the resulting system emerges as a fractal are found, the fractal dimension of the system is given, and the relationship between this fractal dimension and a conserved quantity is pointed out.
Fractal aggregates in tennis ball systems
NASA Astrophysics Data System (ADS)
Sabin, J.; Bandín, M.; Prieto, G.; Sarmiento, F.
2009-09-01
We present a new practical exercise to explain the mechanisms of aggregation of some colloids which are otherwise not easy to understand. We have used tennis balls to simulate, in a visual way, the aggregation of colloids under reaction-limited colloid aggregation (RLCA) and diffusion-limited colloid aggregation (DLCA) regimes. We have used the images of the cluster of balls, following Forrest and Witten's pioneering studies on the aggregation of smoke particles, to estimate their fractal dimension.
Fractal analysis of circulating platelets in type 2 diabetic patients.
Bianciardi, G; Tanganelli, I
2015-01-01
This paper investigates the use of computerized fractal analysis for objective characterization by means of transmission electron microscopy of the complexity of circulating platelets collected from healthy individuals and from type 2 diabetic patients, a pathologic condition in which platelet hyperreactivity has been described. Platelet boundaries were extracted by means of automatically image analysis. Local fractal dimension by box counting (measure of geometric complexity) was automatically calculated. The results showed that the platelet boundary observed by electron microscopy is fractal and that the shape of the circulating platelets is significantly more complex in the diabetic patients in comparison to healthy subjects (p < 0.01), with 100% correct classification. In vitro activated platelets from healthy subjects show an analogous increase of geometric complexity. Computerized fractal analysis of platelet shape by transmission electron microscopy can provide accurate, quantitative, data to study platelet activation in diabetes mellitus.
Fractal Particles: Titan's Thermal Structure and IR Opacity
NASA Technical Reports Server (NTRS)
McKay, C. P.; Rannou, P.; Guez, L.; Young, E. F.; DeVincenzi, Donald (Technical Monitor)
1998-01-01
Titan's haze particles are the principle opacity at solar wavelengths. Most past work in modeling these particles has assumed spherical particles. However, observational evidence strongly favors fractal shapes for the haze particles. We consider the implications of fractal particles for the thermal structure and near infrared opacity of Titan's atmosphere. We find that assuming fractal particles with the optical properties based on laboratory tholin material and with a production rate that allows for a match to the geometric albedo results in warmer troposphere and surface temperatures compared to spherical particles. In the near infrared (1-3 microns) the predicted opacity of the fractal particles is up to a factor of two less than for spherical particles. This has implications for the ability of Cassini to image Titan's surface at 1 micron.
Is fractal geometry useful in medicine and biomedical sciences?
Heymans, O; Fissette, J; Vico, P; Blacher, S; Masset, D; Brouers, F
2000-03-01
Fractal geometry has become very useful in the understanding of many phenomena in various fields such as astrophysics, economy or agriculture and recently in medicine. After a brief intuitive introduction to the basis of fractal geometry, the clue is made about the correlation between Df and the complexity or the irregularity of a structure. However, fractal analysis must be applied with certain caution in natural objects such as bio-medical ones. The cardio-vascular system remains one of the most important fields of application of these kinds of approach. Spectral analysis of the R-R interval, morphology of the distal coronary arteries constitute two examples. Other very interesting applications are founded in bacteriology, medical imaging or ophthalmology. In our institution, we apply fractal analysis in order to quantitate angiogenesis and other vascular processes.
Fractal properties of aggregates of metal nanoclusters on solid surface
NASA Astrophysics Data System (ADS)
Samsonov, V. M.; Kuznetsova, Yu. V.; D'yakova, E. V.
2016-02-01
AFM images are used to determine and analyze fractal characteristics (cluster fraction dimension and lacunarity) of aggregates of Au and Ag nanoclusters on metal films of the same metal produced with the aid of thermal vacuum deposition on mica surface. A fractal dimension of 1.6 that corresponds to typical samples with relatively uniform distribution of nanoclusters on the film surface is in agreement with the mean value calculated from experimental data of Belko et al., who studied the fractal dimension of Au nanoclusters on a different dielectric (quartz) surface. When a compact single aggregate of Au nanoclusters is formed on a certain active center or defect, the fractal cluster dimension decreases to 1.4. The experimental data are compared with the results of existing theoretical models of association of nanoclusters in 2D systems.
Image reconstruction with analytical point spread functions
NASA Astrophysics Data System (ADS)
Asensio Ramos, A.; López Ariste, A.
2010-07-01
Context. The image degradation produced by atmospheric turbulence and optical aberrations is usually alleviated using post-facto image reconstruction techniques, even when observing with adaptive optics systems. Aims: These techniques rely on the development of the wavefront using Zernike functions and the non-linear optimization of a certain metric. The resulting optimization procedure is computationally heavy. Our aim is to alleviate this computational burden. Methods: We generalize the extended Zernike-Nijboer theory to carry out the analytical integration of the Fresnel integral and present a natural basis set for the development of the point spread function when the wavefront is described using Zernike functions. Results: We present a linear expansion of the point spread function in terms of analytic functions, which, in addition, takes defocusing into account in a natural way. This expansion is used to develop a very fast phase-diversity reconstruction technique, which is demonstrated in terms of some applications. Conclusions: We propose that the linear expansion of the point spread function can be applied to accelerate other reconstruction techniques in use that are based on blind deconvolution.
Numeric character recognition method based on fractal dimension
NASA Astrophysics Data System (ADS)
He, Tao; Xie, Yulang; Chen, Jiuyin; Cheng, Longfei; Yuan, Ye
2013-10-01
An image processing method based on fractal dimension is proposed in this paper. This method uses fractal dimension to process the character images firstly, and rises the analysis of each grid to the analysis of interrelation between the grids to eliminate interference. Box-counting method is commonly used for calculating fractal dimension of fractal, which uses small box whose side length is r ,that is the topological dimension of the box is d, to cover up the image. Because there are various levels of cavities and cracks, some small boxes are empty and some small boxes cover a part of fractal image which is called non-empty box (here refers to the average gray of the part that contained in the small box is larger than a certain threshold). We note down the number of non-empty boxes, analyze and calculate them. The method is used to image process the polluted characters, which can remove ink and scratches around the contour of the characters and remain basic contour, then the characters can be recognized by using template matching. In computer simulation experiment for polluted character recognition, this method can recognize the polluted characters quickly, which improve the accuracy of the recognition of the polluted characters.
Time evolution of the fractal dimension of a mixing front
NASA Astrophysics Data System (ADS)
Lopez Gonzalez-Nieto, P.; Grau, J.
2009-04-01
We present a description of an experimental study of an array of turbulent plumes (from one to nine plumes), investigating the time evolution of the fractal dimension of the plumes and also the spatial evolution of the fractal dimension from one plume to other. We also investigate the effects of bouyancy (different Atwood numbers), the number of plumes and the height of the bouyancy source on the fractal dimension. The plumes are formed by injecting a dense fluid from a small source (from one to nine orifices) into a stationary body of lighter brime (saline solution) contained in a tank. The source fluid was dyed with fluorescein and we use the LIF technique. The plumes were fully turbulent and we have both momentum and bouyancy regimes. The fractal dimensions of contours of concentration were measured. The fractal analysis of the turbulent convective plumes was performed with the box counting algorithm for different intensities of evolving plume images using the special software Ima_Calc. Fractal dimensions between 1.3 and 1.35 are obtained from box counting methods for free convection and neutral boundary layers. Other results have been published which use the box counting method to analyze images of jet sections -produced from LIF techniques. The regions where most of the mixing takes place are also compared with Reactive flow experiments using phenolphthalein and acid-base interfaces performed by Redondo(1994) IMA 43. Eds M. Farge, JC Hunt and C. Vassilicos.
Electromagnetic inverse applications for functional brain imaging
Wood, C.C.
