Partial iterated function system-based fractal image coding
NASA Astrophysics Data System (ADS)
Wang, Zhou; Yu, Ying Lin
1996-06-01
A recent trend in computer graphics and image processing has been to use iterated function system (IFS) to generate and describe images. Barnsley et al. presented the conception of fractal image compression and Jacquin was the first to propose a fully automatic gray scale still image coding algorithm. This paper introduces a generalization of basic IFS, leading to a conception of partial iterated function system (PIFS). A PIFS operator is contractive under certain conditions and when it is applied to generate an image, only part of it is actually iteratedly applied. PIFS provides us a flexible way to combine fractal coding with other image coding techniques and many specific algorithms can be derived from it. On the basis of PIFS, we implement a partial fractal block coding (PFBC) algorithm and compare it with basic IFS based fractal block coding algorithm. Experimental results show that coding efficiency is improved and computation time is reduced while image fidelity does not degrade very much.
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.
Fractal images induce fractal pupil dilations and constrictions.
Moon, P; Muday, J; Raynor, S; Schirillo, J; Boydston, C; Fairbanks, M S; Taylor, R P
2014-09-01
Fractals are self-similar structures or patterns that repeat at increasingly fine magnifications. Research has revealed fractal patterns in many natural and physiological processes. This article investigates pupillary size over time to determine if their oscillations demonstrate a fractal pattern. We predict that pupil size over time will fluctuate in a fractal manner and this may be due to either the fractal neuronal structure or fractal properties of the image viewed. We present evidence that low complexity fractal patterns underlie pupillary oscillations as subjects view spatial fractal patterns. We also present evidence implicating the autonomic nervous system's importance in these patterns. Using the variational method of the box-counting procedure we demonstrate that low complexity fractal patterns are found in changes within pupil size over time in millimeters (mm) and our data suggest that these pupillary oscillation patterns do not depend on the fractal properties of the image viewed. PMID:24978815
Fractal-based image processing for mine detection
NASA Astrophysics Data System (ADS)
Nelson, Susan R.; Tuovila, Susan M.
1995-06-01
A fractal-based analysis algorithm has been developed to perform the task of automated recognition of minelike targets in side scan sonar images. Because naturally occurring surfaces, such as the sea bottom, are characterized by irregular textures they are well suited to modeling as fractal surfaces. Manmade structures, including mines, are composed of Euclidean shapes, which makes fractal-based analysis highly appropriate for discrimination of mines from a natural background. To that end, a set of fractal features, including fractal dimension, was developed to classify image areas as minelike targets, nonmine areas, or clutter. Four different methods of fractal dimension calculation were compared and the Weierstrass function was used to study the effect of various signal processing procedures on the fractal qualities of an image. The difference in fractal dimension between different images depends not only on the physical features extant in the images but in the underlying statistical characteristics of the processing procedures applied to the images and the underlying mathematical assumptions of the fractal dimension calculation methods. For the image set studied, fractal-based analysis achieved a classification rate similar to human operators, and was very successful in identifying areas of clutter. The analysis technique presented here is applicable to any type of signal that may be configured as an image, making this technique suitable for multisensor systems.
Engineering images designed by fractal subdivision scheme.
Mustafa, Ghulam; Bari, Mehwish; Jamil, Saba
2016-01-01
This paper is concerned with the modeling of engineering images by the fractal properties of 6-point binary interpolating scheme. Association between the fractal behavior of the limit curve/surface and the parameter is obtained. The relationship between the subdivision parameter and the fractal dimension of the limit fractal curve of subdivision fractal is also presented. Numerical examples and visual demonstrations show that 6-point scheme is good choice for the generation of fractals for the modeling of fractal antennas, bearings, garari's and rock etc. PMID:27652066
Fractal calculus involving gauge function
NASA Astrophysics Data System (ADS)
Golmankhaneh, Alireza K.; Baleanu, Dumitru
2016-08-01
Henstock-Kurzweil integral or gauge integral is the generalization of the Riemann integral. The functions which are not integrable because of singularity in the senses of Lebesgue or Riemann are gauge integrable. In this manuscript, we have generalized Fα-calculus using the gauge integral method for the integrating of the functions on fractal set subset of real-line where they have singularities. The suggested new method leads to the wider class of functions on the fractal subset of real-line that are *Fα-integrable. Using gauge function we define *Fα-derivative of functions their Fα-derivative is not exist. The reported results can be used for generalizing the fundamental theorem of Fα-calculus.
Multi-Scale Fractal Analysis of Image Texture and Pattern
NASA Technical Reports Server (NTRS)
Emerson, Charles W.
1998-01-01
Fractals embody important ideas of self-similarity, in which the spatial behavior or appearance of a system is largely independent of scale. Self-similarity is defined as a property of curves or surfaces where each part is indistinguishable from the whole, or where the form of the curve or surface is invariant with respect to scale. An ideal fractal (or monofractal) curve or surface has a constant dimension over all scales, although it may not be an integer value. This is in contrast to Euclidean or topological dimensions, where discrete one, two, and three dimensions describe curves, planes, and volumes. Theoretically, if the digital numbers of a remotely sensed image resemble an ideal fractal surface, then due to the self-similarity property, the fractal dimension of the image will not vary with scale and resolution. However, most geographical phenomena are not strictly self-similar at all scales, but they can often be modeled by a stochastic fractal in which the scaling and self-similarity properties of the fractal have inexact patterns that can be described by statistics. Stochastic fractal sets relax the monofractal self-similarity assumption and measure many scales and resolutions in order to represent the varying form of a phenomenon as a function of local variables across space. In image interpretation, pattern is defined as the overall spatial form of related features, and the repetition of certain forms is a characteristic pattern found in many cultural objects and some natural features. Texture is the visual impression of coarseness or smoothness caused by the variability or uniformity of image tone or color. A potential use of fractals concerns the analysis of image texture. In these situations it is commonly observed that the degree of roughness or inexactness in an image or surface is a function of scale and not of experimental technique. The fractal dimension of remote sensing data could yield quantitative insight on the spatial complexity and
Estimating fractal dimension of medical images
NASA Astrophysics Data System (ADS)
Penn, Alan I.; Loew, Murray H.
1996-04-01
Box counting (BC) is widely used to estimate the fractal dimension (fd) of medical images on the basis of a finite set of pixel data. The fd is then used as a feature to discriminate between healthy and unhealthy conditions. We show that BC is ineffective when used on small data sets and give examples of published studies in which researchers have obtained contradictory and flawed results by using BC to estimate the fd of data-limited medical images. We present a new method for estimating fd of data-limited medical images. In the new method, fractal interpolation functions (FIFs) are used to generate self-affine models of the underlying image; each model, upon discretization, approximates the original data points. The fd of each FIF is analytically evaluated. The mean of the fds of the FIFs is the estimate of the fd of the original data. The standard deviation of the fds of the FIFs is a confidence measure of the estimate. The goodness-of-fit of the discretized models to the original data is a measure of self-affinity of the original data. In a test case, the new method generated a stable estimate of fd of a rib edge in a standard chest x-ray; box counting failed to generate a meaningful estimate of the same image.
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…
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.
Fractal steganography using artificially generated images
NASA Astrophysics Data System (ADS)
Agaian, Sos S.; Susmilch, Johanna M.
2008-04-01
Steganography is the art of hiding information in a cover image so it is not readily apparent to a third party observer. There exist a variety of fractal steganographic methods for embedding information in an image. The main contribution of the previous work was to embed data by modifying the original, pre-existing image or embedding an encrypted datastream in an image. In this paper we propose a new fractal steganographic method. The fractal parameters of the image are altered by the steganographic data while the image is generated. This results in an image that is generated with the data already hidden in it and not added after the fact. We show that the input parameters of the algorithm, such as the type of fractal and number of iterations, will serve as a simple secret key for extracting the hidden information. We explain how the capacity of the image is affected by the variation of the parameters. We also demonstrate how standard steganographic detection algorithms perform against the generated images and analyze their capability to detect information hidden with this new technique
Fast fractal image compression with triangulation wavelets
NASA Astrophysics Data System (ADS)
Hebert, D. J.; Soundararajan, Ezekiel
1998-10-01
We address the problem of improving the performance of wavelet based fractal image compression by applying efficient triangulation methods. We construct iterative function systems (IFS) in the tradition of Barnsley and Jacquin, using non-uniform triangular range and domain blocks instead of uniform rectangular ones. We search for matching domain blocks in the manner of Zhang and Chen, performing a fast wavelet transform on the blocks and eliminating low resolution mismatches to gain speed. We obtain further improvements by the efficiencies of binary triangulations (including the elimination of affine and symmetry calculations and reduced parameter storage), and by pruning the binary tree before construction of the IFS. Our wavelets are triangular Haar wavelets and `second generation' interpolation wavelets as suggested by Sweldens' recent work.
A simple method for estimating the fractal dimension from digital images: The compression dimension
NASA Astrophysics Data System (ADS)
Chamorro-Posada, Pedro
2016-10-01
The fractal structure of real world objects is often analyzed using digital images. In this context, the compression fractal dimension is put forward. It provides a simple method for the direct estimation of the dimension of fractals stored as digital image files. The computational scheme can be implemented using readily available free software. Its simplicity also makes it very interesting for introductory elaborations of basic concepts of fractal geometry, complexity, and information theory. A test of the computational scheme using limited-quality images of well-defined fractal sets obtained from the Internet and free software has been performed. Also, a systematic evaluation of the proposed method using computer generated images of the Weierstrass cosine function shows an accuracy comparable to those of the methods most commonly used to estimate the dimension of fractal data sequences applied to the same test problem.
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.
Pyramidal fractal dimension for high resolution images
NASA Astrophysics Data System (ADS)
Mayrhofer-Reinhartshuber, Michael; Ahammer, Helmut
2016-07-01
Fractal analysis (FA) should be able to yield reliable and fast results for high-resolution digital images to be applicable in fields that require immediate outcomes. Triggered by an efficient implementation of FA for binary images, we present three new approaches for fractal dimension (D) estimation of images that utilize image pyramids, namely, the pyramid triangular prism, the pyramid gradient, and the pyramid differences method (PTPM, PGM, PDM). We evaluated the performance of the three new and five standard techniques when applied to images with sizes up to 8192 × 8192 pixels. By using artificial fractal images created by three different generator models as ground truth, we determined the scale ranges with minimum deviations between estimation and theory. All pyramidal methods (PM) resulted in reasonable D values for images of all generator models. Especially, for images with sizes ≥1024 ×1024 pixels, the PMs are superior to the investigated standard approaches in terms of accuracy and computation time. A measure for the possibility to differentiate images with different intrinsic D values did show not only that the PMs are well suited for all investigated image sizes, and preferable to standard methods especially for larger images, but also that results of standard D estimation techniques are strongly influenced by the image size. Fastest results were obtained with the PDM and PGM, followed by the PTPM. In terms of absolute D values best performing standard methods were magnitudes slower than the PMs. Concluding, the new PMs yield high quality results in short computation times and are therefore eligible methods for fast FA of high-resolution images.
Pyramidal fractal dimension for high resolution images.
Mayrhofer-Reinhartshuber, Michael; Ahammer, Helmut
2016-07-01
Fractal analysis (FA) should be able to yield reliable and fast results for high-resolution digital images to be applicable in fields that require immediate outcomes. Triggered by an efficient implementation of FA for binary images, we present three new approaches for fractal dimension (D) estimation of images that utilize image pyramids, namely, the pyramid triangular prism, the pyramid gradient, and the pyramid differences method (PTPM, PGM, PDM). We evaluated the performance of the three new and five standard techniques when applied to images with sizes up to 8192 × 8192 pixels. By using artificial fractal images created by three different generator models as ground truth, we determined the scale ranges with minimum deviations between estimation and theory. All pyramidal methods (PM) resulted in reasonable D values for images of all generator models. Especially, for images with sizes ≥1024×1024 pixels, the PMs are superior to the investigated standard approaches in terms of accuracy and computation time. A measure for the possibility to differentiate images with different intrinsic D values did show not only that the PMs are well suited for all investigated image sizes, and preferable to standard methods especially for larger images, but also that results of standard D estimation techniques are strongly influenced by the image size. Fastest results were obtained with the PDM and PGM, followed by the PTPM. In terms of absolute D values best performing standard methods were magnitudes slower than the PMs. Concluding, the new PMs yield high quality results in short computation times and are therefore eligible methods for fast FA of high-resolution images. PMID:27475069
Fractality of pulsatile flow in speckle images
NASA Astrophysics Data System (ADS)
Nemati, M.; Kenjeres, S.; Urbach, H. P.; Bhattacharya, N.
2016-05-01
The scattering of coherent light from a system with underlying flow can be used to yield essential information about dynamics of the process. In the case of pulsatile flow, there is a rapid change in the properties of the speckle images. This can be studied using the standard laser speckle contrast and also the fractality of images. In this paper, we report the results of experiments performed to study pulsatile flow with speckle images, under different experimental configurations to verify the robustness of the techniques for applications. In order to study flow under various levels of complexity, the measurements were done for three in-vitro phantoms and two in-vivo situations. The pumping mechanisms were varied ranging from mechanical pumps to the human heart for the in vivo case. The speckle images were analyzed using the techniques of fractal dimension and speckle contrast analysis. The results of these techniques for the various experimental scenarios were compared. The fractal dimension is a more sensitive measure to capture the complexity of the signal though it was observed that it is also extremely sensitive to the properties of the scattering medium and cannot recover the signal for thicker diffusers in comparison to speckle contrast.
a Type of Fractal Interpolation Functions and Their Fractional Calculus
NASA Astrophysics Data System (ADS)
Liang, Yong-Shun; Zhang, Qi
2016-05-01
Combine Chebyshev systems with fractal interpolation, certain continuous functions have been approximated by fractal interpolation functions unanimously. Local structure of these fractal interpolation functions (FIF) has been discussed. The relationship between order of Riemann-Liouville fractional calculus and Box dimension of FIF has been investigated.
Fractal image compression: A resolution independent representation for imagery
NASA Technical Reports Server (NTRS)
Sloan, Alan D.
1993-01-01
A deterministic fractal is an image which has low information content and no inherent scale. Because of their low information content, deterministic fractals can be described with small data sets. They can be displayed at high resolution since they are not bound by an inherent scale. A remarkable consequence follows. Fractal images can be encoded at very high compression ratios. This fern, for example is encoded in less than 50 bytes and yet can be displayed at resolutions with increasing levels of detail appearing. The Fractal Transform was discovered in 1988 by Michael F. Barnsley. It is the basis for a new image compression scheme which was initially developed by myself and Michael Barnsley at Iterated Systems. The Fractal Transform effectively solves the problem of finding a fractal which approximates a digital 'real world image'.
Multi-Scale Fractal Analysis of Image Texture and Pattern
NASA Technical Reports Server (NTRS)
Emerson, Charles W.; Lam, Nina Siu-Ngan; Quattrochi, Dale A.
1999-01-01
Analyses of the fractal dimension of Normalized Difference Vegetation Index (NDVI) images of homogeneous land covers near Huntsville, Alabama revealed that the fractal dimension of an image of an agricultural land cover indicates greater complexity as pixel size increases, a forested land cover gradually grows smoother, and an urban image remains roughly self-similar over the range of pixel sizes analyzed (10 to 80 meters). A similar analysis of Landsat Thematic Mapper images of the East Humboldt Range in Nevada taken four months apart show a more complex relation between pixel size and fractal dimension. The major visible difference between the spring and late summer NDVI images 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.
Smitha, K A; Gupta, A K; Jayasree, R S
2015-09-01
Glioma, the heterogeneous tumors originating from glial cells, generally exhibit varied grades and are difficult to differentiate using conventional MR imaging techniques. When this differentiation is crucial in the disease prognosis and treatment, even the advanced MR imaging techniques fail to provide a higher discriminative power for the differentiation of malignant tumor from benign ones. A powerful image processing technique applied to the imaging techniques is expected to provide a better differentiation. The present study focuses on the fractal analysis of fluid attenuation inversion recovery MR images, for the differentiation of glioma. For this, we have considered the most important parameters of fractal analysis, fractal dimension and lacunarity. While fractal analysis assesses the malignancy and complexity of a fractal object, lacunarity gives an indication on the empty space and the degree of inhomogeneity in the fractal objects. Box counting method with the preprocessing steps namely binarization, dilation and outlining was used to obtain the fractal dimension and lacunarity in glioma. Statistical analysis such as one-way analysis of variance and receiver operating characteristic (ROC) curve analysis helped to compare the mean and to find discriminative sensitivity of the results. It was found that the lacunarity of low and high grade gliomas vary significantly. ROC curve analysis between low and high grade glioma for fractal dimension and lacunarity yielded 70.3% sensitivity and 66.7% specificity and 70.3% sensitivity and 88.9% specificity, respectively. The study observes that fractal dimension and lacunarity increases with an increase in the grade of glioma and lacunarity is helpful in identifying most malignant grades.
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.
An image retrieval system based on fractal dimension.
Yao, Min; Yi, Wen-Sheng; Shen, Bin; Dai, Hong-Hua
2003-01-01
This paper presents a new kind of image retrieval system which obtains the feature vectors of images by estimating their fractal dimension; and at the same time establishes a tree-structure image database. After preprocessing and feature extracting, a given image is matched with the standard images in the image database using a hierarchical method of image indexing.
Fractal dimension of cerebral surfaces using magnetic resonance images
Majumdar, S.; Prasad, R.R.
1988-11-01
The calculation of the fractal dimension of the surface bounded by the grey matter in the normal human brain using axial, sagittal, and coronal cross-sectional magnetic resonance (MR) images is presented. The fractal dimension in this case is a measure of the convolutedness of this cerebral surface. It is proposed that the fractal dimension, a feature that may be extracted from MR images, may potentially be used for image analysis, quantitative tissue characterization, and as a feature to monitor and identify cerebral abnormalities and developmental changes.
Evaluation of Two Fractal Methods for Magnetogram Image Analysis
NASA Technical Reports Server (NTRS)
Stark, B.; Adams, M.; Hathaway, D. H.; Hagyard, M. J.
1997-01-01
Fractal and multifractal techniques have been applied to various types of solar data to study the fractal properties of sunspots as well as the distribution of photospheric magnetic fields and the role of random motions on the solar surface in this distribution. Other research includes the investigation of changes in the fractal dimension as an indicator for solar flares. Here we evaluate the efficacy of two methods for determining the fractal dimension of an image data set: the Differential Box Counting scheme and a new method, the Jaenisch scheme. To determine the sensitivity of the techniques to changes in image complexity, various types of constructed images are analyzed. In addition, we apply this method to solar magnetogram data from Marshall Space Flight Centers vector magnetograph.
Unification of two fractal families
NASA Astrophysics Data System (ADS)
Liu, Ying
1995-06-01
Barnsley and Hurd classify the fractal images into two families: iterated function system fractals (IFS fractals) and fractal transform fractals, or local iterated function system fractals (LIFS fractals). We will call IFS fractals, class 2 fractals and LIFS fractals, class 3 fractals. In this paper, we will unify these two approaches plus another family of fractals, the class 5 fractals. The basic idea is given as follows: a dynamical system can be represented by a digraph, the nodes in a digraph can be divided into two parts: transient states and persistent states. For bilevel images, a persistent node is a black pixel. A transient node is a white pixel. For images with more than two gray levels, a stochastic digraph is used. A transient node is a pixel with the intensity of 0. The intensity of a persistent node is determined by a relative frequency. In this way, the two families of fractals can be generated in a similar way. In this paper, we will first present a classification of dynamical systems and introduce the transformation based on digraphs, then we will unify the two approaches for fractal binary images. We will compare the decoding algorithms of the two families. Finally, we will generalize the discussion to continuous-tone images.
Wavelet and fractal analysis of ground-vehicle images
NASA Astrophysics Data System (ADS)
Gorsich, David J.; Tolle, Charles R.; Karlsen, Robert E.; Gerhart, Grant R.
1996-10-01
A large number of terrain images were taken at Aberdeen Proving Grounds, some containing ground vehicles. Is it possible to screen the images for possible targets in a short amount of time using the fractal dimension to detect texture variations. The fractal dimension is determined using the wavelet transform for these visual images. The vehicles are positioned within the grass and in different locations. Since it has been established that natural terrain exhibits a statistical l/f self-similarity property and the psychophysical perception of roughness can be quantified by the same self-similarity, fractal dimensions estimates should vary only at texture boundaries and breaks in the tree and grass patterns. Breaks in the patterns are found using contour plots of the dimension estimates and are considered as perceptual texture variations. Variation in the dimension estimate is considered more important than the accuracy of the actual dimensions number. Accurate variation estimates are found even with low resolution images.
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.
Human discrimination of surface slant in fractal and related textured images.
Passmore, P J; Johnston, A
1995-01-01
Slant-discrimination thresholds were measured for textures with the property that their power spectra, when log transformed, are inversely proportional to log spatial frequency: P(f) alpha f-beta. As the exponent beta changes from high values to low values, the slope of the power spectrum of the image decreases. As the parameter passes through values in the fractal range the resulting texture changes from having the appearance of a cloud-like surface through to a granite-like surface. Exponents below the fractal range produce textures that converge towards the appearance of a random grey-level noise pattern. Since fractal patterns are self-similar at a range of scales, one might think it would be difficult to recover changes in depth in fractal images; however, slant-discrimination thresholds did not differ substantially as a function of the slope of the power spectrum. Reducing the size of the viewing aperture increased thresholds significantly, suggesting that slant discrimination benefits from a global analysis. The effect of texture regularity on perceived slant was investigated using bandpassed fractal textures. As the bandwidth of a bandpass filter is reduced, the bandpassed texture was perceived to be increasingly more slanted than its fractal counterpart.
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.
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.
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.
Fractal Analysis of Laplacian Pyramidal Filters Applied to Segmentation of Soil Images
de Castro, J.; Méndez, A.; Tarquis, A. M.
2014-01-01
The laplacian pyramid is a well-known technique for image processing in which local operators of many scales, but identical shape, serve as the basis functions. The required properties to the pyramidal filter produce a family of filters, which is unipara metrical in the case of the classical problem, when the length of the filter is 5. We pay attention to gaussian and fractal behaviour of these basis functions (or filters), and we determine the gaussian and fractal ranges in the case of single parameter a. These fractal filters loose less energy in every step of the laplacian pyramid, and we apply this property to get threshold values for segmenting soil images, and then evaluate their porosity. Also, we evaluate our results by comparing them with the Otsu algorithm threshold values, and conclude that our algorithm produce reliable test results. PMID:25114957
Fractal analysis of laplacian pyramidal filters applied to segmentation of soil images.
de Castro, J; Ballesteros, F; Méndez, A; Tarquis, A M
2014-01-01
The laplacian pyramid is a well-known technique for image processing in which local operators of many scales, but identical shape, serve as the basis functions. The required properties to the pyramidal filter produce a family of filters, which is unipara metrical in the case of the classical problem, when the length of the filter is 5. We pay attention to gaussian and fractal behaviour of these basis functions (or filters), and we determine the gaussian and fractal ranges in the case of single parameter a. These fractal filters loose less energy in every step of the laplacian pyramid, and we apply this property to get threshold values for segmenting soil images, and then evaluate their porosity. Also, we evaluate our results by comparing them with the Otsu algorithm threshold values, and conclude that our algorithm produce reliable test results. PMID:25114957
Fractal image analysis - Application to the topography of Oregon and synthetic images.
NASA Technical Reports Server (NTRS)
Huang, Jie; Turcotte, Donald L.
1990-01-01
Digitized topography for the state of Oregon has been used to obtain maps of fractal dimension and roughness amplitude. The roughness amplitude correlates well with variations in relief and is a promising parameter for the quantitative classification of landforms. The spatial variations in fractal dimension are low and show no clear correlation with different tectonic settings. For Oregon the mean fractal dimension from a two-dimensional spectral analysis is D = 2.586, and for a one-dimensional spectral analysis the mean fractal dimension is D = 1.487, which is close to the Brown noise value D = 1.5. Synthetic two-dimensional images have also been generated for a range of D values. For D = 2.6, the synthetic image has a mean one-dimensional spectral fractal dimension D = 1.58, which is consistent with the results for Oregon. This approach can be easily applied to any digitzed image that obeys fractal statistics.
Multi-Scale Fractal Analysis of Image Texture and Pattern
NASA Technical Reports Server (NTRS)
Emerson, Charles W.; Quattrochi, Dale A.; Luvall, Jeffrey C.
1997-01-01
Fractals embody important ideas of self-similarity, in which the spatial behavior or appearance of a system is largely scale-independent. Self-similarity is a property of curves or surfaces where each part is indistinguishable from the whole. The fractal dimension D of remote sensing data yields quantitative insight on the spatial complexity and information content contained within these data. Analyses of Normalized Difference Vegetation Index (NDVI) images of homogeneous land covers near Huntsville, Alabama revealed that the fractal dimension of an image of an agricultural land cover indicates greater complexity as pixel size increases, a forested land cover gradually grows smoother, and an urban image remains roughly self-similar over the range of pixel sizes analyzed(l0 to 80 meters). The forested scene behaves as one would expect-larger pixel sizes decrease the complexity of the image as individual clumps of trees are averaged into larger blocks. The increased complexity of the agricultural image with increasing pixel size results from the loss of homogeneous groups of pixels in the large fields to mixed pixels composed of varying combinations of NDVI values that correspond to roads and vegetation. The same process occur's in the urban image to some extent, but the lack of large, homogeneous areas in the high resolution NDVI image means the initially high D value is maintained as pixel size increases. The slope of the fractal dimension-resolution relationship provides indications of how image classification or feature identification will be affected by changes in sensor resolution.
FIRE: fractal indexing with robust extensions for image databases.
Distasi, Riccardo; Nappi, Michele; Tucci, Maurizio
2003-01-01
As already documented in the literature, fractal image encoding is a family of techniques that achieves a good compromise between compression and perceived quality by exploiting the self-similarities present in an image. Furthermore, because of its compactness and stability, the fractal approach can be used to produce a unique signature, thus obtaining a practical image indexing system. Since fractal-based indexing systems are able to deal with the images in compressed form, they are suitable for use with large databases. We propose a system called FIRE, which is then proven to be invariant under three classes of pixel intensity transformations and under geometrical isometries such as rotations by multiples of /spl pi//2 and reflections. This property makes the system robust with respect to a large class of image transformations that can happen in practical applications: the images can be retrieved even in the presence of illumination and/or color alterations. Additionally, the experimental results show the effectiveness of FIRE in terms of both compression and retrieval accuracy.
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.
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.
Log-periodic route to fractal functions.
Gluzman, S; Sornette, D
2002-03-01
Log-periodic oscillations have been found to decorate the usual power-law behavior found to describe the approach to a critical point, when the continuous scale-invariance symmetry is partially broken into a discrete-scale invariance symmetry. For Ising or Potts spins with ferromagnetic interactions on hierarchical systems, the relative magnitude of the log-periodic corrections are usually very small, of order 10(-5). In growth processes [diffusion limited aggregation (DLA)], rupture, earthquake, and financial crashes, log-periodic oscillations with amplitudes of the order of 10% have been reported. We suggest a "technical" explanation for this 4 order-of-magnitude difference based on the property of the "regular function" g(x) embodying the effect of the microscopic degrees of freedom summed over in a renormalization group (RG) approach F(x)=g(x)+mu(-1)F(gamma x) of an observable F as a function of a control parameter x. For systems for which the RG equation has not been derived, the previous equation can be understood as a Jackson q integral, which is the natural tool for describing discrete-scale invariance. We classify the "Weierstrass-type" solutions of the RG into two classes characterized by the amplitudes A(n) of the power-law series expansion. These two classes are separated by a novel "critical" point. Growth processes (DLA), rupture, earthquake, and financial crashes thus seem to be characterized by oscillatory or bounded regular microscopic functions that lead to a slow power-law decay of A(n), giving strong log-periodic amplitudes. If in addition, the phases of A(n) are ergodic and mixing, the observable presents self-affine nondifferentiable properties. In contrast, the regular function of statistical physics models with "ferromagnetic"-type interactions at equilibrium involves unbound logarithms of polynomials of the control variable that lead to a fast exponential decay of A(n) giving weak log-periodic amplitudes and smoothed observables. PMID
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.
Aliasing removing of hyperspectral image based on fractal structure matching
NASA Astrophysics Data System (ADS)
Wei, Ran; Zhang, Ye; Zhang, Junping
2015-05-01
Due to the richness on high frequency components, hyperspectral image (HSI) is more sensitive to distortion like aliasing. Many methods aiming at removing such distortion have been proposed. However, seldom of them are suitable to HSI, due to low spatial resolution characteristic of HSI. Fortunately, HSI contains plentiful spectral information, which can be exploited to overcome such difficulties. Motivated by this, we proposed an aliasing removing method for HSI. The major differences between proposed and current methods is that proposed algorithm is able to utilize fractal structure information, thus the dilemma originated from low-resolution of HSI is solved. Experiments on real HSI data demonstrated subjectively and objectively that proposed method can not only remove annoying visual effect brought by aliasing, but also recover more high frequency component.
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 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.
Fractal analysis of scatter imaging signatures to distinguish breast pathologies
NASA Astrophysics Data System (ADS)
Eguizabal, Alma; Laughney, Ashley M.; Krishnaswamy, Venkataramanan; Wells, Wendy A.; Paulsen, Keith D.; Pogue, Brian W.; López-Higuera, José M.; Conde, Olga M.
2013-02-01
Fractal analysis combined with a label-free scattering technique is proposed for describing the pathological architecture of tumors. Clinicians and pathologists are conventionally trained to classify abnormal features such as structural irregularities or high indices of mitosis. The potential of fractal analysis lies in the fact of being a morphometric measure of the irregular structures providing a measure of the object's complexity and self-similarity. As cancer is characterized by disorder and irregularity in tissues, this measure could be related to tumor growth. Fractal analysis has been probed in the understanding of the tumor vasculature network. This work addresses the feasibility of applying fractal analysis to the scattering power map (as a physical modeling) and principal components (as a statistical modeling) provided by a localized reflectance spectroscopic system. Disorder, irregularity and cell size variation in tissue samples is translated into the scattering power and principal components magnitude and its fractal dimension is correlated with the pathologist assessment of the samples. The fractal dimension is computed applying the box-counting technique. Results show that fractal analysis of ex-vivo fresh tissue samples exhibits separated ranges of fractal dimension that could help classifier combining the fractal results with other morphological features. This contrast trend would help in the discrimination of tissues in the intraoperative context and may serve as a useful adjunct to surgeons.
Analysis of fractal dimensions of rat bones from film and digital images
NASA Technical Reports Server (NTRS)
Pornprasertsuk, S.; Ludlow, J. B.; Webber, R. L.; Tyndall, D. A.; Yamauchi, M.
2001-01-01
OBJECTIVES: (1) To compare the effect of two different intra-oral image receptors on estimates of fractal dimension; and (2) to determine the variations in fractal dimensions between the femur, tibia and humerus of the rat and between their proximal, middle and distal regions. METHODS: The left femur, tibia and humerus from 24 4-6-month-old Sprague-Dawley rats were radiographed using intra-oral film and a charge-coupled device (CCD). Films were digitized at a pixel density comparable to the CCD using a flat-bed scanner. Square regions of interest were selected from proximal, middle, and distal regions of each bone. Fractal dimensions were estimated from the slope of regression lines fitted to plots of log power against log spatial frequency. RESULTS: The fractal dimensions estimates from digitized films were significantly greater than those produced from the CCD (P=0.0008). Estimated fractal dimensions of three types of bone were not significantly different (P=0.0544); however, the three regions of bones were significantly different (P=0.0239). The fractal dimensions estimated from radiographs of the proximal and distal regions of the bones were lower than comparable estimates obtained from the middle region. CONCLUSIONS: Different types of image receptors significantly affect estimates of fractal dimension. There was no difference in the fractal dimensions of the different bones but the three regions differed significantly.
Intelligent fuzzy approach for fast fractal image compression
NASA Astrophysics Data System (ADS)
Nodehi, Ali; Sulong, Ghazali; Al-Rodhaan, Mznah; Al-Dhelaan, Abdullah; Rehman, Amjad; Saba, Tanzila
2014-12-01
Fractal image compression (FIC) is recognized as a NP-hard problem, and it suffers from a high number of mean square error (MSE) computations. In this paper, a two-phase algorithm was proposed to reduce the MSE computation of FIC. In the first phase, based on edge property, range and domains are arranged. In the second one, imperialist competitive algorithm (ICA) is used according to the classified blocks. For maintaining the quality of the retrieved image and accelerating algorithm operation, we divided the solutions into two groups: developed countries and undeveloped countries. Simulations were carried out to evaluate the performance of the developed approach. Promising results thus achieved exhibit performance better than genetic algorithm (GA)-based and Full-search algorithms in terms of decreasing the number of MSE computations. The number of MSE computations was reduced by the proposed algorithm for 463 times faster compared to the Full-search algorithm, although the retrieved image quality did not have a considerable change.
Loh, N. Duane
2012-06-20
This deposition includes the aerosol diffraction images used for phasing, fractal morphology, and time-of-flight mass spectrometry. Files in this deposition are ordered in subdirectories that reflect the specifics.
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
A new version of Visual tool for estimating the fractal dimension of images
NASA Astrophysics Data System (ADS)
Grossu, I. V.; Felea, D.; Besliu, C.; Jipa, Al.; Bordeianu, C. C.; Stan, E.; Esanu, T.
2010-04-01
-dimensional case. Summary of revisions:The application interface was changed from SDI (single document interface) to MDI (multi-document interface). One form was added in order to provide a graphical user interface for the new functionalities (fractal analysis of 2D and 3D images stored in csv files). Additional comments: User friendly graphical interface; Easy deployment mechanism. Running time: In the first approximation, the algorithm is linear. References:[1] I.V. Grossu, C. Besliu, M.V. Rusu, Al. Jipa, C.C. Bordeianu, D. Felea, Comput. Phys. Comm. 180 (2009) 1999-2001.[2] F. Balena, Programming Microsoft Visual Basic 6.0, Microsoft Press, US, 1999.
Hurst exponent for fractal characterization of LANDSAT images
NASA Astrophysics Data System (ADS)
Valdiviezo-N., Juan C.; Castro, Raul; Cristóbal, Gabriel; Carbone, Anna
2014-10-01
In this research the Hurst exponent H is used for quantifying the fractal features of LANDSAT images. The Hurst exponent is estimated by means of the Detrending Moving Average (DMA), an algorithm based on a generalized high-dimensional variance around a moving average low-pass filter. Hence, for a two-dimensional signal, the algorithm first generates an average response for different subarrays by varying the size of the moving low-pass filter. For each subarray the corresponding variance value is calculated by the difference between the original and the averaged signals. The value of the variance obtained at each subarray is then plotted on log-log axes, with the slope of the regression line corresponding to the Hurst exponent. The application of the algorithm to a set of LANDSAT imagery has allowed us to estimate the Hurst exponent of specific areas on Earth surface at subsequent time instances. According to the presented results, the value of the Hurst exponent is directly related to the changes in land use, showing a decreasing value when the area under study has been modified by natural processes or human intervention. Interestingly, natural areas presenting a gradual growth of man made activities or an increasing degree of pollution have a considerable reduction in their corresponding Hurst exponent.
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.
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.
A Lossless hybrid wavelet-fractal compression for welding radiographic images.
Mekhalfa, Faiza; Avanaki, Mohammad R N; Berkani, Daoud
2016-01-01
In this work a lossless wavelet-fractal image coder is proposed. The process starts by compressing and decompressing the original image using wavelet transformation and fractal coding algorithm. The decompressed image is removed from the original one to obtain a residual image which is coded by using Huffman algorithm. Simulation results show that with the proposed scheme, we achieve an infinite peak signal to noise ratio (PSNR) with higher compression ratio compared to typical lossless method. Moreover, the use of wavelet transform speeds up the fractal compression algorithm by reducing the size of the domain pool. The compression results of several welding radiographic images using the proposed scheme are evaluated quantitatively and compared with the results of Huffman coding algorithm. PMID:26890900
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.
Edge detection and image segmentation of space scenes using fractal analyses
NASA Technical Reports Server (NTRS)
Cleghorn, Timothy F.; Fuller, J. J.
1992-01-01
A method was developed for segmenting images of space scenes into manmade and natural components, using fractal dimensions and lacunarities. Calculations of these parameters are presented. Results are presented for a variety of aerospace images, showing that it is possible to perform edge detections of manmade objects against natural background such as those seen in an aerospace environment.
NASA Technical Reports Server (NTRS)
Emerson, Charles W.; Sig-NganLam, Nina; Quattrochi, Dale A.
2004-01-01
The accuracy of traditional multispectral maximum-likelihood image classification is limited by the skewed statistical distributions of reflectances from the complex heterogenous mixture of land cover types in urban areas. This work examines the utility of local variance, fractal dimension and Moran's I index of spatial autocorrelation in segmenting multispectral satellite imagery. Tools available in the Image Characterization and Modeling System (ICAMS) were used to analyze Landsat 7 imagery of Atlanta, Georgia. Although segmentation of panchromatic images is possible using indicators of spatial complexity, different land covers often yield similar values of these indices. Better results are obtained when a surface of local fractal dimension or spatial autocorrelation is combined as an additional layer in a supervised maximum-likelihood multispectral classification. The addition of fractal dimension measures is particularly effective at resolving land cover classes within urbanized areas, as compared to per-pixel spectral classification techniques.
NASA Astrophysics Data System (ADS)
Tremberger, George, Jr.; Flamholz, A.; Cheung, E.; Sullivan, R.; Subramaniam, R.; Schneider, P.; Brathwaite, G.; Boteju, J.; Marchese, P.; Lieberman, D.; Cheung, T.; Holden, Todd
2007-09-01
The absorption effect of the back surface boundary of a diffuse layer was studied via laser generated reflection speckle pattern. The spatial speckle intensity provided by a laser beam was measured. The speckle data were analyzed in terms of fractal dimension (computed by NIH ImageJ software via the box counting fractal method) and weak localization theory based on Mie scattering. Bar code imaging was modeled as binary absorption contrast and scanning resolution in millimeter range was achieved for diffusive layers up to thirty transport mean free path thick. Samples included alumina, porous glass and chicken tissue. Computer simulation was used to study the effect of speckle spatial distribution and observed fractal dimension differences were ascribed to variance controlled speckle sizes. Fractal dimension suppressions were observed in samples that had thickness dimensions around ten transport mean free path. Computer simulation suggested a maximum fractal dimension of about 2 and that subtracting information could lower fractal dimension. The fractal dimension was shown to be sensitive to sample thickness up to about fifteen transport mean free paths, and embedded objects which modified 20% or more of the effective thickness was shown to be detectable. The box counting fractal method was supplemented with the Higuchi data series fractal method and application to architectural distortion mammograms was demonstrated. The use of fractals in diffusive analysis would provide a simple language for a dialog between optics experts and mammography radiologists, facilitating the applications of laser diagnostics in tissues.
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.
NASA Technical Reports Server (NTRS)
Huang, J.; Turcotte, D. L.
1989-01-01
The concept of fractal mapping is introduced and applied to digitized topography of Arizona. It is shown that the fractal statistics satisfy the topography of the state to a good approximation. The fractal dimensions and roughness amplitudes from subregions are used to construct maps of these quantities. It is found that the fractal dimension of actual two-dimensional topography is not affected by the adding unity to the fractal dimension of one-dimensional topographic tracks. In addition, consideration is given to the production of fractal maps from synthetically derived topography.
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.
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)
Saremi, Saeed; Sejnowski, Terrence J.
2016-01-01
Natural images are scale invariant with structures at all length scales. We formulated a geometric view of scale invariance in natural images using percolation theory, which describes the behavior of connected clusters on graphs. We map images to the percolation model by defining clusters on a binary representation for images. We show that critical percolating structures emerge in natural images and study their scaling properties by identifying fractal dimensions and exponents for the scale-invariant distributions of clusters. This formulation leads to a method for identifying clusters in images from underlying structures as a starting point for image segmentation. PMID:26415153
NASA Astrophysics Data System (ADS)
Grossu, I. V.; El-Shamali, S. A.
2013-07-01
This work presents a new version of a Visual Basic 6.0 application for estimating the fractal dimension of images and 4D objects (Grossu et al. 2013 [1]). Following our attempt of investigating artistic works by fractal analysis of craquelure, we encountered important difficulties in filtering real information from noise. In this context, trying to avoid a sharp delimitation of "black" and "white" pixels, we implemented a fuzzy box-counting algorithm. Hyper-Fractal Analysis v04 example of use. Fuzzy fractal dimension of painting craquelure. Running time: In a first approximation, the algorithm is linear [2].
Fractal methods for extracting artificial objects from the unmanned aerial vehicle images
NASA Astrophysics Data System (ADS)
Markov, Eugene
2016-04-01
Unmanned aerial vehicles (UAVs) have become used increasingly in earth surface observations, with a special interest put into automatic modes of environmental control and recognition of artificial objects. Fractal methods for image processing well detect the artificial objects in digital space images but were not applied previously to the UAV-produced imagery. Parameters of photography, on-board equipment, and image characteristics differ considerably for spacecrafts and UAVs. Therefore, methods that work properly with space images can produce different results for the UAVs. In this regard, testing the applicability of fractal methods for the UAV-produced images and determining the optimal range of parameters for these methods represent great interest. This research is dedicated to the solution of this problem. Specific features of the earth's surface images produced with UAVs are described in the context of their interpretation and recognition. Fractal image processing methods for extracting artificial objects are described. The results of applying these methods to the UAV images are presented.