1997-10-01
This is the final report of a one-year, Laboratory Directed Research and Development (LDRD) project at Los Alamos National Laboratory (LANL). This project addresses an important mathematical and computational problem in functional brain imaging, namely the electromagnetic {open_quotes}inverse problem.{close_quotes} Electromagnetic brain imaging techniques, magnetoencephalography (MEG) and electroencephalography (EEG), are based on measurements of electrical potentials and magnetic fields at hundreds of locations outside the human head. The inverse problem is the estimation of the locations, magnitudes, and time-sources of electrical currents in the brain from surface measurements. This project extends recent progress on the inverse problem by combining the use of anatomical constraints derived from magnetic resonance imaging (MRI) with Bayesian and other novel algorithmic approaches. The results suggest that we can achieve significant improvements in the accuracy and robustness of inverse solutions by these two approaches.
Functional lung imaging using hyperpolarized gas MRI.
Fain, Sean B; Korosec, Frank R; Holmes, James H; O'Halloran, Rafael; Sorkness, Ronald L; Grist, Thomas M
2007-05-01
The noninvasive assessment of lung function using imaging is increasingly of interest for the study of lung diseases, including chronic obstructive pulmonary disease (COPD) and asthma. Hyperpolarized gas MRI (HP MRI) has demonstrated the ability to detect changes in ventilation, perfusion, and lung microstructure that appear to be associated with both normal lung development and disease progression. The physical characteristics of HP gases and their application to MRI are presented with an emphasis on current applications. Clinical investigations using HP MRI to study asthma, COPD, cystic fibrosis, pediatric chronic lung disease, and lung transplant are reviewed. Recent advances in polarization, pulse sequence development for imaging with Xe-129, and prototype low magnetic field systems dedicated to lung imaging are highlighted as areas of future development for this rapidly evolving technology.
Billock, V A; Cunningham, D W; Havig, P R; Tsou, B H
2001-10-01
Recent work establishes that static and dynamic natural images have fractal-like l/falpha spatiotemporal spectra. Artifical textures, with randomized phase spectra, and 1/falpha amplitude spectra are also used in studies of texture and noise perception. Influenced by colorimetric principles and motivated by the ubiquity of 1/falpha spatial and temporal image spectra, we treat the spatial and temporal frequency exponents as the dimensions characterizing a dynamic texture space, and we characterize two key attributes of this space, the spatiotemporal appearance map and the spatiotemporal discrimination function (a map of MacAdam-like just-noticeable-difference contours).
Effect of angle of deposition on the Fractal properties of ZnO thin film surface
NASA Astrophysics Data System (ADS)
Yadav, R. P.; Agarwal, D. C.; Kumar, Manvendra; Rajput, Parasmani; Tomar, D. S.; Pandey, S. N.; Priya, P. K.; Mittal, A. K.
2017-09-01
Zinc oxide (ZnO) thin films were prepared by atom beam sputtering at various deposition angles in the range of 20-75°. The deposited thin films were examined by glancing angle X-ray diffraction and atomic force microscopy (AFM). Scaling law analysis was performed on AFM images to show that the thin film surfaces are self-affine. Fractal dimension of each of the 256 vertical sections along the fast scan direction of a discretized surface, obtained from the AFM height data, was estimated using the Higuchi's algorithm. Hurst exponent was computed from the fractal dimension. The grain sizes, as determined by applying self-correlation function on AFM micrographs, varied with the deposition angle in the same manner as the Hurst exponent.
Effects of Image Contrast on Functional MRI Image Registration
Gonzalez-Castillo, Javier; Duthie, Kristen N.; Saad, Ziad S.; Chu, Carlton; Bandettini, Peter A.; Luh, Wen-Ming
2012-01-01
Lack of tissue contrast and existing inhomogeneous bias fields from multi-channel coils have the potential to degrade the output of registration algorithms; and consequently degrade group analysis and any attempt to accurately localize brain function. Non-invasive ways to improve tissue contrast in fMRI images include the use of low flip angles (FAs) well below the Ernst angle and longer repetition times (TR). Techniques to correct intensity inhomogeneity are also available in most mainstream fMRI data analysis packages; but are not used as part of the pre-processing pipeline in many studies. In this work, we use a combination of real data and simulations to show that simple-to-implement acquisition/pre-processing techniques can significantly improve the outcome of both functional-to-functional and anatomical-to-functional image registrations. We also emphasize the need of tissue contrast on EPI images to be able to appropriately evaluate the quality of the alignment. In particular, we show that the use of low FAs (e.g., θ≤40°), when physiological noise considerations permit such an approach, significantly improves accuracy, consistency and stability of registration for data acquired at relatively short TRs (TR≤2s). Moreover, we also show that the application of bias correction techniques significantly improves alignment both for array-coil data (known to contain high intensity inhomogeneity) as well as birdcage-coil data. Finally, improvements in alignment derived from the use of the first infinite-TR volumes (ITVs) as targets for registration are also demonstrated. For the purpose of quantitatively evaluating the different scenarios, two novel metrics were developed: Mean Voxel Distance (MVD) to evaluate registration consistency, and Deviation of Mean Voxel Distance (dMVD) to evaluate registration stability across successive alignment attempts. PMID:23128074
Multilayer adsorption on fractal surfaces.
Vajda, Péter; Felinger, Attila
2014-01-10
Multilayer adsorption is often observed in liquid chromatography. The most frequently employed model for multilayer adsorption is the BET isotherm equation. In this study we introduce an interpretation of multilayer adsorption measured on liquid chromatographic stationary phases based on the fractal theory. The fractal BET isotherm model was successfully used to determine the apparent fractal dimension of the adsorbent surface. The nonlinear fitting of the fractal BET equation gives us the estimation of the adsorption equilibrium constants and the monolayer saturation capacity of the adsorbent as well. In our experiments, aniline and proline were used as test molecules on reversed phase and normal phase columns, respectively. Our results suggest an apparent fractal dimension 2.88-2.99 in the case of reversed phase adsorbents, in the contrast with a bare silica column with a fractal dimension of 2.54. Copyright © 2013 The Authors. Published by Elsevier B.V. All rights reserved.
Huang, F.; Peng, R. D.; Liu, Y. H.; Chen, Z. Y.; Ye, M. F.; Wang, L.
2012-09-15
Fractal dust grains of different shapes are observed in a radially confined magnetized radio frequency plasma. The fractal dimensions of the dust structures in two-dimensional (2D) horizontal dust layers are calculated, and their evolution in the dust growth process is investigated. It is found that as the dust grains grow the fractal dimension of the dust structure decreases. In addition, the fractal dimension of the center region is larger than that of the entire region in the 2D dust layer. In the initial growth stage, the small dust particulates at a high number density in a 2D layer tend to fill space as a normal surface with fractal dimension D = 2. The mechanism of the formation of fractal dust grains is discussed.
Fractals in geology and geophysics
NASA Technical Reports Server (NTRS)
Turcotte, Donald L.
1989-01-01
The definition of a fractal distribution is that the number of objects N with a characteristic size greater than r scales with the relation N of about r exp -D. The frequency-size distributions for islands, earthquakes, fragments, ore deposits, and oil fields often satisfy this relation. This application illustrates a fundamental aspect of fractal distributions, scale invariance. The requirement of an object to define a scale in photograhs of many geological features is one indication of the wide applicability of scale invariance to geological problems; scale invariance can lead to fractal clustering. Geophysical spectra can also be related to fractals; these are self-affine fractals rather than self-similar fractals. Examples include the earth's topography and geoid.
Diffusion on regular random fractals
NASA Astrophysics Data System (ADS)
Aarão Reis, Fábio D. A.
1996-12-01
We study random walks on structures intermediate to statistical and deterministic fractals called regular random fractals, constructed introducing randomness in the distribution of lacunas of Sierpinski carpets. Random walks are simulated on finite stages of these fractals and the scaling properties of the mean square displacement 0305-4470/29/24/007/img1 of N-step walks are analysed. The anomalous diffusion exponents 0305-4470/29/24/007/img2 obtained are very near the estimates for the carpets with the same dimension. This result motivates a discussion on the influence of some types of lattice irregularity (random structure, dead ends, lacunas) on 0305-4470/29/24/007/img2, based on results on several fractals. We also propose to use these and other regular random fractals as models for real self-similar structures and to generalize results for statistical systems on fractals.
Fractals in geology and geophysics
NASA Technical Reports Server (NTRS)
Turcotte, Donald L.