Plant Identification Based on Leaf Midrib Cross-Section Images Using Fractal Descriptors
da Silva, Núbia Rosa; Florindo, João Batista; Gómez, María Cecilia; Rossatto, Davi Rodrigo; Kolb, Rosana Marta; Bruno, Odemir Martinez
2015-01-01
The correct identification of plants is a common necessity not only to researchers but also to the lay public. Recently, computational methods have been employed to facilitate this task, however, there are few studies front of the wide diversity of plants occurring in the world. This study proposes to analyse images obtained from cross-sections of leaf midrib using fractal descriptors. These descriptors are obtained from the fractal dimension of the object computed at a range of scales. In this way, they provide rich information regarding the spatial distribution of the analysed structure and, as a consequence, they measure the multiscale morphology of the object of interest. In Biology, such morphology is of great importance because it is related to evolutionary aspects and is successfully employed to characterize and discriminate among different biological structures. Here, the fractal descriptors are used to identify the species of plants based on the image of their leaves. A large number of samples are examined, being 606 leaf samples of 50 species from Brazilian flora. The results are compared to other imaging methods in the literature and demonstrate that fractal descriptors are precise and reliable in the taxonomic process of plant species identification. PMID:26091501
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.
Foulsham, Tom; Kingstone, Alan
2010-04-01
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.
Differential Diagnosis: Shape and Function, Fractal Tools in the Pathology Lab.
Bianciardi, Giorgio
2015-10-01
Fractal analysis is a useful objective tool in describing complexity of shapes and signals providing information for understanding pathological changes. We present fractal approaches and software used in our pathology laboratory to analyze shapes of tumors in tissues and cells, to evaluate the microvessel network complexity in hereditary diseases or the complexity of the surface of blood cells in atherosclerosis-linked condition, as well to analyze function in vasculopathic subjects by chaotic analysis of electrocardiographic signals, in order to perform differential diagnosis. The fractal parameters appear to converge towards distinct values in pathological conditions compared to healthy, approaching the characteristics values of a percolation process or the diffusion-limited aggregation process, respectively: a bifurcation that allows to support the diagnostic process of the pathologist in his daily work. These methods, presented here as a kind of a cookbook ready for the pathologist, are low cost and not time consuming. PMID:26375935
Differential Diagnosis: Shape and Function, Fractal Tools in the Pathology Lab.
Bianciardi, Giorgio
2015-10-01
Fractal analysis is a useful objective tool in describing complexity of shapes and signals providing information for understanding pathological changes. We present fractal approaches and software used in our pathology laboratory to analyze shapes of tumors in tissues and cells, to evaluate the microvessel network complexity in hereditary diseases or the complexity of the surface of blood cells in atherosclerosis-linked condition, as well to analyze function in vasculopathic subjects by chaotic analysis of electrocardiographic signals, in order to perform differential diagnosis. The fractal parameters appear to converge towards distinct values in pathological conditions compared to healthy, approaching the characteristics values of a percolation process or the diffusion-limited aggregation process, respectively: a bifurcation that allows to support the diagnostic process of the pathologist in his daily work. These methods, presented here as a kind of a cookbook ready for the pathologist, are low cost and not time consuming.
Radial distribution function for hard spheres in fractal dimensions: A heuristic approximation
NASA Astrophysics Data System (ADS)
Santos, Andrés; de Haro, Mariano López
2016-06-01
Analytic approximations for the radial distribution function, the structure factor, and the equation of state of hard-core fluids in fractal dimension d (1 ≤d ≤3 ) are developed as heuristic interpolations from the knowledge of the exact and Percus-Yevick results for the hard-rod and hard-sphere fluids, respectively. In order to assess their value, such approximate results are compared with those of recent Monte Carlo simulations and numerical solutions of the Percus-Yevick equation for a fractal dimension [M. Heinen et al., Phys. Rev. Lett. 115, 097801 (2015), 10.1103/PhysRevLett.115.097801], a good agreement being observed.
Alzheimer's Disease Detection in Brain Magnetic Resonance Images Using Multiscale Fractal Analysis
Lahmiri, Salim; Boukadoum, Mounir
2013-01-01
We present a new automated system for the detection of brain magnetic resonance images (MRI) affected by Alzheimer's disease (AD). The MRI is analyzed by means of multiscale analysis (MSA) to obtain its fractals at six different scales. The extracted fractals are used as features to differentiate healthy brain MRI from those of AD by a support vector machine (SVM) classifier. The result of classifying 93 brain MRIs consisting of 51 images of healthy brains and 42 of brains affected by AD, using leave-one-out cross-validation method, yielded 99.18% ± 0.01 classification accuracy, 100% sensitivity, and 98.20% ± 0.02 specificity. These results and a processing time of 5.64 seconds indicate that the proposed approach may be an efficient diagnostic aid for radiologists in the screening for AD. PMID:24967286
NASA Astrophysics Data System (ADS)
Ahammer, Helmut; DeVaney, Trevor T. J.
2004-03-01
The boundary of a fractal object, represented in a two-dimensional space, is theoretically a line with an infinitely small width. In digital images this boundary or contour is limited to the pixel resolution of the image and the width of the line commonly depends on the edge detection algorithm used. The Minkowski dimension was evaluated by using three different edge detection algorithms (Sobel, Roberts, and Laplace operator). These three operators were investigated because they are very widely used and because their edge detection result is very distinct concerning the line width. Very common fractals (Sierpinski carpet and Koch islands) were investigated as well as the binary images from a cancer invasion assay taken with a confocal laser scanning microscope. The fractal dimension is directly proportional to the width of the contour line and the fact, that in practice very often the investigated objects are fractals only within a limited resolution range is considered too.
NASA Astrophysics Data System (ADS)
Liang, Yingjie; Ye, Allen Q.; Chen, Wen; Gatto, Rodolfo G.; Colon-Perez, Luis; Mareci, Thomas H.; Magin, Richard L.
2016-10-01
Non-Gaussian (anomalous) diffusion is wide spread in biological tissues where its effects modulate chemical reactions and membrane transport. When viewed using magnetic resonance imaging (MRI), anomalous diffusion is characterized by a persistent or 'long tail' behavior in the decay of the diffusion signal. Recent MRI studies have used the fractional derivative to describe diffusion dynamics in normal and post-mortem tissue by connecting the order of the derivative with changes in tissue composition, structure and complexity. In this study we consider an alternative approach by introducing fractal time and space derivatives into Fick's second law of diffusion. This provides a more natural way to link sub-voxel tissue composition with the observed MRI diffusion signal decay following the application of a diffusion-sensitive pulse sequence. Unlike previous studies using fractional order derivatives, here the fractal derivative order is directly connected to the Hausdorff fractal dimension of the diffusion trajectory. The result is a simpler, computationally faster, and more direct way to incorporate tissue complexity and microstructure into the diffusional dynamics. Furthermore, the results are readily expressed in terms of spectral entropy, which provides a quantitative measure of the overall complexity of the heterogeneous and multi-scale structure of biological tissues. As an example, we apply this new model for the characterization of diffusion in fixed samples of the mouse brain. These results are compared with those obtained using the mono-exponential, the stretched exponential, the fractional derivative, and the diffusion kurtosis models. Overall, we find that the order of the fractal time derivative, the diffusion coefficient, and the spectral entropy are potential biomarkers to differentiate between the microstructure of white and gray matter. In addition, we note that the fractal derivative model has practical advantages over the existing models from the
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.
Zone Specific Fractal Dimension of Retinal Images as Predictor of Stroke Incidence
Kumar, Dinesh Kant; Hao, Hao; Unnikrishnan, Premith; Kawasaki, Ryo; Mitchell, Paul
2014-01-01
Fractal dimensions (FDs) are frequently used for summarizing the complexity of retinal vascular. However, previous techniques on this topic were not zone specific. A new methodology to measure FD of a specific zone in retinal images has been developed and tested as a marker for stroke prediction. Higuchi's fractal dimension was measured in circumferential direction (FDC) with respect to optic disk (OD), in three concentric regions between OD boundary and 1.5 OD diameter from its margin. The significance of its association with future episode of stroke event was tested using the Blue Mountain Eye Study (BMES) database and compared against spectrum fractal dimension (SFD) and box-counting (BC) dimension. Kruskal-Wallis analysis revealed FDC as a better predictor of stroke (H = 5.80, P = 0.016, α = 0.05) compared with SFD (H = 0.51, P = 0.475, α = 0.05) and BC (H = 0.41, P = 0.520, α = 0.05) with overall lower median value for the cases compared to the control group. This work has shown that there is a significant association between zone specific FDC of eye fundus images with future episode of stroke while this difference is not significant when other FD methods are employed. PMID:25485298
Using fractal compression scheme to embed a digital signature into an image
NASA Astrophysics Data System (ADS)
Puate, Joan; Jordan, Frederic D.
1997-01-01
With the increase in the number of digital networks and recording devices, digital images appear to be a material, especially still images, whose ownership is widely threatened due to the availability of simple, rapid and perfect duplication and distribution means. It is in this context that several European projects are devoted to finding a technical solution which, as it applies to still images, introduces a code or watermark into the image data itself. This watermark should not only allow one to determine the owner of the image, but also respect its quality and be difficult to revoke. An additional requirement is that the code should be retrievable by the only mean of the protected information. In this paper, we propose a new scheme based on fractal coding and decoding. In general terms, a fractal coder exploits the spatial redundancy within the image by establishing a relationship between its different parts. We describe a way to use this relationship as a means of embedding a watermark. Tests have been performed in order to measure the robustness of the technique against JPEG conversion and low pass filtering. In both cases, very promising results have been obtained.
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
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.
Optical fractal synthesizer - Concept and experimental verification
NASA Astrophysics Data System (ADS)
Tanida, Jun; Uemoto, Atsushi; Ichioka, Yoshiki
1993-02-01
Generation of fractal images with an iterated function system (IFS) (Barnsley, 1988) that can be easily implemented using optical techniques is considered. An optical fractal synthesizer (OFS) is described which is capable of effectively computing the iterated function systems taking advantage of optical processing in data continuity and parallelism. An experimental system based on two optical subsystems for affine transformation and a TV-feedback line has been constructed to demonstrate the processing capability of the OFS.
Azevedo-Marques, P M; Spagnoli, H F; Frighetto-Pereira, L; Menezes-Reis, R; Metzner, G A; Rangayyan, R M; Nogueira-Barbosa, M H
2015-08-01
Fractures with partial collapse of vertebral bodies are generically referred to as "vertebral compression fractures" or VCFs. VCFs can have different etiologies comprising trauma, bone failure related to osteoporosis, or metastatic cancer affecting bone. VCFs related to osteoporosis (benign fractures) and to cancer (malignant fractures) are commonly found in the elderly population. In the clinical setting, the differentiation between benign and malignant fractures is complex and difficult. This paper presents a study aimed at developing a system for computer-aided diagnosis to help in the differentiation between malignant and benign VCFs in magnetic resonance imaging (MRI). We used T1-weighted MRI of the lumbar spine in the sagittal plane. Images from 47 consecutive patients (31 women, 16 men, mean age 63 years) were studied, including 19 malignant fractures and 54 benign fractures. Spectral and fractal features were extracted from manually segmented images of 73 vertebral bodies with VCFs. The classification of malignant vs. benign VCFs was performed using the k-nearest neighbor classifier with the Euclidean distance. Results obtained show that combinations of features derived from Fourier and wavelet transforms, together with the fractal dimension, were able to obtain correct classification rate up to 94.7% with area under the receiver operating characteristic curve up to 0.95. PMID:26736364
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.
Radial distribution function for hard spheres in fractal dimensions: A heuristic approximation.
Santos, Andrés; de Haro, Mariano López
2016-06-01
Analytic approximations for the radial distribution function, the structure factor, and the equation of state of hard-core fluids in fractal dimension d (1≤d≤3) are developed as heuristic interpolations from the knowledge of the exact and Percus-Yevick results for the hard-rod and hard-sphere fluids, respectively. In order to assess their value, such approximate results are compared with those of recent Monte Carlo simulations and numerical solutions of the Percus-Yevick equation for a fractal dimension [M. Heinen et al., Phys. Rev. Lett. 115, 097801 (2015)PRLTAO0031-900710.1103/PhysRevLett.115.097801], a good agreement being observed. PMID:27415227
Evaluation of super-resolution imager with binary fractal test target
NASA Astrophysics Data System (ADS)
Landeau, Stéphane
2014-10-01
Today, new generation of powerful non-linear image processing are used for real time super-resolution or noise reduction. Optronic imagers with such features are becoming difficult to assess, because spatial resolution and sensitivity are now related to scene content. Many algorithms include regularization process, which usually reduces image complexity to enhance spread edges or contours. Small important scene details can be then deleted by this kind of processing. In this paper, a binary fractal test target is presented, with a structured clutter pattern and an interesting autosimilarity multi-scale property. The apparent structured clutter of this test target gives a trade-off between a white noise, unlikely in real scenes, and very structured targets like MTF targets. Together with the fractal design of the target, an assessment method has been developed to evaluate automatically the non-linear effects on the acquired and processed image of the imager. The calculated figure of merit is to be directly comparable to the linear Fourier MTF. For this purpose the Haar wavelet elements distributed spatially and at different scales on the target are assimilated to the sine Fourier cycles at different frequencies. The probability of correct resolution indicates the ability to read correct Haar contrast among all Haar wavelet elements with a position constraint. For the method validation, a simulation of two different imager types has been done, a well-sampled linear system and an under-sampled one, coupled with super-resolution or noise reduction algorithms. The influence of the target contrast on the figures of merit is analyzed. Finally, the possible introduction of this new figure of merit in existing analytical range performance models, such as TRM4 (Fraunhofer IOSB) or NVIPM (NVESD) is discussed. Benefits and limitations of the method are also compared to the TOD (TNO) evaluation method.
NASA Technical Reports Server (NTRS)
Quattrochi, Dale A.; Emerson, Charles W.; Lam, Nina Siu-Ngan; Laymon, Charles A.
1997-01-01
The Image Characterization And Modeling System (ICAMS) is a public domain software package that is designed to provide scientists with innovative spatial analytical tools to visualize, measure, and characterize landscape patterns so that environmental conditions or processes can be assessed and monitored more effectively. In this study ICAMS has been used to evaluate how changes in fractal dimension, as a landscape characterization index, and resolution, are related to differences in Landsat images collected at different dates for the same area. Landsat Thematic Mapper (TM) data obtained in May and August 1993 over a portion of the Great Basin Desert in eastern Nevada were used for analysis. These data represent contrasting periods of peak "green-up" and "dry-down" for the study area. The TM data sets were converted into Normalized Difference Vegetation Index (NDVI) images to expedite analysis of differences in fractal dimension between the two dates. These NDVI images were also resampled to resolutions of 60, 120, 240, 480, and 960 meters from the original 30 meter pixel size, to permit an assessment of how fractal dimension varies with spatial resolution. Tests of fractal dimension for two dates at various pixel resolutions show that the D values in the August image become increasingly more complex as pixel size increases to 480 meters. The D values in the May image show an even more complex relationship to pixel size than that expressed in the August image. Fractal dimension for a difference image computed for the May and August dates increase with pixel size up to a resolution of 120 meters, and then decline with increasing pixel size. This means that the greatest complexity in the difference images occur around a resolution of 120 meters, which is analogous to the operational domain of changes in vegetation and snow cover that constitute differences between the two dates.
NASA Astrophysics Data System (ADS)
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.
Medical image retrieval and analysis by Markov random fields and multi-scale fractal dimension.
Backes, André Ricardo; Gerhardinger, Leandro Cavaleri; Batista Neto, João do Espírito Santo; Bruno, Odemir Martinez
2015-02-01
Many Content-based Image Retrieval (CBIR) systems and image analysis tools employ color, shape and texture (in a combined fashion or not) as attributes, or signatures, to retrieve images from databases or to perform image analysis in general. Among these attributes, texture has turned out to be the most relevant, as it allows the identification of a larger number of images of a different nature. This paper introduces a novel signature which can be used for image analysis and retrieval. It combines texture with complexity extracted from objects within the images. The approach consists of a texture segmentation step, modeled as a Markov Random Field process, followed by the estimation of the complexity of each computed region. The complexity is given by a Multi-scale Fractal Dimension. Experiments have been conducted using an MRI database in both pattern recognition and image retrieval contexts. The results show the accuracy of the proposed method in comparison with other traditional texture descriptors and also indicate how the performance changes as the level of complexity is altered.
Fractal-based description of natural scenes.
Pentland, A P
1984-06-01
This paper addresses the problems of 1) representing natural shapes such as mountains, trees, and clouds, and 2) computing their description from image data. To solve these problems, we must be able to relate natural surfaces to their images; this requires a good model of natural surface shapes. Fractal functions are a good choice for modeling 3-D natural surfaces because 1) many physical processes produce a fractal surface shape, 2) fractals are widely used as a graphics tool for generating natural-looking shapes, and 3) a survey of natural imagery has shown that the 3-D fractal surface model, transformed by the image formation process, furnishes an accurate description of both textured and shaded image regions. The 3-D fractal model provides a characterization of 3-D surfaces and their images for which the appropriateness of the model is verifiable. Furthermore, this characterization is stable over transformations of scale and linear transforms of intensity. The 3-D fractal model has been successfully applied to the problems of 1) texture segmentation and classification, 2) estimation of 3-D shape information, and 3) distinguishing between perceptually ``smooth'' and perceptually ``textured'' surfaces in the scene.
Mossotti, Victor G.; Eldeeb, A. Raouf
2000-01-01
Turcotte, 1997, and Barton and La Pointe, 1995, have identified many potential uses for the fractal dimension in physicochemical models of surface properties. The image-analysis program described in this report is an extension of the program set MORPH-I (Mossotti and others, 1998), which provided the fractal analysis of electron-microscope images of pore profiles (Mossotti and Eldeeb, 1992). MORPH-II, an integration of the modified kernel of the program MORPH-I with image calibration and editing facilities, was designed to measure the fractal dimension of the exposed surfaces of stone specimens as imaged in cross section in an electron microscope.
Characterizing Hyperspectral Imagery (AVIRIS) Using Fractal Technique
NASA Technical Reports Server (NTRS)
Qiu, Hong-Lie; Lam, Nina Siu-Ngan; Quattrochi, Dale
1997-01-01
With the rapid increase in hyperspectral data acquired by various experimental hyperspectral imaging sensors, it is necessary to develop efficient and innovative tools to handle and analyze these data. The objective of this study is to seek effective spatial analytical tools for summarizing the spatial patterns of hyperspectral imaging data. In this paper, we (1) examine how fractal dimension D changes across spectral bands of hyperspectral imaging data and (2) determine the relationships between fractal dimension and image content. It has been documented that fractal dimension changes across spectral bands for the Landsat-TM data and its value [(D)] is largely a function of the complexity of the landscape under study. The newly available hyperspectral imaging data such as that from the Airborne Visible Infrared Imaging Spectrometer (AVIRIS) which has 224 bands, covers a wider spectral range with a much finer spectral resolution. Our preliminary result shows that fractal dimension values of AVIRIS scenes from the Santa Monica Mountains in California vary between 2.25 and 2.99. However, high fractal dimension values (D > 2.8) are found only from spectral bands with high noise level and bands with good image quality have a fairly stable dimension value (D = 2.5 - 2.6). This suggests that D can also be used as a summary statistics to represent the image quality or content of spectral bands.
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.
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)
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…
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
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.
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.
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
Field Emission and Radial Distribution Function Studies of Fractal-like Amorphous Carbon Nanotips
NASA Astrophysics Data System (ADS)
Solá, F.; Biaggi-Labiosa, A.; Fonseca, L. F.; Resto, O.; Lebrón-Colón, M.; Meador, M. A.
2009-05-01
The short-range order of individual fractal-like amorphous carbon nanotips was investigated by means of energy-filtered electron diffraction in a transmission electron microscope (TEM). The nanostructures were grown in porous silicon substrates in situ within the TEM by the electron beam-induced deposition method. The structure factor S( k) and the reduced radial distribution function G( r) were calculated. From these calculations a bond angle of 124° was obtained which suggests a distorted graphitic structure. Field emission was obtained from individual nanostructures using two micromanipulators with sub-nanometer positioning resolution. A theoretical three-stage model that accounts for the geometry of the nanostructures provides a value for the field enhancement factor close to the one obtained experimentally from the Fowler-Nordheim law.
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
2012-06-28
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.
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
2012-06-28
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. PMID:22739316
NASA Astrophysics Data System (ADS)
Mosquera Lopez, Clara; Agaian, Sos
2013-02-01
Prostate cancer detection and staging is an important step towards patient treatment selection. Advancements in digital pathology allow the application of new quantitative image analysis algorithms for computer-assisted diagnosis (CAD) on digitized histopathology images. In this paper, we introduce a new set of features to automatically grade pathological images using the well-known Gleason grading system. The goal of this study is to classify biopsy images belonging to Gleason patterns 3, 4, and 5 by using a combination of wavelet and fractal features. For image classification we use pairwise coupling Support Vector Machine (SVM) classifiers. The accuracy of the system, which is close to 97%, is estimated through three different cross-validation schemes. The proposed system offers the potential for automating classification of histological images and supporting prostate cancer diagnosis.
ERIC Educational Resources Information Center
Simoson, Andrew J.
2009-01-01
This article presents a fun activity of generating a double-minded fractal image for a linear algebra class once the idea of rotation and scaling matrices are introduced. In particular the fractal flip-flops between two words, depending on the level at which the image is viewed. (Contains 5 figures.)
Image analysis of human corneal endothelial cells based on fractal theory
NASA Astrophysics Data System (ADS)
Zhang, Zhi; Luo, Qingming; Zeng, Shaoqun; Zhang, Xinyu; Huang, Dexiu; Chen, Weiguo
1999-09-01
A fast method is developed to quantitatively characterize the shape of human corneal endothelial cells with fractal theory and applied to analyze microscopic photographs of human corneal endothelial cells. The results show that human corneal endothelial cells possess the third characterization parameter-- fractal dimension, besides another two characterization parameter (its size and shape). Compared with tradition method, this method has many advantages, such as automatism, speediness, parallel processing and can be used to analyze large numbers of endothelial cells, the obtained values are statistically significant, it offers a new approach for clinic diagnosis of endothelial cells.
2006-01-01
Executive Summary Objective The objective of this analysis is to review a spectrum of functional brain imaging technologies to identify whether there are any imaging modalities that are more effective than others for various brain pathology conditions. This evidence-based analysis reviews magnetoencephalography (MEG), magnetic resonance spectroscopy (MRS), positron emission tomography (PET), and functional magnetic resonance imaging (fMRI) for the diagnosis or surgical management of the following conditions: Alzheimer’s disease (AD), brain tumours, epilepsy, multiple sclerosis (MS), and Parkinson’s disease (PD). Clinical Need: Target Population and Condition Alzheimer’s disease is a progressive, degenerative, neurologic condition characterized by cognitive impairment and memory loss. The Canadian Study on Health and Aging estimated that there will be 97,000 incident cases (about 60,000 women) of dementia (including AD) in Canada in 2006. In Ontario, there will be an estimated 950 new cases and 580 deaths due to brain cancer in 2006. Treatments for brain tumours include surgery and radiation therapy. However, one of the limitations of radiation therapy is that it damages tissue though necrosis and scarring. Computed tomography (CT) and magnetic resonance imaging (MRI) may not distinguish between radiation effects and resistant tissue, creating a potential role for functional brain imaging. Epilepsy is a chronic disorder that provokes repetitive seizures. In Ontario, the rate of epilepsy is estimated to be 5 cases per 1,000 people. Most people with epilepsy are effectively managed with drug therapy; but about 50% do not respond to drug therapy. Surgical resection of the seizure foci may be considered in these patients, and functional brain imaging may play a role in localizing the seizure foci. Multiple sclerosis is a progressive, inflammatory, demyelinating disease of the central nervous system (CNS). The cause of MS is unknown; however, it is thought to be
Fractal Feature Analysis Of Beef Marblingpatterns
NASA Astrophysics Data System (ADS)
Chen, Kunjie; Qin, Chunfang
The purpose of this study is to investigate fractal behavior of beef marbling patterns and to explore relationships between fractal dimensions and marbling scores. Authors firstly extracted marbling images from beef rib-eye crosssection images using computer image processing technologies and then implemented the fractal analysis on these marbling images based on the pixel covering method. Finally box-counting fractal dimension (BFD) and informational fractal dimension (IFD) of one hundred and thirty-five beef marbling images were calculated and plotted against the beef marbling scores. The results showed that all beef marbling images exhibit fractal behavior over the limited range of scales accessible to analysis. Furthermore, their BFD and IFD are closely related to the score of beef marbling, suggesting that fractal analyses can provide us a potential tool to calibrate the score of beef marbling.
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
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.
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.
Characterization of branch complexity by fractal analyses and detect plant functional adaptations
Alados, C.L.; Escos, J.; Emlen, J.M.; Freeman, D.C.
1999-01-01
The comparison between complexity in the sense of space occupancy (box-counting fractal dimension Dc and information dimension DI ) and heterogeneity in the sense of space distribution (average evenness index and evenness variation coefficient JCV) were investigated in mathematical fractal objects and natural branch ¯ J structures. In general, increased fractal dimension was paired with low heterogeneity. Comparisons between branch architecture in Anthyllis cytisoides under different slope exposure and grazing impact revealed that branches were more complex and more homogeneously distributed for plants on northern exposures than southern, while grazing had no impact during a wet year. Developmental instability was also investigated by the statistical noise of the allometric relation between internode length and node order. In conclusion, our study demonstrated that fractal dimension of branch structure can be used to analyze the structural organization of plants, especially if we consider not only fractal dimension but also shoot distribution within the canopy (lacunarity). These indexes together with developmental instability analyses are good indicators of growth responses to the environment.
Fractal 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 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.
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.
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.
Study of fractal dimension in chest images using normal and interstitial lung disease cases
NASA Astrophysics Data System (ADS)
Tucker, Douglas M.; Correa, Jose L.; Souto, Miguel; Malagari, Katerina S.
1993-09-01
A quantitative computerized method which provides accurate discrimination between chest radiographs with positive findings of interstitial disease patterns and normal chest radiographs may increase the efficacy of radiologic screening of the chest and the utility of digital radiographic systems. This report is a comparison of fractal dimension measured in normal chest radiographs and in radiographs with abnormal lungs having reticular, nodular, reticulonodular and linear patterns of interstitial disease. Six regions of interest (ROI's) from each of 33 normal chest radiographs and 33 radiographs with positive findings of interstitial disease were studied. Results indicate that there is a statistically significant difference between the distribution of the fractal dimension in normal radiographs and radiographs where disease is present.
Fractal metrology for biogeosystems analysis
NASA Astrophysics Data System (ADS)
Torres-Argüelles, V.; Oleschko, K.; Tarquis, A. M.; Korvin, G.; Gaona, C.; Parrot, J.-F.; Ventura-Ramos, E.
2010-06-01
The solid-pore distribution pattern plays an important role in soil functioning being related with the main physical, chemical and biological multiscale and multitemporal processes. In the present research, this pattern is extracted from the digital images of three soils (Chernozem, Solonetz and "Chocolate'' Clay) and compared in terms of roughness of the gray-intensity distribution (the measurand) quantified by several measurement techniques. Special attention was paid to the uncertainty of each of them and to the measurement function which best fits to the experimental results. Some of the applied techniques are known as classical in the fractal context (box-counting, rescaling-range and wavelets analyses, etc.) while the others have been recently developed by our Group. The combination of all these techniques, coming from Fractal Geometry, Metrology, Informatics, Probability Theory and Statistics is termed in this paper Fractal Metrology (FM). We show the usefulness of FM through a case study of soil physical and chemical degradation applying the selected toolbox to describe and compare the main structural attributes of three porous media with contrasting structure but similar clay mineralogy dominated by montmorillonites.
Fractal electronic devices: simulation and implementation.
Fairbanks, M S; McCarthy, D N; Scott, S A; Brown, S A; Taylor, R P
2011-09-01
Many natural structures have fractal geometries that exhibit useful functional properties. These properties, which exploit the recurrence of patterns at increasingly small scales, are often desirable in applications and, consequently, fractal geometry is increasingly employed in diverse technologies ranging from radio antennae to storm barriers. In this paper, we explore the application of fractal geometry to electrical devices. First, we lay the foundations for the implementation of fractal devices by considering diffusion-limited aggregation (DLA) of atomic clusters. Under appropriate growth conditions, atomic clusters of various elements form fractal patterns driven by DLA. We perform a fractal analysis of both simulated and physical devices to determine their spatial scaling properties and demonstrate their potential as fractal circuit elements. Finally, we simulate conduction through idealized and DLA fractal devices and show that their fractal scaling properties generate novel, nonlinear conduction properties in response to depletion by electrostatic gates. PMID:21841218
Fractal electronic devices: simulation and implementation
NASA Astrophysics Data System (ADS)
Fairbanks, M. S.; McCarthy, D. N.; Scott, S. A.; Brown, S. A.; Taylor, R. P.
2011-09-01
Many natural structures have fractal geometries that exhibit useful functional properties. These properties, which exploit the recurrence of patterns at increasingly small scales, are often desirable in applications and, consequently, fractal geometry is increasingly employed in diverse technologies ranging from radio antennae to storm barriers. In this paper, we explore the application of fractal geometry to electrical devices. First, we lay the foundations for the implementation of fractal devices by considering diffusion-limited aggregation (DLA) of atomic clusters. Under appropriate growth conditions, atomic clusters of various elements form fractal patterns driven by DLA. We perform a fractal analysis of both simulated and physical devices to determine their spatial scaling properties and demonstrate their potential as fractal circuit elements. Finally, we simulate conduction through idealized and DLA fractal devices and show that their fractal scaling properties generate novel, nonlinear conduction properties in response to depletion by electrostatic gates.
Functional magnetic resonance imaging.
Buchbinder, Bradley R
2016-01-01
Functional magnetic resonance imaging (fMRI) maps the spatiotemporal distribution of neural activity in the brain under varying cognitive conditions. Since its inception in 1991, blood oxygen level-dependent (BOLD) fMRI has rapidly become a vital methodology in basic and applied neuroscience research. In the clinical realm, it has become an established tool for presurgical functional brain mapping. This chapter has three principal aims. First, we review key physiologic, biophysical, and methodologic principles that underlie BOLD fMRI, regardless of its particular area of application. These principles inform a nuanced interpretation of the BOLD fMRI signal, along with its neurophysiologic significance and pitfalls. Second, we illustrate the clinical application of task-based fMRI to presurgical motor, language, and memory mapping in patients with lesions near eloquent brain areas. Integration of BOLD fMRI and diffusion tensor white-matter tractography provides a road map for presurgical planning and intraoperative navigation that helps to maximize the extent of lesion resection while minimizing the risk of postoperative neurologic deficits. Finally, we highlight several basic principles of resting-state fMRI and its emerging translational clinical applications. Resting-state fMRI represents an important paradigm shift, focusing attention on functional connectivity within intrinsic cognitive networks. PMID:27432660
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.
Matsueda, Hiroaki; Lee, Ching Hua
2015-03-10
We examine singular value spectrum of a class of two-dimensional fractal images. We find that the spectra can be mapped onto entanglement spectra of free fermions in one dimension. This exact mapping tells us that the singular value decomposition is a way of detecting a holographic relation between classical and quantum systems.
Fractal Metrology for biogeosystems analysis
NASA Astrophysics Data System (ADS)
Torres-Argüelles, V.; Oleschko, K.; Tarquis, A. M.; Korvin, G.; Gaona, C.; Parrot, J.-F.; Ventura-Ramos, E.
2010-11-01
The solid-pore distribution pattern plays an important role in soil functioning being related with the main physical, chemical and biological multiscale and multitemporal processes of this complex system. In the present research, we studied the aggregation process as self-organizing and operating near a critical point. The structural pattern is extracted from the digital images of three soils (Chernozem, Solonetz and "Chocolate" Clay) and compared in terms of roughness of the gray-intensity distribution quantified by several measurement techniques. Special attention was paid to the uncertainty of each of them measured in terms of standard deviation. Some of the applied methods are known as classical in the fractal context (box-counting, rescaling-range and wavelets analyses, etc.) while the others have been recently developed by our Group. The combination of these techniques, coming from Fractal Geometry, Metrology, Informatics, Probability Theory and Statistics is termed in this paper Fractal Metrology (FM). We show the usefulness of FM for complex systems analysis through a case study of the soil's physical and chemical degradation applying the selected toolbox to describe and compare the structural attributes of three porous media with contrasting structure but similar clay mineralogy dominated by montmorillonites.
Fractal analysis for assessing tumour grade in microscopic images of breast tissue
NASA Astrophysics Data System (ADS)
Tambasco, Mauro; Costello, Meghan; Newcomb, Chris; Magliocco, Anthony M.
2007-03-01
In 2006, breast cancer is expected to continue as the leading form of cancer diagnosed in women, and the second leading cause of cancer mortality in this group. A method that has proven useful for guiding the choice of treatment strategy is the assessment of histological tumor grade. The grading is based upon the mitosis count, nuclear pleomorphism, and tubular formation, and is known to be subject to inter-observer variability. Since cancer grade is one of the most significant predictors of prognosis, errors in grading can affect patient management and outcome. Hence, there is a need to develop a breast cancer-grading tool that is minimally operator dependent to reduce variability associated with the current grading system, and thereby reduce uncertainty that may impact patient outcome. In this work, we explored the potential of a computer-based approach using fractal analysis as a quantitative measure of cancer grade for breast specimens. More specifically, we developed and optimized computational tools to compute the fractal dimension of low- versus high-grade breast sections and found them to be significantly different, 1.3+/-0.10 versus 1.49+/-0.10, respectively (Kolmogorov-Smirnov test, p<0.001). These results indicate that fractal dimension (a measure of morphologic complexity) may be a useful tool for demarcating low- versus high-grade cancer specimens, and has potential as an objective measure of breast cancer grade. Such prognostic value could provide more sensitive and specific information that would reduce inter-observer variability by aiding the pathologist in grading cancers.
NASA Astrophysics Data System (ADS)
Lehtonen, Juha; Andriyashin, Alexey; Parkkinen, Jussi; Leisti, Tuomas; Nyman, Göte
2006-10-01
The visual quality of images is outward in image presentation, compression and analysis. Depending on the use, the quality of images may give more information or more experiences to the viewer. However, the relations between mathematical and human methods for grouping the images are not obvious. For example, different humans think differently and so, they make the grouping differently. However, there may be some connections between image mathematical features and human selections. Here we try to find such relations that could give more possibilities for developing the actual quality of images for different purposes. In this study, we present some methods and preliminary results that are based on psychological tests to humans, MPEG-7 based features of the images and face detection methods. We also show some notes and questions belonging to this problem and plans for the future research.
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.
NASA Technical Reports Server (NTRS)
Bruno, B. C.; Taylor, G. J.; Rowland, S. K.; Lucey, P. G.; Self, S.
1992-01-01
Results are presented of a preliminary investigation of the fractal nature of the plan-view shapes of lava flows in Hawaii (based on field measurements and aerial photographs), as well as in Idaho and the Galapagos Islands (using aerial photographs only). The shapes of the lava flow margins are found to be fractals: lava flow shape is scale-invariant. This observation suggests that nonlinear forces are operating in them because nonlinear systems frequently produce fractals. A'a and pahoehoe flows can be distinguished by their fractal dimensions (D). The majority of the a'a flows measured have D between 1.05 and 1.09, whereas the pahoehoe flows generally have higher D (1.14-1.23). The analysis is extended to other planetary bodies by measuring flows from orbital images of Venus, Mars, and the moon. All are fractal and have D consistent with the range of terrestrial a'a and have D consistent with the range of terrestrial a'a and pahoehoe values.
NASA Technical Reports Server (NTRS)
Lam, Nina Siu-Ngan; Qiu, Hong-Lie; Quattrochi, Dale A.; Emerson, Charles W.; Arnold, James E. (Technical Monitor)
2001-01-01
The rapid increase in digital data volumes from new and existing sensors necessitates the need for efficient analytical tools for extracting information. We developed an integrated software package called ICAMS (Image Characterization and Modeling System) to provide specialized spatial analytical functions for interpreting remote sensing data. This paper evaluates the three fractal dimension measurement methods: isarithm, variogram, and triangular prism, along with the spatial autocorrelation measurement methods Moran's I and Geary's C, that have been implemented in ICAMS. A modified triangular prism method was proposed and implemented. Results from analyzing 25 simulated surfaces having known fractal dimensions show that both the isarithm and triangular prism methods can accurately measure a range of fractal surfaces. The triangular prism method is most accurate at estimating the fractal dimension of higher spatial complexity, but it is sensitive to contrast stretching. The variogram method is a comparatively poor estimator for all of the surfaces, particularly those with higher fractal dimensions. Similar to the fractal techniques, the spatial autocorrelation techniques are found to be useful to measure complex images but not images with low dimensionality. These fractal measurement methods can be applied directly to unclassified images and could serve as a tool for change detection and data mining.
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.
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).
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
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
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.
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
Mesh generation/refinement using fractal concepts and iterated function systems
NASA Technical Reports Server (NTRS)
Bova, S. W.; Carey, G. F.
1992-01-01
A novel method of mesh generation is proposed which is based on the use of fractal concepts to derive contractive, affine transformations. The transformations are constructed in such a manner that the attractors of the resulting maps are a union of the points, lines and surfaces in the domain. In particular, the mesh nodes may be generated recursively as a sequence of points which are obtained by applying the transformations to a coarse background mesh constructed from the given boundary data. A Delaunay triangulation or similar edge connection approach can then be performed on the resulting set of nodes in order to generate the mesh. Local refinement of an existing mesh can also be performed using the procedure. The method is easily extended to three dimensions, in which case the Delaunay triangulation is replaced by an analogous 3D tesselation.
Investigation into How 8th Grade Students Define Fractals
ERIC Educational Resources Information Center
Karakus, Fatih
2015-01-01
The analysis of 8th grade students' concept definitions and concept images can provide information about their mental schema of fractals. There is limited research on students' understanding and definitions of fractals. Therefore, this study aimed to investigate the elementary students' definitions of fractals based on concept image and concept…
A Brief Historical Introduction to Fractals and Fractal Geometry
ERIC Educational Resources Information Center
Debnath, Lokenath
2006-01-01
This paper deals with a brief historical introduction to fractals, fractal dimension and fractal geometry. Many fractals including the Cantor fractal, the Koch fractal, the Minkowski fractal, the Mandelbrot and Given fractal are described to illustrate self-similar geometrical figures. This is followed by the discovery of dynamical systems and…
NASA 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.
Fractals, Coherence and Brain Dynamics
NASA Astrophysics Data System (ADS)
Vitiello, Giuseppe
2010-11-01
I show that the self-similarity property of deterministic fractals provides a direct connection with the space of the entire analytical functions. Fractals are thus described in terms of coherent states in the Fock-Bargmann representation. Conversely, my discussion also provides insights on the geometrical properties of coherent states: it allows to recognize, in some specific sense, fractal properties of coherent states. In particular, the relation is exhibited between fractals and q-deformed coherent states. The connection with the squeezed coherent states is also displayed. In this connection, the non-commutative geometry arising from the fractal relation with squeezed coherent states is discussed and the fractal spectral properties are identified. I also briefly discuss the description of neuro-phenomenological data in terms of squeezed coherent states provided by the dissipative model of brain and consider the fact that laboratory observations have shown evidence that self-similarity characterizes the brain background activity. This suggests that a connection can be established between brain dynamics and the fractal self-similarity properties on the basis of the relation discussed in this report between fractals and squeezed coherent states. Finally, I do not consider in this paper the so-called random fractals, namely those fractals obtained by randomization processes introduced in their iterative generation. Since self-similarity is still a characterizing property in many of such random fractals, my conjecture is that also in such cases there must exist a connection with the coherent state algebraic structure. In condensed matter physics, in many cases the generation by the microscopic dynamics of some kind of coherent states is involved in the process of the emergence of mesoscopic/macroscopic patterns. The discussion presented in this paper suggests that also fractal generation may provide an example of emergence of global features, namely long range
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.
Functional imaging in lung cancer
Harders, S W; Balyasnikowa, S; Fischer, B M
2014-01-01
Lung cancer represents an increasingly frequent cancer diagnosis worldwide. An increasing awareness on smoking cessation as an important mean to reduce lung cancer incidence and mortality, an increasing number of therapy options and a steady focus on early diagnosis and adequate staging have resulted in a modestly improved survival. For early diagnosis and precise staging, imaging, especially positron emission tomography combined with CT (PET/CT), plays an important role. Other functional imaging modalities such as dynamic contrast-enhanced CT (DCE-CT) and diffusion-weighted MR imaging (DW-MRI) have demonstrated promising results within this field. The purpose of this review is to provide the reader with a brief and balanced introduction to these three functional imaging modalities and their current or potential application in the care of patients with lung cancer. PMID:24289258
Fractal analysis: A new remote sensing tool for lava flows
NASA Technical Reports Server (NTRS)
Bruno, B. C.; Taylor, G. J.; Rowland, S. K.; Lucey, P. G.; Self, S.
1992-01-01
Many important quantitative parameters have been developed that relate to the rheology and eruption and emplacement mechanics of lavas. This research centers on developing additional, unique parameters, namely the fractal properties of lava flows, to add to this matrix of properties. There are several methods of calculating the fractal dimension of a lava flow margin. We use the 'structured walk' or 'divider' method. In this method, we measure the length of a given lava flow margin by walking rods of different lengths along the margin. Since smaller rod lengths transverse more smaller-scaled features in the flow margin, the apparent length of the flow outline will increase as the length of the measuring rod decreases. By plotting the apparent length of the flow outline as a function of the length of the measuring rod on a log-log plot, fractal behavior can be determined. A linear trend on a log-log plot indicates that the data are fractal. The fractal dimension can then be calculated from the slope of the linear least squares fit line to the data. We use this 'structured walk' method to calculate the fractal dimension of many lava flows using a wide range of rod lengths, from 1/8 to 16 meters, in field studies of the Hawaiian islands. We also use this method to calculate fractal dimensions from aerial photographs of lava flows, using lengths ranging from 20 meters to over 2 kilometers. Finally, we applied this method to orbital images of extraterrestrial lava flows on Venus, Mars, and the Moon, using rod lengths up to 60 kilometers.
Fractal signatures in the aperiodic Fibonacci grating.
Verma, Rupesh; Banerjee, Varsha; Senthilkumaran, Paramasivam
2014-05-01
The Fibonacci grating (FbG) is an archetypal example of aperiodicity and self-similarity. While aperiodicity distinguishes it from a fractal, self-similarity identifies it with a fractal. Our paper investigates the outcome of these complementary features on the FbG diffraction profile (FbGDP). We find that the FbGDP has unique characteristics (e.g., no reduction in intensity with increasing generations), in addition to fractal signatures (e.g., a non-integer fractal dimension). These make the Fibonacci architecture potentially useful in image forming devices and other emerging technologies. PMID:24784044
Changes in fractal dimension during aggregation.
Chakraborti, Rajat K; Gardner, Kevin H; Atkinson, Joseph F; Van Benschoten, John E
2003-02-01
Experiments were performed to evaluate temporal changes in the fractal dimension of aggregates formed during flocculation of an initially monodisperse suspension of latex microspheres. Particle size distributions and aggregate geometrical information at different mixing times were obtained using a non-intrusive optical sampling and digital image analysis technique, under variable conditions of mixing speed, coagulant (alum) dose and particle concentration. Pixel resolution required to determine aggregate size and geometric measures including the fractal dimension is discussed and a quantitative measure of accuracy is developed. The two-dimensional fractal dimension was found to range from 1.94 to 1.48, corresponding to aggregates that are either relatively compact or loosely structured, respectively. Changes in fractal dimension are explained using a conceptual model, which describes changes in fractal dimension associated with aggregate growth and changes in aggregate structure. For aggregation of an initially monodisperse suspension, the fractal dimension was found to decrease over time in the initial stages of floc formation.
Functional imaging for regenerative medicine.
Leahy, Martin; Thompson, Kerry; Zafar, Haroon; Alexandrov, Sergey; Foley, Mark; O'Flatharta, Cathal; Dockery, Peter
2016-01-01
In vivo imaging is a platform technology with the power to put function in its natural structural context. With the drive to translate stem cell therapies into pre-clinical and clinical trials, early selection of the right imaging techniques is paramount to success. There are many instances in regenerative medicine where the biological, biochemical, and biomechanical mechanisms behind the proposed function of stem cell therapies can be elucidated by appropriate imaging. Imaging techniques can be divided according to whether labels are used and as to whether the imaging can be done in vivo. In vivo human imaging places additional restrictions on the imaging tools that can be used. Microscopies and nanoscopies, especially those requiring fluorescent markers, have made an extraordinary impact on discovery at the molecular and cellular level, but due to their very limited ability to focus in the scattering tissues encountered for in vivo applications they are largely confined to superficial imaging applications in research laboratories. Nanoscopy, which has tremendous benefits in resolution, is limited to the near-field (e.g. near-field scanning optical microscope (NSNOM)) or to very high light intensity (e.g. stimulated emission depletion (STED)) or to slow stochastic events (photo-activated localization microscopy (PALM) and stochastic optical reconstruction microscopy (STORM)). In all cases, nanoscopy is limited to very superficial applications. Imaging depth may be increased using multiphoton or coherence gating tricks. Scattering dominates the limitation on imaging depth in most tissues and this can be mitigated by the application of optical clearing techniques that can impose mild (e.g. topical application of glycerol) or severe (e.g. CLARITY) changes to the tissue to be imaged. Progression of therapies through to clinical trials requires some thought as to the imaging and sensing modalities that should be used. Smoother progression is facilitated by the use of
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.
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.
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 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.
NASA Technical Reports Server (NTRS)
Makikallio, T. H.; Hoiber, S.; Kober, L.; Torp-Pedersen, C.; Peng, C. K.; Goldberger, A. L.; Huikuri, H. V.
1999-01-01
A number of new methods have been recently developed to quantify complex heart rate (HR) dynamics based on nonlinear and fractal analysis, but their value in risk stratification has not been evaluated. This study was designed to determine whether selected new dynamic analysis methods of HR variability predict mortality in patients with depressed left ventricular (LV) function after acute myocardial infarction (AMI). Traditional time- and frequency-domain HR variability indexes along with short-term fractal-like correlation properties of RR intervals (exponent alpha) and power-law scaling (exponent beta) were studied in 159 patients with depressed LV function (ejection fraction <35%) after an AMI. By the end of 4-year follow-up, 72 patients (45%) had died and 87 (55%) were still alive. Short-term scaling exponent alpha (1.07 +/- 0.26 vs 0.90 +/- 0.26, p <0.001) and power-law slope beta (-1.35 +/- 0.23 vs -1.44 +/- 0.25, p <0.05) differed between survivors and those who died, but none of the traditional HR variability measures differed between these groups. Among all analyzed variables, reduced scaling exponent alpha (<0.85) was the best univariable predictor of mortality (relative risk 3.17, 95% confidence interval 1.96 to 5.15, p <0.0001), with positive and negative predictive accuracies of 65% and 86%, respectively. In the multivariable Cox proportional hazards analysis, mortality was independently predicted by the reduced exponent alpha (p <0.001) after adjustment for several clinical variables and LV function. A short-term fractal-like scaling exponent was the most powerful HR variability index in predicting mortality in patients with depressed LV function. Reduction in fractal correlation properties implies more random short-term HR dynamics in patients with increased risk of death after AMI.
Fractal 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.
Functional imaging in Huntington's disease.
Paulsen, Jane S
2009-04-01
Huntington's disease (HD) is a genetic brain disease characterized by loss of capacity in movement control, cognition, and emotional regulation over a period of about 30 years. Since it is well established that clinical impairments and brain atrophy can be detected decades prior to receiving a clinical diagnosis, functional neuroimaging efforts have gained momentum in HD research. In most brain disorders, there is accumulating evidence that the clinical manifestations of disease do not simply depend on the extent of tissue loss, but represent a complex balance among neuronal dysfunction, tissue repair, and circuitry reorganization. Based upon this premise, functional neuroimaging modalities may be more sensitive to the earliest changes in HD than are structural imaging approaches. For this review, PET and fMRI studies conducted in HD samples were summarized. Strengths and limitations of the utilization of functional imaging in HD are discussed and recommendations are offered to facilitate future research endeavors.
Dynamic imaging of brain function
Hyder, Fahmeed
2013-01-01
In recent years, there have been unprecedented methodological advances in the dynamic imaging of brain activities. Electrophysiological, optical, and magnetic resonance methods now allow mapping of functional activation (or deactivation) by measurement of neuronal activity (e.g., membrane potential, ion flux, neurotransmitter flux), energy metabolism (e.g., glucose consumption, oxygen consumption, creatine kinase flux), and functional hyperemia (e.g., blood oxygenation, blood flow, blood volume). Properties of the glutamatergic synapse are used as a model to reveal activities at the nerve terminal and their associated changes in energy demand and blood flow. This approach reveals that each method measures different tissue- and/or cell-specific components with specified spatiotemporal resolution. While advantages and disadvantages of different methods are apparent and often used to supersede one another in terms of specificity and/or sensitivity, no particular technique is the optimal dynamic brain imaging method because each method is unique in some respect. Because the demand for energy substrates is a fundamental requirement for function, energy-based methods may allow quantitative dynamic imaging in vivo. However there are exclusive neurobiological insights gained by combining some of these different dynamic imaging techniques. PMID:18839085
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
2014-01-01
Background 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. Methods 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. Results 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. Conclusion 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. PMID:25298774
Fractal vector optical fields.
Pan, Yue; Gao, Xu-Zhen; Cai, Meng-Qiang; Zhang, Guan-Lin; Li, Yongnan; Tu, Chenghou; Wang, Hui-Tian
2016-07-15
We introduce the concept of a fractal, which provides an alternative approach for flexibly engineering the optical fields and their focal fields. We propose, design, and create a new family of optical fields-fractal vector optical fields, which build a bridge between the fractal and vector optical fields. The fractal vector optical fields have polarization states exhibiting fractal geometry, and may also involve the phase and/or amplitude simultaneously. The results reveal that the focal fields exhibit self-similarity, and the hierarchy of the fractal has the "weeding" role. The fractal can be used to engineer the focal field. PMID:27420485
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.
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.
Fractals in art and nature: why do we like them?
NASA Astrophysics Data System (ADS)
Spehar, Branka; Taylor, Richard P.
2013-03-01
Fractals have experienced considerable success in quantifying the visual complexity exhibited by many natural patterns, and continue to capture the imagination of scientists and artists alike. Fractal patterns have also been noted for their aesthetic appeal, a suggestion further reinforced by the discovery that the poured patterns of the American abstract painter Jackson Pollock are also fractal, together with the findings that many forms of art resemble natural scenes in showing scale-invariant, fractal-like properties. While some have suggested that fractal-like patterns are inherently pleasing because they resemble natural patterns and scenes, the relation between the visual characteristics of fractals and their aesthetic appeal remains unclear. Motivated by our previous findings that humans display a consistent preference for a certain range of fractal dimension across fractal images of various types we turn to scale-specific processing of visual information to understand this relationship. Whereas our previous preference studies focused on fractal images consisting of black shapes on white backgrounds, here we extend our investigations to include grayscale images in which the intensity variations exhibit scale invariance. This scale-invariance is generated using a 1/f frequency distribution and can be tuned by varying the slope of the rotationally averaged Fourier amplitude spectrum. Thresholding the intensity of these images generates black and white fractals with equivalent scaling properties to the original grayscale images, allowing a direct comparison of preferences for grayscale and black and white fractals. We found no significant differences in preferences between the two groups of fractals. For both set of images, the visual preference peaked for images with the amplitude spectrum slopes from 1.25 to 1.5, thus confirming and extending the previously observed relationship between fractal characteristics of images and visual preference.
Surface topography characterization of automotive cylinder liner surfaces using fractal methods
NASA Astrophysics Data System (ADS)
Lawrence K, Deepak; Ramamoorthy, B.
2013-09-01
This paper explores the use of fractal approaches for the possible characterization of automotive cylinder bore surface topography by employing methods such as differential box counting method, power spectral method and structure function method. Three stage plateau honing experiments were conducted to manufacture sixteen cylinder liner surfaces with different surface topographies, for the study. The three fractal methods are applied on the image data obtained using a computer vision system and 3-D profile data obtained using vertical scanning white light interferometer from the cylinder liner surfaces. The computed fractal parameters (fractal dimension and topothesy) are compared and correlated with the measured 3-D Abbott-Firestone curve parameters (Sk, Spk, Svk, Sr1 and Sr2) that are currently used for the surface topography characterization cylinder liner surfaces. The analyses of the results indicated that the fractal dimension (D) computed using the vision data as well as 3-D profile data by employing three different fractal methods consistantly showed a negative correlation with the functional surface topographical parameters that represents roughness at peak (Spk),core (Sk) and valley (Svk) regions and positive correlation with the upper bearing area (Sr1) and lower bearing area (Sr2) of the automotive of cylinder bore surface.
Diffraction from fractal grating Cantor sets
NASA Astrophysics Data System (ADS)
Golmankhaneh, Alireza K.; Baleanu, D.
2016-08-01
In this paper, we have generalized the Fα-calculus by suggesting Fourier and Laplace transformations of the function with support of the fractals set which are the subset of the real line. Using this generalization, we have found the diffraction fringes from the fractal grating Cantor sets.
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.
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
Functional imaging in Tourette's syndrome.
Adams, J R; Troiano, A R; Calne, D B
2004-10-01
The cause or causes of Tourette's syndrome (TS) remain unknown. Functional imaging studies have evaluated several implicated neurotransmitter systems and focused predominantly on the frequency or severity of tics. The results have been inconclusive and frequently contradictory with little light shed on pathogenetic mechanisms. However, metabolic derangements have been demonstrated within regions of the basal ganglia, limbic system and sensori-motor cortex and are in keeping with the concept of TS as both a motor and behavioral disorder. TS has long been regarded an involuntary movement disorder. However, many patients have stated that without the premonitory sensation, there would be no tics. For this reason, it has been suggested that the premonitory urge may be considered the involuntary component of TS and the performance of the tic merely a voluntary response. Future studies are needed to differentiate functional changes relating to urge from those associated with the performance of tics and tic suppression.
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
Multiresolution processing for fractal analysis of airborne remotely sensed data
NASA Technical Reports Server (NTRS)
Jaggi, S.; Quattrochi, D.; Lam, N.
1992-01-01
Images acquired by NASA's Calibrated Airborne Multispectral Scanner are used to compute the fractal dimension as a function of spatial resolution. Three methods are used to determine the fractal dimension: Shelberg's (1982, 1983) line-divider method, the variogram method, and the triangular prism method. A description of these methods and the result of applying these methods to a remotely-sensed image is also presented. The scanner data was acquired over western Puerto Rico in January, 1990 over land and water. The aim is to study impacts of man-induced changes on land that affect sedimentation into the near-shore environment. The data were obtained over the same area at three different pixel sizes: 10 m, 20 m, and 30 m.
Shirazinodeh, Alireza; Noubari, Hossein Ahmadi; Rabbani, Hossein; Dehnavi, Alireza Mehri
2015-01-01
Recent studies on wavelet transform and fractal modeling applied on mammograms for the detection of cancerous tissues indicate that microcalcifications and masses can be utilized for the study of the morphology and diagnosis of cancerous cases. It is shown that the use of fractal modeling, as applied to a given image, can clearly discern cancerous zones from noncancerous areas. In this paper, for fractal modeling, the original image is first segmented into appropriate fractal boxes followed by identifying the fractal dimension of each windowed section using a computationally efficient two-dimensional box-counting algorithm. Furthermore, using appropriate wavelet sub-bands and image Reconstruction based on modified wavelet coefficients, it is shown that it is possible to arrive at enhanced features for detection of cancerous zones. In this paper, we have attempted to benefit from the advantages of both fractals and wavelets by introducing a new algorithm. By using a new algorithm named F1W2, the original image is first segmented into appropriate fractal boxes, and the fractal dimension of each windowed section is extracted. Following from that, by applying a maximum level threshold on fractal dimensions matrix, the best-segmented boxes are selected. In the next step, the segmented Cancerous zones which are candidates are then decomposed by utilizing standard orthogonal wavelet transform and db2 wavelet in three different resolution levels, and after nullifying wavelet coefficients of the image at the first scale and low frequency band of the third scale, the modified reconstructed image is successfully utilized for detection of breast cancer regions by applying an appropriate threshold. For detection of cancerous zones, our simulations indicate the accuracy of 90.9% for masses and 88.99% for microcalcifications detection results using the F1W2 method. For classification of detected mictocalcification into benign and malignant cases, eight features are identified and
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
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.
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)
Routes to fractality and entropy in Liesegang systems
Kalash, Leen; Sultan, Rabih
2014-06-01
Liesegang bands are formed when solutions of co-precipitate ions interdiffuse in a 1D gel matrix. In a recent study [R. F. Sultan, Acta. Mech. Sin. 27, 119 (2011)], Liesegang patterns have been characterized as fractal structures. In addition to experimentally obtained patterns, geometric Liesegang patterns were constructed in conformity with the well-known empirical laws. Both mathematical fractal dimensions and box count dimensions for images of PbF{sub 2} and PbI{sub 2} Liesegang patterns have been calculated. Liesegang patterns can also be described by the entropy state function, and categorized as more or less ordered structures. We revisit the relation between entropy and fractal dimension, and apply it to simulated geometrical Liesegang patterns. We have resort to three different routes for the estimation of the entropy of a Liesegang pattern. The HarFA software enabled the calculation of the Hausdorff dimension and the topological entropy, then the information dimension and the Shannon entropy. In a third pathway, analytical calculations were carried out by estimating the probability of occurrence of a fractal element or coverage. The product of Shannon entropy and Boltzmann constant yields the thermodynamic entropy. The values for PbF{sub 2} and PbI{sub 2} Liesegang patterns attained the order of magnitude of the reported Third Law entropies, but yet remained lower, in conformity with the more ordered Liesegang structures.
Routes to fractality and entropy in Liesegang systems
NASA Astrophysics Data System (ADS)
Kalash, Leen; Sultan, Rabih
2014-06-01
Liesegang bands are formed when solutions of co-precipitate ions interdiffuse in a 1D gel matrix. In a recent study [R. F. Sultan, Acta. Mech. Sin. 27, 119 (2011)], Liesegang patterns have been characterized as fractal structures. In addition to experimentally obtained patterns, geometric Liesegang patterns were constructed in conformity with the well-known empirical laws. Both mathematical fractal dimensions and box count dimensions for images of PbF2 and PbI2 Liesegang patterns have been calculated. Liesegang patterns can also be described by the entropy state function, and categorized as more or less ordered structures. We revisit the relation between entropy and fractal dimension, and apply it to simulated geometrical Liesegang patterns. We have resort to three different routes for the estimation of the entropy of a Liesegang pattern. The HarFA software enabled the calculation of the Hausdorff dimension and the topological entropy, then the information dimension and the Shannon entropy. In a third pathway, analytical calculations were carried out by estimating the probability of occurrence of a fractal element or coverage. The product of Shannon entropy and Boltzmann constant yields the thermodynamic entropy. The values for PbF2 and PbI2 Liesegang patterns attained the order of magnitude of the reported Third Law entropies, but yet remained lower, in conformity with the more ordered Liesegang structures.
Time evolution of quantum fractals
Wojcik; Bialynicki-Birula; Zyczkowski
2000-12-11
We propose a general construction of wave functions of arbitrary prescribed fractal dimension, for a wide class of quantum problems, including the infinite potential well, harmonic oscillator, linear potential, and free particle. The box-counting dimension of the probability density P(t)(x) = |Psi(x,t)|(2) is shown not to change during the time evolution. We prove a universal relation D(t) = 1+Dx/2 linking the dimensions of space cross sections Dx and time cross sections D(t) of the fractal quantum carpets.
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.
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
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
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…
Feasibility of functional imaging for brachytherapy
2009-01-01
This review summarizes the current understanding of the feasibility of functional imaging for brachytherapy. In following subsections the role of ultrasound, power doppler imaging, positron emission tomography, magnetic resonance imaging, dynamic dose calculation and targeted brachytherapy is analyzed. The combination of functional imaging with the new tools for intraoperative dose calculation and optimization opens new and exciting times in brachytherapy. New optimized protocols are needed and should be tested in controlled trials, to demonstrate an advantage of such a new paradigm.
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.
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
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.
Characteristic functionals in imaging and image-quality assessment: tutorial.
Clarkson, Eric; Barrett, Harrison H
2016-08-01
Characteristic functionals are one of the main analytical tools used to quantify the statistical properties of random fields and generalized random fields. The viewpoint taken here is that a random field is the correct model for the ensemble of objects being imaged by a given imaging system. In modern digital imaging systems, random fields are not used to model the reconstructed images themselves since these are necessarily finite dimensional. After a brief introduction to the general theory of characteristic functionals, many examples relevant to imaging applications are presented. The propagation of characteristic functionals through both a binned and list-mode imaging system is also discussed. Methods for using characteristic functionals and image data to estimate population parameters and classify populations of objects are given. These methods are based on maximum likelihood and maximum a posteriori techniques in spaces generated by sampling the relevant characteristic functionals through the imaging operator. It is also shown how to calculate a Fisher information matrix in this space. These estimators and classifiers, and the Fisher information matrix, can then be used for image quality assessment of imaging systems.
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.
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
2015-10-01
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.
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.…
Edges of Saturn's rings are fractal.
Li, Jun; Ostoja-Starzewski, Martin
2015-01-01
The images recently sent by the Cassini spacecraft mission (on the NASA website http://saturn.jpl.nasa.gov/photos/halloffame/) show the complex and beautiful rings of Saturn. Over the past few decades, various conjectures were advanced that Saturn's rings are Cantor-like sets, although no convincing fractal analysis of actual images has ever appeared. Here we focus on four images sent by the Cassini spacecraft mission (slide #42 "Mapping Clumps in Saturn's Rings", slide #54 "Scattered Sunshine", slide #66 taken two weeks before the planet's Augus't 200'9 equinox, and slide #68 showing edge waves raised by Daphnis on the Keeler Gap) and one image from the Voyager 2' mission in 1981. Using three box-counting methods, we determine the fractal dimension of edges of rings seen here to be consistently about 1.63 ~ 1.78. This clarifies in what sense Saturn's rings are fractal. PMID:25883885
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.
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.
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)
GENERATING FRACTAL PATTERNS BY USING p-CIRCLE INVERSION
NASA Astrophysics Data System (ADS)
Ramírez, José L.; Rubiano, Gustavo N.; Zlobec, Borut Jurčič
2015-10-01
In this paper, we introduce the p-circle inversion which generalizes the classical inversion with respect to a circle (p = 2) and the taxicab inversion (p = 1). We study some basic properties and we also show the inversive images of some basic curves. We apply this new transformation to well-known fractals such as Sierpinski triangle, Koch curve, dragon curve, Fibonacci fractal, among others. Then we obtain new fractal patterns. Moreover, we generalize the method called circle inversion fractal be means of the p-circle inversion.
Fractal 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.
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. PMID:25227013
NASA Technical Reports Server (NTRS)
Turcotte, D. L.
1986-01-01
The use of renormalization group techniques on fragmentation problems is examined. The equations which represent fractals and the size-frequency distributions of fragments are presented. Method for calculating the size distributions of asteriods and meteorites are described; the frequency-mass distribution for these interplanetary objects are due to fragmentation. The application of two renormalization group models to fragmentation is analyzed. It is observed that the models yield a fractal behavior for fragmentation; however, different values for the fractal dimension are produced . It is concluded that fragmentation is a scale invariant process and that the fractal dimension is a measure of the fragility of the fragmented material.
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.
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
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.
Spin Transport in Multiply Connected Fractal Conductors
NASA Astrophysics Data System (ADS)
Lee, Bo-Ray; Chang, Ching-Ray; Klik, Ivo
2014-12-01
We consider spin and charge transport in a Sierpinski planar carpet; the interest here is its unique geometry. We analyze the fractal conductor as a combination of multiply connected quantum wires, and we observe the evolution of the transmission envelope in different fractal generations. For a fractal conductor dominated by resonant modes the transmission is characterized by strong fluctuations and conduction gaps. We show that charge and spin transport have different responses both to the presence of defects and to applied bias. At a high bias, or in a high-order fractal generation, spin accumulation is separated from charge accumulation because the larger drift velocity needs a longer polarization length, and the sample may turn into an insulator by the action of the defects. Our results are calculated numerically using the Keldysh Green function within the tight-binding framework.
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.
Molecular and Functional Imaging of Internet Addiction
Zhu, Yunqi; Zhang, Hong; Tian, Mei
2015-01-01
Maladaptive use of the Internet results in Internet addiction (IA), which is associated with various negative consequences. Molecular and functional imaging techniques have been increasingly used for analysis of neurobiological changes and neurochemical correlates of IA. This review summarizes molecular and functional imaging findings on neurobiological mechanisms of IA, focusing on magnetic resonance imaging (MRI) and nuclear imaging modalities including positron emission tomography (PET) and single photon emission computed tomography (SPECT). MRI studies demonstrate that structural changes in frontal cortex are associated with functional abnormalities in Internet addicted subjects. Nuclear imaging findings indicate that IA is associated with dysfunction of the brain dopaminergic systems. Abnormal dopamine regulation of the prefrontal cortex (PFC) could underlie the enhanced motivational value and uncontrolled behavior over Internet overuse in addicted subjects. Further investigations are needed to determine specific changes in the Internet addictive brain, as well as their implications for behavior and cognition. PMID:25879023
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.
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
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.
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.
Functional imaging of the musculoskeletal system.
Griffith, James F
2015-06-01
Functional imaging, which provides information of how tissues function rather than structural information, is well established in neuro- and cardiac imaging. Many musculoskeletal structures, such as ligaments, fascia and mineralized bone, have by definition a mainly structural role and clearly don't have the same functional capacity as the brain, heart, liver or kidney. The main functionally responsive musculoskeletal tissues are the bone marrow, muscle and nerve and, as such, magnetic resonance (MR) functional imaging has primarily addressed these areas. Proton or phosphorus spectroscopy, other fat quantification techniques, perfusion imaging, BOLD imaging, diffusion and diffusion tensor imaging (DTI) are the main functional techniques applied. The application of these techniques in the musculoskeletal system has mainly been research orientated where they have already greatly enhanced our understanding of marrow physiology, muscle physiology and neural function. Going forwards, they will have a greater clinical impact helping to bridge the disconnect often seen between structural appearances and clinical symptoms, allowing a greater understanding of disease processes and earlier recognition of disease, improving prognostic prediction and optimizing the monitoring of treatment effect. PMID:26029633
Fractal Analysis of Cervical Intraepithelial Neoplasia
Fabrizii, Markus; Moinfar, Farid; Jelinek, Herbert F.; Karperien, Audrey; Ahammer, Helmut
2014-01-01
Introduction Cervical intraepithelial neoplasias (CIN) represent precursor lesions of cervical cancer. These neoplastic lesions are traditionally subdivided into three categories CIN 1, CIN 2, and CIN 3, using microscopical criteria. The relation between grades of cervical intraepithelial neoplasia (CIN) and its fractal dimension was investigated to establish a basis for an objective diagnosis using the method proposed. Methods Classical evaluation of the tissue samples was performed by an experienced gynecologic pathologist. Tissue samples were scanned and saved as digital images using Aperio scanner and software. After image segmentation the box counting method as well as multifractal methods were applied to determine the relation between fractal dimension and grades of CIN. A total of 46 images were used to compare the pathologist's neoplasia grades with the predicted groups obtained by fractal methods. Results Significant or highly significant differences between all grades of CIN could be found. The confusion matrix, comparing between pathologist's grading and predicted group by fractal methods showed a match of 87.1%. Multifractal spectra were able to differentiate between normal epithelium and low grade as well as high grade neoplasia. Conclusion Fractal dimension can be considered to be an objective parameter to grade cervical intraepithelial neoplasia. PMID:25302712
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.
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.
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 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.
Phase transfer function of digital imaging systems
NASA Astrophysics Data System (ADS)
Bhakta, Vikrant R.
For the past several decades, optical engineering has relied heavily on Fourier analysis of linear systems as a valuable aid in realizing numerous imaging applications. Today, spatial frequency analysis via the optical transfer function (OTF) remains an integral tool for the design, characterization and testing of incoherent imaging systems. The magnitude of the complex OTF is known as the modulation transfer function (MTF) and its phase is given by the phase transfer function (PTF). The MTF represents the contrast reduction at each spatial frequency; whereas, the PTF represents the spatial shift of these frequencies. While the MTF has been used extensively to characterize imaging systems, the PTF has long been ignored because it was thought to have an insignificant presence and to be difficult to understand and measure. Through theoretical analysis and experimental demonstrations, this work addresses all of these issues and shows that the PTF is a valuable tool for modern-day digital imaging systems. The effects of optical aberrations on the PTF of an imaging system in the absence of aliasing have been analyzed in detail. However, for the digital imaging systems, the effect of aliasing on the overall system behavior becomes an important consideration. To this end, the effects of aliasing on the PTF of the sampled imaging system are described and its key properties are derived. The role of PTF as an essential metric in today's imaging systems necessitates practical PTF measurement techniques. Two, easy-to-implement, image-based methods for PTF measurement are described and experimentally validated. These measurement methods and the insights gained from the theoretical analysis are leveraged for several applications spanning diverse fields such as optical system characterization, computational imaging, and image processing.
Fractal analysis of DNA sequence data
Berthelsen, C.L.
1993-01-01
DNA sequence databases are growing at an almost exponential rate. New analysis methods are needed to extract knowledge about the organization of nucleotides from this vast amount of data. Fractal analysis is a new scientific paradigm that has been used successfully in many domains including the biological and physical sciences. Biological growth is a nonlinear dynamic process and some have suggested that to consider fractal geometry as a biological design principle may be most productive. This research is an exploratory study of the application of fractal analysis to DNA sequence data. A simple random fractal, the random walk, is used to represent DNA sequences. The fractal dimension of these walks is then estimated using the [open quote]sandbox method[close quote]. Analysis of 164 human DNA sequences compared to three types of control sequences (random, base-content matched, and dimer-content matched) reveals that long-range correlations are present in DNA that are not explained by base or dimer frequencies. The study also revealed that the fractal dimension of coding sequences was significantly lower than sequences that were primarily noncoding, indicating the presence of longer-range correlations in functional sequences. The multifractal spectrum is used to analyze fractals that are heterogeneous and have a different fractal dimension for subsets with different scalings. The multifractal spectrum of the random walks of twelve mitochondrial genome sequences was estimated. Eight vertebrate mtDNA sequences had uniformly lower spectra values than did four invertebrate mtDNA sequences. Thus, vertebrate mitochondria show significantly longer-range correlations than to invertebrate mitochondria. The higher multifractal spectra values for invertebrate mitochondria suggest a more random organization of the sequences. This research also includes considerable theoretical work on the effects of finite size, embedding dimension, and scaling ranges.
Fractal Analysis of DNA Sequence Data
NASA Astrophysics Data System (ADS)
Berthelsen, Cheryl Lynn
DNA sequence databases are growing at an almost exponential rate. New analysis methods are needed to extract knowledge about the organization of nucleotides from this vast amount of data. Fractal analysis is a new scientific paradigm that has been used successfully in many domains including the biological and physical sciences. Biological growth is a nonlinear dynamic process and some have suggested that to consider fractal geometry as a biological design principle may be most productive. This research is an exploratory study of the application of fractal analysis to DNA sequence data. A simple random fractal, the random walk, is used to represent DNA sequences. The fractal dimension of these walks is then estimated using the "sandbox method." Analysis of 164 human DNA sequences compared to three types of control sequences (random, base -content matched, and dimer-content matched) reveals that long-range correlations are present in DNA that are not explained by base or dimer frequencies. The study also revealed that the fractal dimension of coding sequences was significantly lower than sequences that were primarily noncoding, indicating the presence of longer-range correlations in functional sequences. The multifractal spectrum is used to analyze fractals that are heterogeneous and have a different fractal dimension for subsets with different scalings. The multifractal spectrum of the random walks of twelve mitochondrial genome sequences was estimated. Eight vertebrate mtDNA sequences had uniformly lower spectra values than did four invertebrate mtDNA sequences. Thus, vertebrate mitochondria show significantly longer-range correlations than do invertebrate mitochondria. The higher multifractal spectra values for invertebrate mitochondria suggest a more random organization of the sequences. This research also includes considerable theoretical work on the effects of finite size, embedding dimension, and scaling ranges.
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
Modeling of functional brain imaging data
NASA Astrophysics Data System (ADS)
Horwitz, Barry
1999-03-01
The richness and complexity of data sets obtained from functional neuroimaging studies of human cognitive behavior, using techniques such as positron emission tomography and functional magnetic resonance imaging, have until recently not been exploited by computational neural modeling methods. In this article, following a brief introduction to functional neuroimaging methodology, two neural modeling approaches for use with functional brain imaging data are described. One, which uses structural equation modeling, examines the effective functional connections between various brain regions during specific cognitive tasks. The second employs large-scale neural modeling to relate functional neuroimaging signals in multiple, interconnected brain regions to the underlying neurobiological time-varying activities in each region. These two modeling procedures are illustrated using a visual processing paradigm.
Image sharpness function based on edge feature
NASA Astrophysics Data System (ADS)
Jun, Ni
2009-11-01
Autofocus technique has been widely used in optical tracking and measure system, but it has problem that when the autofocus device should to work. So, no-reference image sharpness assessment has become an important issue. A new Sharpness Function that can estimate current frame image be in focus or not is proposed in this paper. According to current image whether in focus or not and choose the time of auto focus automatism. The algorithm measures object typical edge and edge direction, and then get image local kurtosis information to determine the degree of image sharpness. It firstly select several grads points cross the edge line, secondly calculates edge sharpness value and get the cure of the kurtosis, according the measure precision of optical-equipment, a threshold value will be set beforehand. If edge kurtosis value is more than threshold, it can conclude current frame image is in focus. Otherwise, it is out of focus. If image is out of focus, optics system then takes autofocus program. This algorithm test several thousands of digital images captured from optical tracking and measure system. The results show high correlation with subjective sharpness assessment for s images of sky object.
Landini, G
2011-01-01
Fractal geometry, developed by B. Mandelbrot, has provided new key concepts necessary to the understanding and quantification of some aspects of pattern and shape randomness, irregularity, complexity and self-similarity. In the field of microscopy, fractals have profound implications in relation to the effects of magnification and scaling on morphology and to the methodological approaches necessary to measure self-similar structures. In this article are reviewed the fundamental concepts on which fractal geometry is based, their relevance to the microscopy field as well as a number of technical details that can help improving the robustness of morphological analyses when applied to microscopy problems.
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.
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.
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.
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.
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
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.
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)
Classification of impervious land cover using fractals
NASA Astrophysics Data System (ADS)
Quackenbush, Lindi J.
Runoff from urban areas is a leading source of nonpoint source pollution in estuaries, lakes, and streams. The extent and type of impervious land cover are considered to be critical factors in evaluating runoff amounts and the potential for environmental damage. Land cover information for watershed modeling is frequently derived using remote sensing techniques, and improvements in image classification are expected to enhance the reliability of runoff models. In order to understand potential pollutant loads there is a need to characterize impervious areas based on land use. However, distinguishing between impervious features such as roofs and roads using only spectral information is often challenging due to the similarity in construction materials. Since spectral information alone is often lacking, spatial complexity measured using fractal dimension was analyzed to determine its utility in performing detailed classification. Fractal dimension describes the complexity of curves and surfaces in non-integer dimensions. Statistical analysis demonstrated that fractal dimension varies between roofs, roads, and driveways. Analysis also observed the impact of scale by determining statistical differences in fractal dimension, based on the size of the window considered and the ground sampled distance of the pixels under consideration. The statistical differences in fractal dimension translated to minor improvements in classification accuracy when separating roofs, roads, and driveways.
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.
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.
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.
Functional lumen imaging of the gastrointestinal tract.
Lottrup, Christian; Gregersen, Hans; Liao, Donghua; Fynne, Lotte; Frøkjær, Jens Brøndum; Krogh, Klaus; Regan, Julie; Kunwald, Peter; McMahon, Barry P
2015-10-01
This nonsystematic review aims to describe recent developments in the use of functional lumen imaging in the gastrointestinal tract stimulated by the introduction of the functional lumen imaging probe. When ingested food in liquid and solid form is transported along the gastrointestinal tract, sphincters provide an important role in the flow and control of these contents. Inadequate function of sphincters is the basis of many gastrointestinal diseases. Despite this, traditional methods of sphincter diagnosis and measurement such as fluoroscopy, manometry, and the barostat are limited in what they can tell us. It has long been thought that measurement of sphincter function through resistance to distension is a better approach, now more commonly known as distensibility testing. The functional lumen imaging probe is the first medical measurement device that purports in a practical way to provide geometric profiling and measurement of distensibility in sphincters. With use of impedance planimetry, an axial series of cross-sectional areas and pressure in a catheter-mounted allantoid bag are used for the calculation of distensibility parameters. The technique has been trialed in many valvular areas of the gastrointestinal tract, including the upper esophageal sphincter, the esophagogastric junction, and the anorectal region. It has shown potential in the biomechanical assessment of sphincter function and characterization of swallowing disorders, gastroesophageal reflux disease, eosinophilic esophagitis, achalasia, and fecal incontinence. From this early work, the functional lumen imaging technique has the potential to contribute to a better and more physiological understanding of narrowing regions in the gastrointestinal tract in general and sphincters in particular. PMID:25980822
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. PMID:11051496
Fractal interpolation on the Sierpinski Gasket
NASA Astrophysics Data System (ADS)
Çelik, Derya; Koçak, Sahin; Özdemir, Yunus
2008-01-01
We prove for the Sierpinski Gasket (SG) an analogue of the fractal interpolation theorem of Barnsley. Let V0={p1,p2,p3} be the set of vertices of SG and the three contractions of the plane, of which the SG is the attractor. Fix a number n and consider the iterations uw=uw1uw2...uwn for any sequence w=(w1,w2,...,wn)[set membership, variant]{1,2,3}n. The union of the images of V0 under these iterations is the set of nth stage vertices Vn of SG. Let be any function. Given any numbers [alpha]w (w[set membership, variant]{1,2,3}n) with 0<[alpha]w<1, there exists a unique continuous extension of F, such thatf(uw(x))=[alpha]wf(x)+hw(x) for x[set membership, variant]SG, where hw are harmonic functions on SG for w[set membership, variant]{1,2,3}n. Interpreting the harmonic functions as the "degree 1 polynomials" on SG is thus a self-similar interpolation obtained for any start function .
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
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.
Functional imaging in freely moving animals.
Kerr, Jason N D; Nimmerjahn, Axel
2012-02-01
Uncovering the relationships between animal behavior and cellular activity in the brain has been one of the key aims of neuroscience research for decades, and still remains so. Electrophysiological approaches have enabled sparse sampling from electrically excitable cells in freely moving animals that has led to the identification of important phenomena such as place, grid and head-direction cells. Optical imaging in combination with newly developed labeling approaches now allows minimally invasive and comprehensive sampling from dense networks of electrically and chemically excitable cells such as neurons and glia during self-determined behavior. To achieve this two main imaging avenues have been followed: Optical recordings in head-restrained, mobile animals and miniature microscope-bearing freely moving animals. Here we review progress made toward functional cellular imaging in freely moving rodents, focusing on developments over the past few years. We discuss related challenges and biological applications.
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.
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.
Problems of Geophysics that Inspired Fractal Geometry
NASA Astrophysics Data System (ADS)
Mandelbrot, B. B.
2001-12-01
Fractal geometry arose when the speaker used then esoteric mathematics and the concept of invariance as a tool to understand diverse ``down-to-earth'' practical needs. The first step consisted in using discontinuous functions to represent the variation of speculative prices. The next several steps consisted in introducing infinite-range (global) dependence to handle data from geophysics, beginning with hydrology (and also again in finance). This talk will detail the speaker's debt and gratitude toward several specialists from diverse areas of geophysics who had the greatest impact on fractal geometry in its formative period.
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.
[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.
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. PMID:26651668
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.
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.
Preliminary Study of 2D Fracture Upscaling of Geothermal Rock Using IFS Fractal Model
NASA Astrophysics Data System (ADS)
Tobing, Prana F. L.; Feranie, Selly; Latief, Fourier D. E.
2016-08-01
Fractured rock plays important role in reservoir production. In larger scale, fractures are more likely to be heterogeneous and considered to be fractal in its nature. One of the characteristics of fractal structure is the scale independence. An investigation of fractal properties on natural fractured rock is therefore needed for modelling larger fracture. We have investigated the possibilities of fractal upscaling method to produce a larger geothermal fracture model based on smaller fracture data. We generate Iterated Function System (IFS) fractal model using parameters e.g. scale factor, angle between branch, initial line direction, and branch thickness. All the model parameters are obtained from smaller fracture data. We generate higher iteration model to be compared with larger geothermal fracture. The similarity between the IFS fractal model and natural fracture is measured by 2D box counting fractal dimension (D). The fractal dimension of first to fourth generation fractal model is (1.86 ± 0.02). The fractal dimension of the reference geothermal site is (1.86 ± 0.04). Besides of D, we found significant similarity of fracture parameters there are intensity and density between fracture model and natural fracture. Based on these result, we conclude that fractal upscaling using IFS fractal model is potential to model larger scale of 2D fracture.
Functional magnetic resonance imaging using RASER
Goerke, Ute; Garwood, Michael; Ugurbil, Kamil
2010-01-01
Although functional imaging of neuronal activity by magnetic resonance imaging (fMRI) has become the primary methodology employed in studying the brain, significant portions of the brain are inaccessible by this methodology due to its sensitivity to macroscopic magnetic field inhomogeneities induced near air filled cavities in the head. In this paper, we demonstrate that this sensitivity is eliminated by a novel pulse sequence, RASER (rapid acquisition by sequential excitation and refocusing) (Chamberlain et al., 2007), that can generate functional maps. This is accomplished because RASER acquired signals are purely and perfectly T2 weighted, without any T2*-effects that are inherent in the other image acquisition schemes employed to date. T2-weighted fMRI sequences are also more specific to the site of neuronal activity at ultrahigh magnetic fields than T2*-variations since they are dominated by signal components originating from the tissue in the capillary bed. The RASER based fMRI response is quantified; it is shown to have inherently less noisy time series and to provide fMRI in brain regions, such as the orbitofrontal cortex, which are challenging to image with conventional techniques. PMID:20699123
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.
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. PMID:10466140
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.