1989-01-01
The definition of a fractal distribution is that the number of objects N with a characteristic size greater than r scales with the relation N of about r exp -D. The frequency-size distributions for islands, earthquakes, fragments, ore deposits, and oil fields often satisfy this relation. This application illustrates a fundamental aspect of fractal distributions, scale invariance. The requirement of an object to define a scale in photograhs of many geological features is one indication of the wide applicability of scale invariance to geological problems; scale invariance can lead to fractal clustering. Geophysical spectra can also be related to fractals; these are self-affine fractals rather than self-similar fractals. Examples include the earth's topography and geoid.
Visual Function Assessment in Medical Imaging Research.
Lança, Carla; Thompson, John D; Lança, Luis; Hogg, Peter
2015-01-01
Medical image perception research relies on visual data to study the diagnostic relationship between observers and medical images. A consistent method to assess visual function for participants in medical imaging research has not been developed and represents a significant gap in existing research. Three visual assessment factors appropriate to observer studies were identified: visual acuity, contrast sensitivity, and stereopsis. A test was designed for each, and 30 radiography observers (mean age 31.6 years) participated in each test. Mean binocular visual acuity for distance was 20/14 for all observers. The difference between observers who did and did not use corrective lenses was not statistically significant (P = .12). All subjects had a normal value for near visual acuity and stereoacuity. Contrast sensitivity was better than population norms. All observers had normal visual function and could participate in medical imaging visual analysis studies. Protocols of evaluation and populations norms are provided. Further studies are necessary to understand fully the relationship between visual performance on tests and diagnostic accuracy in practice.
Fast Optical Imaging of Human Brain Function
Gratton, Gabriele; Fabiani, Monica
2010-01-01
Great advancements in brain imaging during the last few decades have opened a large number of new possibilities for neuroscientists. The most dominant methodologies (electrophysiological and magnetic resonance-based methods) emphasize temporal and spatial information, respectively. However, theorizing about brain function has recently emphasized the importance of rapid (within 100 ms or so) interactions between different elements of complex neuronal networks. Fast optical imaging, and in particular the event-related optical signal (EROS, a technology that has emerged over the last 15 years) may provide descriptions of localized (to sub-cm level) brain activity with a temporal resolution of less than 100 ms. The main limitations of EROS are its limited penetration, which allows us to image cortical structures not deeper than 3 cm from the surface of the head, and its low signal-to-noise ratio. Advantages include the fact that EROS is compatible with most other imaging methods, including electrophysiological, magnetic resonance, and trans-cranial magnetic stimulation techniques, with which can be recorded concurrently. In this paper we present a summary of the research that has been conducted so far on fast optical imaging, including evidence for the possibility of recording neuronal signals with this method, the properties of the signals, and various examples of applications to the study of human cognitive neuroscience. Extant issues, controversies, and possible future developments are also discussed. PMID:20631845
Pediatric Epilepsy: Neurology, Functional Imaging, and Neurosurgery.
Mountz, James M; Patterson, Christina M; Tamber, Mandeep S
2017-03-01
In this chapter we provide a comprehensive review of the current role that functional imaging can have in the care of the pediatric epilepsy patient from the perspective of the epilepsy neurologist and the epilepsy neurosurgeon. In the neurology section, the diagnosis and classification of epilepsy adapted by the International League Against Epilepsy as well as the etiology and incidence of the disease is presented. The neuroimaging section describes how advanced nuclear medicine imaging methods can be synergized to provide a maximum opportunity to localize an epileptogenic focus. This section described the value of FDG-PET and regional cerebral blood flow SPECT in the identification of an epileptogenic focus. The imaging section also emphasizes the importance on developing a dedicated epilepsy management team, comprised of an epilepsy imaging specialist, epilepsy neurologist and epilepsy neurosurgeon, to provide the maximum benefit to each child with epilepsy. An emphasis is placed on preparation for ictal SPECT injection procedures, including the critical role of an automated injector well as the use of state-of-the-art dedicated nuclear medicine imaging and analysis protocols to correctly localize the epileptogenic focus location. In the final section, surgical options, approaches and expected outcomes for the different classes of epilepsy is presented.
Wang Xujing; Becker, Frederick F.; Gascoyne, Peter R. C.
2010-12-15
The scale-invariant property of the cytoplasmic membrane of biological cells is examined by applying the Minkowski-Bouligand method to digitized scanning electron microscopy images of the cell surface. The membrane is found to exhibit fractal behavior, and the derived fractal dimension gives a good description of its morphological complexity. Furthermore, we found that this fractal dimension correlates well with the specific membrane dielectric capacitance derived from the electrorotation measurements. Based on these findings, we propose a new fractal single-shell model to describe the dielectrics of mammalian cells, and compare it with the conventional single-shell model (SSM). We found that while both models fit with experimental data well, the new model is able to eliminate the discrepancy between the measured dielectric property of cells and that predicted by the SSM.
Wang, Xujing; Becker, Frederick F.; Gascoyne, Peter R. C.
2010-01-01
The scale-invariant property of the cytoplasmic membrane of biological cells is examined by applying the Minkowski–Bouligand method to digitized scanning electron microscopy images of the cell surface. The membrane is found to exhibit fractal behavior, and the derived fractal dimension gives a good description of its morphological complexity. Furthermore, we found that this fractal dimension correlates well with the specific membrane dielectric capacitance derived from the electrorotation measurements. Based on these findings, we propose a new fractal single-shell model to describe the dielectrics of mammalian cells, and compare it with the conventional single-shell model (SSM). We found that while both models fit with experimental data well, the new model is able to eliminate the discrepancy between the measured dielectric property of cells and that predicted by the SSM. PMID:21198103
Applications of fractal geometry to dynamical evolution of sunspots
Milovanov, A.V.; Zelenyi, L.M. )
1993-07-01
A fractal model for sunspot dynamics is presented. Formation of a sunspot in the solar photosphere is considered from the viewpoint of aggregation of magnetic flux tubes on a fractal geometry. Fine structure of the magnetic flux tubes is analyzed for a broad class of non-Maxwellian plasma distribution functions. The sunspot fractal dimension is proved to depend on the parameters of the plasma distribution function, enabling one to investigate intrinsic properties of the solar plasma by means of powerful geometrical methods. Magnetic field dissipation in the tubes is shown to result in effective sunspot decay. Sunspot formation and decay times as well as the diffusion constant [ital K] deduced by using the fractal model, are in a good agreement with observational data. Disappearance of umbras in decaying sunspots is interpreted as a second-order phase transition reminiscent of the transition through the Curie point in ferromagnetics.
Fractal polyzirconosiloxane cluster coatings
Sugama, T.
1992-08-01
Fractal polyzirconosiloxane (PZS) cluster films were prepared through the hydrolysis-polycondensation-pyrolysis synthesis of two-step HCl acid-NaOH base catalyzed sol precursors consisting of N-[3-(triethoxysilyl)propyl]-4,5-dihydroimidazole, Zr(OC{sub 3}H{sub 7}){sub 4}, methanol, and water. When amorphous PZSs were applied to aluminum as protective coatings against NaCl-induced corrosion, the effective film was that derived from the sol having a pH near the isoelectric point in the positive zeta potential region. The following four factors played an important role in assembling the protective PZS coating films: (1) a proper rate of condensation, (2) a moderate ratio of Si-O-Si to Si-O-Zr linkages formed in the PZS network, (3) hydrophobic characteristics, and (4) a specific microstructural geometry, in which large fractal clusters were linked together.
Fractal polyzirconosiloxane cluster coatings
Sugama, T.
1992-01-01
Fractal polyzirconosiloxane (PZS) cluster films were prepared through the hydrolysis-polycondensation-pyrolysis synthesis of two-step HCl acid-NaOH base catalyzed sol precursors consisting of N-(3-(triethoxysilyl)propyl)-4,5-dihydroimidazole, Zr(OC{sub 3}H{sub 7}){sub 4}, methanol, and water. When amorphous PZSs were applied to aluminum as protective coatings against NaCl-induced corrosion, the effective film was that derived from the sol having a pH near the isoelectric point in the positive zeta potential region. The following four factors played an important role in assembling the protective PZS coating films: (1) a proper rate of condensation, (2) a moderate ratio of Si-O-Si to Si-O-Zr linkages formed in the PZS network, (3) hydrophobic characteristics, and (4) a specific microstructural geometry, in which large fractal clusters were linked together.