Kopelman, R
1988-09-23
Classical reaction kinetics has been found to be unsatisfactory when the reactants are spatially constrained on the microscopic level by either walls, phase boundaries, or force fields. Recently discovered theories of heterogeneous reaction kinetics have dramatic consequences, such as fractal orders for elementary reactions, self-ordering and self-unmixing of reactants, and rate coefficients with temporal "memories." The new theories were needed to explain the results of experiments and supercomputer simulations of reactions that were confined to low dimensions or fractal dimensions or both. Among the practical examples of "fractal-like kinetics" are chemical reactions in pores of membranes, excitation trapping in molecular aggregates, exciton fusion in composite materials, and charge recombination in colloids and clouds.
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
Fractal dimensions of sinkholes
NASA Astrophysics Data System (ADS)
Reams, Max W.
1992-05-01
Sinkhole perimeters are probably fractals ( D=1.209-1.558) for sinkholes with areas larger than 10,000 m 2, based on area-perimeter plots of digitized data from karst surfaces developed on six geologic units in the United States. The sites in Florida, Kentucky, Indiana and Missouri were studied using maps with a scale of 1:24, 000. Size-number distributions of sinkhole perimeters and areas may also be fractal, although data for small sinkholes is needed for verification. Studies based on small-scale maps are needed to evaluate the number and roughness of small sinkhole populations.
NASA Astrophysics Data System (ADS)
Meir, Yigal; Aharony, Amnon
1989-05-01
We investigate the problem of flow in porous media near the percolation threshold by studying the generelized model of Viscous Fingering (VF) on fractal structures. We obtain analytic expressions for the fractal dimensions of the resulting structures, which are in excellent agreement with existing experimental results, and exact relations for the exponent Dt, which describes the scaling of the time it takes the fluid to cross the sample, with the sample size, in terms of geometrical exponents for various experimental situations. Lastly, we discuss the relation between the continuous viscous fingers model and stochastic processes such as dielectric breakdown model (DBM) and diffusion limited aggregation (DLA).
Imaging control functions of optical scanners
NASA Astrophysics Data System (ADS)
Nishinaga, Hisashi; Hirayama, Toru; Fujii, Daiyu; Yamamoto, Hajime; Irihama, Hiroshi; Ogata, Taro; Koizumi, Yukio; Suzuki, Kenta; Fujishima, Yohei; Matsuyama, Tomoyuki; Kawaguchi, Ryoichi
2014-03-01
For future printing based on multiple patterning and directed self-assembly, critical dimension and overlay requirements become tighter for immersion lithography. Thermal impact of exposure to both the projection lens and reticle expansion becomes the dominant factor for high volume production. A new procedure to tune the thermal control function is needed to maintain the tool conditions to obtain high productivity and accuracy. Additionally, new functions of both hardware and software are used to improve the imaging performance even during exposure with high-dose conditions. In this paper, we describe the procedure to tune the thermal control parameters which indicate the response of projection lens aberration and reticle expansion separately. As new functionalities to control the thermal lens aberration, wavefront-based lens control software and reticle bending hardware are introduced. By applying these functions, thermal focus control can be improved drastically. Further, the capability of prediction of reticle expansion is discussed, including experimental data from overlay exposure and aerial image sensor results.
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.
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
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
Classical Liquids in Fractal Dimension.
Heinen, Marco; Schnyder, Simon K; Brady, John F; Löwen, Hartmut
2015-08-28
We introduce fractal liquids by generalizing classical liquids of integer dimensions d=1,2,3 to a noninteger dimension dl. The particles composing the liquid are fractal objects and their configuration space is also fractal, with the same dimension. Realizations of our generic model system include microphase separated binary liquids in porous media, and highly branched liquid droplets confined to a fractal polymer backbone in a gel. Here, we study the thermodynamics and pair correlations of fractal liquids by computer simulation and semianalytical statistical mechanics. Our results are based on a model where fractal hard spheres move on a near-critical percolating lattice cluster. The predictions of the fractal Percus-Yevick liquid integral equation compare well with our simulation results.
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.
Seven topics in functional magnetic resonance imaging.
Bandettini, Peter A
2009-09-01
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.
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
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
Infrared Imaging System for Studying Brain Function
NASA Technical Reports Server (NTRS)
Mintz, Frederick; Mintz, Frederick; Gunapala, Sarath
2007-01-01
A proposed special-purpose infrared imaging system would be a compact, portable, less-expensive alternative to functional magnetic resonance imaging (fMRI) systems heretofore used to study brain function. Whereas a typical fMRI system fills a large room, and must be magnetically isolated, this system would fit into a bicycle helmet. The system would include an assembly that would be mounted inside the padding in a modified bicycle helmet or other suitable headgear. The assembly would include newly designed infrared photodetectors and data-acquisition circuits on integrated-circuit chips on low-thermal-conductivity supports in evacuated housings (see figure) arranged in multiple rows and columns that would define image coordinates. Each housing would be spring-loaded against the wearer s head. The chips would be cooled by a small Stirling Engine mounted contiguous to, but thermally isolated from, the portions of the assembly in thermal contact with the wearer s head. Flexible wires or cables for transmitting data from the aforementioned chips would be routed to an integrated, multichannel transmitter and thence through the top of the assembly to a patch antenna on the outside of the helmet. The multiple streams of data from the infrared-detector chips would be sent to a remote site, where they would be processed, by software, into a three-dimensional display of evoked potentials that would represent firing neuronal bundles and thereby indicate locations of neuronal activity associated with mental or physical activity. The 3D images will be analogous to current fMRI images. The data would also be made available, in real-time, for comparison with data in local or internationally accessible relational databases that already exist in universities and research centers. Hence, this system could be used in research on, and for the diagnosis of response from the wearer s brain to physiological, psychological, and environmental changes in real time. The images would also be
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)
Theoretical study of statistical fractal model with applications to mineral resource prediction
NASA Astrophysics Data System (ADS)
Wei, Shen; Pengda, Zhao
2002-04-01
The statistical estimation of fractal dimensions is an important topic of investigation. Current solutions emphsize visual straight-line fitting, but nonlinear statistical modeling has the potential of making valuable contributions in this field. In this paper, we present the concepts of generalized fractal models and generalized fractal dimension and conclude that many geological models are special cases of the generalized models. We show that the power-function distribution possesses the fractal property of scaling invariance under upper truncation, which may help in lead statistical fractal modeling. A new method is developed on the basis of nonlinear regression to estimate fractal parameters. This method has advantages with respect to the traditional method based on linear regression for estimating the fractal dimension. Finally, the new method is illustrated by means of application to a real data set.
Intravital multiphoton microscopy for imaging hepatobiliary function
NASA Astrophysics Data System (ADS)
Li, Feng-Chieh; Sun, Tzu-Lin; Lee, Hsuan-Shu; Yang, Shu-Mei; Dong, Chen-Yuan
2007-07-01
Liver is the chemical factory in body responsible for important functions such as metabolism and detoxification. When liver can not be regenerated in time to amend damages that has occurred, failure of hepatic functions can result. Traditionally, the study of liver pathology has depended on histological techniques, but such methods are limited to ex-vivo observation. In order to study hepatic metabolism in vivo, we have designed a hepatic imaging chamber made of biocompatible titanium alloy (6V4Al-Ti, ELI grade). In combination with multiphoton and second harmonic generation microscopy, our approach allows the intravital observation of hepatic intravital activities to be achieved. Processes such as hepatic metabolism and disease progression can be studied using this methodology.
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.
Imaging Functional Nucleic Acid Delivery to Skin.
Kaspar, Roger L; Hickerson, Robyn P; González-González, Emilio; Flores, Manuel A; Speaker, Tycho P; Rogers, Faye A; Milstone, Leonard M; Contag, Christopher H
2016-01-01
Monogenic skin diseases arise from well-defined single gene mutations, and in some cases a single point mutation. As the target cells are superficial, these diseases are ideally suited for treatment by nucleic acid-based therapies as well as monitoring through a variety of noninvasive imaging technologies. Despite the accessibility of the skin, there remain formidable barriers for functional delivery of nucleic acids to the target cells within the dermis and epidermis. These barriers include the stratum corneum and the layered structure of the skin, as well as more locally, the cellular, endosomal and nuclear membranes. A wide range of technologies for traversing these barriers has been described and moderate success has been reported for several approaches. The lessons learned from these studies include the need for combinations of approaches to facilitate nucleic acid delivery across these skin barriers and then functional delivery across the cellular and nuclear membranes for expression (e.g., reporter genes, DNA oligonucleotides or shRNA) or into the cytoplasm for regulation (e.g., siRNA, miRNA, antisense oligos). The tools for topical delivery that have been evaluated include chemical, physical and electrical methods, and the development and testing of each of these approaches has been greatly enabled by imaging tools. These techniques allow delivery and real time monitoring of reporter genes, therapeutic nucleic acids and also triplex nucleic acids for gene editing. Optical imaging is comprised of a number of modalities based on properties of light-tissue interaction (e.g., scattering, autofluorescence, and reflectance), the interaction of light with specific molecules (e.g., absorbtion, fluorescence), or enzymatic reactions that produce light (bioluminescence). Optical imaging technologies operate over a range of scales from macroscopic to microscopic and if necessary, nanoscopic, and thus can be used to assess nucleic acid delivery to organs, regions, cells
Imaging Functional Nucleic Acid Delivery to Skin.
Kaspar, Roger L; Hickerson, Robyn P; González-González, Emilio; Flores, Manuel A; Speaker, Tycho P; Rogers, Faye A; Milstone, Leonard M; Contag, Christopher H
2016-01-01
Monogenic skin diseases arise from well-defined single gene mutations, and in some cases a single point mutation. As the target cells are superficial, these diseases are ideally suited for treatment by nucleic acid-based therapies as well as monitoring through a variety of noninvasive imaging technologies. Despite the accessibility of the skin, there remain formidable barriers for functional delivery of nucleic acids to the target cells within the dermis and epidermis. These barriers include the stratum corneum and the layered structure of the skin, as well as more locally, the cellular, endosomal and nuclear membranes. A wide range of technologies for traversing these barriers has been described and moderate success has been reported for several approaches. The lessons learned from these studies include the need for combinations of approaches to facilitate nucleic acid delivery across these skin barriers and then functional delivery across the cellular and nuclear membranes for expression (e.g., reporter genes, DNA oligonucleotides or shRNA) or into the cytoplasm for regulation (e.g., siRNA, miRNA, antisense oligos). The tools for topical delivery that have been evaluated include chemical, physical and electrical methods, and the development and testing of each of these approaches has been greatly enabled by imaging tools. These techniques allow delivery and real time monitoring of reporter genes, therapeutic nucleic acids and also triplex nucleic acids for gene editing. Optical imaging is comprised of a number of modalities based on properties of light-tissue interaction (e.g., scattering, autofluorescence, and reflectance), the interaction of light with specific molecules (e.g., absorbtion, fluorescence), or enzymatic reactions that produce light (bioluminescence). Optical imaging technologies operate over a range of scales from macroscopic to microscopic and if necessary, nanoscopic, and thus can be used to assess nucleic acid delivery to organs, regions, cells
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).
Fractal dimension based corneal fungal infection diagnosis
NASA Astrophysics Data System (ADS)
Balasubramanian, Madhusudhanan; Perkins, A. Louise; Beuerman, Roger W.; Iyengar, S. Sitharama
2006-08-01
We present a fractal measure based pattern classification algorithm for automatic feature extraction and identification of fungus associated with an infection of the cornea of the eye. A white-light confocal microscope image of suspected fungus exhibited locally linear and branching structures. The pixel intensity variation across the width of a fungal element was gaussian. Linear features were extracted using a set of 2D directional matched gaussian-filters. Portions of fungus profiles that were not in the same focal plane appeared relatively blurred. We use gaussian filters of standard deviation slightly larger than the width of a fungus to reduce discontinuities. Cell nuclei of cornea and nerves also exhibited locally linear structure. Cell nuclei were excluded by their relatively shorter lengths. Nerves in the cornea exhibited less branching compared with the fungus. Fractal dimensions of the locally linear features were computed using a box-counting method. A set of corneal images with fungal infection was used to generate class-conditional fractal measure distributions of fungus and nerves. The a priori class-conditional densities were built using an adaptive-mixtures method to reflect the true nature of the feature distributions and improve the classification accuracy. A maximum-likelihood classifier was used to classify the linear features extracted from test corneal images as 'normal' or 'with fungal infiltrates', using the a priori fractal measure distributions. We demonstrate the algorithm on the corneal images with culture-positive fungal infiltrates. The algorithm is fully automatic and will help diagnose fungal keratitis by generating a diagnostic mask of locations of the fungal infiltrates.
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.
Functional optical imaging at the microscopic level
Salazar Vázquez, Beatriz Y.; Hightower, Ciel Makena; Sapuppo, Francesca; Tartakovsky, Daniel M.; Intaglietta, Marcos
2010-01-01
Functional microscopic imaging of in vivo tissues aims at characterizing parameters at the level of the unitary cellular components under normal conditions, in the presence of blood flow, to understand and monitor phenomena that lead to maintaining homeostatic balance. Of principal interest are the setting of shear stress on the endothelium; formation of the plasma layer, where the balance between nitric oxide production and scavenging is established; and formation of the oxygen gradients that determine the distribution of oxygen from blood into the tissue. Optical techniques that enable the analysis of functional microvascular processes are the measurement of blood vessel dimensions by image shearing, the photometric analysis of the extent of the plasma layer, the dual-slit methodology for measuring blood flow velocity, and the direct measurement of oxygen concentration in blood and tissue. Each of these technologies includes the development of paired, related mathematical approaches that enable characterizing the transport properties of the blood tissue system. While the technology has been successful in analyzing the living tissue in experimental conditions, deployment to clinical settings remains an elusive goal, due to the difficulty of obtaining optical access to the depth of the tissue. PMID:20210428
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.
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. PMID:25996738
Turbulence on a Fractal Fourier Set.
Lanotte, Alessandra S; Benzi, Roberto; Malapaka, Shiva K; Toschi, Federico; Biferale, Luca
2015-12-31
A novel investigation of the nature of intermittency in incompressible, homogeneous, and isotropic turbulence is performed by a numerical study of the Navier-Stokes equations constrained on a fractal Fourier set. The robustness of the energy transfer and of the vortex stretching mechanisms is tested by changing the fractal dimension D from the original three dimensional case to a strongly decimated system with D=2.5, where only about 3% of the Fourier modes interact. This is a unique methodology to probe the statistical properties of the turbulent energy cascade, without breaking any of the original symmetries of the equations. While the direct energy cascade persists, deviations from the Kolmogorov scaling are observed in the kinetic energy spectra. A model in terms of a correction with a linear dependency on the codimension of the fractal set E(k)∼k(-5/3+3-D) explains the results. At small scales, the intermittency of the vorticity field is observed to be quasisingular as a function of the fractal mode reduction, leading to an almost Gaussian statistics already at D∼2.98. These effects must be connected to a genuine modification in the triad-to-triad nonlinear energy transfer mechanism. PMID:26764993
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.
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.
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.
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.
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.
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.
Eliazar, Iddo; Klafter, Joseph
2008-06-01
We explore six classes of fractal probability laws defined on the positive half-line: Weibull, Frechét, Lévy, hyper Pareto, hyper beta, and hyper shot noise. Each of these classes admits a unique statistical power-law structure, and is uniquely associated with a certain operation of renormalization. All six classes turn out to be one-dimensional projections of underlying Poisson processes which, in turn, are the unique fixed points of Poissonian renormalizations. The first three classes correspond to linear Poissonian renormalizations and are intimately related to extreme value theory (Weibull, Frechét) and to the central limit theorem (Lévy). The other three classes correspond to nonlinear Poissonian renormalizations. Pareto's law--commonly perceived as the "universal fractal probability distribution"--is merely a special case of the hyper Pareto class.
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.
Fractal Analysis on Morphology of Laser Irradiated Vanadium Surfaces Under Different Ambient
NASA Astrophysics Data System (ADS)
Szkiva, Zs.; Bálint, Á. M.; Füle, M.; Nánai, L.
2013-12-01
Pulsed laser irradiated vanadium surface morphology under different ambient has been prepared and characterized using fractal dimension analysis method on scanning electron microscopy (SEM) images. In presence of different ambient, self-periodic and self-similar surface patterns (e.g. dots, islands, and pins) were grown and appeared in different shapes. The fractal dimension (FD) of this developed vanadium nanostructure was calculated by fractal box count method (FBM). The calculated fractal dimension (FD, Df) shows dependence on the different type on ambient and the number of laser shots.
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.
Characterisation of human non-proliferative diabetic retinopathy using the fractal analysis
Ţălu, Ştefan; Călugăru, Dan Mihai; Lupaşcu, Carmen Alina
2015-01-01
AIM To investigate and quantify changes in the branching patterns of the retina vascular network in diabetes using the fractal analysis method. METHODS This was a clinic-based prospective study of 172 participants managed at the Ophthalmological Clinic of Cluj-Napoca, Romania, between January 2012 and December 2013. A set of 172 segmented and skeletonized human retinal images, corresponding to both normal (24 images) and pathological (148 images) states of the retina were examined. An automatic unsupervised method for retinal vessel segmentation was applied before fractal analysis. The fractal analyses of the retinal digital images were performed using the fractal analysis software ImageJ. Statistical analyses were performed for these groups using Microsoft Office Excel 2003 and GraphPad InStat software. RESULTS It was found that subtle changes in the vascular network geometry of the human retina are influenced by diabetic retinopathy (DR) and can be estimated using the fractal geometry. The average of fractal dimensions D for the normal images (segmented and skeletonized versions) is slightly lower than the corresponding values of mild non-proliferative DR (NPDR) images (segmented and skeletonized versions). The average of fractal dimensions D for the normal images (segmented and skeletonized versions) is higher than the corresponding values of moderate NPDR images (segmented and skeletonized versions). The lowest values were found for the corresponding values of severe NPDR images (segmented and skeletonized versions). CONCLUSION The fractal analysis of fundus photographs may be used for a more complete undeTrstanding of the early and basic pathophysiological mechanisms of diabetes. The architecture of the retinal microvasculature in diabetes can be quantitative quantified by means of the fractal dimension. Microvascular abnormalities on retinal imaging may elucidate early mechanistic pathways for microvascular complications and distinguish patients with DR from
Forthergillian Lecture. Imaging human brain function.
Frackowiak, R S
The non-invasive brain scanning techniques introduced a quarter of a century ago have become crucial for diagnosis in clinical neurology. They have also been used to investigate brain function and have provided information about normal activity and pathogenesis. They have been used to investigate functional specialization in the brain and how specialized areas communicate to generate complex integrated functions such as speech, memory, the emotions and so on. The phenomenon of brain plasticity is poorly understood and yet clinical neurologists are aware, from everyday observations, that spontaneous recovery from brain lesions is common. An improved understanding of the mechanisms of recovery may generate new therapeutic strategies and indicate ways of modulating mechanisms that promote plastic compensation for loss of function. The main methods used to investigate these issues are positron emission tomography and magnetic resonance imaging (M.R.I.). M.R.I. is also used to map brain structure. The techniques of functional brain mapping and computational morphometrics depend on high performance scanners and a validated set of analytic statistical procedures that generate reproducible data and meaningful inferences from brain scanning data. The motor system presents a good paradigm to illustrate advances made by scanning towards an understanding of plasticity at the level of brain areas. The normal motor system is organized in a nested hierarchy. Recovery from paralysis caused by internal capsule strokes involves functional reorganization manifesting itself as changed patterns of activity in the component brain areas of the normal motor system. The pattern of plastic modification depends in part on patterns of residual or disturbed connectivity after brain injury. Therapeutic manipulations in patients with Parkinson's disease using deep brain stimulation, dopaminergic agents or fetal mesencephalic transplantation provide a means to examine mechanisms underpinning
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.
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.
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)
NASA Astrophysics Data System (ADS)
Burdzy, Krzysztof; Hołyst, Robert; Pruski, Łukasz
2013-05-01
We investigate a process of random walks of a point particle on a two-dimensional square lattice of size n×n with periodic boundary conditions. A fraction p⩽20% of the lattice is occupied by holes (p represents macroporosity). A site not occupied by a hole is occupied by an obstacle. Upon a random step of the walker, a number of obstacles, M, can be pushed aside. The system approaches equilibrium in (nlnn)2 steps. We determine the distribution of M pushed in a single move at equilibrium. The distribution F(M) is given by Mγ where γ=-1.18 for p=0.1, decreasing to γ=-1.28 for p=0.01. Irrespective of the initial distribution of holes on the lattice, the final equilibrium distribution of holes forms a fractal with fractal dimension changing from a=1.56 for p=0.20 to a=1.42 for p=0.001 (for n=4,000). The trace of a random walker forms a distribution with expected fractal dimension 2.
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!
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 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 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. PMID:16351924
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.
Simulation of geological surfaces using fractals
Yfantis, E.A.; Flatman, G.T.; Englund, E.J.
1988-08-01
Methods suggests in the past for simulated ore concentration or pollution concentration over an area of interest, subject to the condition that the simulated surface is passing through specifying points, are based on the assumption of normality. A new method is introduced here which is a generalization of the subdivision method used in fractals. This method is based on the construction of a fractal plane-to-line function f(x, y, R, e, u), where (x, y) is in (a, b) x (c, d), R is the autocorrelation function, e is the resolution limit, and u is a random real function on (-l, l). The simulation using fractals escapes from any distribution assumptions of the data. The given network of points is connected to form quadrilaterals; each one of the quadrilaterals is split based on ways which are extensions of the well-known subdivision method. The quadrilaterals continue to split and grow until resolution obtained in both x and y directions is smaller than a prespecified resolution. If the x coordinate of the ith quadrilateral is in (a/sub i/, b/sub i/) and the y coordinate is in (c/sub i/, d/sub i/), the growth of this quadrilateral is a function of (b/sub i/ - a/sub i/) and (d/sub i/ - c/sub i/); the quadrilateral could grow toward the positive or negative z axis with equal probability forming four new quadrilaterals having a common vertex.
Static friction between rigid fractal surfaces
NASA Astrophysics Data System (ADS)
Alonso-Marroquin, Fernando; Huang, Pengyu; Hanaor, Dorian A. H.; Flores-Johnson, E. A.; Proust, Gwénaëlle; Gan, Yixiang; Shen, Luming
2015-09-01
Using spheropolygon-based simulations and contact slope analysis, we investigate the effects of surface topography and atomic scale friction on the macroscopically observed friction between rigid blocks with fractal surface structures. From our mathematical derivation, the angle of macroscopic friction is the result of the sum of the angle of atomic friction and the slope angle between the contact surfaces. The latter is obtained from the determination of all possible contact slopes between the two surface profiles through an alternative signature function. Our theory is validated through numerical simulations of spheropolygons with fractal Koch surfaces and is applied to the description of frictional properties of Weierstrass-Mandelbrot surfaces. The agreement between simulations and theory suggests that for interpreting macroscopic frictional behavior, the descriptors of surface morphology should be defined from the signature function rather than from the slopes of the contacting surfaces.
Robust Sierpiński triangle fractals on symmetry-mismatched Ag(100).
Zhang, Xue; Li, Na; Liu, Liwei; Gu, Gaochen; Li, Chao; Tang, Hao; Peng, Lianmao; Hou, Shimin; Wang, Yongfeng
2016-08-18
Sierpiński triangle fractals were constructed on both Ag(111) and symmetry-mismatched fourfold Ag(100) surfaces through chemical reaction between H3PH molecules and Fe atoms under vacuum. Density functional theory calculations revealed that the fractals were stabilized by the strong coordination interaction between Fe and O atoms. In comparison, pure H3PH molecules formed fractals via moderately strong hydrogen bonds only on Ag(111), not on Ag(100).
Robust Sierpiński triangle fractals on symmetry-mismatched Ag(100).
Zhang, Xue; Li, Na; Liu, Liwei; Gu, Gaochen; Li, Chao; Tang, Hao; Peng, Lianmao; Hou, Shimin; Wang, Yongfeng
2016-08-18
Sierpiński triangle fractals were constructed on both Ag(111) and symmetry-mismatched fourfold Ag(100) surfaces through chemical reaction between H3PH molecules and Fe atoms under vacuum. Density functional theory calculations revealed that the fractals were stabilized by the strong coordination interaction between Fe and O atoms. In comparison, pure H3PH molecules formed fractals via moderately strong hydrogen bonds only on Ag(111), not on Ag(100). PMID:27498982
Relationship between Fractal Dimension and Agreeability of Facial Imagery
NASA Astrophysics Data System (ADS)
Oyama-Higa, Mayumi; Miao, Tiejun; Ito, Tasuo
2007-11-01
Why do people feel happy and good or equivalently empathize more, with smiling face imageries than with ones of expressionless face? To understand what the essential factors are underlying imageries in relating to the feelings, we conducted an experiment by 84 subjects asked to estimate the degree of agreeability about expressionless and smiling facial images taken from 23 young persons to whom the subjects were no any pre-acquired knowledge. Images were presented one at a time to each subject who was asked to rank agreeability on a scale from 1 to 10. Fractal dimensions of facial images were obtained in order to characterize the complexity of the imageries by using of two types of fractal analysis methods, i.e., planar and cubic analysis methods, respectively. The results show a significant difference in the fractal dimension values between expressionless faces and smiling ones. Furthermore, we found a well correlation between the degree of agreeability and fractal dimensions, implying that the fractal dimension optically obtained in relation to complexity in imagery information is useful to characterize the psychological processes of cognition and awareness.
The fractal structure of the mitochondrial genomes
NASA Astrophysics Data System (ADS)
Oiwa, Nestor N.; Glazier, James A.
2002-08-01
The mitochondrial DNA genome has a definite multifractal structure. We show that loops, hairpins and inverted palindromes are responsible for this self-similarity. We can thus establish a definite relation between the function of subsequences and their fractal dimension. Intriguingly, protein coding DNAs also exhibit palindromic structures, although they do not appear in the sequence of amino acids. These structures may reflect the stabilization and transcriptional control of DNA or the control of posttranscriptional editing of mRNA.
Entropy computing via integration over fractal measures.
Słomczynski, Wojciech; Kwapien, Jarosław; Zyczkowski, Karol
2000-03-01
We discuss the properties of invariant measures corresponding to iterated function systems (IFSs) with place-dependent probabilities and compute their Renyi entropies, generalized dimensions, and multifractal spectra. It is shown that with certain dynamical systems, one can associate the corresponding IFSs in such a way that their generalized entropies are equal. This provides a new method of computing entropy for some classical and quantum dynamical systems. Numerical techniques are based on integration over the fractal measures. (c) 2000 American Institute of Physics.
Relativistic scattering from moving fractally corrugated surfaces.
De Cupis, P
2003-05-15
The solution to the problem of optical or electromagnetic-wave scattering from perfectly conducting rough surfaces modeled by a multiscale fractal function is generalized to the case of relative uniform translating motion with respect to the observer. The presence of motion can be treated by the relativistic frame hopping method by means of plane-wave simplification techniques, since the solution relevant to the static case is expressed in terms of a generalized expansion of Floquet modes.
Application of fractal dimensions to study the structure of flocs formed in lime softening process.
Vahedi, Arman; Gorczyca, Beata
2011-01-01
The use of fractal dimensions to study the internal structure and settling of flocs formed in lime softening process was investigated. Fractal dimensions of flocs were measured directly on floc images and indirectly from their settling velocity. An optical microscope with a motorized stage was used to measure the fractal dimensions of lime softening flocs directly on their images in 2 and 3D space. The directly determined fractal dimensions of the lime softening flocs were 1.11-1.25 for floc boundary, 1.82-1.99 for cross-sectional area and 2.6-2.99 for floc volume. The fractal dimension determined indirectly from the flocs settling rates was 1.87 that was different from the 3D fractal dimension determined directly on floc images. This discrepancy is due to the following incorrect assumptions used for fractal dimensions determined from floc settling rates: linear relationship between square settling velocity and floc size (Stokes' Law), Euclidean relationship between floc size and volume, constant fractal dimensions and one primary particle size describing entire population of flocs. Floc settling model incorporating variable floc fractal dimensions as well as variable primary particle size was found to describe the settling velocity of large (>50 μm) lime softening flocs better than Stokes' Law. Settling velocities of smaller flocs (<50 μm) could still be quite well predicted by Stokes' Law. The variation of fractal dimensions with lime floc size in this study indicated that two mechanisms are involved in the formation of these flocs: cluster-cluster aggregation for small flocs (<50 μm) and diffusion-limited aggregation for large flocs (>50 μm). Therefore, the relationship between the floc fractal dimension and floc size appears to be determined by floc formation mechanisms. PMID:20937512
Fractals analysis of cardiac arrhythmias.
Saeed, Mohammed
2005-09-01
Heart rhythms are generated by complex self-regulating systems governed by the laws of chaos. Consequently, heart rhythms have fractal organization, characterized by self-similar dynamics with long-range order operating over multiple time scales. This allows for the self-organization and adaptability of heart rhythms under stress. Breakdown of this fractal organization into excessive order or uncorrelated randomness leads to a less-adaptable system, characteristic of aging and disease. With the tools of nonlinear dynamics, this fractal breakdown can be quantified with potential applications to diagnostic and prognostic clinical assessment. In this paper, I review the methodologies for fractal analysis of cardiac rhythms and the current literature on their applications in the clinical context. A brief overview of the basic mathematics of fractals is also included. Furthermore, I illustrate the usefulness of these powerful tools to clinical medicine by describing a novel noninvasive technique to monitor drug therapy in atrial fibrillation.
Measuring border irregularities of skin lesions using fractal dimensions
NASA Astrophysics Data System (ADS)
Ng, Vincent T. Y.; Lee, Tim K.
1996-09-01
Malignant melanoma is the most common cancer in people less than 35 years of age and incident rates are increasing by approximately 5 percent per annum in many white populations, including British Columbia, Canada. In 1994, a clinical study has been established to digitize melanocytic lesions under a controlled environment. Lesions are digitized from patients who are referred to the Colored Pigment Lesion Clinic in the University of British Columbia. In this paper, we investigate how to use fractal dimensions (FDs) in measuring the irregularity of a skin lesion. In a previous project, we have experimented with 6 different methods to calculate fractal dimensions on a small number of images of skin lesions, and the simple box-counting method performed the best. However, the method did not exploit the intensity information of the images. With the new set of images which are digitized under the controlled environment, we utilize the differential box counting method to exploit such information. Four FD measures, including the direct FD, the horizontal and the vertical smoothing FDs, and the multi- fractal dimension of order two, are calculated based on the original color images. In addition, these 4 FD features are repeatedly calculate for the blue band of the images. This paper reports the different features through the calculations of the fractal dimensions and compares their differentiation power in the use of diagnosis of images of skin lesions.
Functional Calcium Imaging in Developing Cortical Networks
Dawitz, Julia; Kroon, Tim; Hjorth, J.J. Johannes; Meredith, Rhiannon M.
2011-01-01
A hallmark pattern of activity in developing nervous systems is spontaneous, synchronized network activity. Synchronized activity has been observed in intact spinal cord, brainstem, retina, cortex and dissociated neuronal culture preparations. During periods of spontaneous activity, neurons depolarize to fire single or bursts of action potentials, activating many ion channels. Depolarization activates voltage-gated calcium channels on dendrites and spines that mediate calcium influx. Highly synchronized electrical activity has been measured from local neuronal networks using field electrodes. This technique enables high temporal sampling rates but lower spatial resolution due to integrated read-out of multiple neurons at one electrode. Single cell resolution of neuronal activity is possible using patch-clamp electrophysiology on single neurons to measure firing activity. However, the ability to measure from a network is limited to the number of neurons patched simultaneously, and typically is only one or two neurons. The use of calcium-dependent fluorescent indicator dyes has enabled the measurement of synchronized activity across a network of cells. This technique gives both high spatial resolution and sufficient temporal sampling to record spontaneous activity of the developing network. A key feature of newly-forming cortical and hippocampal networks during pre- and early postnatal development is spontaneous, synchronized neuronal activity (Katz & Shatz, 1996; Khaziphov & Luhmann, 2006). This correlated network activity is believed to be essential for the generation of functional circuits in the developing nervous system (Spitzer, 2006). In both primate and rodent brain, early electrical and calcium network waves are observed pre- and postnatally in vivo and in vitro (Adelsberger et al., 2005; Garaschuk et al., 2000; Lamblin et al., 1999). These early activity patterns, which are known to control several developmental processes including neuronal differentiation
Self-organized one-atom thick fractal nanoclusters via field-induced atomic transport
NASA Astrophysics Data System (ADS)
Batabyal, R.; Mahato, J. C.; Das, Debolina; Roy, Anupam; Dev, B. N.
2013-08-01
We report on the growth of a monolayer thick fractal nanostructures of Ag on flat-top Ag islands, grown on Si(111). Upon application of a voltage pulse at an edge of the flat-top Ag island from a scanning tunneling microscope tip, Ag atoms climb from the edge onto the top of the island. These atoms aggregate to form precisely one-atom thick nanostructures of fractal nature. The fractal (Hausdorff) dimension, DH = 1.75 ± 0.05, of this nanostructure has been determined by analyzing the morphology of the growing nanocluster, imaged by scanning tunneling microscopy, following the application of the voltage pulse. This value of the fractal dimension is consistent with the diffusion limited aggregation (DLA) model. We also determined two other fractal dimensions based on perimeter-radius-of-gyration (DP) and perimeter-area (D'P) relationship. Simulations of the DLA process, with varying sticking probability, lead to different cluster morphologies [P. Meakin, Phys. Rev. A 27, 1495 (1983)]; however, the value of DH is insensitive to this difference in morphology. We suggest that the morphology can be characterized by additional fractal dimension(s) DP and/or D'P, besides DH. We also show that within the DLA process DP = DH [C. Amitrano et al., Phys. Rev. A 40, 1713 (1989)] is only a special case; in general, DP and DH can be unequal. Characterization of fractal morphology is important for fractals in nanoelectronics, as fractal morphology would determine the electron transport behavior.
Anatomic and functional imaging of tagged molecules in animals
Weisenberger, Andrew G.; Majewski, Stanislaw; Paulus, Michael J.; Gleason, Shaun S.
2007-04-24
A novel functional imaging system for use in the imaging of unrestrained and non-anesthetized small animals or other subjects and a method for acquiring such images and further registering them with anatomical X-ray images previously or subsequently acquired. The apparatus comprises a combination of an IR laser profilometry system and gamma, PET and/or SPECT, imaging system, all mounted on a rotating gantry, that permits simultaneous acquisition of positional and orientational information and functional images of an unrestrained subject that are registered, i.e. integrated, using image processing software to produce a functional image of the subject without the use of restraints or anesthesia. The functional image thus obtained can be registered with a previously or subsequently obtained X-ray CT image of the subject. The use of the system described herein permits functional imaging of a subject in an unrestrained/non-anesthetized condition thereby reducing the stress on the subject and eliminating any potential interference with the functional testing that such stress might induce.
Universal characteristics of fractal fluctuations in prime number distribution
NASA Astrophysics Data System (ADS)
Selvam, A. M.
2014-11-01
The frequency of occurrence of prime numbers at unit number spacing intervals exhibits self-similar fractal fluctuations concomitant with inverse power law form for power spectrum generic to dynamical systems in nature such as fluid flows, stock market fluctuations and population dynamics. The physics of long-range correlations exhibited by fractals is not yet identified. A recently developed general systems theory visualizes the eddy continuum underlying fractals to result from the growth of large eddies as the integrated mean of enclosed small scale eddies, thereby generating a hierarchy of eddy circulations or an inter-connected network with associated long-range correlations. The model predictions are as follows: (1) The probability distribution and power spectrum of fractals follow the same inverse power law which is a function of the golden mean. The predicted inverse power law distribution is very close to the statistical normal distribution for fluctuations within two standard deviations from the mean of the distribution. (2) Fractals signify quantum-like chaos since variance spectrum represents probability density distribution, a characteristic of quantum systems such as electron or photon. (3) Fractal fluctuations of frequency distribution of prime numbers signify spontaneous organization of underlying continuum number field into the ordered pattern of the quasiperiodic Penrose tiling pattern. The model predictions are in agreement with the probability distributions and power spectra for different sets of frequency of occurrence of prime numbers at unit number interval for successive 1000 numbers. Prime numbers in the first 10 million numbers were used for the study.
Inverted fractal analysis of TiOx thin layers grown by inverse pulsed laser deposition
NASA Astrophysics Data System (ADS)
Égerházi, L.; Smausz, T.; Bari, F.
2013-08-01
Inverted fractal analysis (IFA), a method developed for fractal analysis of scanning electron microscopy images of cauliflower-like thin films is presented through the example of layers grown by inverse pulsed laser deposition (IPLD). IFA uses the integrated fractal analysis module (FracLac) of the image processing software ImageJ, and an objective thresholding routine that preserves the characteristic features of the images, independently of their brightness and contrast. IFA revealed fD = 1.83 ± 0.01 for TiOx layers grown at 5-50 Pa background pressures. For a series of images, this result was verified by evaluating the scaling of the number of still resolved features on the film, counted manually. The value of fD not only confirms the fractal structure of TiOx IPLD thin films, but also suggests that the aggregation of plasma species in the gas atmosphere may have only limited contribution to the deposition.
Fractal characteristics for binary noise radar waveform
NASA Astrophysics Data System (ADS)
Li, Bing C.
2016-05-01
Noise radars have many advantages over conventional radars and receive great attentions recently. The performance of a noise radar is determined by its waveforms. Investigating characteristics of noise radar waveforms has significant value for evaluating noise radar performance. In this paper, we use binomial distribution theory to analyze general characteristics of binary phase coded (BPC) noise waveforms. Focusing on aperiodic autocorrelation function, we demonstrate that the probability distributions of sidelobes for a BPC noise waveform depend on the distances of these sidelobes to the mainlobe. The closer a sidelobe to the mainlobe, the higher the probability for this sidelobe to be a maximum sidelobe. We also develop Monte Carlo framework to explore the characteristics that are difficult to investigate analytically. Through Monte Carlo experiments, we reveal the Fractal relationship between the code length and the maximum sidelobe value for BPC waveforms, and propose using fractal dimension to measure noise waveform performance.
A tutorial introduction to adaptive fractal analysis
Riley, Michael A.; Bonnette, Scott; Kuznetsov, Nikita; Wallot, Sebastian; Gao, Jianbo
2012-01-01
The authors present a tutorial description of adaptive fractal analysis (AFA). AFA utilizes an adaptive detrending algorithm to extract globally smooth trend signals from the data and then analyzes the scaling of the residuals to the fit as a function of the time scale at which the fit is computed. The authors present applications to synthetic mathematical signals to verify the accuracy of AFA and demonstrate the basic steps of the analysis. The authors then present results from applying AFA to time series from a cognitive psychology experiment on repeated estimation of durations of time to illustrate some of the complexities of real-world data. AFA shows promise in dealing with many types of signals, but like any fractal analysis method there are special challenges and considerations to take into account, such as determining the presence of linear scaling regions. PMID:23060804
Burgers Turbulence on a Fractal Fourier set
NASA Astrophysics Data System (ADS)
Buzzicotti, Michele; Biferale, Luca; Frisch, Uriel; Ray, Samriddhi
2014-11-01
We present a systematic investigation of the effects introduced by a fractal decimation in Fourier space on stochastically forced one-dimensional Burgers equations. The aim is to understand the statistical robustness of the shock singularity under different reductions of the number of the degrees of freedom. We perform a series of direct numerical simulations by using a pseudo-spectral code with resolution up to 16384 points and for various dimensions of the fractal set of Fourier modes DF <1. We present results concerning the scaling properties of statistical measures in real space and the probability distribution functions of local and non-local triads in Fourier space. Partially supported by ERC Grant No 339032.
Optical imaging of fast, dynamic neurophysiological function.
Rector, D. M.; Carter, K. M.; Yao, X.; George, J. S.
2002-01-01
Fast evoked responses were imaged from rat dorsal medulla and whisker barrel cortex. To investigate the biophysical mechanisms involved, fast optical responses associated with isolated crustacean nerve stimulation were recorded using birefringence and scattered light. Such studies allow optimization of non-invasive imaging techniques being developed for use in humans.
Fractal texture analysis of the healing process after bone loss.
Borowska, Marta; Szarmach, Janusz; Oczeretko, Edward
2015-12-01
Radiological assessment of treatment effectiveness of guided bone regeneration (GBR) method in postresectal and postcystal bone loss cases, observed for one year. Group of 25 patients (17 females and 8 males) who underwent root resection with cystectomy were evaluated. The following combination therapy of intraosseous deficits was used, consisting of bone augmentation with xenogenic material together with covering regenerative membranes and tight wound closure. The bone regeneration process was estimated, comparing the images taken on the day of the surgery and 12 months later, by means of Kodak RVG 6100 digital radiography set. The interpretation of the radiovisiographic image depends on the evaluation ability of the eye looking at it, which leaves a large margin of uncertainty. So, several texture analysis techniques were developed and used sequentially on the radiographic image. For each method, the results were the mean from the 25 images. These methods compute the fractal dimension (D), each one having its own theoretic basis. We used five techniques for calculating fractal dimension: power spectral density method, triangular prism surface area method, blanket method, intensity difference scaling method and variogram analysis. Our study showed a decrease of fractal dimension during the healing process after bone loss. We also found evidence that various methods of calculating fractal dimension give different results. During the healing process after bone loss, the surfaces of radiographic images became smooth. The result obtained show that our findings may be of great importance for diagnostic purpose.
Trabecular Bone Mechanical Properties and Fractal Dimension
NASA Technical Reports Server (NTRS)
Hogan, Harry A.
1996-01-01
Countermeasures for reducing bone loss and muscle atrophy due to extended exposure to the microgravity environment of space are continuing to be developed and improved. An important component of this effort is finite element modeling of the lower extremity and spinal column. These models will permit analysis and evaluation specific to each individual and thereby provide more efficient and effective exercise protocols. Inflight countermeasures and post-flight rehabilitation can then be customized and targeted on a case-by-case basis. Recent Summer Faculty Fellowship participants have focused upon finite element mesh generation, muscle force estimation, and fractal calculations of trabecular bone microstructure. Methods have been developed for generating the three-dimensional geometry of the femur from serial section magnetic resonance images (MRI). The use of MRI as an imaging modality avoids excessive exposure to radiation associated with X-ray based methods. These images can also detect trabecular bone microstructure and architecture. The goal of the current research is to determine the degree to which the fractal dimension of trabecular architecture can be used to predict the mechanical properties of trabecular bone tissue. The elastic modulus and the ultimate strength (or strain) can then be estimated from non-invasive, non-radiating imaging and incorporated into the finite element models to more accurately represent the bone tissue of each individual of interest. Trabecular bone specimens from the proximal tibia are being studied in this first phase of the work. Detailed protocols and procedures have been developed for carrying test specimens through all of the steps of a multi-faceted test program. The test program begins with MRI and X-ray imaging of the whole bones before excising a smaller workpiece from the proximal tibia region. High resolution MRI scans are then made and the piece further cut into slabs (roughly 1 cm thick). The slabs are X-rayed again
Dynamic Ultrasound Imaging Applications to Quantify Musculoskeletal Function
Sikdar, Siddhartha; Wei, Qi; Cortes, Nelson
2014-01-01
Advances in imaging methods have led to new capability to study muscle and tendon motion in vivo. Direct measurements of muscle and tendon kinematics using imaging may lead to improved understanding of musculoskeletal function. This review presents quantitative ultrasound methods for muscle dynamics that can be used to assess in vivo musculoskeletal function when integrated with other conventional biomechanical measurements. PMID:24949846
Wavelet transform modulus maxima based fractal correlation analysis
NASA Astrophysics Data System (ADS)
Lin, D. C.; Sharif, A.
2007-12-01
The wavelet transform modulus maxima (WTMM) used in the singularity analysis of one fractal function is extended to study the fractal correlation of two multifractal functions. The technique is developed in the framework of joint partition function analysis (JPFA) proposed by Meneveau et al. [C. Meneveau, K.R. Sreenivasan, Phys. Rev. A 41, 894 (1990)] and is shown to be equally effective. In addition, we show that another leading approach developed for the same purpose, namely, relative multifractal analysis, can be considered as a special case of JPFA at a particular parameter setting.
Subband/Transform MATLAB Functions For Processing Images
NASA Technical Reports Server (NTRS)
Glover, D.
1995-01-01
SUBTRANS software is package of routines implementing image-data-processing functions for use with MATLAB*(TM) software. Provides capability to transform image data with block transforms and to produce spatial-frequency subbands of transformed data. Functions cascaded to provide further decomposition into more subbands. Also used in image-data-compression systems. For example, transforms used to prepare data for lossy compression. Written for use in MATLAB mathematical-analysis environment.
Exterior dimension of fat fractals
NASA Technical Reports Server (NTRS)
Grebogi, C.; Mcdonald, S. W.; Ott, E.; Yorke, J. A.
1985-01-01
Geometric scaling properties of fat fractal sets (fractals with finite volume) are discussed and characterized via the introduction of a new dimension-like quantity which is called the exterior dimension. In addition, it is shown that the exterior dimension is related to the 'uncertainty exponent' previously used in studies of fractal basin boundaries, and it is shown how this connection can be exploited to determine the exterior dimension. Three illustrative applications are described, two in nonlinear dynamics and one dealing with blood flow in the body. Possible relevance to porous materials and ballistic driven aggregation is also noted.
Generating Text from Functional Brain Images
Pereira, Francisco; Detre, Greg; Botvinick, Matthew
2011-01-01
Recent work has shown that it is possible to take brain images acquired during viewing of a scene and reconstruct an approximation of the scene from those images. Here we show that it is also possible to generate text about the mental content reflected in brain images. We began with images collected as participants read names of concrete items (e.g., “Apartment’’) while also seeing line drawings of the item named. We built a model of the mental semantic representation of concrete concepts from text data and learned to map aspects of such representation to patterns of activation in the corresponding brain image. In order to validate this mapping, without accessing information about the items viewed for left-out individual brain images, we were able to generate from each one a collection of semantically pertinent words (e.g., “door,” “window” for “Apartment’’). Furthermore, we show that the ability to generate such words allows us to perform a classification task and thus validate our method quantitatively. PMID:21927602
Overcoming Resistance with Fractals. A New Way to Teach Elementary Circuits.
ERIC Educational Resources Information Center
Ching, W. K.; And Others
1994-01-01
Students construct a Sierpinski gasket from resistors and measure its resistance as a function of size. Provides a brief review of what it means geometrically for the Sierpinski gasket to be fractal, followed by an explanation of how to analyze the electrical resistance on a gasket to find its fractal behavior. (MVL)
Three-Dimensional Surface Parameters and Multi-Fractal Spectrum of Corroded Steel
Shanhua, Xu; Songbo, Ren; Youde, Wang
2015-01-01
To study multi-fractal behavior of corroded steel surface, a range of fractal surfaces of corroded surfaces of Q235 steel were constructed by using the Weierstrass-Mandelbrot method under a high total accuracy. The multi-fractal spectrum of fractal surface of corroded steel was calculated to study the multi-fractal characteristics of the W-M corroded surface. Based on the shape feature of the multi-fractal spectrum of corroded steel surface, the least squares method was applied to the quadratic fitting of the multi-fractal spectrum of corroded surface. The fitting function was quantitatively analyzed to simplify the calculation of multi-fractal characteristics of corroded surface. The results showed that the multi-fractal spectrum of corroded surface was fitted well with the method using quadratic curve fitting, and the evolution rules and trends were forecasted accurately. The findings can be applied to research on the mechanisms of corroded surface formation of steel and provide a new approach for the establishment of corrosion damage constitutive models of steel. PMID:26121468
Three-Dimensional Surface Parameters and Multi-Fractal Spectrum of Corroded Steel.
Shanhua, Xu; Songbo, Ren; Youde, Wang
2015-01-01
To study multi-fractal behavior of corroded steel surface, a range of fractal surfaces of corroded surfaces of Q235 steel were constructed by using the Weierstrass-Mandelbrot method under a high total accuracy. The multi-fractal spectrum of fractal surface of corroded steel was calculated to study the multi-fractal characteristics of the W-M corroded surface. Based on the shape feature of the multi-fractal spectrum of corroded steel surface, the least squares method was applied to the quadratic fitting of the multi-fractal spectrum of corroded surface. The fitting function was quantitatively analyzed to simplify the calculation of multi-fractal characteristics of corroded surface. The results showed that the multi-fractal spectrum of corroded surface was fitted well with the method using quadratic curve fitting, and the evolution rules and trends were forecasted accurately. The findings can be applied to research on the mechanisms of corroded surface formation of steel and provide a new approach for the establishment of corrosion damage constitutive models of steel.
Map of fluid flow in fractal porous medium into fractal continuum flow.
Balankin, Alexander S; Elizarraraz, Benjamin Espinoza
2012-05-01
This paper is devoted to fractal continuum hydrodynamics and its application to model fluid flows in fractally permeable reservoirs. Hydrodynamics of fractal continuum flow is developed on the basis of a self-consistent model of fractal continuum employing vector local fractional differential operators allied with the Hausdorff derivative. The generalized forms of Green-Gauss and Kelvin-Stokes theorems for fractional calculus are proved. The Hausdorff material derivative is defined and the form of Reynolds transport theorem for fractal continuum flow is obtained. The fundamental conservation laws for a fractal continuum flow are established. The Stokes law and the analog of Darcy's law for fractal continuum flow are suggested. The pressure-transient equation accounting the fractal metric of fractal continuum flow is derived. The generalization of the pressure-transient equation accounting the fractal topology of fractal continuum flow is proposed. The mapping of fluid flow in a fractally permeable medium into a fractal continuum flow is discussed. It is stated that the spectral dimension of the fractal continuum flow d(s) is equal to its mass fractal dimension D, even when the spectral dimension of the fractally porous or fissured medium is less than D. A comparison of the fractal continuum flow approach with other models of fluid flow in fractally permeable media and the experimental field data for reservoir tests are provided.
Fractal Character of Titania Nanoparticles Formed by Laser Ablation
Musaev, O.; Midgley, A; Wrobel, J; Yan, J; Kruger, M
2009-01-01
Titania nanoparticles were fabricated by laser ablation of polycrystalline rutile in water at room temperature. The resulting nanoparticles were analyzed with x-ray diffraction, Raman spectroscopy, and transmission electron microscopy. The electron micrograph image of deposited nanoparticles demonstrates fractal properties.
Controlling Molecular Growth between Fractals and Crystals on Surfaces.
Zhang, Xue; Li, Na; Gu, Gao-Chen; Wang, Hao; Nieckarz, Damian; Szabelski, Paweł; He, Yang; Wang, Yu; Xie, Chao; Shen, Zi-Yong; Lü, Jing-Tao; Tang, Hao; Peng, Lian-Mao; Hou, Shi-Min; Wu, Kai; Wang, Yong-Feng
2015-12-22
Recent studies demonstrate that simple functional molecules, which usually form two-dimensional (2D) crystal structures when adsorbed on solid substrates, are also able to self-assemble into ordered openwork fractal aggregates. To direct and control the growth of such fractal supramolecules, it is necessary to explore the conditions under which both fractal and crystalline patterns develop and coexist. In this contribution, we study the coexistence of Sierpiński triangle (ST) fractals and 2D molecular crystals that were formed by 4,4″-dihydroxy-1,1':3',1″-terphenyl molecules on Au(111) in ultrahigh vacuum. Growth competition between the STs and 2D crystals was realized by tuning substrate and molecular surface coverage and changing the functional groups of the molecular building block. Density functional theory calculations and Monte Carlo simulations are used to characterize the process. Both experimental and theoretical results demonstrate the possibility of steering the surface self-assembly to generate fractal and nonfractal structures made up of the same molecular building block.
Controlling Molecular Growth between Fractals and Crystals on Surfaces.
Zhang, Xue; Li, Na; Gu, Gao-Chen; Wang, Hao; Nieckarz, Damian; Szabelski, Paweł; He, Yang; Wang, Yu; Xie, Chao; Shen, Zi-Yong; Lü, Jing-Tao; Tang, Hao; Peng, Lian-Mao; Hou, Shi-Min; Wu, Kai; Wang, Yong-Feng
2015-12-22
Recent studies demonstrate that simple functional molecules, which usually form two-dimensional (2D) crystal structures when adsorbed on solid substrates, are also able to self-assemble into ordered openwork fractal aggregates. To direct and control the growth of such fractal supramolecules, it is necessary to explore the conditions under which both fractal and crystalline patterns develop and coexist. In this contribution, we study the coexistence of Sierpiński triangle (ST) fractals and 2D molecular crystals that were formed by 4,4″-dihydroxy-1,1':3',1″-terphenyl molecules on Au(111) in ultrahigh vacuum. Growth competition between the STs and 2D crystals was realized by tuning substrate and molecular surface coverage and changing the functional groups of the molecular building block. Density functional theory calculations and Monte Carlo simulations are used to characterize the process. Both experimental and theoretical results demonstrate the possibility of steering the surface self-assembly to generate fractal and nonfractal structures made up of the same molecular building block. PMID:26502984
A Fractal Approach to Assess the Risks of Nitroamine Explosives
NASA Astrophysics Data System (ADS)
Song, Xiaolan; Li, Fengsheng; Wang, Yi; An, Chongwei; Wang, Jingyu; Zhang, Jinglin
2012-01-01
To the best of our knowledge, this work represents the first thermal conductivity theory for fractal energetic particle groups to combine fractal and hot-spot theories. We considered the influence of the fractal dimensions of particles on their thermal conductivity and even on the sensitivity of the explosive. Based on this theory, two types of nitroamine explosives (hexahydro-1,3,5-trinitro-1,3,5-triazine [RDX] and hexanitrohexaazaisowurtzitane [HNIW]) with different sizes, size distributions, and microscale morphologies were prepared using wet milling, solvent/nonsolvent, and ridding methods. The dependence of the explosive sensitivity on the fractal characteristics of the particles was investigated. Specifically, the size distributions and scanning electron microscopy (SEM) images of the samples were used to obtain the fractal dimension (D) and surface fractal dimension (Ds), respectively, by using a least-squares method and fractal image processing software (FIPS). The mechanical sensitivity and thermal stability of the samples were characterized using mechanical sensitivity tests and differential scanning calorimetry (DSC) and were further compared with the previous results upon the investigation about HMX (octahydro-1.3.5.7-tetranitro-1,3,5,7-tetrazocine). The results indicate that the sensitivity of nitroamine explosives largely depends on the fractal dimensions of the particles. Specifically, the sample with a higher D value is more insensitive to impact action, whereas the sample with a higher Ds value is more sensitive to friction action. In addition, the sample with both higher D and Ds values has less heat release and a slower rate of thermal decomposition. All of the above observations can be attributed to the alternation of the formation of hot spots that was controlled by heat mass and thermal conductivity due to the increase of D and Ds values caused by changes in parameters such as fine particle content, specific surface area, porosity content
A Novel Fractal Coding Method Based on M-J Sets
Sun, Yuanyuan; Xu, Rudan; Chen, Lina; Kong, Ruiqing; Hu, Xiaopeng
2014-01-01
In this paper, we present a novel fractal coding method with the block classification scheme based on a shared domain block pool. In our method, the domain block pool is called dictionary and is constructed from fractal Julia sets. The image is encoded by searching the best matching domain block with the same BTC (Block Truncation Coding) value in the dictionary. The experimental results show that the scheme is competent both in encoding speed and in reconstruction quality. Particularly for large images, the proposed method can avoid excessive growth of the computational complexity compared with the traditional fractal coding algorithm. PMID:25010686
Fractals and dynamics in art and design.
Guastello, Stephen J
2015-01-01
Many styles of visual art that build on fractal imagery and chaotic dynamics in the creative process have been examined in NDPLS in recent years. This article presents a gallery of artwork turned into design that appeared in the promotional products of the Society for Chaos Theory in Psychology & Life Sciences. The gallery showcases a variety of new imaging styles, including photography, that reflect a deepening perspective on nonlinear dynamics and art. The contributing artworks in design formats combine to render the verve that transcends the boundaries between the artistic and scientific communities.
Ugurbil, Kamil
2016-10-01
When we consider all of the methods we employ to detect brain function, from electrophysiology to optical techniques to functional magnetic resonance imaging (fMRI), we do not really have a 'golden technique' that meets all of the needs for studying the brain. We have methods, each of which has significant limitations but provide often complimentary information. Clearly, there are many questions that need to be answered about fMRI, which unlike other methods, allows us to study the human brain. However, there are also extraordinary accomplishments or demonstration of the feasibility of reaching new and previously unexpected scales of function in the human brain. This article reviews some of the work we have pursued, often with extensive collaborations with other co-workers, towards understanding the underlying mechanisms of the methodology, defining its limitations, and developing solutions to advance it. No doubt, our knowledge of human brain function has vastly expanded since the introduction of fMRI. However, methods and instrumentation in this dynamic field have evolved to a state that discoveries about the human brain based on fMRI principles, together with information garnered at a much finer spatial and temporal scale through other methods, are poised to significantly accelerate in the next decade.This article is part of the themed issue 'Interpreting BOLD: a dialogue between cognitive and cellular neuroscience'. PMID:27574313
Ugurbil, Kamil
2016-10-01
When we consider all of the methods we employ to detect brain function, from electrophysiology to optical techniques to functional magnetic resonance imaging (fMRI), we do not really have a 'golden technique' that meets all of the needs for studying the brain. We have methods, each of which has significant limitations but provide often complimentary information. Clearly, there are many questions that need to be answered about fMRI, which unlike other methods, allows us to study the human brain. However, there are also extraordinary accomplishments or demonstration of the feasibility of reaching new and previously unexpected scales of function in the human brain. This article reviews some of the work we have pursued, often with extensive collaborations with other co-workers, towards understanding the underlying mechanisms of the methodology, defining its limitations, and developing solutions to advance it. No doubt, our knowledge of human brain function has vastly expanded since the introduction of fMRI. However, methods and instrumentation in this dynamic field have evolved to a state that discoveries about the human brain based on fMRI principles, together with information garnered at a much finer spatial and temporal scale through other methods, are poised to significantly accelerate in the next decade.This article is part of the themed issue 'Interpreting BOLD: a dialogue between cognitive and cellular neuroscience'.
Evolution of Fractal Parameters through Development Stage of Soil Crust
NASA Astrophysics Data System (ADS)
Ospina, Abelardo; Florentino, Adriana; Tarquis, Ana Maria
2016-04-01
Soil surface characteristics are subjected to changes driven by several interactions between water, air, biotic and abiotic components. One of the examples of such interactions is provided through biological soil crusts (BSC) in arid and semi-arid environments. BSC are communities composed of cyanobacteria, fungi, mosses, lichens, algae and liverworts covering the soil surface and play an important role in ecosystem functioning. The characteristics and formation of these BSC influence the soil hydrological balance, control the mass of eroded sediment, increase stability of soil surface, and influence plant productivity through the modification of nitrogen and carbon cycle. The site of this work is located at Quibor and Ojo de Agua (Lara state, Venezuela). The Quibor Depression in Venezuela is a major agricultural area being at semi-arid conditions and limited drainage favor the natural process of salinization. Additionally, the extension and intensification of agriculture has led to over-exploitation of groundwater in the past 30 years (Méndoza et al., 2013). The soil microbial crust develops initially on physical crusts which are mainly generated since wetting and drying, being a recurrent feature in the Quíbor arid zone. The microbiotic crust is organic, composed of macro organisms (bryophytes and lichens) and microorganisms (cyanobacteria, fungi algae, etc.); growing on the ground, forming a thickness no greater than 3 mm. For further details see Toledo and Florentino (2009). This study focus on characterize the development stage of the BSC based on image analysis. To this end, grayscale images of different types of biological soil crust at different stages where taken, each image corresponding to an area of 12.96 cm2 with a resolution of 1024x1024 pixels (Ospina et al., 2015). For each image lacunarity and fractal dimension through the differential box counting method were calculated. These were made with the software ImageJ/Fraclac (Karperien, 2013
NASA Astrophysics Data System (ADS)
Eliazar, Iddo; Klafter, Joseph
2008-09-01
The Central Limit Theorem (CLT) and Extreme Value Theory (EVT) study, respectively, the stochastic limit-laws of sums and maxima of sequences of independent and identically distributed (i.i.d.) random variables via an affine scaling scheme. In this research we study the stochastic limit-laws of populations of i.i.d. random variables via nonlinear scaling schemes. The stochastic population-limits obtained are fractal Poisson processes which are statistically self-similar with respect to the scaling scheme applied, and which are characterized by two elemental structures: (i) a universal power-law structure common to all limits, and independent of the scaling scheme applied; (ii) a specific structure contingent on the scaling scheme applied. The sum-projection and the maximum-projection of the population-limits obtained are generalizations of the classic CLT and EVT results - extending them from affine to general nonlinear scaling schemes.
Fractality of light's darkness.
O'Holleran, Kevin; Dennis, Mark R; Flossmann, Florian; Padgett, Miles J
2008-02-01
Natural light fields are threaded by lines of darkness. For monochromatic light, the phenomenon is familiar in laser speckle, i.e., the black points that appear in the scattered light. These black points are optical vortices that extend as lines throughout the volume of the field. We establish by numerical simulations, supported by experiments, that these vortex lines have the fractal properties of a Brownian random walk. Approximately 73% of the lines percolate through the optical beam, the remainder forming closed loops. Our statistical results are similar to those of vortices in random discrete lattice models of cosmic strings, implying that the statistics of singularities in random optical fields exhibit universal behavior. PMID:18352372
Anomalous Diffusion in Fractal Globules
NASA Astrophysics Data System (ADS)
Tamm, M. V.; Nazarov, L. I.; Gavrilov, A. A.; Chertovich, A. V.
2015-05-01
The fractal globule state is a popular model for describing chromatin packing in eukaryotic nuclei. Here we provide a scaling theory and dissipative particle dynamics computer simulation for the thermal motion of monomers in the fractal globule state. Simulations starting from different entanglement-free initial states show good convergence which provides evidence supporting the existence of a unique metastable fractal globule state. We show monomer motion in this state to be subdiffusive described by ⟨X2(t )⟩˜tαF with αF close to 0.4. This result is in good agreement with existing experimental data on the chromatin dynamics, which makes an additional argument in support of the fractal globule model of chromatin packing.
Thermodynamics of Photons on Fractals
Akkermans, Eric; Dunne, Gerald V.; Teplyaev, Alexander
2010-12-03
A thermodynamical treatment of a massless scalar field (a photon) confined to a fractal spatial manifold leads to an equation of state relating pressure to internal energy, PV{sub s}=U/d{sub s}, where d{sub s} is the spectral dimension and V{sub s} defines the 'spectral volume'. For regular manifolds, V{sub s} coincides with the usual geometric spatial volume, but on a fractal this is not necessarily the case. This is further evidence that on a fractal, momentum space can have a different dimension than position space. Our analysis also provides a natural definition of the vacuum (Casimir) energy of a fractal. We suggest ways that these unusual properties might be probed experimentally.
Fractal identification of supercell storms
NASA Astrophysics Data System (ADS)
Féral, Laurent; Sauvageot, Henri
2002-07-01
The most intense and violent form of convective storm is the supercell storm, usually associated with heavy rain, hail, and destructive gusty winds, downbursts, and tornadoes. Identifying a storm cell as a supercell storm is not easy. What is shown here, from radar data, is that when an ordinary, or multicell storm evolves towards the supercellular organization, its fractal dimension is modified. Whereas the fractal dimension of the ordinary convective storms, including multicell thunderstorms, is observed around 1.35, in agreement with previous results, the fractal dimension of supercell storms is found close to 1.07. This low value is due to the unicellular character of supercells. The present paper suggests that the fractal dimension is a parameter that should be considered to analyse the dynamical organization of a convective field and to detect and identify the supercell storms, either isolated or among a population of convective storms.
Anomalous diffusion in fractal globules.
Tamm, M V; Nazarov, L I; Gavrilov, A A; Chertovich, A V
2015-05-01
The fractal globule state is a popular model for describing chromatin packing in eukaryotic nuclei. Here we provide a scaling theory and dissipative particle dynamics computer simulation for the thermal motion of monomers in the fractal globule state. Simulations starting from different entanglement-free initial states show good convergence which provides evidence supporting the existence of a unique metastable fractal globule state. We show monomer motion in this state to be subdiffusive described by ⟨X(2)(t)⟩∼t(αF) with αF close to 0.4. This result is in good agreement with existing experimental data on the chromatin dynamics, which makes an additional argument in support of the fractal globule model of chromatin packing. PMID:25978267
Anomalous diffusion in fractal globules.
Tamm, M V; Nazarov, L I; Gavrilov, A A; Chertovich, A V
2015-05-01
The fractal globule state is a popular model for describing chromatin packing in eukaryotic nuclei. Here we provide a scaling theory and dissipative particle dynamics computer simulation for the thermal motion of monomers in the fractal globule state. Simulations starting from different entanglement-free initial states show good convergence which provides evidence supporting the existence of a unique metastable fractal globule state. We show monomer motion in this state to be subdiffusive described by ⟨X(2)(t)⟩∼t(αF) with αF close to 0.4. This result is in good agreement with existing experimental data on the chromatin dynamics, which makes an additional argument in support of the fractal globule model of chromatin packing.
Fractal dynamics of bioconvective patterns
NASA Technical Reports Server (NTRS)
Noever, David A.
1991-01-01
Biologically generated cellular patterns, sometimes called bioconvective patterns, are found to cluster into aggregates which follow fractal growth dynamics akin to diffusion-limited aggregation (DLA) models. The pattern formed is self-similar with fractal dimension of 1.66 +/-0.038. Bioconvective DLA branching results from thermal roughening which shifts the balance between ordering viscous forces and disordering cell motility and random diffusion. The phase diagram for pattern morphology includes DLA, boundary spokes, random clusters, and reverse clusters.
Fractal geometry-based classification approach for the recognition of lung cancer cells
NASA Astrophysics Data System (ADS)
Xia, Deshen; Gao, Wenqing; Li, Hua
1994-05-01
This paper describes a new fractal geometry based classification approach for the recognition of lung cancer cells, which is used in the health inspection for lung cancers, because cancer cells grow much faster and more irregularly than normal cells do, the shape of the segmented cancer cells is very irregular and considered as a graph without characteristic length. We use Texture Energy Intensity Rn to do fractal preprocessing to segment the cells from the image and to calculate the fractal dimention value for extracting the fractal features, so that we can get the figure characteristics of different cancer cells and normal cells respectively. Fractal geometry gives us a correct description of cancer-cell shapes. Through this method, a good recognition of Adenoma, Squamous, and small cancer cells can be obtained.
Quantitative Functional Morphology by Imaging Flow Cytometry.
Vorobjev, Ivan A; Barteneva, Natasha S
2016-01-01
This chapter describes advantages and limitations of imaging flow cytometry (IFC) based on Imagestream instrumentation using a hybrid approach of morphometric measurement and quantitation of multiparametric fluorescent intensities' distribution in cells and particles. Brief comparison is given of IFC with conventional flow cytometry and fluorescent microscopy. Some future directions of the IFC technology are described and discussed. PMID:27460234
Image based physiological monitoring of cardiac function
NASA Astrophysics Data System (ADS)
Maier, Corinna S.; Bock, Michael; Semmler, Wolfhard; Lorenz, Christine H.
2008-03-01
A new framework for image based physiological cardiac monitoring is proposed based on repeated imaging of critical slice locations in an interventional MRI environment. The aim of this work is to provide a method of detecting pathological changes in the left ventricular (LV) myocardial wall motion where the standard ECG methods are not possible due to distortions by the magnetic field. First MRI LV short axis images are acquired for different phases of the cardiac cycle over RR intervals. Then LV contours are detected based on an established segmentation algorithm. The contour's Fourier Descriptors are calculated to classify myocardial wall into two classes: contracted or not contracted. The classifier is trained during an initial observation period before a pathological change might occur during an intervention. A contour rejected by the classifier using the unconditional, predictive probability of the contour's observation vector as confidence measure is interpreted as a probably pathologic change in the LV myocardial wall motion. To evaluate the performance of the classifier a simple model is introduced for simulating the contours of a pathological, ischemic, LV myocardial wall. The overall performance of the classifier on 516 samples based on healthy volunteer images and 3096 simulated ischemic samples yielded a mean classification error for supervised training of 5.7% and for unsupervised training of 8.7%.
Quantitative Functional Morphology by Imaging Flow Cytometry.
Vorobjev, Ivan A; Barteneva, Natasha S
2016-01-01
This chapter describes advantages and limitations of imaging flow cytometry (IFC) based on Imagestream instrumentation using a hybrid approach of morphometric measurement and quantitation of multiparametric fluorescent intensities' distribution in cells and particles. Brief comparison is given of IFC with conventional flow cytometry and fluorescent microscopy. Some future directions of the IFC technology are described and discussed.
Random walk through fractal environments.
Isliker, H; Vlahos, L
2003-02-01
We analyze random walk through fractal environments, embedded in three-dimensional, permeable space. Particles travel freely and are scattered off into random directions when they hit the fractal. The statistical distribution of the flight increments (i.e., of the displacements between two consecutive hittings) is analytically derived from a common, practical definition of fractal dimension, and it turns out to approximate quite well a power-law in the case where the dimension D(F) of the fractal is less than 2, there is though, always a finite rate of unaffected escape. Random walks through fractal sets with D(F)< or =2 can thus be considered as defective Levy walks. The distribution of jump increments for D(F)>2 is decaying exponentially. The diffusive behavior of the random walk is analyzed in the frame of continuous time random walk, which we generalize to include the case of defective distributions of walk increments. It is shown that the particles undergo anomalous, enhanced diffusion for D(F)<2, the diffusion is dominated by the finite escape rate. Diffusion for D(F)>2 is normal for large times, enhanced though for small and intermediate times. In particular, it follows that fractals generated by a particular class of self-organized criticality models give rise to enhanced diffusion. The analytical results are illustrated by Monte Carlo simulations.
Towards a More General Type of Univariate Constrained Interpolation with Fractal Splines
NASA Astrophysics Data System (ADS)
Chand, A. K. B.; Viswanathan, P.; Reddy, K. M.
2015-09-01
Recently, in [Electron. Trans. Numer. Anal. 41 (2014) 420-442] authors introduced a new class of rational cubic fractal interpolation functions with linear denominators via fractal perturbation of traditional nonrecursive rational cubic splines and investigated their basic shape preserving properties. The main goal of the current paper is to embark on univariate constrained fractal interpolation that is more general than what was considered so far. To this end, we propose some strategies for selecting the parameters of the rational fractal spline so that the interpolating curves lie strictly above or below a prescribed linear or a quadratic spline function. Approximation property of the proposed rational cubic fractal spine is broached by using the Peano kernel theorem as an interlude. The paper also provides an illustration of background theory, veined by examples.
Local fractal dimension based approaches for colonic polyp classification.
Häfner, Michael; Tamaki, Toru; Tanaka, Shinji; Uhl, Andreas; Wimmer, Georg; Yoshida, Shigeto
2015-12-01
This work introduces texture analysis methods that are based on computing the local fractal dimension (LFD; or also called the local density function) and applies them for colonic polyp classification. The methods are tested on 8 HD-endoscopic image databases, where each database is acquired using different imaging modalities (Pentax's i-Scan technology combined with or without staining the mucosa) and on a zoom-endoscopic image database using narrow band imaging. In this paper, we present three novel extensions to a LFD based approach. These extensions additionally extract shape and/or gradient information of the image to enhance the discriminativity of the original approach. To compare the results of the LFD based approaches with the results of other approaches, five state of the art approaches for colonic polyp classification are applied to the employed databases. Experiments show that LFD based approaches are well suited for colonic polyp classification, especially the three proposed extensions. The three proposed extensions are the best performing methods or at least among the best performing methods for each of the employed databases. The methods are additionally tested by means of a public texture image database, the UIUCtex database. With this database, the viewpoint invariance of the methods is assessed, an important features for the employed endoscopic image databases. Results imply that most of the LFD based methods are more viewpoint invariant than the other methods. However, the shape, size and orientation adapted LFD approaches (which are especially designed to enhance the viewpoint invariance) are in general not more viewpoint invariant than the other LFD based approaches.
On the response function separability of hyperspectral imaging systems
NASA Astrophysics Data System (ADS)
Jemec, Jurij; Pernuš, Franjo; Likar, Boštjan; Bürmen, Miran
2015-05-01
Hyperspectral imaging systems effectively collect information across the spectral and two spatial dimensions by employing three main components: the front lens, the light-diffraction element and a camera. Imperfections in these components introduce spectral and spatial dependent distortions in the recorded hyperspectral image. These can be characterized by a 3D response function that is subsequently used to remove distortions and enhance the resolution of the recorded images by deconvolution. The majority of existing characterization methods assume spatial and spectral separability of the 3D response function. In this way, the complex problem of 3D response function characterization is reduced to independent characterizations of the three orthogonal response function components. However, if the 3D response function is non-separable, such characterization can lead to poor response function estimates, and hence inaccurate and distorted results of the subsequent deconvolution-based calibration and image enhancement. In this paper, we evaluate the influence of the spatial response function non-separability on the results of the calibration by deconvolution. For this purpose, a novel procedure for direct measurement of the 2D spatial response function is proposed along with a quantitative measure of the spatial response function non-separability. The quality of deconvolved images is assessed in terms of full width at half maximum (FWHM) and step edge overshoot magnitude observed in the deconvolved images of slanted edges, images of biological slides, and 1951 USAF resolution test chart. Results show that there are cases, when nonseparability of the system response function is significant and should be considered by the deconvolution-based calibration and image enhancement methods.
Automatic extraction of faults and fractal analysis from remote sensing data
NASA Astrophysics Data System (ADS)
Gloaguen, R.; Marpu, P. R.; Niemeyer, I.
2007-03-01
Object-based classification is a promising technique for image classification. Unlike pixel-based methods, which only use the measured radiometric values, the object-based techniques can also use shape and context information of scene textures. These extra degrees of freedom provided by the objects allow the automatic identification of geological structures. In this article, we present an evaluation of object-based classification in the context of extraction of geological faults. Digital elevation models and radar data of an area near Lake Magadi (Kenya) have been processed. We then determine the statistics of the fault populations. The fractal dimensions of fault dimensions are similar to fractal dimensions directly measured on remote sensing images of the study area using power spectra (PSD) and variograms. These methods allow unbiased statistics of faults and help us to understand the evolution of the fault systems in extensional domains. Furthermore, the direct analysis of image texture is a good indicator of the fault statistics and allows us to classify the intensity and type of deformation. We propose that extensional fault networks can be modeled by iterative function system (IFS).
Fractal dimension analysis of malignant and benign endobronchial ultrasound nodes
2014-01-01
Background Endobronchial ultrasonography (EBUS) has been applied as a routine procedure for the diagnostic of hiliar and mediastinal nodes. The authors assessed the relationship between the echographic appearance of mediastinal nodes, based on endobronchial ultrasound images, and the likelihood of malignancy. Methods The images of twelve malignant and eleven benign nodes were evaluated. A previous processing method was applied to improve the quality of the images and to enhance the details. Texture and morphology parameters analyzed were: the image texture of the echographies and a fractal dimension that expressed the relationship between area and perimeter of the structures that appear in the image, and characterizes the convoluted inner structure of the hiliar and mediastinal nodes. Results Processed images showed that relationship between log perimeter and log area of hilar nodes was lineal (i.e. perimeter vs. area follow a power law). Fractal dimension was lower in the malignant nodes compared with non-malignant nodes (1.47(0.09), 1.53(0.10) mean(SD), Mann–Whitney U test p < 0.05)). Conclusion Fractal dimension of ultrasonographic images of mediastinal nodes obtained through endobronchial ultrasound differ in malignant nodes from non-malignant. This parameter could differentiate malignat and non-malignat mediastinic and hiliar nodes. PMID:24920158
Small-angle scattering from fat fractals
NASA Astrophysics Data System (ADS)
Anitas, Eugen M.
2014-06-01
A number of experimental small-angle scattering (SAS) data are characterized by a succession of power-law decays with arbitrarily decreasing values of scattering exponents. To describe such data, here we develop a new theoretical model based on 3D fat fractals (sets with fractal structure, but nonzero volume) and show how one can extract structural information about the underlying fractal structure. We calculate analytically the monodisperse and polydisperse SAS intensity (fractal form factor and structure factor) of a newly introduced model of fat fractals and study its properties in momentum space. The system is a 3D deterministic mass fractal built on an extension of the well-known Cantor fractal. The model allows us to explain a succession of power-law decays and respectively, of generalized power-law decays (GPLD; superposition of maxima and minima on a power-law decay) with arbitrarily decreasing scattering exponents in the range from zero to three. We show that within the model, the present analysis allows us to obtain the edges of all the fractal regions in the momentum space, the number of fractal iteration and the fractal dimensions and scaling factors at each structural level in the fractal. We applied our model to calculate an analytical expression for the radius of gyration of the fractal. The obtained quantities characterizing the fat fractal are correlated to variation of scaling factor with the iteration number.
Ethical issues of brain functional imaging: reading your mind.
Karanasiou, Irene S; Biniaris, Christos G; Marsh, Andrew J
2008-01-01
Neuroimaging practice and research are overviewed in this paper through an ethics lens. The main ethical implications in biomedical research concerning functional brain imaging are discussed with the focus on issues related to imaging of personal information and privacy. Specific norms and guidelines will be eventually formed in the future under the umbrella of the new discipline of Neuroethics.
Hemodynamic responses to functional activation accessed by optical imaging
NASA Astrophysics Data System (ADS)
Ni, Songlin; Li, Pengcheng; Yang, Yuanyuan; Lv, Xiaohua; Luo, Qingming
2006-01-01
A multi-wavelength light-emitting diode (LED) and laser diode (LD) based optical imaging system was developed to visualize the changes in cerebral blood flow, oxygenation following functional activation simultaneously in rodent cortex. The 2-D blood flow image was accessed by laser speckle contrast imaging, and the spectroscopic imaging of intrinsic signal was used for the calculation of oxyhemoglobin (HbO), deoxyhemoglobin (Hb) and total hemoglobin (HbT) concentration. The combination of spectroscopic imaging and laser speckle contrast imaging provides the capability to simultaneously investigate the spatial and temporal blood flow and hemoglobin concentration changes with high resolution, which may lead to a better understanding of the coupling between neuronal activation and vascular responses. The optical imaging system been built is compact and convenient to investigators. And it is reliable to acquire raw data. In present study, the hemodynamic responses to cortical spreading depression (CSD) in parietal cortex of ~-chloralose/urethan anesthetized rats were demonstrated.
Magnetic resonance imaging in the evaluation of cognitive function.
Bigler, Erin D
2014-10-01
Image quality of magnetic resonance imaging (MRI) scans of the brain currently approximate gross anatomy as would be viewed at autopsy. During the first decade of the 21st Century incredible advances in image processing and quantification have occurred permitting more refined methods for studying brain-behavior-cognitive functioning. The current presentation overviews the current status of MRI methods for routine clinical assessment of brain pathology, how these techniques identify neuropathology and how pathological findings are quantified. Diffusion tensor imaging (DTI), functional MRI (fMRI), and resting state fMRI are all reviewed, emphasizing how these techniques permit an examination of brain function and connectivity. General regional relationships of brain function associated with cognitive control will be highlighted.
The topological insulator in a fractal space
Song, Zhi-Gang; Zhang, Yan-Yang; Li, Shu-Shen
2014-06-09
We investigate the band structures and transport properties of a two-dimensional model of topological insulator, with a fractal edge or a fractal bulk. A fractal edge does not affect the robust transport even when the fractal pattern has reached the resolution of the atomic-scale, because the bulk is still well insulating against backscattering. On the other hand, a fractal bulk can support the robust transport only when the fractal resolution is much larger than a critical size. Smaller resolution of bulk fractal pattern will lead to remarkable backscattering and localization, due to strong couplings of opposite edge states on narrow sub-edges which appear almost everywhere in the fractal bulk.
Analysis of fractals with combined partition
NASA Astrophysics Data System (ADS)
Dedovich, T. G.; Tokarev, M. V.
2016-03-01
The space—time properties in the general theory of relativity, as well as the discreteness and non-Archimedean property of space in the quantum theory of gravitation, are discussed. It is emphasized that the properties of bodies in non-Archimedean spaces coincide with the properties of the field of P-adic numbers and fractals. It is suggested that parton showers, used for describing interactions between particles and nuclei at high energies, have a fractal structure. A mechanism of fractal formation with combined partition is considered. The modified SePaC method is offered for the analysis of such fractals. The BC, PaC, and SePaC methods for determining a fractal dimension and other fractal characteristics (numbers of levels and values of a base of forming a fractal) are considered. It is found that the SePaC method has advantages for the analysis of fractals with combined partition.
Hermann, Philipp; Mrkvička, Tomáš; Mattfeldt, Torsten; Minárová, Mária; Helisová, Kateřina; Nicolis, Orietta; Wartner, Fabian; Stehlík, Milan
2015-08-15
Fractals are models of natural processes with many applications in medicine. The recent studies in medicine show that fractals can be applied for cancer detection and the description of pathological architecture of tumors. This fact is not surprising, as due to the irregular structure, cancerous cells can be interpreted as fractals. Inspired by Sierpinski carpet, we introduce a flexible parametric model of random carpets. Randomization is introduced by usage of binomial random variables. We provide an algorithm for estimation of parameters of the model and illustrate theoretical and practical issues in generation of Sierpinski gaskets and Hausdorff measure calculations. Stochastic geometry models can also serve as models for binary cancer images. Recently, a Boolean model was applied on the 200 images of mammary cancer tissue and 200 images of mastopathic tissue. Here, we describe the Quermass-interaction process, which can handle much more variations in the cancer data, and we apply it to the images. It was found out that mastopathic tissue deviates significantly stronger from Quermass-interaction process, which describes interactions among particles, than mammary cancer tissue does. The Quermass-interaction process serves as a model describing the tissue, which structure is broken to a certain level. However, random fractal model fits well for mastopathic tissue. We provide a novel discrimination method between mastopathic and mammary cancer tissue on the basis of complex wavelet-based self-similarity measure with classification rates more than 80%. Such similarity measure relates to Hurst exponent and fractional Brownian motions. The R package FractalParameterEstimation is developed and introduced in the paper.
Applications of Fractal Analytical Techniques in the Estimation of Operational Scale
NASA Technical Reports Server (NTRS)
Emerson, Charles W.; Quattrochi, Dale A.