NASA Astrophysics Data System (ADS)
Latka, Miroslaw; Glaubic-Latka, Marta; Latka, Dariusz; West, Bruce J.
2004-04-01
We study the middle cerebral artery blood flow velocity (MCAfv) in humans using transcranial Doppler ultrasonography (TCD). Scaling properties of time series of the axial flow velocity averaged over a cardiac beat interval may be characterized by two exponents. The short time scaling exponent (STSE) determines the statistical properties of fluctuations of blood flow velocities in short-time intervals while the Hurst exponent describes the long-term fractal properties. In many migraineurs the value of the STSE is significantly reduced and may approach that of the Hurst exponent. This change in dynamical properties reflects the significant loss of short-term adaptability and the overall hyperexcitability of the underlying cerebral blood flow control system. We call this effect fractal rigidity.
One-stop-shop stroke imaging with functional CT.
Tong, Elizabeth; Komlosi, Peter; Wintermark, Max
2015-12-01
Advanced imaging techniques have extended beyond traditional anatomic imaging and progressed to dynamic, physiologic and functional imaging. Neuroimaging is no longer a mere diagnostic tool. Multimodal functional CT, comprising of NCCT, PCT and CTA, provides a one-stop-shop for rapid stroke imaging. Integrating those imaging findings with pertinent clinical information can help guide subsequent treatment decisions, medical management and follow-up imaging selection. This review article will briefly discuss the indication and utility of each modality in acute stroke imaging.
Fuzzy membership functions for analysis of high-resolution CT images of diffuse pulmonary diseases.
Almeida, Eliana; Rangayyan, Rangaraj M; Azevedo-Marques, Paulo M
2015-08-01
We propose the use of fuzzy membership functions to analyze images of diffuse pulmonary diseases (DPDs) based on fractal and texture features. The features were extracted from preprocessed regions of interest (ROIs) selected from high-resolution computed tomography images. The ROIs represent five different patterns of DPDs and normal lung tissue. A Gaussian mixture model (GMM) was constructed for each feature, with six Gaussians modeling the six patterns. Feature selection was performed and the GMMs of the five significant features were used. From the GMMs, fuzzy membership functions were obtained by a probability-possibility transformation and further statistical analysis was performed. An average classification accuracy of 63.5% was obtained for the six classes. For four of the six classes, the classification accuracy was superior to 65%, and the best classification accuracy was 75.5% for one class. The use of fuzzy membership functions to assist in pattern classification is an alternative to deterministic approaches to explore strategies for medical diagnosis.
Turbulent wakes of fractal objects.
Staicu, Adrian; Mazzi, Biagio; Vassilicos, J C; van de Water, Willem
2003-06-01
Turbulence of a windtunnel flow is stirred using objects that have a fractal structure. The strong turbulent wakes resulting from three such objects which have different fractal dimensions are probed using multiprobe hot-wire anemometry in various configurations. Statistical turbulent quantities are studied within inertial and dissipative range scales in an attempt to relate changes in their self-similar behavior to the scaling of the fractal objects.
Langevin Equation on Fractal Curves
NASA Astrophysics Data System (ADS)
Satin, Seema; Gangal, A. D.
2016-07-01
We analyze random motion of a particle on a fractal curve, using Langevin approach. This involves defining a new velocity in terms of mass of the fractal curve, as defined in recent work. The geometry of the fractal curve, plays an important role in this analysis. A Langevin equation with a particular model of noise is proposed and solved using techniques of the Fα-Calculus.
The Calculation of Fractal Dimension in the Presence of Non-Fractal Clutter
NASA Technical Reports Server (NTRS)
Herren, Kenneth A.; Gregory, Don A.
1999-01-01
The area of information processing has grown dramatically over the last 50 years. In the areas of image processing and information storage the technology requirements have far outpaced the ability of the community to meet demands. The need for faster recognition algorithms and more efficient storage of large quantities of data has forced the user to accept less than lossless retrieval of that data for analysis. In addition to clutter that is not the object of interest in the data set, often the throughput requirements forces the user to accept "noisy" data and to tolerate the clutter inherent in that data. It has been shown that some of this clutter, both the intentional clutter (clouds, trees, etc) as well as the noise introduced on the data by processing requirements can be modeled as fractal or fractal-like. Traditional methods using Fourier deconvolution on these sources of noise in frequency space leads to loss of signal and can, in many cases, completely eliminate the target of interest. The parameters that characterize fractal-like noise (predominately the fractal dimension) have been investigated and a technique to reduce or eliminate noise from real scenes has been developed. Examples of clutter reduced images are presented.
The Calculation of Fractal Dimension in the Presence of Non-Fractal Clutter
NASA Technical Reports Server (NTRS)
Herren, Kenneth A.; Gregory, Don A.
1999-01-01
The area of information processing has grown dramatically over the last 50 years. In the areas of image processing and information storage the technology requirements have far outpaced the ability of the community to meet demands. The need for faster recognition algorithms and more efficient storage of large quantities of data has forced the user to accept less than lossless retrieval of that data for analysis. In addition to clutter that is not the object of interest in the data set, often the throughput requirements forces the user to accept "noisy" data and to tolerate the clutter inherent in that data. It has been shown that some of this clutter, both the intentional clutter (clouds, trees, etc) as well as the noise introduced on the data by processing requirements can be modeled as fractal or fractal-like. Traditional methods using Fourier deconvolution on these sources of noise in frequency space leads to loss of signal and can, in many cases, completely eliminate the target of interest. The parameters that characterize fractal-like noise (predominately the fractal dimension) have been investigated and a technique to reduce or eliminate noise from real scenes has been developed. Examples of clutter reduced images are presented.
Electroencephalographic imaging of higher brain function
NASA Technical Reports Server (NTRS)
Gevins, A.; Smith, M. E.; McEvoy, L. K.; Leong, H.; Le, J.
1999-01-01
High temporal resolution is necessary to resolve the rapidly changing patterns of brain activity that underlie mental function. Electroencephalography (EEG) provides temporal resolution in the millisecond range. However, traditional EEG technology and practice provide insufficient spatial detail to identify relationships between brain electrical events and structures and functions visualized by magnetic resonance imaging or positron emission tomography. Recent advances help to overcome this problem by recording EEGs from more electrodes, by registering EEG data with anatomical images, and by correcting the distortion caused by volume conduction of EEG signals through the skull and scalp. In addition, statistical measurements of sub-second interdependences between EEG time-series recorded from different locations can help to generate hypotheses about the instantaneous functional networks that form between different cortical regions during perception, thought and action. Example applications are presented from studies of language, attention and working memory. Along with its unique ability to monitor brain function as people perform everyday activities in the real world, these advances make modern EEG an invaluable complement to other functional neuroimaging modalities.
Imaging visual function of the human brain
Marg, E.
1988-10-01
Imaging of human brain structure and activity with particular reference to visual function is reviewed along with methods of obtaining the data including computed tomographic (CT) scan, magnetic resonance imaging (MRI), magnetic resonance spectroscopy (MRS), and positron emission tomography (PET). The literature is reviewed and the potential for a new understanding of brain visual function is discussed. PET is reviewed from basic physical principles to the most recent visual brain findings with oxygen-15. It is shown that there is a potential for submillimeter localization of visual functions with sequentially different visual stimuli designed for the temporal separation of the responses. Single photon emission computed tomography (SPECT), a less expensive substitute for PET, is also discussed. MRS is covered from basic physical principles to the current state of the art of in vivo biochemical analysis. Future possible clinical applications are discussed. Improved understanding of the functional neural organization of vision and brain will open a window to maps and circuits of human brain function.119 references.
Electroencephalographic imaging of higher brain function
NASA Technical Reports Server (NTRS)
Gevins, A.; Smith, M. E.; McEvoy, L. K.; Leong, H.; Le, J.
1999-01-01
High temporal resolution is necessary to resolve the rapidly changing patterns of brain activity that underlie mental function. Electroencephalography (EEG) provides temporal resolution in the millisecond range. However, traditional EEG technology and practice provide insufficient spatial detail to identify relationships between brain electrical events and structures and functions visualized by magnetic resonance imaging or positron emission tomography. Recent advances help to overcome this problem by recording EEGs from more electrodes, by registering EEG data with anatomical images, and by correcting the distortion caused by volume conduction of EEG signals through the skull and scalp. In addition, statistical measurements of sub-second interdependences between EEG time-series recorded from different locations can help to generate hypotheses about the instantaneous functional networks that form between different cortical regions during perception, thought and action. Example applications are presented from studies of language, attention and working memory. Along with its unique ability to monitor brain function as people perform everyday activities in the real world, these advances make modern EEG an invaluable complement to other functional neuroimaging modalities.
Fractal multifiber microchannel plates
NASA Technical Reports Server (NTRS)
Cook, Lee M.; Feller, W. B.; Kenter, Almus T.; Chappell, Jon H.
1992-01-01
The construction and performance of microchannel plates (MCPs) made using fractal tiling mehtods are reviewed. MCPs with 40 mm active areas having near-perfect channel ordering were produced. These plates demonstrated electrical performance characteristics equivalent to conventionally constructed MCPs. These apparently are the first MCPs which have a sufficiently high degree of order to permit single channel addressability. Potential applications for these devices and the prospects for further development are discussed.
NASA Astrophysics Data System (ADS)
Martin, Demetri
2015-03-01
Demetri Maritn prepared this palindromic poem as his project for Michael Frame's fractal geometry class at Yale. Notice the first, fourth, and seventh words in the second and next-to-second lines are palindromes, the first two and last two lines are palindromes, the middle line, "Be still if I fill its ebb" minus its last letter is a palindrome, and the entire poem is a palindrome...
NASA Astrophysics Data System (ADS)
Besselink, R.; Stawski, T. M.; Van Driessche, A. E. S.; Benning, L. G.
2016-12-01
Densely packed surface fractal aggregates form in systems with high local volume fractions of particles with very short diffusion lengths, which effectively means that particles have little space to move. However, there are no prior mathematical models, which would describe scattering from such surface fractal aggregates and which would allow the subdivision between inter- and intraparticle interferences of such aggregates. Here, we show that by including a form factor function of the primary particles building the aggregate, a finite size of the surface fractal interfacial sub-surfaces can be derived from a structure factor term. This formalism allows us to define both a finite specific surface area for fractal aggregates and the fraction of particle interfacial sub-surfaces at the perimeter of an aggregate. The derived surface fractal model is validated by comparing it with an ab initio approach that involves the generation of a "brick-in-a-wall" von Koch type contour fractals. Moreover, we show that this approach explains observed scattering intensities from in situ experiments that followed gypsum (CaSO4 ṡ 2H2O) precipitation from highly supersaturated solutions. Our model of densely packed "brick-in-a-wall" surface fractal aggregates may well be the key precursor step in the formation of several types of mosaic- and meso-crystals.
Suganthi, S S; Pradhap, S Singh Allmin; Ramakrishnan, S
2015-01-01
Observing and classifying the indirect immunofluorescence patterns on HEp-2 cells can help in detecting Anti-Nuclear-Antibodies. A computer algorithm to perform this function can lead to a more standardized, faster and accurate diagnosis of auto-immune diseases such as systemic lupus erythematosus, sjogrens syndrome, and rheumatoid arthritis. In this paper, HEp-2 staining patterns are classified using segmentation based fractal texture features. The images used for this experimentation are obtained from a publicly available database. The features extracted from a cell image is used to classify it into homogenous, fine speckled, coarse speckled, centromere and nucleolus. The cell images are segmented using the ground truth mask provided in the database. Adaptive histogram equalization is applied to the segmented images for contrast enhancement. Three features namely mean intensity, area and Hausdorff fractal dimension of the border are extracted for 8 different Otsu threshold levels. Finally, the 24 features thus extracted are fed to a support vector machine with Gaussian radial basis function kernel. It is observed that the overall accuracy of classification is 65.17%. The accuracy is greatly dependent on scaling and distribution of the features given to SVM. It appears that the segmentation based fractal texture features and SVM could help to build a robust automated diagnosis tool for auto-immune diseases.
Darwinian Evolution and Fractals
NASA Astrophysics Data System (ADS)
Carr, Paul H.
2009-05-01
Did nature's beauty emerge by chance or was it intelligently designed? Richard Dawkins asserts that evolution is blind aimless chance. Michael Behe believes, on the contrary, that the first cell was intelligently designed. The scientific evidence is that nature's creativity arises from the interplay between chance AND design (laws). Darwin's ``Origin of the Species,'' published 150 years ago in 1859, characterized evolution as the interplay between variations (symbolized by dice) and the natural selection law (design). This is evident in recent discoveries in DNA, Madelbrot's Fractal Geometry of Nature, and the success of the genetic design algorithm. Algorithms for generating fractals have the same interplay between randomness and law as evolution. Fractal statistics, which are not completely random, characterize such phenomena such as fluctuations in the stock market, the Nile River, rainfall, and tree rings. As chaos theorist Joseph Ford put it: God plays dice, but the dice are loaded. Thus Darwin, in discovering the evolutionary interplay between variations and natural selection, was throwing God's dice!
Fractals in biology and medicine
NASA Technical Reports Server (NTRS)
Havlin, S.; Buldyrev, S. V.; Goldberger, A. L.; Mantegna, R. N.; Ossadnik, S. M.; Peng, C. K.; Simons, M.; Stanley, H. E.
1995-01-01
Our purpose is to describe some recent progress in applying fractal concepts to systems of relevance to biology and medicine. We review several biological systems characterized by fractal geometry, with a particular focus on the long-range power-law correlations found recently in DNA sequences containing noncoding material. Furthermore, we discuss the finding that the exponent alpha quantifying these long-range correlations ("fractal complexity") is smaller for coding than for noncoding sequences. We also discuss the application of fractal scaling analysis to the dynamics of heartbeat regulation, and report the recent finding that the normal heart is characterized by long-range "anticorrelations" which are absent in the diseased heart.
Fractals in physiology and medicine
NASA Technical Reports Server (NTRS)
Goldberger, Ary L.; West, Bruce J.
1987-01-01
The paper demonstrates how the nonlinear concepts of fractals, as applied in physiology and medicine, can provide an insight into the organization of such complex structures as the tracheobronchial tree and heart, as well as into the dynamics of healthy physiological variability. Particular attention is given to the characteristics of computer-generated fractal lungs and heart and to fractal pathologies in these organs. It is shown that alterations in fractal scaling may underlie a number of pathophysiological disturbances, including sudden cardiac death syndromes.
Fractals in biology and medicine
NASA Technical Reports Server (NTRS)
Havlin, S.; Buldyrev, S. V.; Goldberger, A. L.; Mantegna, R. N.; Ossadnik, S. M.; Peng, C. K.; Simons, M.; Stanley, H. E.
1995-01-01
Our purpose is to describe some recent progress in applying fractal concepts to systems of relevance to biology and medicine. We review several biological systems characterized by fractal geometry, with a particular focus on the long-range power-law correlations found recently in DNA sequences containing noncoding material. Furthermore, we discuss the finding that the exponent alpha quantifying these long-range correlations ("fractal complexity") is smaller for coding than for noncoding sequences. We also discuss the application of fractal scaling analysis to the dynamics of heartbeat regulation, and report the recent finding that the normal heart is characterized by long-range "anticorrelations" which are absent in the diseased heart.
Dimension of fractal basin boundaries
Park, B.S.
1988-01-01
In many dynamical systems, multiple attractors coexist for certain parameter ranges. The set of initial conditions that asymptotically approach each attractor is its basin of attraction. These basins can be intertwined on arbitrary small scales. Basin boundary can be either smooth or fractal. Dynamical systems that have fractal basin boundary show final state sensitivity of the initial conditions. A measure of this sensitivity (uncertainty exponent {alpha}) is related to the dimension of the basin boundary d = D - {alpha}, where D is the dimension of the phase space and d is the dimension of the basin boundary. At metamorphosis values of the parameter, there might happen a conversion from smooth to fractal basin boundary (smooth-fractal metamorphosis) or a conversion from fractal to another fractal basin boundary characteristically different from the previous fractal one (fractal-fractal metamorphosis). The dimension changes continuously with the parameter except at the metamorphosis values where the dimension of the basin boundary jumps discontinuously. We chose the Henon map and the forced damped pendulum to investigate this. Scaling of the basin volumes near the metamorphosis values of the parameter is also being studied for the Henon map. Observations are explained analytically by using low dimensional model map.