2000-01-01
The observational scale and the resolution of remotely sensed imagery are essential considerations in the interpretation process. Many atmospheric, hydrologic, and other natural and human-influenced spatial phenomena are inherently scale dependent and are governed by different physical processes at different spatial domains. This spatial and operational heterogeneity constrains the ability to compare interpretations of phenomena and processes observed in higher spatial resolution imagery to similar interpretations obtained from lower resolution imagery. This is a particularly acute problem, since longterm global change investigations will require high spatial resolution Earth Observing System (EOS), Landsat 7, or commercial satellite data to be combined with lower resolution imagery from older sensors such as Landsat TM and MSS. Fractal analysis is a useful technique for identifying the effects of scale changes on remotely sensed imagery. The fractal dimension of an image is a non-integer value between two and three which indicates the degree of complexity in the texture and shapes depicted in the image. A true fractal surface exhibits self-similarity, a property of curves or surfaces where each part is indistinguishable from the whole, or where the form of the curve or surface is invariant with respect to scale. Theoretically, if the digital numbers of a remotely sensed image resemble an ideal fractal surface, then due to the self-similarity property, the fractal dimension of the image will not vary with scale and resolution, and the slope of the fractal dimension-resolution relationship would be zero. Most geographical phenomena, however, are not self-similar at all scales, but they can be modeled by a stochastic fractal in which the scaling properties of the image exhibit patterns that can be described by statistics such as area-perimeter ratios and autocovariances. Stochastic fractal sets relax the self-similarity assumption and measure many scales and
Fractal dimension in nonhyperbolic chaotic scattering
NASA Technical Reports Server (NTRS)
Lau, Yun-Tung; Finn, John M.; Ott, Edward
1991-01-01
In chaotic scattering there is a Cantor set of input-variable values of zero Lebesgue measure (i.e., zero total length) on which the scattering function is singular. For cases where the dynamics leading to chaotic scattering is nonhyperbolic (e.g., there are Kolmogorov-Arnol'd-Moser tori), the nature of this singular set is fundamentally different from that in the hyperbolic case. In particular, for the nonhyperbolic case, although the singular set has zero total length, strong evidence is presented to show that its fractal dimension is 1.
Optical multipolar spread functions of an aplanatic imaging system
NASA Astrophysics Data System (ADS)
Rouxel, Jérémy R.; Toury, Timothée
2016-07-01
The electromagnetic field near the focus of a perfect imaging system is calculated for different multipolar sources that play an important role in the radiation of nanostructures. Those multipoles are the exact and extended multipoles occurring in electrodynamics. The theory of diffraction of vector waves is reviewed rigorously for a dipolar radiation and applied to the imaging of multipolar sources. Different geometries are considered in order to connect with experiments and the multipolar spread functions are given in a ready-to-use format up to the octupolar order, in the general case and in the paraxial approximation. Defocus imaging is finally considered to provide a first step toward multipolar imaging.
Construction of realistic images using R-functions
Shevchenko, A.N.; Tsukanov, I.G.
1995-09-01
Realistic images are plane images of three-dimensional bodies in which volume effects are conveyed by illumination. This is how volume is displayed in photographs and paintings. Photographs achieve a realistic volume effect by choosing a certain arrangement, brightness, and number of light sources. Painters choose for their paintings a color palette based entirely on sensory perception. In this paper, we consider the construction of realistic images on a computer display. The shape of the imaged objects is not always known in advance: it may be generated as a result of complex mathematical computations. The geometrical information is described using R-functions.
Molecular, Functional, and Structural Imaging of Major Depressive Disorder.
Zhang, Kai; Zhu, Yunqi; Zhu, Yuankai; Wu, Shuang; Liu, Hao; Zhang, Wei; Xu, Caiyun; Zhang, Hong; Hayashi, Takuya; Tian, Mei
2016-06-01
Major depressive disorder (MDD) is a significant cause of morbidity and mortality worldwide, correlating with genetic susceptibility and environmental risk factors. Molecular, functional, and structural imaging approaches have been increasingly used to detect neurobiological changes, analyze neurochemical correlates, and parse pathophysiological mechanisms underlying MDD. We reviewed recent neuroimaging publications on MDD in terms of molecular, functional, and structural alterations as detected mainly by magnetic resonance imaging (MRI) and positron emission tomography. Altered structure and function of brain regions involved in the cognitive control of affective state have been demonstrated. An abnormal default mode network, as revealed by resting-state functional MRI, is likely associated with aberrant metabolic and serotonergic function revealed by radionuclide imaging. Further multi-modal investigations are essential to clarify the characteristics of the cortical network and serotonergic system associated with behavioral and genetic variations in MDD. PMID:27142698
Partially Blended Constrained Rational Cubic Trigonometric Fractal Interpolation Surfaces
NASA Astrophysics Data System (ADS)
Chand, A. K. B.; Tyada, K. R.
2016-08-01
Fractal interpolation is an advance technique for visualization of scientific shaped data. In this paper, we present a new family of partially blended rational cubic trigonometric fractal interpolation surfaces (RCTFISs) with a combination of blending functions and univariate rational trigonometric fractal interpolation functions (FIFs) along the grid lines of the interpolation domain. The developed FIFs use rational trigonometric functions pi,j(θ) qi,j(θ), where pi,j(θ) and qi,j(θ) are cubic trigonometric polynomials with four shape parameters. The convergence analysis of partially blended RCTFIS with the original surface data generating function is discussed. We derive sufficient data-dependent conditions on the scaling factors and shape parameters such that the fractal grid line functions lie above the grid lines of a plane Π, and consequently the proposed partially blended RCTFIS lies above the plane Π. Positivity preserving partially blended RCTFIS is a special case of the constrained partially blended RCTFIS. Numerical examples are provided to support the proposed theoretical results.
Neurovascular coupling: in vivo optical techniques for functional brain imaging
2013-01-01
Optical imaging techniques reflect different biochemical processes in the brain, which is closely related with neural activity. Scientists and clinicians employ a variety of optical imaging technologies to visualize and study the relationship between neurons, glial cells and blood vessels. In this paper, we present an overview of the current optical approaches used for the in vivo imaging of neurovascular coupling events in small animal models. These techniques include 2-photon microscopy, laser speckle contrast imaging (LSCI), voltage-sensitive dye imaging (VSDi), functional photoacoustic microscopy (fPAM), functional near-infrared spectroscopy imaging (fNIRS) and multimodal imaging techniques. The basic principles of each technique are described in detail, followed by examples of current applications from cutting-edge studies of cerebral neurovascular coupling functions and metabolic. Moreover, we provide a glimpse of the possible ways in which these techniques might be translated to human studies for clinical investigations of pathophysiology and disease. In vivo optical imaging techniques continue to expand and evolve, allowing us to discover fundamental basis of neurovascular coupling roles in cerebral physiology and pathophysiology. PMID:23631798
Neurovascular coupling: in vivo optical techniques for functional brain imaging.
Liao, Lun-De; Tsytsarev, Vassiliy; Delgado-Martínez, Ignacio; Li, Meng-Lin; Erzurumlu, Reha; Vipin, Ashwati; Orellana, Josue; Lin, Yan-Ren; Lai, Hsin-Yi; Chen, You-Yin; Thakor, Nitish V
2013-04-30
Optical imaging techniques reflect different biochemical processes in the brain, which is closely related with neural activity. Scientists and clinicians employ a variety of optical imaging technologies to visualize and study the relationship between neurons, glial cells and blood vessels. In this paper, we present an overview of the current optical approaches used for the in vivo imaging of neurovascular coupling events in small animal models. These techniques include 2-photon microscopy, laser speckle contrast imaging (LSCI), voltage-sensitive dye imaging (VSDi), functional photoacoustic microscopy (fPAM), functional near-infrared spectroscopy imaging (fNIRS) and multimodal imaging techniques. The basic principles of each technique are described in detail, followed by examples of current applications from cutting-edge studies of cerebral neurovascular coupling functions and metabolic. Moreover, we provide a glimpse of the possible ways in which these techniques might be translated to human studies for clinical investigations of pathophysiology and disease. In vivo optical imaging techniques continue to expand and evolve, allowing us to discover fundamental basis of neurovascular coupling roles in cerebral physiology and pathophysiology.
A Fractal Nature for Polymerized Laminin
Hochman-Mendez, Camila; Cantini, Marco; Moratal, David; Salmeron-Sanchez, Manuel; Coelho-Sampaio, Tatiana
2014-01-01
Polylaminin (polyLM) is a non-covalent acid-induced nano- and micro-structured polymer of the protein laminin displaying distinguished biological properties. Polylaminin stimulates neuritogenesis beyond the levels achieved by ordinary laminin and has been shown to promote axonal regeneration in animal models of spinal cord injury. Here we used confocal fluorescence microscopy (CFM), scanning electron microscopy (SEM) and atomic force microscopy (AFM) to characterize its three-dimensional structure. Renderization of confocal optical slices of immunostained polyLM revealed the aspect of a loose flocculated meshwork, which was homogeneously stained by the antibody. On the other hand, an ordinary matrix obtained upon adsorption of laminin in neutral pH (LM) was constituted of bulky protein aggregates whose interior was not accessible to the same anti-laminin antibody. SEM and AFM analyses revealed that the seed unit of polyLM was a flat polygon formed in solution whereas the seed structure of LM was highly heterogeneous, intercalating rod-like, spherical and thin spread lamellar deposits. As polyLM was visualized at progressively increasing magnifications, we observed that the morphology of the polymer was alike independently of the magnification used for the observation. A search for the Hausdorff dimension in images of the two matrices showed that polyLM, but not LM, presented fractal dimensions of 1.55, 1.62 and 1.70 after 1, 8 and 12 hours of adsorption, respectively. Data in the present work suggest that the intrinsic fractal nature of polymerized laminin can be the structural basis for the fractal-like organization of basement membranes in the neurogenic niches of the central nervous system. PMID:25296244
Fractal dimension of microbead assemblies used for protein detection
Hecht, Ariel; Commiskey, Patrick; Lazaridis, Filippos; Argyrakis, Panos
2014-01-01
We use fractal analysis to calculate the protein concentration in a rotating magnetic assembly of microbeads of size 1μm, which has optimized parameters of sedimentation, binding sites and magnetic volume. We utilize the original Forrest-Witten method, but due to the relatively small number of bead particles, which is of the order of 500, we use a large number of origins and also a large number of algorithm iterations. We find a value of the fractal dimension in the range 1.70–1.90, as a function of the thrombin concentration, which plays the role of binding the microbeads together. This is in good agreement with previous results from magnetorotation studies. The calculation of the fractal dimension using multiple points of reference can be used for any assembly with a relatively small number of particles. PMID:25195559
Fractal dimension of microbead assemblies used for protein detection.
Hecht, Ariel; Commiskey, Patrick; Lazaridis, Filippos; Argyrakis, Panos; Kopelman, Raoul
2014-11-10
We use fractal analysis to calculate the protein concentration in a rotating magnetic assembly of microbeads of size 1 μm, which has optimized parameters of sedimentation, binding sites and magnetic volume. We utilize the original Forrest-Witten method, but due to the relatively small number of bead particles, which is of the order of 500, we use a large number of origins and also a large number of algorithm iterations. We find a value of the fractal dimension in the range 1.70-1.90, as a function of the thrombin concentration, which plays the role of binding the microbeads together. This is in good agreement with previous results from magnetorotation studies. The calculation of the fractal dimension using multiple points of reference can be used for any assembly with a relatively small number of particles.
Concept of functional imaging of memory decline in Alzheimer's disease.
Drzezga, Alexander
2008-04-01
Functional imaging methods such as Positron Emission Tomography (PET) and functional Magnetic Resonance Imaging (fMRI) have contributed inestimably to the understanding of physiological cognitive processes in the brain in the recent decades. These techniques for the first time allowed the in vivo assessment of different features of brain function in the living human subject. It was therefore obvious to apply these methods to evaluate pathomechanisms of cognitive dysfunction in disorders such as Alzheimer's disease (AD) as well. One of the most dominant symptoms of AD is the impairment of memory. In this context, the term "memory" represents a simplification and summarizes a set of complex cognitive functions associated with encoding and retrieval of different types of information. A number of imaging studies assessed the functional changes of neuronal activity in the brain at rest and also during performance of cognitive work, with regard to specific characteristics of memory decline in AD. In the current article, basic principles of common functional imaging procedures will be explained and it will be discussed how they can be reasonably applied for the assessment of memory decline in AD. Furthermore, it will be illustrated how these imaging procedures have been employed to improve early and specific diagnosis of the disease, to understand specific pathomechanisms of memory dysfunction and associated compensatory mechanisms, and to draw reverse conclusions on physiological function of memory.
Nonlinear dynamics, fractals, cardiac physiology and sudden death
NASA Technical Reports Server (NTRS)
Goldberger, Ary L.
1987-01-01
The authors propose a diametrically opposite viewpoint to the generally accepted tendency of equating healthy function with order and disease with chaos. With regard to the question of sudden cardiac death and chaos, it is suggested that certain features of dynamical chaos related to fractal structure and fractal dynamics may be important organizing principles in normal physiology and that certain pathologies, including ventricular fibrillation, represent a class of 'pathological periodicities'. Some laboratory work bearing on the relation of nonlinear analysis to physiological and pathophysiological data is briefly reviewed, with tentative theories and models described in reference to the mechanism of ventricular fibrillation.
Fractal mechanisms in the electrophysiology of the heart
NASA Technical Reports Server (NTRS)
Goldberger, A. L.
1992-01-01
The mathematical concept of fractals provides insights into complex anatomic branching structures that lack a characteristic (single) length scale, and certain complex physiologic processes, such as heart rate regulation, that lack a single time scale. Heart rate control is perturbed by alterations in neuro-autonomic function in a number of important clinical syndromes, including sudden cardiac death, congestive failure, cocaine intoxication, fetal distress, space sickness and physiologic aging. These conditions are associated with a loss of the normal fractal complexity of interbeat interval dynamics. Such changes, which may not be detectable using conventional statistics, can be quantified using new methods derived from "chaos theory.".
On a mechanism of cardiac electrical stability. The fractal hypothesis.
Goldberger, A L; Bhargava, V; West, B J; Mandell, A J
1985-01-01
Electrical activation of the ventricles via the His-Purkinje system is represented on the body surface by a waveform with a broad range of frequency components. We speculate that this process is mediated by current flow through a fractal-like conduction network and therefore that the broadband spectrum of the depolarization waveform should be scaled as a power-law distribution. The prediction is confirmed by Fourier analysis of electrocardiographic data from healthy men. This observation suggests a new dynamical link between nonlinear (fractal) structure and nonlinear function in a stable physiologic system. PMID:4041542
Image-based modeling of lung structure and function
Tawhai, Merryn H.; Lin, Ching-Long
2010-01-01
Current state-of-the-art in image-based modeling allows derivation of patient-specific models of the lung, lobes, airways, and pulmonary vascular trees. The application of traditional engineering analyses of fluid and structural mechanics to image-based subject-specific models has the potential to provide new insight into structure-function relationships in the individual via functional interpretation that complements imaging and experimental studies. Three major issues that are encountered in studies of air flow through the bronchial airways are the representation of airway geometry, the imposition of physiological boundary conditions, and the treatment of turbulence. Here we review some efforts to resolve each of these issues, with particular focus on image-based models that have been developed to simulate air flow from the mouth to the terminal bronchiole, and subjected to physiologically meaningful boundary conditions via image registration and soft tissue mechanics models. PMID:21105146
A New Fractal Model of Chromosome and DNA Processes
NASA Astrophysics Data System (ADS)
Bouallegue, K.
Dynamic chromosome structure remains unknown. Can fractals and chaos be used as new tools to model, identify and generate a structure of chromosomes?Fractals and chaos offer a rich environment for exploring and modeling the complexity of nature. In a sense, fractal geometry is used to describe, model, and analyze the complex forms found in nature. Fractals have also been widely not only in biology but also in medicine. To this effect, a fractal is considered an object that displays self-similarity under magnification and can be constructed using a simple motif (an image repeated on ever-reduced scales).It is worth noting that the problem of identifying a chromosome has become a challenge to find out which one of the models it belongs to. Nevertheless, the several different models (a hierarchical coiling, a folded fiber, and radial loop) have been proposed for mitotic chromosome but have not reached a dynamic model yet.This paper is an attempt to solve topological problems involved in the model of chromosome and DNA processes. By combining the fractal Julia process and the numerical dynamical system, we have finally found out four main points. First, we have developed not only a model of chromosome but also a model of mitosis and one of meiosis. Equally important, we have identified the centromere position through the numerical model captured below. More importantly, in this paper, we have discovered the processes of the cell divisions of both mitosis and meiosis. All in all, the results show that this work could have a strong impact on the welfare of humanity and can lead to a cure of genetic diseases.
Functional magnetic resonance imaging in neurology.
Auer, Tibor; Schwarcz, Attila; Horváth, Réka A; Barsi, Péter; Janszky, József
2008-01-30
The present contribution discusses the clinical use of functional MRI (fMRI) and its role in the most common neurological diseases. FMRI was found a reliable and reproducible examination tool resulting in a wide distribution of fMRI methods in presurgical evaluation of epilepsy in determining the relationship of eloquent areas and the epileptic focus. Preliminary data suggest that fMRI using memory paradigms can predict the postoperative memory decline in epilepsy surgery by determining whether a reorganization of memory functions took place. Speech-activated fMRI became the most used tool in determining hemispheric dominance. Visual and sensory-motor cortex can also be routinely investigated by fMRI which helps in decision on epilepsy surgery. FMRI combined with EEG is a new diagnostic tool in epilepsy and sleep disorders. FMRI can identify the penumbra after stroke and can provide an additional information on metabolic state of the threatened brain tissue. FMRI has a predictive role in post-stroke recovery. In relapsing-remitting MS an adaptive reorganization can be demonstrated by fMRI affecting the visual, motor, and memory systems, despite preserved functional performance. Much more extensive reorganization can be demonstrated in secondary progressive MS. These findings suggest that the different stages of MS are related to different stages of the reorganization and MS becomes progressive when there is no more reserve capacity in the brain for reorganization. FMRI offers the capability of detecting early functional hemodynamic alterations in Alzheimer's disease before morphological changes. FMRI can be a valuable tool to test and monitor treatment efficacy in AD. FMRI can also provide information about the mechanisms of different therapeutic approaches in Parkinson disorder including drug treatment and deep brain stimulation.
Functional Magnetic Resonance Imaging in Acute Kidney Injury: Present Status
Zhou, Hai Ying; Chen, Tian Wu; Zhang, Xiao Ming
2016-01-01
Acute kidney injury (AKI) is a common complication of hospitalization that is characterized by a sudden loss of renal excretory function and associated with the subsequent development of chronic kidney disease, poor prognosis, and increased mortality. Although the pathophysiology of renal functional impairment in the setting of AKI remains poorly understood, previous studies have identified changes in renal hemodynamics, perfusion, and oxygenation as key factors in the development and progression of AKI. The early assessment of these changes remains a challenge. Many established approaches are not applicable to humans because of their invasiveness. Functional renal magnetic resonance (MR) imaging offers an alternative assessment tool that could be used to evaluate renal morphology and function noninvasively and simultaneously. Thus, the purpose of this review is to illustrate the principle, application, and role of the techniques of functional renal MR imaging, including blood oxygen level-dependent imaging, arterial spin labeling, and diffusion-weighted MR imaging, in the management of AKI. The use of gadolinium in MR imaging may exacerbate renal impairment and cause nephrogenic systemic fibrosis. Therefore, dynamic contrast-enhanced MR imaging will not be discussed in this paper. PMID:26925411
Endoscopic device for functional imaging of the retina
NASA Astrophysics Data System (ADS)
Barriga, Simon; Lohani, Sweyta; Martell, Bret; Soliz, Peter; Ts'o, Dan
2011-03-01
Non-invasive imaging of retinal function based on the recording of spatially distributed reflectance changes evoked by visual stimuli has to-date been performed primarily using modified commercial fundus cameras. We have constructed a prototype retinal functional imager, using a commercial endoscope (Storz) for the frontend optics, and a low-cost back-end that includes the needed dichroic beam splitter to separate the stimulus path from the imaging path. This device has been tested to demonstrate its performance for the delivery of adequate near infrared (NIR) illumination, intensity of the visual stimulus and reflectance return in the imaging path. The current device was found to be capable of imaging reflectance changes of 0.1%, similar to that observable using the modified commercial fundus camera approach. The visual stimulus (a 505nm spot of 0.5secs) was used with an interrogation illumination of 780nm, and a sequence of imaged captured. At each pixel, the imaged signal was subtracted and normalized by the baseline reflectance, so that the measurement was ΔR/R. The typical retinal activity signal observed had a ΔR/R of 0.3-1.0%. The noise levels were measured when no stimulus was applied and found to vary between +/- 0.05%. Functional imaging has been suggested as a means to provide objective information on retina function that may be a preclinical indicator of ocular diseases, such as age-related macular degeneration (AMD), glaucoma, and diabetic retinopathy. The endoscopic approach promises to yield a significantly more economical retinal functional imaging device that would be clinically important.
A Wave Equation Migration Method for Receiver Function Imaging
NASA Astrophysics Data System (ADS)
Chen, L.; Wen, L.; Zheng, T.
2004-12-01
A wave equation based poststack depth migration method is proposed to image the crustal and upper mantle structures using teleseismic receiver functions. By utilizing a frequency-wavenumber domain one-way phase-screen propagator for wavefield extrapolation in the migration scheme, the common conversion point (CCP) stacked receiver functions are backward propagated to construct the subsurface structural images. Synthetic experiments demonstrate the validity of the migration method for a variety of laterally heterogeneous models. The migrated images show considerable improvement over the CCP images in recovering the structural features. The phase-screen propagator migration method proves to be particularly useful for imaging complex structures and deep discontinuities overlain by strong shallow anomalies, because of its capability of handling lateral velocity variations. Influences of several factors on the image quality of the poststack migration are further investigated, including inter-station spacing, noise level of the data, velocity model used in migration, and earthquake distribution (incident direction of source fields). Theoretical derivation and numerical results suggest that both the CCP stacking and the poststack migration of receiver functions need to be designed in a target-oriented way for reliable and efficient imaging, and special consideration on earthquake distribution is particularly required in designing seismic experiments if structures of large dips are present. The proposed wav equation migration scheme is applied to image the Earth's internal structures using a number of dense field data sets collected at many seismic arrays in Asia. The constructed images reveal several interesting subsurface structures of the study regions and synthetic tests indicate that those subsurface features are well resolved by the seismic data. Significant improvements of the image quality demonstrate the great potential and flexibility of the proposed migration
Fractal analysis of time varying data
Vo-Dinh, Tuan; Sadana, Ajit
2002-01-01
Characteristics of time varying data, such as an electrical signal, are analyzed by converting the data from a temporal domain into a spatial domain pattern. Fractal analysis is performed on the spatial domain pattern, thereby producing a fractal dimension D.sub.F. The fractal dimension indicates the regularity of the time varying data.
Fractal Electronic Circuits Assembled From Nanoclusters
NASA Astrophysics Data System (ADS)
Fairbanks, M. S.; McCarthy, D.; Taylor, R. P.; Brown, S. A.
2009-07-01
Many patterns in nature can be described using fractal geometry. The effect of this fractal character is an array of properties that can include high internal connectivity, high dispersivity, and enhanced surface area to volume ratios. These properties are often desirable in applications and, consequently, fractal geometry is increasingly employed in technologies ranging from antenna to storm barriers. In this paper, we explore the application of fractal geometry to electrical circuits, inspired by the pervasive fractal structure of neurons in the brain. We show that, under appropriate growth conditions, nanoclusters of Sb form into islands on atomically flat substrates via a process close to diffusion-limited aggregation (DLA), establishing fractal islands that will form the basis of our fractal circuits. We perform fractal analysis of the islands to determine the spatial scaling properties (characterized by the fractal dimension, D) of the proposed circuits and demonstrate how varying growth conditions can affect D. We discuss fabrication approaches for establishing electrical contact to the fractal islands. Finally, we present fractal circuit simulations, which show that the fractal character of the circuit translates into novel, non-linear conduction properties determined by the circuit's D value.
Fractal characterization of fracture surfaces in concrete
Saouma, V.E.; Barton, C.C.; Gamaleldin, N.A.
1990-01-01
Fractal geometry is used to characterize the roughness of cracked concrete surfaces through a specially built profilometer, and the fractal dimension is subsequently correlated to the fracture toughness and direction of crack propagation. Preliminary results indicate that the fracture surface is indeed fractal over two orders of magnitudes with a dimension of approximately 1.20. ?? 1990.
Myocardial motion and function assessment using 4D images
NASA Astrophysics Data System (ADS)
Shi, Peng-Cheng; Robinson, Glynn P.; Duncan, James S.
1994-09-01
This paper describes efforts aimed at more objectively and accurately quantifying the local, regional and global function of the left ventricle (LV) of the heart from 4D image data. Using our shape-based image analysis methods, point-wise myocardial motion vector fields between successive image frames through the entire cardiac cycle will be computed. Quantitative LV motion, thickening, and strain measurements will then be established from the point correspondence maps. In the paper, we will also briefly describe an in vivo experimental model which uses implanted imaging-opaque markers to validate the results of our image analysis methods. Finally, initial experimental results using image sequences from two different modalities will be presented.
On the Fundamental Theorem of Calculus for Fractal Sets
NASA Astrophysics Data System (ADS)
Bongiorno, Donatella; Corrao, Giuseppa
2015-04-01
The aim of this paper is to formulate the best version of the Fundamental theorem of Calculus for real functions on a fractal subset of the real line. In order to do that an integral of Henstock-Kurzweil type is introduced.
Functional imaging as an indicator of diagnostic information in cardiac magnetic-resonance images
NASA Astrophysics Data System (ADS)
Klingler, Joseph W.; Andrews, Lee T.; Begeman, Michael S.; Zeiss, Jacob; Leighton, Richard F.
1990-08-01
Magnetic Resonance (MR) images of the human heart provide three dimensional geometric information about the location of cardiac structures throughout the cardiac cycle. Analysis of this four dimensional data set allows detection of abnormal cardiac function related to the presence of coronary artery disease. To assist in this analysis, quantitative measurements of cardiac performance are made from the MR data including ejection fractions, regional wall motion and myocardial wall thickening. Analysis of cardiac performance provided by quantitative analysis of MR data can be aided by computer graphics presentation techniques. Two and three dimensional functional images are computed to indicate regions of abnormality based on the previous methods. The two dimensional images are created using color graphics overlays on the original MR image to represent performance. Polygon surface modeling techniques are used to represent data which is three dimensional, such as blood pool volumes. The surface of these images are color encoded by regional ejection fraction, wall motion or wall thickening. A functional image sequence is constructed at each phase of the cardiac cycle and displayed as a movie loop for review by the physician. Selection of a region on the functional image allows visual interpretation of the original MR images, graphical plots of cardiac function and tabular results. Color encoding is based on absolute measurements and comparison to standard normal templates of cardiac performance.
Functional oesophago-gastric junction imaging
McMahon, Barry P; Drewes, Asbjørn Mohr; Gregersen, Hans
2006-01-01
Despite its role in disease there is still no definitive method to assess oesophago-gastric junction competence (OGJ). Traditionally the OGJ has been assessed using manometry with lower oesophageal sphincter pressure as the indicator. More recently this has been shown not to be a very reliable marker of sphincter function and competence against reflux. Disorders such as gastro-oesophageal reflux disease and to a lesser extend achalasia still effects a significant number of patients. This review looks at using a new technique known as impedance planimetry to profile the geometry and pressure in the OGJ during distension of a bag. The data gathered can be reconstructed into a dynamic representation of OGJ action. This has been shown to provide a useful representation of the OGJ and to show changes to the competence of the OGJ in terms of compliance and distensibility as a result of endoluminal therapy. PMID:16718804
Functional magnetic resonance imaging (FMRI) and expert testimony.
Kulich, Ronald; Maciewicz, Raymond; Scrivani, Steven J
2009-03-01
Medical experts frequently use imaging studies to illustrate points in their court testimony. This article reviews how these studies impact the credibility of expert testimony with judges and juries. The apparent "objective" evidence provided by such imaging studies can lend strong credence to a judge's or jury's appraisal of medical expert's testimony. However, as the court usually has no specialized scientific expertise, the use of complex images as part of courtroom testimony also has the potential to mislead or at least inappropriately bias the weight given to expert evidence. Recent advances in brain imaging may profoundly impact forensic expert testimony. Functional magnetic resonance imaging and other physiologic imaging techniques currently allow visualization of the activation pattern of brain regions associated with a wide variety of cognitive and behavioral tasks, and more recently, pain. While functional imaging technology has a valuable role in brain research and clinical investigation, it is important to emphasize that the use of imaging studies in forensic matters requires a careful scientific foundation and a rigorous legal assessment. PMID:19254335
Analysis of soil images applying Laplacian Pyramidal techniques
NASA Astrophysics Data System (ADS)
Ballesteros, F.; de Castro, J.; Tarquis, A. M.; Méndez, A.
2012-04-01
The Laplacian pyramid is a technique for image encoding in which local operators of many scales but identical shape are the basis functions. Our work describes some properties of the filters of the Laplacian pyramid. Specially, we pay attention to Gaussian and fractal behaviour of these filters, and we determine the normal and fractal ranges in the case of single parameter filters, while studying the influence of these filters in soil image processing. One usual property of any image is that neighboring pixels are highly correlated. This property makes inefficient to represent the image directly in terms of the pixel values, because most of the encoded information would be redundant. Burt and Adelson designed a technique, named Laplacian pyramid, for removing image correlation which combines features of predictive and transform methods. This technique is non causal, and its computations are simple and local. The predicted value for each pixel is computed as a local weighted average, using a unimodal weighting function centred on the pixel itself. Pyramid construction is equivalent to convolving the original image with a set of weighting functions determined by a parameter that defines the filter. According to the parameter values, these filters have a behaviour that goes from the Gaussian shape to the fractal. Previous works only analyze Gaussian filters, but we determine the Gaussian and fractal intervals and study the energy of the Laplacian pyramid images according to the filter types. The different behaviour, qualitatively, involves a significant change in statistical characteristics at different levels of iteration, especially the fractal case, which can highlight specific information from the images. Funding provided by Spanish Ministerio de Ciencia e Innovación (MICINN) through project no. AGL2010-21501/AGR is greatly appreciated.
Resource Letter FR-1: Fractals
NASA Astrophysics Data System (ADS)
Hurd, Alan J.
1988-11-01
This Resource Letter provides a guide to the literature on fractals. Although ``fractal'' is a relatively new term in science, unifying many new ideas with established ones, its wide application and general popularity have made it one of the fastest growing fields in statistical physics. The letter E after an item indicates elementary level or material of general interest to persons becoming informed in the field; the letter I, for intermediate level, indicates material of somewhat more specialized nature; and the letter A indicates rather specialized or advanced material. An asterisk (*) indicates those articles to be included in an accompanying Reprint Book.
Fractal universe and quantum gravity.
Calcagni, Gianluca
2010-06-25
We propose a field theory which lives in fractal spacetime and is argued to be Lorentz invariant, power-counting renormalizable, ultraviolet finite, and causal. The system flows from an ultraviolet fixed point, where spacetime has Hausdorff dimension 2, to an infrared limit coinciding with a standard four-dimensional field theory. Classically, the fractal world where fields live exchanges energy momentum with the bulk with integer topological dimension. However, the total energy momentum is conserved. We consider the dynamics and the propagator of a scalar field. Implications for quantum gravity, cosmology, and the cosmological constant are discussed.
CPD - education and self-assessment: functional imaging in epilepsy.
Richardson, M P
2001-03-01
Functional imaging plays a growing role in the clinical assessment and research investigation of patients with epilepsy. This article reviews the literature on functional MRI (fMRI) investigation of EEG activity, fMRI evaluation of cognitive and motor functions, magnetic resonance spectroscopy (MRS), single photon emission computed tomography (SPECT) and positron emission tomography (PET) in epilepsy. The place of these techniques in clinical evaluation and their contribution to a better neurobiological understanding of epilepsy are discussed. PMID:11407959
Designing fractal nanostructured biointerfaces for biomedical applications.
Zhang, Pengchao; Wang, Shutao
2014-06-01
Fractal structures in nature offer a unique "fractal contact mode" that guarantees the efficient working of an organism with an optimized style. Fractal nanostructured biointerfaces have shown great potential for the ultrasensitive detection of disease-relevant biomarkers from small biomolecules on the nanoscale to cancer cells on the microscale. This review will present the advantages of fractal nanostructures, the basic concept of designing fractal nanostructured biointerfaces, and their biomedical applications for the ultrasensitive detection of various disease-relevant biomarkers, such microRNA, cancer antigen 125, and breast cancer cells, from unpurified cell lysates and the blood of patients.
Roughness Perception of Haptically Displayed Fractal Surfaces
NASA Technical Reports Server (NTRS)
Costa, Michael A.; Cutkosky, Mark R.; Lau, Sonie (Technical Monitor)
2000-01-01
Surface profiles were generated by a fractal algorithm and haptically rendered on a force feedback joystick, Subjects were asked to use the joystick to explore pairs of surfaces and report to the experimenter which of the surfaces they felt was rougher. Surfaces were characterized by their root mean square (RMS) amplitude and their fractal dimension. The most important factor affecting the perceived roughness of the fractal surfaces was the RMS amplitude of the surface. When comparing surfaces of fractal dimension 1.2-1.35 it was found that the fractal dimension was negatively correlated with perceived roughness.
Lin, Lian-Yu; Su, Mao-Yuan M; Pham, Van-Truong; Tran, Thi-Thao; Wang, Yung-Hung; Tseng, Wen-Yih I; Lo, Men-Tzung; Lin, Jiunn-Lee
2016-01-01
Left ventricular (LV) trabeculation has been studied in certain forms of cardiomyopathy. However, the changes of LV endocardial trabeculation during the remodeling process leading to heart failure (HF) are unclear. Seventy-four patients with systolic heart failure (SHF), 65 with heart failure with preserved ejection fraction (HFpEF) and 61 without HF were prospectively enrolled. All subjects received magnetic resonance imaging (MRI) study including cine, T1 and late gadolinium enhancement (LGE) images. Trabecular-papillary muscle (TPM) mass, fractal dimension (FD) and extracellular volume (ECV) were derived. The results showed that TPM mass index was higher in patients with SHF than that in patients with HFpEF and non-HF. The TPM mass-LV mass ratio (TPMm/LVM) was higher in SHF group than that in HFpEF and non-HF. FD was not different among groups. The presence of LGE was inversely associated with TPM mass index and TPMm/LVM while the ECV were positively associated with TPMm/LVM. The FD was positively associated with LV chamber size. In conclusion, TPM increases in patients with SHF and are probably related to myocardial cell hypertrophy and fibrotic repair during remodeling. The FD increases with the dilatation of LV chamber but remain unchanged with the deterioration of LV function. PMID:26876005
Lin, Lian-Yu; Su, Mao-Yuan M.; Pham, Van-Truong; Tran, Thi-Thao; Wang, Yung-Hung; Tseng, Wen-Yih I.; Lo, Men-Tzung; Lin, Jiunn-Lee
2016-01-01
Left ventricular (LV) trabeculation has been studied in certain forms of cardiomyopathy. However, the changes of LV endocardial trabeculation during the remodeling process leading to heart failure (HF) are unclear. Seventy-four patients with systolic heart failure (SHF), 65 with heart failure with preserved ejection fraction (HFpEF) and 61 without HF were prospectively enrolled. All subjects received magnetic resonance imaging (MRI) study including cine, T1 and late gadolinium enhancement (LGE) images. Trabecular-papillary muscle (TPM) mass, fractal dimension (FD) and extracellular volume (ECV) were derived. The results showed that TPM mass index was higher in patients with SHF than that in patients with HFpEF and non-HF. The TPM mass-LV mass ratio (TPMm/LVM) was higher in SHF group than that in HFpEF and non-HF. FD was not different among groups. The presence of LGE was inversely associated with TPM mass index and TPMm/LVM while the ECV were positively associated with TPMm/LVM. The FD was positively associated with LV chamber size. In conclusion, TPM increases in patients with SHF and are probably related to myocardial cell hypertrophy and fibrotic repair during remodeling. The FD increases with the dilatation of LV chamber but remain unchanged with the deterioration of LV function. PMID:26876005
Fractal Theory for Permeability Prediction, Venezuelan and USA Wells
NASA Astrophysics Data System (ADS)
Aldana, Milagrosa; Altamiranda, Dignorah; Cabrera, Ana
2014-05-01
Inferring petrophysical parameters such as permeability, porosity, water saturation, capillary pressure, etc, from the analysis of well logs or other available core data has always been of critical importance in the oil industry. Permeability in particular, which is considered to be a complex parameter, has been inferred using both empirical and theoretical techniques. The main goal of this work is to predict permeability values on different wells using Fractal Theory, based on a method proposed by Pape et al. (1999). This approach uses the relationship between permeability and the geometric form of the pore space of the rock. This method is based on the modified equation of Kozeny-Carman and a fractal pattern, which allows determining permeability as a function of the cementation exponent, porosity and the fractal dimension. Data from wells located in Venezuela and the United States of America are analyzed. Employing data of porosity and permeability obtained from core samples, and applying the Fractal Theory method, we calculated the prediction equations for each well. At the beginning, this was achieved by training with 50% of the data available for each well. Afterwards, these equations were tested inferring over 100% of the data to analyze possible trends in their distribution. This procedure gave excellent results in all the wells in spite of their geographic distance, generating permeability models with the potential to accurately predict permeability logs in the remaining parts of the well for which there are no core samples, using even porority logs. Additionally, empirical models were used to determine permeability and the results were compared with those obtained by applying the fractal method. The results indicated that, although there are empirical equations that give a proper adjustment, the prediction results obtained using fractal theory give a better fit to the core reference data.
Current Status of Functional Imaging in Eating Disorders
Frank, Guido K.W.; Kaye, Walter H.
2013-01-01
Eating Disorders are complex psychiatric problems that involve biologic and psychological factors. Brain imaging studies provide insights how functionally connected brain networks may contribute to disturbed eating behavior, resulting in food refusal and altered body weight, but also body preoccupations and heightened anxiety. In this article we review the current state of brain imaging in eating disorders, and how such techniques may help identify pathways that could be important in the treatment of those often detrimental disorders. PMID:22532388
Functional MRI studies of human vision on a clinical imager
George, J.S.; Lewine, J.D.; Aine, C.J.; van Hulsteyn, D.; Wood, C.C. ); Sanders, J.; Maclin, E. ); Belliveau, J.W. ); Caprihan, A. )
1992-01-01
During the past decade, Magnetic Resonance Imaging (MRI) has become the method of choice for imaging the anatomy of the human brain. Recently, Belliveau and colleagues have reported the use of echo planar magnetic resonance imaging (EPI) to image patterns of neural activity. Here, we report functional MR imaging in response to visual stimulation without the use of contrast agents, and without the extensive hardware modifications required for EPI. Regions of activity were observed near the expected locations of V1, V2 and possibly V3 and another active region was observed near the parietal-occipital sulcus on the superior surface of the cerebrum. These locations are consistent with sources observed in neuromagnetic studies of the human visual response.
Functional MRI studies of human vision on a clinical imager
George, J.S.; Lewine, J.D.; Aine, C.J.; van Hulsteyn, D.; Wood, C.C.; Sanders, J.; Maclin, E.; Belliveau, J.W.; Caprihan, A.
1992-09-01
During the past decade, Magnetic Resonance Imaging (MRI) has become the method of choice for imaging the anatomy of the human brain. Recently, Belliveau and colleagues have reported the use of echo planar magnetic resonance imaging (EPI) to image patterns of neural activity. Here, we report functional MR imaging in response to visual stimulation without the use of contrast agents, and without the extensive hardware modifications required for EPI. Regions of activity were observed near the expected locations of V1, V2 and possibly V3 and another active region was observed near the parietal-occipital sulcus on the superior surface of the cerebrum. These locations are consistent with sources observed in neuromagnetic studies of the human visual response.
Basis Functions in Image Reconstruction From Projections: A Tutorial Introduction
NASA Astrophysics Data System (ADS)
Herman, Gabor T.
2015-11-01
The series expansion approaches to image reconstruction from projections assume that the object to be reconstructed can be represented as a linear combination of fixed basis functions and the task of the reconstruction algorithm is to estimate the coefficients in such a linear combination based on the measured projection data. It is demonstrated that using spherically symmetric basis functions (blobs), instead of ones based on the more traditional pixels, yields superior reconstructions of medically relevant objects. The demonstration uses simulated computerized tomography projection data of head cross-sections and the series expansion method ART for the reconstruction. In addition to showing the results of one anecdotal example, the relative efficacy of using pixel and blob basis functions in image reconstruction from projections is also evaluated using a statistical hypothesis testing based task oriented comparison methodology. The superiority of the efficacy of blob basis functions over that of pixel basis function is found to be statistically significant.
Sensitivity analysis of near-infrared functional lymphatic imaging
NASA Astrophysics Data System (ADS)
Weiler, Michael; Kassis, Timothy; Dixon, J. Brandon
2012-06-01
Near-infrared imaging of lymphatic drainage of injected indocyanine green (ICG) has emerged as a new technology for clinical imaging of lymphatic architecture and quantification of vessel function, yet the imaging capabilities of this approach have yet to be quantitatively characterized. We seek to quantify its capabilities as a diagnostic tool for lymphatic disease. Imaging is performed in a tissue phantom for sensitivity analysis and in hairless rats for in vivo testing. To demonstrate the efficacy of this imaging approach to quantifying immediate functional changes in lymphatics, we investigate the effects of a topically applied nitric oxide (NO) donor glyceryl trinitrate ointment. Premixing ICG with albumin induces greater fluorescence intensity, with the ideal concentration being 150 μg/mL ICG and 60 g/L albumin. ICG fluorescence can be detected at a concentration of 150 μg/mL as deep as 6 mm with our system, but spatial resolution deteriorates below 3 mm, skewing measurements of vessel geometry. NO treatment slows lymphatic transport, which is reflected in increased transport time, reduced packet frequency, reduced packet velocity, and reduced effective contraction length. NIR imaging may be an alternative to invasive procedures measuring lymphatic function in vivo in real time.
Functional Doppler optical coherence tomography for cortical blood flow imaging
NASA Astrophysics Data System (ADS)
Yu, Lingfeng; Liu, Gangjun; Nguyen, Elaine; Choi, Bernard; Chen, Zhongping
2010-02-01
Optical methods have been widely used in basic neuroscience research to study the cerebral blood flow dynamics in order to overcome the low spatial resolution associated with magnetic resonance imaging and positron emission tomography. Although laser Doppler imaging and laser speckle imaging can map out en face cortical hemodynamics and columns, depth resolution is not available. Two-photon microscopy has been used for mapping cortical activity. However, flow measurement requires fluorescent dye injection, which can be problematic. The noninvasive and high resolution tomographic capabilities of optical coherence tomography make it a promising technique for mapping depth resolved cortical blood flow. Here, we present a functional Doppler optical coherence tomography (OCT) imaging modality for quantitative evaluation of cortical blood flow in a mouse model. Fast, repeated, Doppler OCT scans across a vessel of interest were performed to record flow dynamic information with a high temporal resolution of the cardiac cycles. Spectral Doppler analysis of continuous Doppler images demonstrates how the velocity components and longitudinally projected flow-volume-rate change over time, thereby providing complementary temporal flow information to the spatially distributed flow information of Doppler OCT. The proposed functional Doppler OCT imaging modality can be used to diagnose vessel stenosis/blockage or monitor blood flow changes due to pharmacological agents/neuronal activities. Non-invasive in-vivo mice experiments were performed to verify the capabilities of function Doppler OCT.
Enhancing images with Intensity-Dependent Spread functions
NASA Technical Reports Server (NTRS)
Reese, Greg
1992-01-01
The theory of Intensity-Dependent Spread functions (IDS), a model of the human visual system proposed by Cornsweet (1985), is applied to image enhancement. An artificial image is examined which illustrates the characteristics of IDS processing and shows how the theoretical results translate into visual effects. Examples of realistic scenes that have been enhanced by IDS are presented. The system is shown to be particularly useful for bringing out detail in regions of low-contrast images. IDS can be readily implemented on a parallel computer.
Challenges of functional imaging research of pain in children
Sava, Simona; Lebel, Alyssa A; Leslie, David S; Drosos, Athena; Berde, Charles; Becerra, Lino; Borsook, David
2009-01-01
Functional imaging has revolutionized the neurosciences. In the pain field it has dramatically altered our understanding of how the brain undergoes significant functional, anatomical and chemical changes in patients with chronic pain. However, most studies have been performed in adults. Because functional imaging is non-invasive and can be performed in awake individuals, applications in children have become more prevalent, but only recently in the pain field. Measures of changes in the brains of children have important implications in understanding neural plasticity in response to acute and chronic pain in the developing brain. Such findings may have implications for treatments in children affected by chronic pain and provide novel insights into chronic pain syndromes in adults. In this review we summarize this potential and discuss specific concerns related to the imaging of pain in children. PMID:19531255
Functional requirements for a central research imaging data repository.
Franke, Thomas; Gruetz, Romanus; Dickmann, Frank
2013-01-01
The current situation at many university medical centers regarding the management of biomedical research imaging data leaves much to be desired. In contrast to the recommendations of the German Research Foundation (DFG) and the German Council of Sciences and Humanities regarding the professional management of research data, there are commonly many individual data pools for research data in each institute and the management remains the responsibility of the researcher. A possible solution for this situation would be to install local central repositories for biomedical research imaging data. In this paper, we developed a scenario based on abstracted use-cases for institutional research undertakings as well as collaborative biomedical research projects and analyzed the functional requirements that a local repository would have to fulfill. We determined eight generic categories of functional requirements, which can be viewed as a basic guideline for the minimum functionality of a central repository for biomedical research imaging data.
Functional imaging of small tissue volumes with diffuse optical tomography
NASA Astrophysics Data System (ADS)
Klose, Alexander D.; Hielscher, Andreas H.
2006-03-01
Imaging of dynamic changes in blood parameters, functional brain imaging, and tumor imaging are the most advanced application areas of diffuse optical tomography (DOT). When dealing with the image reconstruction problem one is faced with the fact that near-infrared photons, unlike X-rays, are highly scattered when they traverse biological tissue. Image reconstruction schemes are required that model the light propagation inside biological tissue and predict measurements on the tissue surface. By iteratively changing the tissue-parameters until the predictions agree with the real measurements, a spatial distribution of optical properties inside the tissue is found. The optical properties can be related to the tissue oxygenation, inflammation, or to the fluorophore concentration of a biochemical marker. If the model of light propagation is inaccurate, the reconstruction process will lead to an inaccurate result as well. Here, we focus on difficulties that are encountered when DOT is employed for functional imaging of small tissue volumes, for example, in cancer studies involving small animals, or human finger joints for early diagnosis of rheumatoid arthritis. Most of the currently employed image reconstruction methods rely on the diffusion theory that is an approximation to the equation of radiative transfer. But, in the cases of small tissue volumes and tissues that contain low scattering regions diffusion theory has been shown to be of limited applicability Therefore, we employ a light propagation model that is based on the equation of radiative transfer, which promises to overcome the limitations.
NASA Astrophysics Data System (ADS)
Tilg, Bernhard; Modre, Robert; Fischer, Gerald; Hanser, Friedrich; Messnarz, Bernd; Schocke, Michael F. H.; Kremser, Christian; Roithinger, Franz
2002-04-01
Inverse electrocardiography has been developing for several years. By coupling electrocardiographic mapping and 3D+time anatomical data, the electrical excitation sequence can be imaged completely noninvasively in the human heart. In this study, a bidomain theory based surface heart model activation time imaging approach was applied to single beat data of atrial and ventricular depolarization. For sinus and paced rhythms, the sites of early activation and the areas with late activation were estimated with sufficient accuracy. In particular for focal arrhythmias, this model-based imaging approach might allow the guidance and evaluation of antiarrhythmic interventions, for instance, in case of catheter ablation or drug therapy.
Fractal statistics of cloud fields
NASA Technical Reports Server (NTRS)
Cahalan, Robert F.; Joseph, Joachim H.
1989-01-01
Landsat Multispectral Scanner (MSS) and Thematic Mapper (TM) data, with 80 and 30 m spatial resolution, respectively, have been employed to study the spatial structure of boundary-layer and intertropical convergence zone (ITCZ) clouds. The probability distributions of cloud areas and cloud perimeters are found to approximately follow a power-law, with a different power (i.e., fractal dimension) for each cloud type. They are better approximated by a double power-law behavior, indicating a change in the fractal dimension at a characteristic size which depends upon cloud type. The fractal dimension also changes with threshold. The more intense cloud areas are found to have a higher perimeter fractal dimension, perhaps indicative of the increased turbulence at cloud top. A detailed picture of the inhomogeneous spatial structure of various cloud types will contribute to a better understanding of basic cloud processes, and also has implications for the remote sensing of clouds, for their effects on remote sensing of other parameters, and for the parameterization of clouds in general circulation models, all of which rely upon plane-parallel radiative transfer algorithms.
Exploring Fractal Geometry with Children.
ERIC Educational Resources Information Center
Vacc, Nancy Nesbitt
1999-01-01
Heightens the awareness of elementary school teachers, teacher educators, and teacher-education researchers of possible applications of fractal geometry with children and, subsequently, initiates discussion about the appropriateness of including this new mathematics in the elementary curriculum. Presents activities for exploring children's…
Zueva, Marina V.
2015-01-01
The theory that ties normal functioning and pathology of the brain and visual system with the spatial–temporal structure of the visual and other sensory stimuli is described for the first time in the present study. The deficit of fractal complexity of environmental influences can lead to the distortion of fractal complexity in the visual pathways of the brain and abnormalities of development or aging. The use of fractal light stimuli and fractal stimuli of other modalities can help to restore the functions of the brain, particularly in the elderly and in patients with neurodegenerative disorders or amblyopia. Non-linear dynamics of these physiological processes have a strong base of evidence, which is seen in the impaired fractal regulation of rhythmic activity in aged and diseased brains. From birth to old age, we live in a non-linear world, in which objects and processes with the properties of fractality and non-linearity surround us. Against this background, the evolution of man took place and all periods of life unfolded. Works of art created by man may also have fractal properties. The positive influence of music on cognitive functions is well-known. Insufficiency of sensory experience is believed to play a crucial role in the pathogenesis of amblyopia and age-dependent diseases. The brain is very plastic in its early development, and the plasticity decreases throughout life. However, several studies showed the possibility to reactivate the adult’s neuroplasticity in a variety of ways. We propose that a non-linear structure of sensory information on many spatial and temporal scales is crucial to the brain health and fractal regulation of physiological rhythms. Theoretical substantiation of the author’s theory is presented. Possible applications and the future research that can experimentally confirm or refute the theoretical concept are considered. PMID:26236232
Zueva, Marina V
2015-01-01
The theory that ties normal functioning and pathology of the brain and visual system with the spatial-temporal structure of the visual and other sensory stimuli is described for the first time in the present study. The deficit of fractal complexity of environmental influences can lead to the distortion of fractal complexity in the visual pathways of the brain and abnormalities of development or aging. The use of fractal light stimuli and fractal stimuli of other modalities can help to restore the functions of the brain, particularly in the elderly and in patients with neurodegenerative disorders or amblyopia. Non-linear dynamics of these physiological processes have a strong base of evidence, which is seen in the impaired fractal regulation of rhythmic activity in aged and diseased brains. From birth to old age, we live in a non-linear world, in which objects and processes with the properties of fractality and non-linearity surround us. Against this background, the evolution of man took place and all periods of life unfolded. Works of art created by man may also have fractal properties. The positive influence of music on cognitive functions is well-known. Insufficiency of sensory experience is believed to play a crucial role in the pathogenesis of amblyopia and age-dependent diseases. The brain is very plastic in its early development, and the plasticity decreases throughout life. However, several studies showed the possibility to reactivate the adult's neuroplasticity in a variety of ways. We propose that a non-linear structure of sensory information on many spatial and temporal scales is crucial to the brain health and fractal regulation of physiological rhythms. Theoretical substantiation of the author's theory is presented. Possible applications and the future research that can experimentally confirm or refute the theoretical concept are considered. PMID:26236232
A simultaneous multimodal imaging system for tissue functional parameters
NASA Astrophysics Data System (ADS)
Ren, Wenqi; Zhang, Zhiwu; Wu, Qiang; Zhang, Shiwu; Xu, Ronald
2014-02-01
Simultaneous and quantitative assessment of skin functional characteristics in different modalities will facilitate diagnosis and therapy in many clinical applications such as wound healing. However, many existing clinical practices and multimodal imaging systems are subjective, qualitative, sequential for multimodal data collection, and need co-registration between different modalities. To overcome these limitations, we developed a multimodal imaging system for quantitative, non-invasive, and simultaneous imaging of cutaneous tissue oxygenation and blood perfusion parameters. The imaging system integrated multispectral and laser speckle imaging technologies into one experimental setup. A Labview interface was developed for equipment control, synchronization, and image acquisition. Advanced algorithms based on a wide gap second derivative reflectometry and laser speckle contrast analysis (LASCA) were developed for accurate reconstruction of tissue oxygenation and blood perfusion respectively. Quantitative calibration experiments and a new style of skinsimulating phantom were designed to verify the accuracy and reliability of the imaging system. The experimental results were compared with a Moor tissue oxygenation and perfusion monitor. For In vivo testing, a post-occlusion reactive hyperemia (PORH) procedure in human subject and an ongoing wound healing monitoring experiment using dorsal skinfold chamber models were conducted to validate the usability of our system for dynamic detection of oxygenation and perfusion parameters. In this study, we have not only setup an advanced multimodal imaging system for cutaneous tissue oxygenation and perfusion parameters but also elucidated its potential for wound healing assessment in clinical practice.
Probe and object function reconstruction in incoherent stem imaging
Nellist, P.D.; Pennycook, S.J.
1996-09-01
Using the phase-object approximation it is shown how an annular dark- field (ADF) detector in a scanning transmission electron microscope (STEM) leads to an image which can be described by an incoherent model. The point spread function is found to be simply the illuminating probe intensity. An important consequence of this is that there is no phase problem in the imaging process, which allows various image processing methods to be applied directly to the image intensity data. Using an image of a GaAs<110>, the probe intensity profile is reconstructed, confirming the existence of a 1.3 {Angstrom} probe in a 300kV STEM. It is shown that simply deconvolving this reconstructed probe from the image data does not improve its interpretability because the dominant effects of the imaging process arise simply from the restricted resolution of the microscope. However, use of the reconstructed probe in a maximum entropy reconstruction is demonstrated, which allows information beyond the resolution limit to be restored and does allow improved image interpretation.
Functional Imaging in OA: Role of Imaging in the Evaluation of Tissue Biomechanics
Neu, Corey P.
2014-01-01
Functional imaging refers broadly to the visualization of organ or tissue physiology using medical image modalities. In load-bearing tissues of the body, including articular cartilage lining the bony ends of joints, changes in strain, stress, and material properties occur in osteoarthritis (OA), providing an opportunity to probe tissue function through the progression of the disease. Here, biomechanical measures in cartilage and related joint tissues are discussed as key imaging biomarkers in the evaluation of OA. Emphasis will be placed on the a) potential of radiography, ultrasound, and magnetic resonance imaging to assess early tissue pathomechanics in OA, b) relative utility of kinematic, structural, morphological, and biomechanical measures as functional imaging biomarkers, and c) improved diagnostic specificity through the combination of multiple imaging biomarkers with unique contrasts, including elastography and quantitative assessments of tissue biochemistry. In comparison to other modalities, magnetic resonance imaging provides an extensive range of functional measures at the tissue level, with conventional and emerging techniques available to potentially to assess the spectrum of preclinical to advance OA. PMID:25278049
New developments in paediatric cardiac functional ultrasound imaging.
de Korte, Chris L; Nillesen, Maartje M; Saris, Anne E C M; Lopata, Richard G P; Thijssen, Johan M; Kapusta, Livia
2014-07-01
Ultrasound imaging can be used to estimate the morphology as well as the motion and deformation of tissues. If the interrogated tissue is actively deforming, this deformation is directly related to its function and quantification of this deformation is normally referred as 'strain imaging'. Tissue can also be deformed by applying an internal or external force and the resulting, induced deformation is a function of the mechanical tissue characteristics. In combination with the load applied, these strain maps can be used to estimate or reconstruct the mechanical properties of tissue. This technique was named 'elastography' by Ophir et al. in 1991. Elastography can be used for atherosclerotic plaque characterisation, while the contractility of the heart or skeletal muscles can be assessed with strain imaging. Rather than using the conventional video format (DICOM) image information, radio frequency (RF)-based ultrasound methods enable estimation of the deformation at higher resolution and with higher precision than commercial methods using Doppler (tissue Doppler imaging) or video image data (2D speckle tracking methods). However, the improvement in accuracy is mainly achieved when measuring strain along the ultrasound beam direction, so it has to be considered a 1D technique. Recently, this method has been extended to multiple directions and precision further improved by using spatial compounding of data acquired at multiple beam steered angles. Using similar techniques, the blood velocity and flow can be determined. RF-based techniques are also beneficial for automated segmentation of the ventricular cavities. In this paper, new developments in different techniques of quantifying cardiac function by strain imaging, automated segmentation, and methods of performing blood flow imaging are reviewed and their application in paediatric cardiology is discussed. PMID:27277901
Hyperpolarized Xenon-129 Magnetic Resonance Imaging of Functional Lung Microstructure
NASA Astrophysics Data System (ADS)
Dregely, Isabel
Hyperpolarized 129Xe (HXe) is a non-invasive contrast agent for lung magnetic resonance imaging (MRI), which upon inhalation follows the functional pathway of oxygen in the lung by dissolving into lung tissue structures and entering the blood stream. HXe MRI therefore provides unique opportunities for functional lung imaging of gas exchange which occurs from alveolar air spaces across the air-blood boundary into parenchymal tissue. However challenges in acquisition speed and signal-to-noise ratio have limited the development of a HXe imaging biomarker to diagnose lung disease. This thesis addresses these challenges by introducing parallel imaging to HXe MRI. Parallel imaging requires dedicated hardware. This work describes design, implementation, and characterization of a 32-channel phased-array chest receive coil with an integrated asymmetric birdcage transmit coil tuned to the HXe resonance on a 3 Tesla MRI system. Using the newly developed human chest coil, a functional HXe imaging method, multiple exchange time xenon magnetization transfer contrast (MXTC) is implemented. MXTC dynamically encodes HXe gas exchange into the image contrast. This permits two parameters to be derived regionally which are related to gas-exchange functionality by characterizing tissue-to-alveolar-volume ratio and alveolar wall thickness in the lung parenchyma. Initial results in healthy subjects demonstrate the sensitivity of MXTC by quantifying the subtle changes in lung microstructure in response to orientation and lung inflation. Our results in subjects with lung disease show that the MXTC-derived functional tissue density parameter exhibits excellent agreement with established imaging techniques. The newly developed dynamic parameter, which characterizes the alveolar wall, was elevated in subjects with lung disease, most likely indicating parenchymal inflammation. In light of these observations we believe that MXTC has potential as a biomarker for the regional quantification of 1
Electromagnetic field of fractal distribution of charged particles
Tarasov, Vasily E.
2005-08-15
Electric and magnetic fields of fractal distribution of charged particles are considered. The fractional integrals are used to describe fractal distribution. The fractional integrals are considered as approximations of integrals on fractals. Using the fractional generalization of integral Maxwell equation, the simple examples of the fields of homogeneous fractal distribution are considered. The electric dipole and quadrupole moments for fractal distribution are derived.
Functional plasticity before the cradle: a review of neural functional imaging in the human fetus.
Anderson, Amy L; Thomason, Moriah E
2013-11-01
The organization of the brain is highly plastic in fetal life. Establishment of healthy neural functional systems during the fetal period is essential to normal growth and development. Across the last several decades, remarkable progress has been made in understanding the development of human fetal functional brain systems. This is largely due to advances in imaging methodologies. Fetal neuroimaging began in the 1950-1970's with fetal electroencephalography (EEG) applied during labor. Later, in the 1980's, magnetoencephalography (MEG) emerged as an effective approach for investigating fetal brain function. Most recently, functional magnetic resonance imaging (fMRI) has arisen as an additional powerful approach for examining fetal brain function. This review will discuss major developmental findings from fetal imaging studies such as the maturation of prenatal sensory system functions, functional hemispheric asymmetry, and sensory-driven neurodevelopment. We describe how with improved imaging and analysis techniques, functional imaging of the fetus has the potential to assess the earliest point of neural maturation and provide insight into the patterning and sequence of normal and abnormal brain development.
NASA Astrophysics Data System (ADS)
Wei, Wei; Cai, Jianchao; Hu, Xiangyun; Han, Qi; Liu, Shuang; Zhou, Yingfang
2016-08-01
A theoretical effective thermal conductivity model for nanofluids is derived based on fractal distribution characteristics of nanoparticle aggregation. Considering two different mechanisms of heat conduction including particle aggregation and convention, the model is expressed as a function of the fractal dimension and concentration. In the model, the change of fractal dimension is related to the variation of aggregation shape. The theoretical computations of the developed model provide a good agreement with the experimental results, which may serve as an effective approach for quantitatively estimating the effective thermal conductivity of nanofluids.
Adaptive sigmoid function bihistogram equalization for image contrast enhancement
NASA Astrophysics Data System (ADS)
Arriaga-Garcia, Edgar F.; Sanchez-Yanez, Raul E.; Ruiz-Pinales, Jose; Garcia-Hernandez, Ma. de Guadalupe
2015-09-01
Contrast enhancement plays a key role in a wide range of applications including consumer electronic applications, such as video surveillance, digital cameras, and televisions. The main goal of contrast enhancement is to increase the quality of images. However, most state-of-the-art methods induce different types of distortion such as intensity shift, wash-out, noise, intensity burn-out, and intensity saturation. In addition, in consumer electronics, simple and fast methods are required in order to be implemented in real time. A bihistogram equalization method based on adaptive sigmoid functions is proposed. It consists of splitting the image histogram into two parts that are equalized independently by using adaptive sigmoid functions. In order to preserve the mean brightness of the input image, the parameter of the sigmoid functions is chosen to minimize the absolute mean brightness metric. Experiments on the Berkeley database have shown that the proposed method improves the quality of images and preserves their mean brightness. An application to improve the colorfulness of images is also presented.
Ultrasound strain imaging for quantification of tissue function: cardiovascular applications
NASA Astrophysics Data System (ADS)
de Korte, Chris L.; Lopata, Richard G. P.; Hansen, Hendrik H. G.
2013-03-01
With ultrasound imaging, the motion and deformation of tissue can be measured. Tissue can be deformed by applying a force on it and the resulting deformation is a function of its mechanical properties. Quantification of this resulting tissue deformation to assess the mechanical properties of tissue is called elastography. If the tissue under interrogation is actively deforming, the deformation is directly related to its function and quantification of this deformation is normally referred as `strain imaging'. Elastography can be used for atherosclerotic plaques characterization, while the contractility of the heart or skeletal muscles can be assessed with strain imaging. We developed radio frequency (RF) based ultrasound methods to assess the deformation at higher resolution and with higher accuracy than commercial methods using conventional image data (Tissue Doppler Imaging and 2D speckle tracking methods). However, the improvement in accuracy is mainly achieved when measuring strain along the ultrasound beam direction, so 1D. We further extended this method to multiple directions and further improved precision by using compounding of data acquired at multiple beam steered angles. In arteries, the presence of vulnerable plaques may lead to acute events like stroke and myocardial infarction. Consequently, timely detection of these plaques is of great diagnostic value. Non-invasive ultrasound strain compounding is currently being evaluated as a diagnostic tool to identify the vulnerability of plaques. In the heart, we determined the strain locally and at high resolution resulting in a local assessment in contrary to conventional global functional parameters like cardiac output or shortening fraction.
Functional DNA Nanomaterials for Sensing and Imaging in Living Cells
Torabi, Seyed-Fakhreddin; Lu, Yi
2014-01-01
Recent developments in integrating high selectivity of functional DNA, such as DNAzyme and aptamers, with efficient DNA delivery into cells by gold nanoparticles or superior near-infrared optical properties of upconversion nanoparticles are reviewed. Their applications in sensing and imaging small organic metabolites, toxins, metal ions, pH, DNA, RNA, proteins, and pathogens are summarized. The advantages and future directions of these functional DNA materials are discussed. PMID:24468446
Light scattering by a reentrant fractal surface.
Mendoza-Suárez, A; Méndez, E R
1997-05-20
Recently, rigorous numerical techniques for treating light scattering problems with one-dimensional rough surfaces have been developed. In their usual formulation, these techniques are based on the solution of two coupled integral equations and are applicable only to surfaces whose profiles can be described by single-valued functions of a coordinate in the mean plane of the surface. In this paper we extend the applicability of the integral equation method to surfaces with multivalued profiles. A procedure for finding a parametric description of a given profile is described, and the scattering equations are established within the framework of this formalism. We then present some results of light scattering from a sequence of one-dimensional flat surfaces with defects in the form of triadic Koch curves. Beyond a certain order of the prefractal, the scattering patterns become stationary (within the numerical accuracy of the method). It can then be argued that the results obtained correspond to a surface with a fractal structure. These constitute, to our knowledge, the first rigorous calculations of light scattering from a reentrant fractal surface. PMID:18253371
Fractal analysis of the hierarchic structure of fossil coal surface
Alekseev, A.D.; Vasilenko, T.A.; Kirillov, A.K.
2008-05-15
The fractal analysis is described as method of studying images of surface of fossil coal, one of the natural sorbent, with the aim of determining its structural surface heterogeneity. The deformation effect as a reduction in the dimensions of heterogeneity boundaries is considered. It is shown that the theory of nonequilibrium dynamic systems permits to assess a formation level of heterogeneities involved into a sorbent composition by means of the Hurst factor.
Functional magnetic resonance imaging in oncology: state of the art*
Guimaraes, Marcos Duarte; Schuch, Alice; Hochhegger, Bruno; Gross, Jefferson Luiz; Chojniak, Rubens; Marchiori, Edson
2014-01-01
In the investigation of tumors with conventional magnetic resonance imaging, both quantitative characteristics, such as size, edema, necrosis, and presence of metastases, and qualitative characteristics, such as contrast enhancement degree, are taken into consideration. However, changes in cell metabolism and tissue physiology which precede morphological changes cannot be detected by the conventional technique. The development of new magnetic resonance imaging techniques has enabled the functional assessment of the structures in order to obtain information on the different physiological processes of the tumor microenvironment, such as oxygenation levels, cellularity and vascularity. The detailed morphological study in association with the new functional imaging techniques allows for an appropriate approach to cancer patients, including the phases of diagnosis, staging, response evaluation and follow-up, with a positive impact on their quality of life and survival rate. PMID:25741058
Live-Animal Imaging of Renal Function by Multiphoton Microscopy
Dunn, Kenneth W.; Sutton, Timothy A.; Sandoval, Ruben M.
2015-01-01
Intravital microscopy, microscopy of living animals, is a powerful research technique that combines the resolution and sensitivity found in microscopic studies of cultured cells with the relevance and systemic influences of cells in the context of the intact animal. The power of intravital microscopy has recently been extended with the development of multiphoton fluorescence microscopy systems capable of collecting optical sections from deep within the kidney at subcellular resolution, supporting high-resolution characterizations of the structure and function of glomeruli, tubules, and vasculature in the living kidney. Fluorescent probes are administered to an anesthetized, surgically prepared animal, followed by image acquisition for up to 3 hr. Images are transferred via a high-speed network to specialized computer systems for digital image analysis. This general approach can be used with different combinations of fluorescent probes to evaluate processes such as glomerular permeability, proximal tubule endocytosis, microvascular flow, vascular permeability, mitochondrial function, and cellular apoptosis/necrosis. PMID:23042524
Functional magnetic resonance imaging in oncology: state of the art.
Guimaraes, Marcos Duarte; Schuch, Alice; Hochhegger, Bruno; Gross, Jefferson Luiz; Chojniak, Rubens; Marchiori, Edson
2014-01-01
In the investigation of tumors with conventional magnetic resonance imaging, both quantitative characteristics, such as size, edema, necrosis, and presence of metastases, and qualitative characteristics, such as contrast enhancement degree, are taken into consideration. However, changes in cell metabolism and tissue physiology which precede morphological changes cannot be detected by the conventional technique. The development of new magnetic resonance imaging techniques has enabled the functional assessment of the structures in order to obtain information on the different physiological processes of the tumor microenvironment, such as oxygenation levels, cellularity and vascularity. The detailed morphological study in association with the new functional imaging techniques allows for an appropriate approach to cancer patients, including the phases of diagnosis, staging, response evaluation and follow-up, with a positive impact on their quality of life and survival rate.
Fractal patterns of fractures in granites
Velde, B.; Dubois, J.; Moore, D.; Touchard, G.
1991-01-01
Fractal measurements using the Cantor's dust method in a linear one-dimensional analysis mode were made on the fracture patterns revealed on two-dimensional, planar surfaces in four granites. This method allows one to conclude that: 1. (1)|The fracture systems seen on two-dimensional surfaces in granites are consistent with the part of fractal theory that predicts a repetition of patterns on different scales of observation, self similarity. Fractal analysis gives essentially the same values of D on the scale of kilometres, metres and centimetres (five orders of magnitude) using mapped, surface fracture patterns in a Sierra Nevada granite batholith (Mt. Abbot quadrangle, Calif.). 2. (2)|Fractures show the same fractal values at different depths in a given batholith. Mapped fractures (main stage ore veins) at three mining levels (over a 700 m depth interval) of the Boulder batholith, Butte, Mont. show the same fractal values although the fracture disposition appears to be different at different levels. 3. (3)|Different sets of fracture planes in a granite batholith, Central France, and in experimental deformation can have different fractal values. In these examples shear and tension modes have the same fractal values while compressional fractures follow a different fractal mode of failure. The composite fracture patterns are also fractal but with a different, median, fractal value compared to the individual values for the fracture plane sets. These observations indicate that the fractal method can possibly be used to distinguish fractures of different origins in a complex system. It is concluded that granites fracture in a fractal manner which can be followed at many scales. It appears that fracture planes of different origins can be characterized using linear fractal analysis. ?? 1991.
The Assessment of Neurological Systems with Functional Imaging
ERIC Educational Resources Information Center
Eidelberg, David
2007-01-01
In recent years a number of multivariate approaches have been introduced to map neural systems in health and disease. In this review, we focus on spatial covariance methods applied to functional imaging data to identify patterns of regional activity associated with behavior. In the rest state, this form of network analysis can be used to detect…
Functional Connectivity Magnetic Resonance Imaging Classification of Autism
ERIC Educational Resources Information Center
Anderson, Jeffrey S.; Nielsen, Jared A.; Froehlich, Alyson L.; DuBray, Molly B.; Druzgal, T. Jason; Cariello, Annahir N.; Cooperrider, Jason R.; Zielinski, Brandon A.; Ravichandran, Caitlin; Fletcher, P. Thomas; Alexander, Andrew L.; Bigler, Erin D.; Lange, Nicholas; Lainhart, Janet E.
2011-01-01
Group differences in resting state functional magnetic resonance imaging connectivity between individuals with autism and typically developing controls have been widely replicated for a small number of discrete brain regions, yet the whole-brain distribution of connectivity abnormalities in autism is not well characterized. It is also unclear…
Coherence imaging by use of a Newton rings sampling function.
Podoleanu, A G; Dobre, G M; Webb, D J; Jackson, D A
1996-11-01
We show that, with suitable optics in the arm of a Michelson interferometer, orthogonal galvo-scanning mirrors build a sampling function in the form of Newton rings when the two interferometer arms are matched. Using a low-coherence source, one can obtain transversal depth-resolved images. A fast display procedure using a storage oscilloscope was devised based on this method.
NASA Technical Reports Server (NTRS)
Jaggi, S.; Quattrochi, Dale A.; Lam, Nina S.-N.
1993-01-01
Fractal geometry is increasingly becoming a useful tool for modeling natural phenomena. As an alternative to Euclidean concepts, fractals allow for a more accurate representation of the nature of complexity in natural boundaries and surfaces. The purpose of this paper is to introduce and implement three algorithms in C code for deriving fractal measurement from remotely sensed data. These three methods are: the line-divider method, the variogram method, and the triangular prism method. Remote-sensing data acquired by NASA's Calibrated Airborne Multispectral Scanner (CAMS) are used to compute the fractal dimension using each of the three methods. These data were obtained as a 30 m pixel spatial resolution over a portion of western Puerto Rico in January 1990. A description of the three methods, their implementation in PC-compatible environment, and some results of applying these algorithms to remotely sensed image data are presented.
Application of the fractal theory on the study of filter cake constructure
Xu, X.; Xu, J.; Deng, C.; Qian, L.; Yan, K.
1995-12-31
Cake filtration is a complex process and the cake constructure is very difficult to describe in theory. Cake constructure parameters, such as the cake porosity, pore size shape and even its distribution, are main factors influencing the filtration results but have not been thoroughly understood yet. In this paper the fractal theory, an effective mathematical method in describing the self-similar phenomenon is used to investigate the filter cake constructure, and the scanning electron microscope and automatic image analyzer are used to measure the cake constructure. Cakes which formed in different conditions are examined and the fractal dimension of the cake are calculated. The study shows that the constructure of the filter cake can be approximated by Sierpinski fractal geometry and that the fractal dimension of filter cake, related to the particle characteristics, slurry concentration and filtration pressure is a good parameter to describe the pore size distribution and the cake penetrability.
Surface characterization of proteins using multi-fractal property of heat-denatured aggregates
Lahiri, Tapobrata; Mishra, Hrishikesh; Sarkar, Subrata; Misra, Krishna
2008-01-01
Multi-fractal property of heat-denatured protein aggregates (HDPA) is characteristic of its individual form. The visual similarity between digitally generated microscopic images of HDPA with that of surface-image of its individual X-ray structures in protein databank (PDB) displayed using Visual Molecular Dynamics (VMD) viewer is the basis of the study. We deigned experiments to view the fractal nature of proteins at different aggregate scales. Intensity based multi-fractal dimensions (ILMFD) extracted from various planes of digital microscopic images of protein aggregates were used to characterize HDPA into different classes. Moreover, the ILMFD parameters extracted from aggregates show similar classification pattern to digital images of protein surface displayed by VMD viewer using PDB entry. We discuss the use of irregular patterns of heat-denatured aggregate proteins to understand various surface properties in native proteins. PMID:18795110
Functional Nanoscale Imaging of Synaptic Vesicle Cycling with Superfast Fixation.
Schikorski, Thomas
2016-01-01
Functional imaging is the measurement of structural changes during an ongoing physiological process over time. In many cases, functional imaging has been implemented by tracking a fluorescent signal in live imaging sessions. Electron microscopy, however, excludes live imaging which has hampered functional imaging approaches on the ultrastructural level. This barrier was broken with the introduction of superfast fixation. Superfast fixation is capable of stopping and fixing membrane traffic at sufficient speed to capture a physiological process at a distinct functional state. Applying superfast fixation at sequential time points allows tracking of membrane traffic in a step-by-step fashion.This technique has been applied to track labeled endocytic vesicles at central synapses as they pass through the synaptic vesicle cycle. At synapses, neurotransmitter is released from synaptic vesicles (SVs) via fast activity-dependent exocytosis. Exocytosis is coupled to fast endocytosis that retrieves SVs components from the plasma membrane shortly after release. Fluorescent FM dyes that bind to the outer leaflet of the plasma membrane enter the endocytic vesicle during membrane retrieval and remain trapped in endocytic vesicles have been widely used to study SV exo-endocytic cycling in live imaging sessions. FM dyes can also be photoconverted into an electron-dense diaminobenzidine polymer which allows the investigation of SV cycling in the electron microscope. The combination of FM labeling with superfast fixation made it possible to track the fine structure of endocytic vesicles at 1 s intervals. Because this combination is not specialized to SV cycling, many other cellular processes can be studied. Furthermore, the technique is easy to set up and cost effective.This chapter describes activity-dependent FM dye labeling of SVs in cultured hippocampal neurons, superfast microwave-assisted fixation, photoconversion of the fluorescent endocytic vesicles, and the analysis of
NASA Astrophysics Data System (ADS)
Squarcina, Letizia; De Luca, Alberto; Bellani, Marcella; Brambilla, Paolo; Turkheimer, Federico E.; Bertoldo, Alessandra
2015-02-01
Fractal geometry can be used to analyze shape and patterns in brain images. With this study we use fractals to analyze T1 data of patients affected by schizophrenia or bipolar disorder, with the aim of distinguishing between healthy and pathological brains using the complexity of brain structure, in particular of grey matter, as a marker of disease. 39 healthy volunteers, 25 subjects affected by schizophrenia and 11 patients affected by bipolar disorder underwent an MRI session. We evaluated fractal dimension of the brain cortex and its substructures, calculated with an algorithm based on the box-count algorithm. We modified this algorithm, with the aim of avoiding the segmentation processing step and using all the information stored in the image grey levels. Moreover, to increase sensitivity to local structural changes, we computed a value of fractal dimension for each slice of the brain or of the particular structure. To have reference values in comparing healthy subjects with patients, we built a template by averaging fractal dimension values of the healthy volunteers data. Standard deviation was evaluated and used to create a confidence interval. We also performed a slice by slice t-test to assess the difference at slice level between the three groups. Consistent average fractal dimension values were found across all the structures in healthy controls, while in the pathological groups we found consistent differences, indicating a change in brain and structures complexity induced by these disorders.
Squarcina, Letizia; De Luca, Alberto; Bellani, Marcella; Brambilla, Paolo; Turkheimer, Federico E; Bertoldo, Alessandra
2015-02-21
Fractal geometry can be used to analyze shape and patterns in brain images. With this study we use fractals to analyze T1 data of patients affected by schizophrenia or bipolar disorder, with the aim of distinguishing between healthy and pathological brains using the complexity of brain structure, in particular of grey matter, as a marker of disease. 39 healthy volunteers, 25 subjects affected by schizophrenia and 11 patients affected by bipolar disorder underwent an MRI session. We evaluated fractal dimension of the brain cortex and its substructures, calculated with an algorithm based on the box-count algorithm. We modified this algorithm, with the aim of avoiding the segmentation processing step and using all the information stored in the image grey levels. Moreover, to increase sensitivity to local structural changes, we computed a value of fractal dimension for each slice of the brain or of the particular structure. To have reference values in comparing healthy subjects with patients, we built a template by averaging fractal dimension values of the healthy volunteers data. Standard deviation was evaluated and used to create a confidence interval. We also performed a slice by slice t-test to assess the difference at slice level between the three groups. Consistent average fractal dimension values were found across all the structures in healthy controls, while in the pathological groups we found consistent differences, indicating a change in brain and structures complexity induced by these disorders.
NASA Astrophysics Data System (ADS)
Westphal, Volker
Optical Coherence Tomography (OCT) is a noninvasive optical imaging technique that allows high-resolution cross-sectional imaging of tissue microstructure, achieving a spatial resolution of about 10 mum. OCT is similar to B-mode ultrasound (US) except that it uses infrared light instead of ultrasound. In contrast to US, no coupling gel is needed, simplifying the image acquisition. Furthermore, the fiber optic implementation of OCT is compatible with endoscopes. In recent years, the transition from slow imaging, bench-top systems to real-time clinical systems has been under way. This has lead to a variety of applications, namely in ophthalmology, gastroenterology, dermatology and cardiology. First, this dissertation will demonstrate that OCT is capable of imaging and differentiating clinically relevant tissue structures in the gastrointestinal tract. A careful in vitro correlation study between endoscopic OCT images and corresponding histological slides was performed. Besides structural imaging, OCT systems were further developed for functional imaging, as for example to visualize blood flow. Previously, imaging flow in small vessels in real-time was not possible. For this research, a new processing scheme similar to real-time Doppler in US was introduced. It was implemented in dedicated hardware to allow real-time acquisition and overlayed display of blood flow in vivo. A sensitivity of 0.5mm/s was achieved. Optical coherence microscopy (OCM) is a variation of OCT, improving the resolution even further to a few micrometers. Advances made in the OCT scan engine for the Doppler setup enabled real-time imaging in vivo with OCM. In order to generate geometrical correct images for all the previous applications in real-time, extensive image processing algorithms were developed. Algorithms for correction of distortions due to non-telecentric scanning, nonlinear scan mirror movements, and refraction were developed and demonstrated. This has led to interesting new
NASA Astrophysics Data System (ADS)
Gao, Wei; Zakharov, Valery P.; Myakinin, Oleg O.; Bratchenko, Ivan A.; Artemyev, Dmitry N.; Kornilin, Dmitry V.
2015-07-01
Optical coherence tomography (OCT) is usually employed for the measurement of retinal thickness characterizing the structural changes of tissue. However, fractal dimension (FD) could also character the structural changes of tissue. Therefore, fractal dimension changes may provide further information regarding cellular layers and early damage in ocular diseases. We investigated the possibility of OCT in detecting changes in fractal dimension from layered retinal structures. OCT images were obtained from diabetic patients without retinopathy (DM, n = 38 eyes) or mild diabetic retinopathy (MDR, n = 43 eyes) and normal healthy subjects (Controls, n = 74 eyes). Fractal dimension was calculated using the differentiate box counting methodology. We evaluated the usefulness of quantifying fractal dimension of layered structures in the detection of retinal damage. Generalized estimating equations considering within-subject intereye relations were used to test for differences between the groups. A modified p value of <0.001 was considered statistically significant. Receiver operating characteristic (ROC) curves were constructed to describe the ability of fractal dimension to discriminate between the eyes of DM, MDR and healthy eyes. Significant decreases of fractal dimension were observed in all layers in the MDR eyes compared with controls except in the inner nuclear layer (INL). Significant decreases of fractal dimension were also observed in all layers in the MDR eyes compared with DM eyes. The highest area under receiver operating characteristic curve (AUROC) values estimated for fractal dimension were observed for the outer plexiform layer (OPL) and outer segment photoreceptors (OS) when comparing MDR eyes with controls. The highest AUROC value estimated for fractal dimension were also observed for the retinal nerve fiber layer (RNFL) and OS when comparing MDR eyes with DM eyes. Our results suggest that fractal dimension of the intraretinal layers may provide useful
Evolving random fractal Cantor superlattices for the infrared using a genetic algorithm.
Bossard, Jeremy A; Lin, Lan; Werner, Douglas H
2016-01-01
Ordered and chaotic superlattices have been identified in Nature that give rise to a variety of colours reflected by the skin of various organisms. In particular, organisms such as silvery fish possess superlattices that reflect a broad range of light from the visible to the UV. Such superlattices have previously been identified as 'chaotic', but we propose that apparent 'chaotic' natural structures, which have been previously modelled as completely random structures, should have an underlying fractal geometry. Fractal geometry, often described as the geometry of Nature, can be used to mimic structures found in Nature, but deterministic fractals produce structures that are too 'perfect' to appear natural. Introducing variability into fractals produces structures that appear more natural. We suggest that the 'chaotic' (purely random) superlattices identified in Nature are more accurately modelled by multi-generator fractals. Furthermore, we introduce fractal random Cantor bars as a candidate for generating both ordered and 'chaotic' superlattices, such as the ones found in silvery fish. A genetic algorithm is used to evolve optimal fractal random Cantor bars with multiple generators targeting several desired optical functions in the mid-infrared and the near-infrared. We present optimized superlattices demonstrating broadband reflection as well as single and multiple pass bands in the near-infrared regime.