Investigating Fractal Geometry Using LOGO.
ERIC Educational Resources Information Center
Thomas, David A.
1989-01-01
Discusses dimensionality in Euclidean geometry. Presents methods to produce fractals using LOGO. Uses the idea of self-similarity. Included are program listings and suggested extension activities. (MVL)
Fractals in physiology and medicine
NASA Technical Reports Server (NTRS)
Goldberger, Ary L.; West, Bruce J.
1987-01-01
The paper demonstrates how the nonlinear concepts of fractals, as applied in physiology and medicine, can provide an insight into the organization of such complex structures as the tracheobronchial tree and heart, as well as into the dynamics of healthy physiological variability. Particular attention is given to the characteristics of computer-generated fractal lungs and heart and to fractal pathologies in these organs. It is shown that alterations in fractal scaling may underlie a number of pathophysiological disturbances, including sudden cardiac death syndromes.
Retinal functional imager (RFI): non-invasive functional imaging of the retina.
Ganekal, S
2013-01-01
Retinal functional imager (RFI) is a unique non-invasive functional imaging system with novel capabilities for visualizing the retina. The objective of this review was to show the utility of non-invasive functional imaging in various disorders. Electronic literature search was carried out using the websites www.pubmed.gov and www.google.com. The search words were retinal functional imager and non-invasive retinal imaging used in combination. The articles published or translated into English were studied. The RFI directly measures hemodynamic parameters such as retinal blood-flow velocity, oximetric state, metabolic responses to photic activation and generates capillary perfusion maps (CPM) that provides retinal vasculature detail similar to flourescein angiography. All of these parameters stand in a direct relationship to the function and therefore the health of the retina, and are known to be degraded in the course of retinal diseases. Detecting changes in retinal function aid early diagnosis and treatment as functional changes often precede structural changes in many retinal disorders.
Is the human left ventricle partially a fractal pump?
NASA Astrophysics Data System (ADS)
Moore, Brandon; Dasi, Lakshmi
2011-11-01
Ventricular systolic and diastolic dysfunctions represent a large portion of healthcare problems in the United States. Many of these problems are caused and/or characterized by their altered fluid-structure mechanics. The structure of the left ventricle in particular is complex with time dependent multi-scale geometric complexity. At relatively small scales, one facet that is still not well understood is the role of trabeculae in the pumping function of the left ventricle. We utilize fractal geometry tools to help characterize the complexity of the inner surface of the left ventricle at different times during the cardiac cycle. A high-resolution three dimensional model of the time dependent ventricular geometry was constructed from computed tomography (CT) images in a human. The scale dependent fractal dimension of the ventricle was determined using the box-counting algorithm over the cardiac cycle. It is shown that the trabeculae may indeed play an integral role in the biomechanics of pumping by regulating the mechanical leverage available to the cardiac muscle fibers.
Using fractal analysis of thermal signatures for thyroid disease evaluation
NASA Astrophysics Data System (ADS)
Gavriloaia, Gheorghe; Sofron, Emil; Gavriloaia, Mariuca-Roxana; Ghemigean, Adina-Mariana
2010-11-01
The skin is the largest organ of the body and it protects against heat, light, injury and infection. Skin temperature is an important parameter for diagnosing diseases. Thermal analysis is non-invasive, painless, and relatively inexpensive, showing a great potential research. Since the thyroid regulates metabolic rate it is intimately connected to body temperature, more than, any modification of its function generates a specific thermal image on the neck skin. The shapes of thermal signatures are often irregular in size and shape. Euclidean geometry is not able to evaluate their shape for different thyroid diseases, and fractal geometry is used in this paper. Different thyroid diseases generate different shapes, and their complexity are evaluated by specific mathematical approaches, fractal analysis, in order to the evaluate selfsimilarity and lacunarity. Two kinds of thyroid diseases, hyperthyroidism and papillary cancer are analyzed in this paper. The results are encouraging and show the ability to continue research for thermal signature to be used in early diagnosis of thyroid diseases.
Global lithospheric imaging using teleseismic receiver functions
NASA Astrophysics Data System (ADS)
Rondenay, S.; Spieker, K.; Halpaap, F.; Farestveit, M.; Sawade, L.; Zijerveld, L.
2015-12-01
Project GLImER (Global Lithospheric Imagining using Earthquake Recordings) aims to conduct a global survey of lithospheric interfaces using converted teleseismic body waves. Data from permanent and temporary seismic networks worldwide will be processed automatically to produce global maps of key interfaces (Moho, intra-lithospheric interfaces, lithosphere-asthenosphere boundary). In this presentation, we discuss the challenges associated with automating the analysis of converted waves and the potential of the resulting data products to be used in novel imaging approaches. With regards to automation, we address in particular the search for an optimal deconvolution method in receiver function analysis. To do so, we carry out a systematic comparison of various commonly used deconvolution methods and find that all methods produce equally robust receiver functions provided that a suitable regularization parameter is found. We further note that a suitable regularization can be found objectively for most approaches, thus challenging the belief that only time-domain deconvolution is a viable option for receiver function automation. With regards to imaging applications, we investigate how the resulting global database of receiver functions will be amenable to existing processing approaches as well as new approaches adapted from seismic exploration, including industry-based interpretation tools.
Fractal analysis of narwhal space use patterns.
Laidre, Kristin L; Heide-Jørgensen, Mads P; Logsdon, Miles L; Hobbs, Roderick C; Dietz, Rune; VanBlaricom, Glenn R
2004-01-01
Quantifying animal movement in response to a spatially and temporally heterogeneous environment is critical to understanding the structural and functional landscape influences on population viability. Generalities of landscape structure can easily be extended to the marine environment, as marine predators inhabit a patchy, dynamic system, which influences animal choice and behavior. An innovative use of the fractal measure of complexity, indexing the linearity of movement paths over replicate temporal scales, was applied to satellite tracking data collected from narwhals (Monodon monoceros) (n = 20) in West Greenland and the eastern Canadian high Arctic. Daily movements of individuals were obtained using polar orbiting satellites via the ARGOS data location and collection system. Geographic positions were filtered to obtain a daily good quality position for each whale. The length of total pathway was measured over seven different temporal length scales (step lengths), ranging from one day to one week, and a seasonal mean was calculated. Fractal dimension (D) was significantly different between seasons, highest during summer (D = 1.61, SE 0.04) and winter (D = 1.69, SE 0.06) when whales made convoluted movements in focal areas. Fractal dimension was lowest during fall (D = 1.34, SE 0.03) when whales were migrating south ahead of the forming sea ice. There were no significant effects of size category or sex on fractal dimension by season. The greater linearity of movement during the migration period suggests individuals do not intensively forage on patchy resources until they arrive at summer or winter sites. The highly convoluted movements observed during summer and winter suggest foraging or searching efforts in localized areas. Significant differences between the fractal dimensions on two separate wintering grounds in Baffin Bay suggest differential movement patterns in response to the dynamics of sea ice.
Fractal analysis of Xylella fastidiosa biofilm formation
NASA Astrophysics Data System (ADS)
Moreau, A. L. D.; Lorite, G. S.; Rodrigues, C. M.; Souza, A. A.; Cotta, M. A.
2009-07-01
We have investigated the growth process of Xylella fastidiosa biofilms inoculated on a glass. The size and the distance between biofilms were analyzed by optical images; a fractal analysis was carried out using scaling concepts and atomic force microscopy images. We observed that different biofilms show similar fractal characteristics, although morphological variations can be identified for different biofilm stages. Two types of structural patterns are suggested from the observed fractal dimensions Df. In the initial and final stages of biofilm formation, Df is 2.73±0.06 and 2.68±0.06, respectively, while in the maturation stage, Df=2.57±0.08. These values suggest that the biofilm growth can be understood as an Eden model in the former case, while diffusion-limited aggregation (DLA) seems to dominate the maturation stage. Changes in the correlation length parallel to the surface were also observed; these results were correlated with the biofilm matrix formation, which can hinder nutrient diffusion and thus create conditions to drive DLA growth.