Evolving random fractal Cantor superlattices for the infrared using a genetic algorithm
Bossard, Jeremy A.; Lin, Lan; Werner, Douglas H.
2016-01-01
Ordered and chaotic superlattices have been identified in Nature that give rise to a variety of colours reflected by the skin of various organisms. In particular, organisms such as silvery fish possess superlattices that reflect a broad range of light from the visible to the UV. Such superlattices have previously been identified as ‘chaotic’, but we propose that apparent ‘chaotic’ natural structures, which have been previously modelled as completely random structures, should have an underlying fractal geometry. Fractal geometry, often described as the geometry of Nature, can be used to mimic structures found in Nature, but deterministic fractals produce structures that are too ‘perfect’ to appear natural. Introducing variability into fractals produces structures that appear more natural. We suggest that the ‘chaotic’ (purely random) superlattices identified in Nature are more accurately modelled by multi-generator fractals. Furthermore, we introduce fractal random Cantor bars as a candidate for generating both ordered and ‘chaotic’ superlattices, such as the ones found in silvery fish. A genetic algorithm is used to evolve optimal fractal random Cantor bars with multiple generators targeting several desired optical functions in the mid-infrared and the near-infrared. We present optimized superlattices demonstrating broadband reflection as well as single and multiple pass bands in the near-infrared regime. PMID:26763335
Separating Fractal and Oscillatory Components in the Power Spectrum of Neurophysiological Signal.
Wen, Haiguang; Liu, Zhongming
2016-01-01
Neurophysiological field-potential signals consist of both arrhythmic and rhythmic patterns indicative of the fractal and oscillatory dynamics arising from likely distinct mechanisms. Here, we present a new method, namely the irregular-resampling auto-spectral analysis (IRASA), to separate fractal and oscillatory components in the power spectrum of neurophysiological signal according to their distinct temporal and spectral characteristics. In this method, we irregularly resampled the neural signal by a set of non-integer factors, and statistically summarized the auto-power spectra of the resampled signals to separate the fractal component from the oscillatory component in the frequency domain. We tested this method on simulated data and demonstrated that IRASA could robustly separate the fractal component from the oscillatory component. In addition, applications of IRASA to macaque electrocorticography and human magnetoencephalography data revealed a greater power-law exponent of fractal dynamics during sleep compared to wakefulness. The temporal fluctuation in the broadband power of the fractal component revealed characteristic dynamics within and across the eyes-closed, eyes-open and sleep states. These results demonstrate the efficacy and potential applications of this method in analyzing electrophysiological signatures of large-scale neural circuit activity. We expect that the proposed method or its future variations would potentially allow for more specific characterization of the differential contributions of oscillatory and fractal dynamics to distributed neural processes underlying various brain functions.
Evolving random fractal Cantor superlattices for the infrared using a genetic algorithm.
Bossard, Jeremy A; Lin, Lan; Werner, Douglas H
2016-01-01
Ordered and chaotic superlattices have been identified in Nature that give rise to a variety of colours reflected by the skin of various organisms. In particular, organisms such as silvery fish possess superlattices that reflect a broad range of light from the visible to the UV. Such superlattices have previously been identified as 'chaotic', but we propose that apparent 'chaotic' natural structures, which have been previously modelled as completely random structures, should have an underlying fractal geometry. Fractal geometry, often described as the geometry of Nature, can be used to mimic structures found in Nature, but deterministic fractals produce structures that are too 'perfect' to appear natural. Introducing variability into fractals produces structures that appear more natural. We suggest that the 'chaotic' (purely random) superlattices identified in Nature are more accurately modelled by multi-generator fractals. Furthermore, we introduce fractal random Cantor bars as a candidate for generating both ordered and 'chaotic' superlattices, such as the ones found in silvery fish. A genetic algorithm is used to evolve optimal fractal random Cantor bars with multiple generators targeting several desired optical functions in the mid-infrared and the near-infrared. We present optimized superlattices demonstrating broadband reflection as well as single and multiple pass bands in the near-infrared regime. PMID:26763335
Launching the chaotic realm of iso-fractals: A short remark
O'Schmidt, Nathan; Katebi, Reza; Corda, Christian
2015-03-10
In this brief note, we introduce the new, emerging sub-discipline of iso-fractals by highlighting and discussing the preliminary results of recent works. First, we note the abundance of fractal, chaotic, non-linear, and self-similar structures in nature while emphasizing the importance of studying such systems because fractal geometry is the language of chaos. Second, we outline the iso-fractal generalization of the Mandelbrot set to exemplify the newly generated Mandelbrot iso-sets. Third, we present the cutting-edge notion of dynamic iso-spaces and explain how a mathematical space can be iso-topically lifted with iso-unit functions that (continuously or discretely) change; in the discrete case examples, we mention that iteratively generated sequences like Fibonacci’s numbers and (the complex moduli of) Mandelbrot’s numbers can supply a deterministic chain of iso-units to construct an ordered series of (magnified and/or de-magnified) iso-spaces that are locally iso-morphic. Fourth, we consider the initiation of iso-fractals with Inopin’s holographic ring (IHR) topology and fractional statistics for 2D and 3D iso-spaces. In total, the reviewed iso-fractal results are a significant improvement over traditional fractals because the application of Santilli’s iso-mathematics arms us an extra degree of freedom for attacking problems in chaos. Finally, we conclude by proposing some questions and ideas for future research work.
The generalized 20/80 law using probabilistic fractals applied to petroleum field size
Crovelli, R.A.
1995-01-01
Fractal properties of the Pareto probability distribution are used to generalize "the 20/80 law." The 20/80 law is a heuristic law that has evolved over the years into the following rule of thumb for many populations: 20 percent of the population accounts for 80 percent of the total value. The general p100/q100 law in probabilistic form is defined with q as a function of p, where p is the population proportion and q is the proportion of total value. Using the Pareto distribution, the p100/q100 law in fractal form is derived with the parameter q being a fractal, where q unexpectedly possesses the scale invariance property. The 20/80 law is a special case of the p100/q100 law in fractal form. The p100/q100 law in fractal form is applied to petroleum fieldsize data to obtain p and q such that p100% of the oil fields greater than any specified scale or size in a geologic play account for q100% of the total oil of the fields. The theoretical percentages of total resources of oil using the fractal q are extremely close to the empirical percentages from the data using the statistic q. Also, the empirical scale invariance property of the statistic q for the petroleum fieldsize data is in excellent agreement with the theoretical scale invariance property of the fractal q. ?? 1995 Oxford University Press.
Microtopographic Inspection and Fractal Analysis of Skin Neoplasia
NASA Astrophysics Data System (ADS)
Costa, Manuel F. M.; Hipolito, Alberto Valencia; Gutierrez, Gustavo Fidel; Chanona, Jorge; Gallegos, Eva Ramón
2008-04-01
Early detection of skin cancer is fundamental to a successful treatment. Changes in the shape, including the relief, of skin lesions are an indicator of a possible malignity. Optical microtopographic inspection of skin lesions can be used to identify diagnostic patterns of benign and malign skin' lesions. Statistical parameters like the mean roughness (Ra) may allow the discrimination between different types of lesions and degree of malignity. Fractal analysis of bi-dimensional and 3D images of skin lesions can validate or complement that assessment by calculation of its fractal dimensions (FD). On the study herein reported the microtopographic inspection of the skin lesions were performed using the optical triangulation based microtopographer developed at the Physics Department of the University of Minho, MICROTOP.03.MFC. The patients that participated in this research work were men and women older than 15 years with the clinical and histopathology diagnoses of: melanoma, basocellular carcinoma, epidermoide carcinoma, actinic keratosis, keratoacantosis and benign nevus. Latex impressions of the lesions were taken and microtopographically analyzed. Characteristic information for each type of studied lesion was obtained. For melanoma it was observed that on the average these tumors present an increased roughness of around 67 percent compared to the roughness of the healthy skin. This feature allows the distinction from other tumors as basocellular carcinoma (were the roughness increase was in the average of 49 percent) and benign lesions as the epidermoide cyst (37 percent) or the seborrhea keratosis (4 percent). Tumor size and roughness are directly proportional to the grade of malignality. The characterization of the fractal geometry of 2D (histological slides) and 3D images of skin lesions was performed by obtaining its FD evaluated by means of the Box counting method. Results obtained showed that the average fractal dimension of histological slide images (FDh
Method for non-referential defect characterization using fractal encoding and active contours
Gleason, Shaun S.; Sari-Sarraf, Hamed
2007-05-15
A method for identification of anomalous structures, such as defects, includes the steps of providing a digital image and applying fractal encoding to identify a location of at least one anomalous portion of the image. The method does not require a reference image to identify the location of the anomalous portion. The method can further include the step of initializing an active contour based on the location information obtained from the fractal encoding step and deforming an active contour to enhance the boundary delineation of the anomalous portion.
Quantum Fractals: From Heisenberg's Uncertainty to Barnsley's Fractality
NASA Astrophysics Data System (ADS)
Jadczyk, Arkadiusz
2014-07-01
This book brings together two concepts. The first is over a hundred years old -- the "quantum", while the second, "fractals", is newer, achieving popularity after the pioneering work of Benoit Mandelbrot. Both areas of research are expanding dramatically day by day. It is somewhat amazing that quantum theory, in spite of its age, is still a boiling mystery as we see in some quotes from recent publications addressed to non-expert readers:...
Mapping Variation in Vegetation Functioning with Imaging Spectroscopy
NASA Astrophysics Data System (ADS)
Townsend, P. A.; Couture, J. J.; Kruger, E. L.; Serbin, S.; Singh, A.
2015-12-01
Imaging spectroscopy (otherwise known as hyperspectral remote sensing) offers the potential to characterize the spatial and temporal variation in biophysical and biochemical properties of vegetation that can be costly or logistically difficult to measure comprehensively using traditional methods. A number of recent studies have illustrated the capacity for imaging spectroscopy data, such as from NASA's AVIRIS sensor, to empirically estimate functional traits related to foliar chemistry and physiology (Singh et al. 2015, Serbin et al. 2015). Here, we present analyses that illustrate the implications of those studies to characterize within-field or -stand variability in ecosystem functioning. In agricultural ecosystems, within-field photosynthetic capacity can vary by 30-50%, likely due to within-field variations in water availability and soil fertility. In general, the variability of foliar traits is lower in forests than agriculture, but can still be significant. Finally, we demonstrate that functional trait variability at the stand scale is strongly related to vegetation diversity. These results have two significant implications: 1) reliance on a small number of field samples to broadly estimate functional traits likely underestimates variability in those traits, and 2) if trait estimations from imaging spectroscopy are reliable, such data offer the opportunity to greatly increase the density of measurements we can use to predict ecosystem function.
Intrinsic signal imaging of brain function using a small implantable CMOS imaging device
NASA Astrophysics Data System (ADS)
Haruta, Makito; Sunaga, Yoshinori; Yamaguchi, Takahiro; Takehara, Hironari; Noda, Toshihiko; Sasagawa, Kiyotaka; Tokuda, Takashi; Ohta, Jun
2015-04-01
A brain functional imaging technique over a long period is important to understand brain functions related to animal behavior. We have developed a small implantable CMOS imaging device for measuring brain activity in freely moving animals. This device is composed of a CMOS image sensor chip and LEDs for illumination. In this study, we demonstrated intrinsic signal imaging of blood flow using the device with a green LED light source at a peak wavelength of 535 nm, which corresponds to one of the absorption spectral peaks of blood cells. Brain activity increases regional blood flow. The device light weight of about 0.02 g makes it possible to stably measure brain activity through blood flow over a long period. The device has successfully measured the intrinsic signal related to sensory stimulation on the primary somatosensory cortex.
Functional Neuro-Imaging and Post-Traumatic Olfactory Impairment
Roberts, Richard J.; Sheehan, William; Thurber, Steven; Roberts, Mary Ann
2010-01-01
Objective: To evaluate via a research literature survey the anterior neurological significance of decreased olfactory functioning following traumatic brain injuries. Materials and Methods: A computer literature review was performed to locate all functional neuro-imaging studies on patients with post-traumatic anosmia and other olfactory deficits. Results: A convergence of findings from nine functional neuro-imaging studies indicating evidence for reduced metabolic activity at rest or relative hypo-perfusion during olfactory activations. Hypo-activation of the prefrontal regions was apparent in all nine post-traumatic samples, with three samples yielding evidence of reduced activity in the temporal regions as well. Conclusions: The practical ramifications include the reasonable hypothesis that a total anosmic head trauma patient likely has frontal lobe involvement. PMID:21716782
Conformal dynamics of fractal growth patterns without randomness
Davidovitch; Feigenbaum; Hentschel; Procaccia
2000-08-01
Many models of fractal growth patterns (such as diffusion limited aggregation and dielectric breakdown models) combine complex geometry with randomness; this double difficulty is a stumbling block to their elucidation. In this paper we introduce a wide class of fractal growth models with highly complex geometry but without any randomness in their growth rules. The models are defined in terms of deterministic itineraries of iterated conformal maps, generating the function Phi((n))(omega) which maps the exterior of the unit circle to the exterior of an n-particle growing aggregate. The complexity of the evolving interfaces is fully contained in the deterministic dynamics of the conformal map Phi((n))(omega). We focus attention on a class of growth models in which the itinerary is quasiperiodic. Such itineraries can be approached via a series of rational approximants. The analytic power gained is used to introduce a scaling theory of the fractal growth patterns and to identify the exponent that determines the fractal dimension.
Multiscale Fractal Characterization of Hierarchical Heterogeneity in Sandstone Reservoirs
NASA Astrophysics Data System (ADS)
Liu, Yanfeng; Liu, Yuetian; Sun, Lu; Liu, Jian
2016-07-01
Heterogeneities affecting reservoirs often develop at different scales. Previous studies have described these heterogeneities using different parameters depending on their size, and there is no one comprehensive method of reservoir evaluation that considers every scale. This paper introduces a multiscale fractal approach to quantify consistently the hierarchical heterogeneities of sandstone reservoirs. Materials taken from typical depositional pattern and aerial photography are used to represent three main types of sandstone reservoir: turbidite, braided, and meandering river system. Subsequent multiscale fractal dimension analysis using the Bouligand-Minkowski method characterizes well the hierarchical heterogeneity of the sandstone reservoirs. The multiscale fractal dimension provides a curve function that describes the heterogeneity at different scales. The heterogeneity of a reservoir’s internal structure decreases as the observational scale increases. The shape of a deposit’s facies is vital for quantitative determination of the sedimentation type, and thus enhanced oil recovery. Characterization of hierarchical heterogeneity by multiscale fractal dimension can assist reservoir evaluation, geological modeling, and even the design of well patterns.
Fractal Reference Signals in Pulse-Width Modulation
NASA Technical Reports Server (NTRS)
Lurie, Boris; Lurie, Helen
2005-01-01
A report proposes the use of waveforms having fractal shapes reminiscent of sawteeth (in contradistinction to conventional regular sawtooth waveforms) as reference signals for pulse-width modulation in control systems for thrusters of spacecraft flying in formation. Fractal reference signals may also be attractive in some terrestrial control systems - especially those in which pulse-width modulation is used for precise control of electric motors. The report asserts that the use of fractal reference signals would enable the synchronous control of several variables of a spacecraft formation, such that consumption of propellant would be minimized, intervals between thruster firings would be long (as preferred for performing scientific observations), and delays in controlling large-thrust maneuvers for retargeting would be minimized. The report further asserts that whereas different controllers would be needed for different modes of operation if conventional pulsewidth modulation were used, the use of fractal reference signals would enable the same controller to function nearly optimally in all regimes of operation, so that only this one controller would be needed.
Fractal applications to complex crustal problems
NASA Technical Reports Server (NTRS)
Turcotte, Donald L.
1989-01-01
Complex scale-invariant problems obey fractal statistics. The basic definition of a fractal distribution is that the number of objects with a characteristic linear dimension greater than r satisfies the relation N = about r exp -D where D is the fractal dimension. Fragmentation often satisfies this relation. The distribution of earthquakes satisfies this relation. The classic relationship between the length of a rocky coast line and the step length can be derived from this relation. Power law relations for spectra can also be related to fractal dimensions. Topography and gravity are examples. Spectral techniques can be used to obtain maps of fractal dimension and roughness amplitude. These provide a quantitative measure of texture analysis. It is argued that the distribution of stress and strength in a complex crustal region, such as the Alps, is fractal. Based on this assumption, the observed frequency-magnitude relation for the seismicity in the region can be derived.
Group theoretic reduction of Laplacian dynamical problems on fractal lattices
Schwalm, W.A.; Schwalm, M.K.; Giona, M.
1997-06-01
Discrete forms of the Schr{umlt o}dinger equation, the diffusion equation, the linearized Landau-Ginzburg equation, and discrete models for vibrations and spin dynamics belong to a class of Laplacian-based finite difference models. Real-space renormalization of such models on finitely ramified regular fractals is known to give exact recursion relations. It is shown that these recursions commute with Lie groups representing continuous symmetries of the discrete models. Each such symmetry reduces the order of the renormalization recursions by one, resulting in a system of recursions with one fewer variable. Group trajectories are obtained from inverse images of fixed and invariant sets of the recursions. A subset of the Laplacian finite difference models can be mapped by change of boundary conditions and time dependence to a diffusion problem with closed boundaries. In such cases conservation of mass simplifies the group flow and obtaining the groups becomes easier. To illustrate this, the renormalization recursions for Green functions on four standard examples are decoupled. The examples are (1) the linear chain, (2) an anisotropic version of Dhar{close_quote}s 3-simplex, similar to a model dealt with by Hood and Southern, (3) the fourfold coordinated Sierpi{acute n}ski lattice of Rammal and of Domany {ital et al.}, and (4) a form of the Vicsek lattice. Prospects for applying the group theoretic method to more general dynamical systems are discussed. {copyright} {ital 1997} {ital The American Physical Society}
A method for functional magnetic resonance imaging of olfaction.
Sobel, N; Prabhakaran, V; Desmond, J E; Glover, G H; Sullivan, E V; Gabrieli, J D
1997-12-30
A method for generating olfactory stimuli for humans within a functional magnetic resonance imaging (fMRI) experimental design is described. The system incorporates a nasal-mask in which the change from odorant to no-odorant conditions occurs in less than 500 ms and is not accompanied by visual, auditory, tactile, or thermal cues. The mask provides an ordorant-free environment following prolonged ordorant presence. Specific imaging parameters that are conducive to the study of the human olfactory system are described. In a pilot study performed using these methods, the specific patterns of activation observed converged with published experimental and clinical findings. PMID:9497007
Emission of terahertz radiations from fractal antennas
NASA Astrophysics Data System (ADS)
Miyamaru, F.; Saito, Y.; Takeda, M. W.; Liu, L.; Hou, B.; Wen, W.; Sheng, Ping
2009-11-01
We investigate the emission of terahertz radiation from a photoconductive fractal antenna fabricated on a semi-insulating gallium arsenide substrate. Owing to the self-similarity of fractal structures, our fractal antenna shows a multiband emission of terahertz radiation. The emission intensity at peak frequency is about twice that from a bow-tie antenna. We also investigate the mechanism of the multiband emission by using the finite-difference time-domain calculation.
Ghosh, Subrata; Dutta, Mrinal; Ray, Kanad; Fujita, Daisuke; Bandyopadhyay, Anirban
2016-06-01
We introduce a new class of fractal reaction kinetics wherein two or more distinct fractal structures are synthesized as parts of a singular cascade reaction in a single chemical beaker. Two examples: sphere ↔ spiral & triangle ↔ square fractals, grow 10(6) orders from a single dendrimer (8 nm) to the visible scale. PMID:27166589
Fractal model of anomalous diffusion.
Gmachowski, Lech
2015-12-01
An equation of motion is derived from fractal analysis of the Brownian particle trajectory in which the asymptotic fractal dimension of the trajectory has a required value. The formula makes it possible to calculate the time dependence of the mean square displacement for both short and long periods when the molecule diffuses anomalously. The anomalous diffusion which occurs after long periods is characterized by two variables, the transport coefficient and the anomalous diffusion exponent. An explicit formula is derived for the transport coefficient, which is related to the diffusion constant, as dependent on the Brownian step time, and the anomalous diffusion exponent. The model makes it possible to deduce anomalous diffusion properties from experimental data obtained even for short time periods and to estimate the transport coefficient in systems for which the diffusion behavior has been investigated. The results were confirmed for both sub and super-diffusion.
Surface fractals in liposome aggregation.
Roldán-Vargas, Sándalo; Barnadas-Rodríguez, Ramon; Quesada-Pérez, Manuel; Estelrich, Joan; Callejas-Fernández, José
2009-01-01
In this work, the aggregation of charged liposomes induced by magnesium is investigated. Static and dynamic light scattering, Fourier-transform infrared spectroscopy, and cryotransmission electron microscopy are used as experimental techniques. In particular, multiple intracluster scattering is reduced to a negligible amount using a cross-correlation light scattering scheme. The analysis of the cluster structure, probed by means of static light scattering, reveals an evolution from surface fractals to mass fractals with increasing magnesium concentration. Cryotransmission electron microscopy micrographs of the aggregates are consistent with this interpretation. In addition, a comparative analysis of these results with those previously reported in the presence of calcium suggests that the different hydration energy between lipid vesicles when these divalent cations are present plays a fundamental role in the cluster morphology. This suggestion is also supported by infrared spectroscopy data. The kinetics of the aggregation processes is also analyzed through the time evolution of the mean diffusion coefficient of the aggregates. PMID:19257067
Surface fractals in liposome aggregation.
Roldán-Vargas, Sándalo; Barnadas-Rodríguez, Ramon; Quesada-Pérez, Manuel; Estelrich, Joan; Callejas-Fernández, José
2009-01-01
In this work, the aggregation of charged liposomes induced by magnesium is investigated. Static and dynamic light scattering, Fourier-transform infrared spectroscopy, and cryotransmission electron microscopy are used as experimental techniques. In particular, multiple intracluster scattering is reduced to a negligible amount using a cross-correlation light scattering scheme. The analysis of the cluster structure, probed by means of static light scattering, reveals an evolution from surface fractals to mass fractals with increasing magnesium concentration. Cryotransmission electron microscopy micrographs of the aggregates are consistent with this interpretation. In addition, a comparative analysis of these results with those previously reported in the presence of calcium suggests that the different hydration energy between lipid vesicles when these divalent cations are present plays a fundamental role in the cluster morphology. This suggestion is also supported by infrared spectroscopy data. The kinetics of the aggregation processes is also analyzed through the time evolution of the mean diffusion coefficient of the aggregates.
Fuzzy fractals, chaos, and noise
Zardecki, A.
1997-05-01
To distinguish between chaotic and noisy processes, the authors analyze one- and two-dimensional chaotic mappings, supplemented by the additive noise terms. The predictive power of a fuzzy rule-based system allows one to distinguish ergodic and chaotic time series: in an ergodic series the likelihood of finding large numbers is small compared to the likelihood of finding them in a chaotic series. In the case of two dimensions, they consider the fractal fuzzy sets whose {alpha}-cuts are fractals, arising in the context of a quadratic mapping in the extended complex plane. In an example provided by the Julia set, the concept of Hausdorff dimension enables one to decide in favor of chaotic or noisy evolution.
Vectorial point spread function and optical transfer function in oblique plane imaging.
Kim, Jeongmin; Li, Tongcang; Wang, Yuan; Zhang, Xiang
2014-05-01
Oblique plane imaging, using remote focusing with a tilted mirror, enables direct two-dimensional (2D) imaging of any inclined plane of interest in three-dimensional (3D) specimens. It can image real-time dynamics of a living sample that changes rapidly or evolves its structure along arbitrary orientations. It also allows direct observations of any tilted target plane in an object of which orientational information is inaccessible during sample preparation. In this work, we study the optical resolution of this innovative wide-field imaging method. Using the vectorial diffraction theory, we formulate the vectorial point spread function (PSF) of direct oblique plane imaging. The anisotropic lateral resolving power caused by light clipping from the tilted mirror is theoretically analyzed for all oblique angles. We show that the 2D PSF in oblique plane imaging is conceptually different from the inclined 2D slice of the 3D PSF in conventional lateral imaging. Vectorial optical transfer function (OTF) of oblique plane imaging is also calculated by the fast Fourier transform (FFT) method to study effects of oblique angles on frequency responses.
The fractal dimensions of the spatial distribution of young open clusters in the solar neighbourhood
NASA Astrophysics Data System (ADS)
de La Fuente Marcos, R.; de La Fuente Marcos, C.
2006-06-01
Context: .Fractals are geometric objects with dimensionalities that are not integers. They play a fundamental role in the dynamics of chaotic systems. Observation of fractal structure in both the gas and the star-forming sites in galaxies suggests that the spatial distribution of young open clusters should follow a fractal pattern, too. Aims: .Here we investigate the fractal pattern of the distribution of young open clusters in the Solar Neighbourhood using a volume-limited sample from WEBDA and a multifractal analysis. By counting the number of objects inside spheres of different radii centred on clusters, we study the homogeneity of the distribution. Methods: .The fractal dimension D of the spatial distribution of a volume-limited sample of young open clusters is determined by analysing different moments of the count-in-cells. The spectrum of the Minkowski-Bouligand dimension of the distribution is studied as a function of the parameter q. The sample is corrected for dynamical effects. Results: .The Minkowski-Bouligand dimension varies with q in the range 0.71-1.77, therefore the distribution of young open clusters is fractal. We estimate that the average value of the fractal dimension is < D> = 1.7± 0.2 for the distribution of young open clusters studied. Conclusions: .The spatial distribution of young open clusters in the Solar Neighbourhood exhibits multifractal structure. The fractal dimension is time-dependent, increasing over time. The values found are consistent with the fractal dimension of star-forming sites in other spiral galaxies.
Fractal superconductivity near localization threshold
Feigel'man, M.V.; Ioffe, L.B.; Kravtsov, V.E.; Cuevas, E.
2010-07-15
We develop a semi-quantitative theory of electron pairing and resulting superconductivity in bulk 'poor conductors' in which Fermi energy E{sub F} is located in the region of localized states not so far from the Anderson mobility edge E{sub c}. We assume attractive interaction between electrons near the Fermi surface. We review the existing theories and experimental data and argue that a large class of disordered films is described by this model. Our theoretical analysis is based on analytical treatment of pairing correlations, described in the basis of the exact single-particle eigenstates of the 3D Anderson model, which we combine with numerical data on eigenfunction correlations. Fractal nature of critical wavefunction's correlations is shown to be crucial for the physics of these systems. We identify three distinct phases: 'critical' superconductive state formed at E{sub F} = E{sub c}, superconducting state with a strong pseudo-gap, realized due to pairing of weakly localized electrons and insulating state realized at E{sub F} still deeper inside a localized band. The 'critical' superconducting phase is characterized by the enhancement of the transition temperature with respect to BCS result, by the inhomogeneous spatial distribution of superconductive order parameter and local density of states. The major new feature of the pseudo-gapped state is the presence of two independent energy scales: superconducting gap {Delta}, that is due to many-body correlations and a new 'pseudo-gap' energy scale {Delta}{sub P} which characterizes typical binding energy of localized electron pairs and leads to the insulating behavior of the resistivity as a function of temperature above superconductive T{sub c}. Two gap nature of the pseudo-gapped superconductor is shown to lead to specific features seen in scanning tunneling spectroscopy and point-contact Andreev spectroscopy. We predict that pseudo-gapped superconducting state demonstrates anomalous behavior of the optical
Functional laser speckle imaging of cerebral blood flow under hypothermia
NASA Astrophysics Data System (ADS)
Li, Minheng; Miao, Peng; Zhu, Yisheng; Tong, Shanbao
2011-08-01
Hypothermia can unintentionally occur in daily life, e.g., in cardiovascular surgery or applied as therapeutics in the neurosciences critical care unit. So far, the temperature-induced spatiotemporal responses of the neural function have not been fully understood. In this study, we investigated the functional change in cerebral blood flow (CBF), accompanied with neuronal activation, by laser speckle imaging (LSI) during hypothermia. Laser speckle images from Sprague-Dawley rats (n = 8, male) were acquired under normothermia (37°C) and moderate hypothermia (32°C). For each animal, 10 trials of electrical hindpaw stimulation were delivered under both temperatures. Using registered laser speckle contrast analysis and temporal clustering analysis (TCA), we found a delayed response peak and a prolonged response window under hypothermia. Hypothermia also decreased the activation area and the amplitude of the peak CBF. The combination of LSI and TCA is a high-resolution functional imaging method to investigate the spatiotemporal neurovascular coupling in both normal and pathological brain functions.
Functional imaging of the lungs with gas agents.
Kruger, Stanley J; Nagle, Scott K; Couch, Marcus J; Ohno, Yoshiharu; Albert, Mitchell; Fain, Sean B
2016-02-01
This review focuses on the state-of-the-art of the three major classes of gas contrast agents used in magnetic resonance imaging (MRI)-hyperpolarized (HP) gas, molecular oxygen, and fluorinated gas--and their application to clinical pulmonary research. During the past several years there has been accelerated development of pulmonary MRI. This has been driven in part by concerns regarding ionizing radiation using multidetector computed tomography (CT). However, MRI also offers capabilities for fast multispectral and functional imaging using gas agents that are not technically feasible with CT. Recent improvements in gradient performance and radial acquisition methods using ultrashort echo time (UTE) have contributed to advances in these functional pulmonary MRI techniques. The relative strengths and weaknesses of the main functional imaging methods and gas agents are compared and applications to measures of ventilation, diffusion, and gas exchange are presented. Functional lung MRI methods using these gas agents are improving our understanding of a wide range of chronic lung diseases, including chronic obstructive pulmonary disease, asthma, and cystic fibrosis in both adults and children.
Dopaminergic action beyond its effects on motor function: imaging studies.
Brooks, David J
2006-08-01
Along with motor programming, it is now thought that tonic release of dopamine in the striatum acts to focus and filter non-motor activities such as working memory, implicit learning, decision making, and planning. Additionally, thresholds to painful stimuli may well be dopamine dependant. Phasic (burst) release of dopamine in the basal ganglia and frontal areas is thought to play a role in alerting organisms to novel and potentially rewarding stimuli and in mediating contextual learning. Dopamine release also drives a craving for stimuli and facilitates their enjoyment. Functional imaging can help elucidate the role of dopamine in mediating non-motor activities. The integrity of dopamine terminal function can be measured with PET and SPECT in vivo in health and Parkinson's disease (PD) and this can be correlated with performance of executive tasks. In addition, these imaging modalities allow dopamine release in response to stimuli (both rewarding and unrewarding) to be detected, as reflected by changes in D2 receptor availability to radioligands. Finally, the functional effects of dopamine deficiency and its replacement can be monitored by studying patterns of brain activation, as evidenced by regional blood flow changes. In this review, some of the insights that imaging has given us concerning the role of dopamine in non-motor functions is presented.
Order-fractal transitions in abstract paintings
NASA Astrophysics Data System (ADS)
de la Calleja, E. M.; Cervantes, F.; de la Calleja, J.
2016-08-01
In this study, we determined the degree of order for 22 Jackson Pollock paintings using the Hausdorff-Besicovitch fractal dimension. Based on the maximum value of each multi-fractal spectrum, the artworks were classified according to the year in which they were painted. It has been reported that Pollock's paintings are fractal and that this feature was more evident in his later works. However, our results show that the fractal dimension of these paintings ranges among values close to two. We characterize this behavior as a fractal-order transition. Based on the study of disorder-order transition in physical systems, we interpreted the fractal-order transition via the dark paint strokes in Pollock's paintings as structured lines that follow a power law measured by the fractal dimension. We determined self-similarity in specific paintings, thereby demonstrating an important dependence on the scale of observations. We also characterized the fractal spectrum for the painting entitled Teri's Find. We obtained similar spectra for Teri's Find and Number 5, thereby suggesting that the fractal dimension cannot be rejected completely as a quantitative parameter for authenticating these artworks.
Some problems in fractal differential equations
NASA Astrophysics Data System (ADS)
Su, Weiyi
2016-06-01
Based upon the fractal calculus on local fields, or p-type calculus, or Gibbs-Butzer calculus ([1],[2]), we suggest a constructive idea for "fractal differential equations", beginning from some special examples to a general theory. However, this is just an original idea, it needs lots of later work to support. In [3], we show example "two dimension wave equations with fractal boundaries", and in this note, other examples, as well as an idea to construct fractal differential equations are shown.
Stability limits for bioconvective fractals - Microgravity prospects
NASA Technical Reports Server (NTRS)
Noever, David A.
1992-01-01
Fractal objects are delicate aggregates which show self-similar behavior and vanishing density for increasing length scales. In practice real fractals in nature however possess only a limited region of verifiable self-similarity. As natural fractal objects increase in size, they become easier to disrupt mechanically. Herein the effects of thermal vibrations and gravity are investigated as deforming forces on fractal aggregation. Example calculations are carried out on a biological fractal formed from the surface aggregation of various cells such as alga and bacteria. For typical cell parameters, the predicted diameter of this so-called 'bioconvective' fractal agrees well with the observed limits of about 5 cm. On earth, this size represents an experimental maximum for finding bioconvective fractal objects. To extend this size range of fractals available for statistical study, a reduced gravity environment offers one way to achieve larger fractals. For these enhanced sizes, the present scaling predicts that microgravity can yield up to a 35-fold improvement in extending statistical resolution.
Electrodynamic properties of fractal clusters
NASA Astrophysics Data System (ADS)
Maksimenko, V. V.; Zagaynov, V. A.; Agranovski, I. E.
2014-07-01
An influence of interference on a character of light interaction both with individual fractal cluster (FC) consisting of nanoparticles and with agglomerates of such clusters is investigated. Using methods of the multiple scattering theory, effective dielectric permeability of a micron-size FC composed of non-absorbing nanoparticles is calculated. The cluster could be characterized by a set of effective dielectric permeabilities. Their number coincides with the number of particles, where space arrangement in the cluster is correlated. If the fractal dimension is less than some critical value and frequency corresponds to the frequency of the visible spectrum, then the absolute value of effective dielectric permeability becomes very large. This results in strong renormalization (decrease) of the incident radiation wavelength inside the cluster. The renormalized photons are cycled or trapped inside the system of multi-scaled cavities inside the cluster. A lifetime of a photon localized inside an agglomerate of FCs is a macroscopic value allowing to observe the stimulated emission of the localized light. The latter opens up a possibility for creation of lasers without inverse population of energy levels. Moreover, this allows to reconsider problems of optical cloaking of macroscopic objects. One more feature of fractal structures is a possibility of unimpeded propagation of light when any resistance associated with scattering disappears.
Is Hydroclimate Fractal? Another Look
NASA Astrophysics Data System (ADS)
Fleming, S. W.
2012-04-01
Fractal dynamics, defined for our purposes as log-space linear scaling of the power spectrum, are important to water resource scientists for two broad reasons. The first is fundamental: such behaviour is commonly believed to be very widespread in nature, and is therefore a central and important feature of physical systems - including watershed hydrological systems. The second is practical: associated properties, such as runs and clustering, violate the usual assumptions of many standard statistical and time series analysis techniques in applied hydrology and climatology, such as flood frequency analysis and long-term trend analysis. Recent work, however, has indicated that some instrumental climatic and hydroclimatic records, which seem initially suggestive of 1/f ^β scaling, may in fact be insufficiently long to reliably distinguish between fractal dynamics and simpler, low-order linear memory processes which are also known to be common in such systems. With the aim of more carefully assessing the general presence of fractal dynamics in light of historical environmental dataset limitations, we apply here a simple new rule-of-thumb for record length sufficiency, in conjunction with standard Fourier transform-based spectral analysis techniques, to a smorgasbord of long-term time series drawn from watershed hydrology, climatology, and glaciology at various study sites worldwide.
Longitudinal, multimodal functional imaging of microvascular response to photothermal therapy
Bui, Albert K.; Teves, Kathleen M.; Indrawan, Elmer; Jia, Wangcun; Choi, Bernard
2012-01-01
Although studies have shown that photothermal therapy can coagulate selectively abnormal vasculature, the ability of this method to achieve consistent, complete removal of the vasculature is questionable. We present the use of multimodal, wide-field functional imaging to study, in greater detail, the biological response to selective laser injury. Specifically, a single-platform instrument capable of coregistered fluorescence imaging and laser speckle imaging was utilized to monitor vascular endothelial growth factor gene expression and blood flow, respectively, in a transgenic rodent model. Collectively, the longitudinal, in vivo data collected with our instrument suggest that the biological response to selective laser injury involves early-stage redistribution of blood flow, followed by increased vascular endothelial growth factor promoter activity to stimulate pro-angiogenic events. PMID:20890338
Azevedo, S.G.; Fitch, J.P.
1987-10-21
Conventional software interfaces that use imperative computer commands or menu interactions are often restrictive environments when used for researching new algorithms or analyzing processed experimental data. We found this to be true with current signal-processing software (SIG). As an alternative, ''functional language'' interfaces provide features such as command nesting for a more natural interaction with the data. The Image and Signal LISP Environment (ISLE) is an example of an interpreted functional language interface based on common LISP. Advantages of ISLE include multidimensional and multiple data-type independence through dispatching functions, dynamic loading of new functions, and connections to artificial intelligence (AI) software. 10 refs.
Azevedo, S.G.; Fitch, J.P.
1987-05-01
Conventional software interfaces which utilize imperative computer commands or menu interactions are often restrictive environments when used for researching new algorithms or analyzing processed experimental data. We found this to be true with current signal processing software (SIG). Existing ''functional language'' interfaces provide features such as command nesting for a more natural interaction with the data. The Image and Signal Lisp Environment (ISLE) will be discussed as an example of an interpreted functional language interface based on Common LISP. Additional benefits include multidimensional and multiple data-type independence through dispatching functions, dynamic loading of new functions, and connections to artificial intelligence software.
Fractal analysis of radiologists' visual scanning pattern in screening mammography
NASA Astrophysics Data System (ADS)
Alamudun, Folami T.; Yoon, Hong-Jun; Hudson, Kathy; Morin-Ducote, Garnetta; Tourassi, Georgia
2015-03-01
Several researchers have investigated radiologists' visual scanning patterns with respect to features such as total time examining a case, time to initially hit true lesions, number of hits, etc. The purpose of this study was to examine the complexity of the radiologists' visual scanning pattern when viewing 4-view mammographic cases, as they typically do in clinical practice. Gaze data were collected from 10 readers (3 breast imaging experts and 7 radiology residents) while reviewing 100 screening mammograms (24 normal, 26 benign, 50 malignant). The radiologists' scanpaths across the 4 mammographic views were mapped to a single 2-D image plane. Then, fractal analysis was applied on the composite 4- view scanpaths. For each case, the complexity of each radiologist's scanpath was measured using fractal dimension estimated with the box counting method. The association between the fractal dimension of the radiologists' visual scanpath, case pathology, case density, and radiologist experience was evaluated using fixed effects ANOVA. ANOVA showed that the complexity of the radiologists' visual search pattern in screening mammography is dependent on case specific attributes (breast parenchyma density and case pathology) as well as on reader attributes, namely experience level. Visual scanning patterns are significantly different for benign and malignant cases than for normal cases. There is also substantial inter-observer variability which cannot be explained only by experience level.
Fractal dimension and mechanism of aggregation of apple juice particles.
Benítez, E I; Lozano, J E; Genovese, D B
2010-04-01
Turbidity of freshly squeezed apple juice is produced by a polydisperse suspension of particles coming from the cellular tissue. After precipitation of coarse particles by gravity, only fine-colloidal particles remain in suspension. Aggregation of colloidal particles leads to the formation of fractal structures. The fractal dimension is a measure of the internal density of these aggregates and depends on their mechanism of aggregation. Digitized images of primary particles and aggregates of depectinized, diafiltered cloudy apple juice were obtained by scanning electron microscopy (SEM). Average radius of the primary particles was found to be a = 40 ± 11 nm. Maximum radius of the aggregates, R(L), ranged between 250 and 7750 nm. Fractal dimension of the aggregates was determined by analyzing SEM images with the variogram method, obtaining an average value of D(f) = 2.3 ± 0.1. This value is typical of aggregates formed by rapid flocculation or diffusion limited aggregation. Diafiltration process was found to reduce the average size and polydispersity of the aggregates, determined by photon correlation spectroscopy. Average gyration radius of the aggregates before juice diafiltration was found to be R(g) = 629 ± 87 nm. Average number of primary particles per aggregate was calculated to be N = 1174. PMID:21339133
Functional transcranial brain imaging by optical-resolution photoacoustic microscopy
NASA Astrophysics Data System (ADS)
Hu, Song; Maslov, Konstantin; Tsytsarev, Vassiliy; Wang, Lihong V.
2009-07-01
Optical-resolution photoacoustic microscopy (OR-PAM) is applied to functional brain imaging in living mice. A near-diffraction-limited bright-field optical illumination is employed to achieve micrometer lateral resolution, and a dual-wavelength measurement is utilized to extract the blood oxygenation information. The variation in hemoglobin oxygen saturation (sO2) along vascular branching has been imaged in a precapillary arteriolar tree and a postcapillary venular tree, respectively. To the best of our knowledge, this is the first report on in vivo volumetric imaging of brain microvascular morphology and oxygenation down to single capillaries through intact mouse skulls. It is anticipated that: (i) chronic imaging enabled by this minimally invasive procedure will advance the study of cortical plasticity and neurological diseases; (ii) revealing the neuroactivity-dependent changes in hemoglobin concentration and oxygenation will facilitate the understanding of neurovascular coupling at the capillary level; and (iii) combining functional OR-PAM and high-resolution blood flowmetry will have the potential to explore cellular pathways of brain energy metabolism.