Fractal analysis of bone structure with applications to osteoporosis and microgravity effects
Acharya, R.S.; Swarnarkar, V.; Krishnamurthy, R.; Hausman, E.; LeBlanc, A.; Lin, C.; Shackelford, L.
1995-12-31
The authors characterize the trabecular structure with the aid of fractal dimension. The authors use Alternating Sequential filters to generate a nonlinear pyramid for fractal dimension computations. The authors do not make any assumptions of the statistical distributions of the underlying fractal bone structure. The only assumption of the scheme is the rudimentary definition of self similarity. This allows them the freedom of not being constrained by statistical estimation schemes. With mathematical simulations, the authors have shown that the ASF methods outperform other existing methods for fractal dimension estimation. They have shown that the fractal dimension remains the same when computed with both the X-Ray images and the MRI images of the patella. They have shown that the fractal dimension of osteoporotic subjects is lower than that of the normal subjects. In animal models, the authors have shown that the fractal dimension of osteoporotic rats was lower than that of the normal rats. In a 17 week bedrest study, they have shown that the subject`s prebedrest fractal dimension is higher than that of the postbedrest fractal dimension.
Fractal analysis of bone structure with applications to osteoporosis and microgravity effects
NASA Astrophysics Data System (ADS)
Acharya, Raj S.; LeBlanc, Adrian; Shackelford, Linda; Swarnakar, Vivek; Krishnamurthy, Ram; Hausman, E.; Lin, Chin-Shoou
1995-05-01
We characterize the trabecular structure with the aid of fractal dimension. We use alternating sequential filters (ASF) to generate a nonlinear pyramid for fractal dimension computations. We do not make any assumptions of the statistical distributions of the underlying fractal bone structure. The only assumption of our scheme is the rudimentary definition of self-similarity. This allows us the freedom of not being constrained by statistical estimation schemes. With mathematical simulations, we have shown that the ASF methods outperform other existing methods for fractal dimension estimation. We have shown that the fractal dimension remains the same when computed with both the x-ray images and the MRI images of the patella. We have shown that the fractal dimension of osteoporotic subjects is lower than that of the normal subjects. In animal models, we have shown that the fractal dimension of osteoporotic rats was lower than that of the normal rats. In a 17 week bedrest study, we have shown that the subject's prebedrest fractal dimension is higher than that of the postbedrest fractal dimension.
Functional MRI using regularized parallel imaging acquisition.
Lin, Fa-Hsuan; Huang, Teng-Yi; Chen, Nan-Kuei; Wang, Fu-Nien; Stufflebeam, Steven M; Belliveau, John W; Wald, Lawrence L; Kwong, Kenneth K
2005-08-01
Parallel MRI techniques reconstruct full-FOV images from undersampled k-space data by using the uncorrelated information from RF array coil elements. One disadvantage of parallel MRI is that the image signal-to-noise ratio (SNR) is degraded because of the reduced data samples and the spatially correlated nature of multiple RF receivers. Regularization has been proposed to mitigate the SNR loss originating due to the latter reason. Since it is necessary to utilize static prior to regularization, the dynamic contrast-to-noise ratio (CNR) in parallel MRI will be affected. In this paper we investigate the CNR of regularized sensitivity encoding (SENSE) acquisitions. We propose to implement regularized parallel MRI acquisitions in functional MRI (fMRI) experiments by incorporating the prior from combined segmented echo-planar imaging (EPI) acquisition into SENSE reconstructions. We investigated the impact of regularization on the CNR by performing parametric simulations at various BOLD contrasts, acceleration rates, and sizes of the active brain areas. As quantified by receiver operating characteristic (ROC) analysis, the simulations suggest that the detection power of SENSE fMRI can be improved by regularized reconstructions, compared to unregularized reconstructions. Human motor and visual fMRI data acquired at different field strengths and array coils also demonstrate that regularized SENSE improves the detection of functionally active brain regions.
Functional MRI Using Regularized Parallel Imaging Acquisition
Lin, Fa-Hsuan; Huang, Teng-Yi; Chen, Nan-Kuei; Wang, Fu-Nien; Stufflebeam, Steven M.; Belliveau, John W.; Wald, Lawrence L.; Kwong, Kenneth K.
2013-01-01
Parallel MRI techniques reconstruct full-FOV images from undersampled k-space data by using the uncorrelated information from RF array coil elements. One disadvantage of parallel MRI is that the image signal-to-noise ratio (SNR) is degraded because of the reduced data samples and the spatially correlated nature of multiple RF receivers. Regularization has been proposed to mitigate the SNR loss originating due to the latter reason. Since it is necessary to utilize static prior to regularization, the dynamic contrast-to-noise ratio (CNR) in parallel MRI will be affected. In this paper we investigate the CNR of regularized sensitivity encoding (SENSE) acquisitions. We propose to implement regularized parallel MRI acquisitions in functional MRI (fMRI) experiments by incorporating the prior from combined segmented echo-planar imaging (EPI) acquisition into SENSE reconstructions. We investigated the impact of regularization on the CNR by performing parametric simulations at various BOLD contrasts, acceleration rates, and sizes of the active brain areas. As quantified by receiver operating characteristic (ROC) analysis, the simulations suggest that the detection power of SENSE fMRI can be improved by regularized reconstructions, compared to unregularized reconstructions. Human motor and visual fMRI data acquired at different field strengths and array coils also demonstrate that regularized SENSE improves the detection of functionally active brain regions. PMID:16032694
Structural and functional brain imaging in schizophrenia.
Cleghorn, J M; Zipursky, R B; List, S J
1991-01-01
We present an evaluation of the contribution of structural and functional brain imaging to our understanding of schizophrenia. Methodological influences on the validity of the data generated by these new technologies include problems with measurement and clinical and anatomic heterogeneity. These considerations greatly affect the interpretation of the data generated by these technologies. Work in these fields to date, however, has produced strong evidence which suggests that schizophrenia is a disease which involves abnormalities in the structure and function of many brain areas. Structural brain imaging studies of schizophrenia using computed tomography (CT) and magnetic resonance imaging (MRI) are reviewed and their contribution to current theories of the pathogenesis of schizophrenia are discussed. Positron emission tomography (PET) studies of brain metabolic activity and dopamine receptor binding in schizophrenia are summarized and the critical questions raised by these studies are outlined. Future studies in these fields have the potential to yield critical insights into the pathophysiology of schizophrenia; new directions for studies of schizophrenia using these technologies are identified. PMID:1911736
Fractal properties of macrophage membrane studied by AFM.
Bitler, A; Dover, R; Shai, Y
2012-12-01
Complexity of cell membrane poses difficulties to quantify corresponding morphology changes during cell proliferation and damage. We suggest using fractal dimension of the cell membrane to quantify its complexity and track changes produced by various treatments. Glutaraldehyde fixed mouse RAW 264.7 macrophage membranes were chosen as model system and imaged in PeakForce QNM (quantitative nanomechanics) mode of AFM (atomic force microscope). The morphology of the membranes was characterized by fractal dimension. The parameter was calculated for set of AFM images by three different methods. The same calculations were done for the AFM images of macrophages treated with colchicine, an inhibitor of the microtubule polymerization, and microtubule stabilizing agent taxol. We conclude that fractal dimension can be additional and useful parameter to characterize the cell membrane complexity and track the morphology changes produced by different treatments.
NASA Astrophysics Data System (ADS)
Boyko, Anton N.; Pyatilova, Olga V.; Kalmykov, Rustam M.; Gaev, Dahir S.; Timoshenkov, Sergei P.; Gavrilov, Sergei A.
2016-12-01
Study of new materials and composites based on porous silicon is of great interest for electronics and microelectronics industry. Functional characteristics of structured layers are closely associated with their morphology properties and treatment conditions correspondently. In this work a porous silicon layers formed by metal-assisted chemical etching (MACE) with the use of gas adsorption-desorption method, scanning electron microscopy (SEM) and fractal geometry have been examined. Specific surface area given by multi-point BET method was about of 7 m2/g and 13 m2/g for n-Si and p-Si specimens correspondently. Surface fractal dimension Ds was estimated for p-type mesoporous silicon from BET results using Neimark's thermodynamic approach, the value is Ds=2.86. "Slit islands" Mandelbrot's algorithm was applied for analysis of SEM images and calculations of surface fractal dimension Ds, computation gives Ds = 2.52 for n-Si sample and Ds = 2.84 for p-Si sample. The study testified the fractal nature of porous layers formed by MACE and exhibits correlation between different methods of fractal dimension estimation. The results can be applied for improvement of methods of structured solids characterization.
ERIC Educational Resources Information Center
Geake, John
1992-01-01
Examined how exposure to a program of fractal computer graphics affected the perceptual sensitivity of sixth-grade students (n=197) to the natural visual environment. MANCOVA analysis of collected data and students' written responses to questions indicated that environmental perceptual sensitivity was higher for subjects exposed to fractal images.…
Overview of Functional Magnetic Resonance Imaging
Glover, Gary H.
2010-01-01
Synopsis Blood Oxygen Level Dependent (BOLD) functional magnetic resonance imaging (fMRI) depicts changes in deoxyhemoglobin concentration consequent to task-induced or spontaneous modulation of neural metabolism. Since its inception in 1990, this method has been widely employed in thousands of studies of cognition for clinical applications such as surgical planning, for monitoring treatment outcomes, and as a biomarker in pharmacologic and training programs. Technical developments have solved most of the challenges of applying fMRI in practice. These challenges include low contrast to noise ratio of BOLD signals, image distortion, and signal dropout. More recently, attention is turning to the use of pattern classification and other statistical methods to draw increasingly complex inferences about cognitive brain states from fMRI data. This paper reviews the methods, some of the challenges and the future of fMRI. PMID:21435566
Fractal analysis of lumbar vertebral cancellous bone architecture.
Feltrin, G P; Macchi, V; Saccavini, C; Tosi, E; Dus, C; Fassina, A; Parenti, A; De Caro, R
2001-11-01
Osteoporosis is characterized by bone mineral density (BMD) decreasing and spongy bone rearrangement with consequent loss of elasticity and increased bone fragility. Quantitative computed tomography (QCT) quantifies bone mineral content but does not describe spongy architecture. Analysis of trabecular pattern may provide additional information to evaluate osteoporosis. The aim of this study was to determine whether the fractal analysis of the microradiography of lumbar vertebrae provides a reliable assessment of bone texture, which correlates with the BMD. The lumbar segment of the spine was removed from 22 cadavers with no history of back pain and examined with standard x-ray, traditional tomography, and quantitative computed tomography to measure BMD. The fractal dimension, which quantifies the image fractal complexity, was calculated on microradiographs of axial sections of the fourth lumbar vertebra to determine its characteristic spongy network. The relationship between the values of the BMD and those of the fractal dimension was evaluated by linear regression and a statistically significant correlation (R = 0.96) was found. These findings suggest that the application of fractal analysis to radiological analyses can provide valuable information on the trabecular pattern of vertebrae. Thus, fractal dimensions of trabecular bone structure should be considered as a supplement to BMD evaluation in the assessment of osteoporosis.
Fractal analysis: methodologies for biomedical researchers.
Ristanović, Dusan; Milosević, Nebojsa T
2012-01-01
Fractal analysis has become a popular method in all branches of scientific investigations including biology and medicine. Although there is a growing interest in the application of fractal analysis in biological sciences, questions about the methodology of fractal analysis have partly restricted its wider and comprehensible application. It is a notable fact that fractal analysis is derived from fractal geometry, but there are some unresolved issues that need to be addressed. In this respect, we discuss several related underlying principles for fractal analysis and establish the meaningful relationship between fractal analysis and fractal geometry. Since some concepts in fractal analysis are determined descriptively and/or qualitatively, this paper provides their exact mathematical definitions or explanations. Another aim of this study is to show that nowadays fractal analysis is an independent mathematical and experimental method based on Mandelbrot's fractal geometry, Euclidean traditiontal geometry and Richardson's coastline method.
Origins of fractality in the growth of complex networks
NASA Astrophysics Data System (ADS)
Song, Chaoming; Havlin, Shlomo; Makse, Hernán A.
2006-04-01
Complex networks from such different fields as biology, technology or sociology share similar organization principles. The possibility of a unique growth mechanism promises to uncover universal origins of collective behaviour. In particular, the emergence of self-similarity in complex networks raises the fundamental question of the growth process according to which these structures evolve. Here we investigate the concept of renormalization as a mechanism for the growth of fractal and non-fractal modular networks. We show that the key principle that gives rise to the fractal architecture of networks is a strong effective `repulsion' (or, disassortativity) between the most connected nodes (that is, the hubs) on all length scales, rendering them very dispersed. More importantly, we show that a robust network comprising functional modules, such as a cellular network, necessitates a fractal topology, suggestive of an evolutionary drive for their existence.
Accuracy of the box-counting algorithm for noisy fractals
NASA Astrophysics Data System (ADS)
Górski, A. Z.; Stróż, M.; Oświȩcimka, P.; Skrzat, J.
2016-04-01
The box-counting (BC) algorithm is applied to calculate fractal dimensions of four fractal sets. The sets are contaminated with an additive noise with amplitude γ=10-5-10-1. The accuracy of calculated numerical values of the fractal dimensions is analyzed as a function of γ for different sizes of the data sample. In particular, it has been found that even in case of pure fractals (γ=0) as well as for tiny noise (γ≈10-5) one has considerable error for the calculated exponents of order 0.01. For larger noise the error is growing up to 0.1 and more, with natural saturation limited by the embedding dimension. This prohibits the power-like scaling of the error. Moreover, the noise effect cannot be cured by taking larger data samples.
SEVEN TOPICS IN FUNCTIONAL MAGNETIC RESONANCE IMAGING
BANDETTINI, PETER A.
2010-01-01
Functional MRI (fMRI) is a non-invasive brain imaging methodology that started in 1991 and allows human brain activation to be imaged at high resolution within only a few minutes. Because it has extremely high sensitivity, is relatively easy to implement, and can be performed on most standard clinical MRI scanners. It continues to grow at an explosive rate throughout the world. Over the years, at any given time, fMRI has been defined by only a handful of major topics that have been the focus of researchers using and developing the methodology. In this review, I attempt to take a snapshot of the field of fMRI as it is in mid-2009 by discussing the seven topics that I feel are most on the minds of fMRI researchers. The topics are, in no particular order or grouping: (1) Clinical impact, (2) Utilization of individual functional maps, (3) fMRI signal interpretation, (4) Pattern effect mapping and decoding, (5) Endogenous oscillations, (6) MRI technology, and (7) Alternative functional contrast mechanisms. Most of these topics are highly interdependent, each advancing as the others advance. While most fMRI involves applications towards clinical or neuroscience questions, all applications are fundamentally dependent on advances in basic methodology as well as advances in our understanding of the relationship between neuronal activity and fMRI signal changes. This review neglects almost completely an in-depth discussion of applications. Rather the discussions are on the methods and interpretation. PMID:19938211
Functional CT imaging of prostate cancer
NASA Astrophysics Data System (ADS)
Henderson, Elizabeth; Milosevic, Michael F.; Haider, Masoom A.; Yeung, Ivan W. T.
2003-09-01
The purpose of this paper is to investigate the distribution of blood flow (F), mean capillary transit time (Tc), capillary permeability (PS) and blood volume (vb) in prostate cancer using contrast-enhanced CT. Nine stage T2-T3 prostate cancer patients were enrolled in the study. Following bolus injection of a contrast agent, a time series of CT images of the prostate was acquired. Functional maps showing the distribution of F, Tc, PS and vb within the prostate were generated using a distributed parameter tracer kinetic model, the adiabatic approximation to the tissue homogeneity model. The precision of the maps was assessed using covariance matrix analysis. Finally, maps were compared to the findings of standard clinical investigations. Eight of the functional maps demonstrated regions of increased F, PS and vb, the locations of which were consistent with the results of standard clinical investigations. However, model parameters other than F could only be measured precisely within regions of high F. In conclusion functional CT images of cancer-containing prostate glands demonstrate regions of elevated F, PS and vb. However, caution should be used when applying a complex tracer kinetic model to the study of prostate cancer since not all parameters can be measured precisely in all areas.