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.
NASA Astrophysics Data System (ADS)
Jia, Peng; Cai, Dongmei; Wang, Dong
2014-11-01
A parallel blind deconvolution algorithm is presented. The algorithm contains the constraints of the point spread function (PSF) derived from the physical process of the imaging. Additionally, in order to obtain an effective restored image, the fractal energy ratio is used as an evaluation criterion to estimate the quality of the image. This algorithm is fine-grained parallelized to increase the calculation speed. Results of numerical experiments and real experiments indicate that this algorithm is effective.
Study on Huber fractal image compression.
Jeng, Jyh-Horng; Tseng, Chun-Chieh; Hsieh, Jer-Guang
2009-05-01
In this paper, a new similarity measure for fractal image compression (FIC) is introduced. In the proposed Huber fractal image compression (HFIC), the linear Huber regression technique from robust statistics is embedded into the encoding procedure of the fractal image compression. When the original image is corrupted by noises, we argue that the fractal image compression scheme should be insensitive to those noises presented in the corrupted image. This leads to a new concept of robust fractal image compression. The proposed HFIC is one of our attempts toward the design of robust fractal image compression. The main disadvantage of HFIC is the high computational cost. To overcome this drawback, particle swarm optimization (PSO) technique is utilized to reduce the searching time. Simulation results show that the proposed HFIC is robust against outliers in the image. Also, the PSO method can effectively reduce the encoding time while retaining the quality of the retrieved image.
Fractal-based image edge detection
NASA Astrophysics Data System (ADS)
Luo, Huiguo; Zhu, Yaoting; Zhu, Guang-Xi; Wan, Faguang; Zhang, Ping
1993-08-01
Image edge is an important feature of image. Usually, we use Laplacian or Sober operator to get an image edge. In this paper, we use fractal method to get the edge. After introducing Fractal Brownian Random (FBR) field, we give the definition of Discrete Fractal Brownian Increase Random (DFBIR) field and discuss its properties, then we apply the DFBIR field to detect the edge of an image. According to the parameters H and D of DFBIR, we give a measure M equals (alpha) H + (beta) D. From the M value of each pixel, we can detect the edge of image.
Multi-Scale Fractal Analysis of Image Texture and Pattern
NASA Technical Reports Server (NTRS)
Emerson, Charles W.
1998-01-01
Fractals embody important ideas of self-similarity, in which the spatial behavior or appearance of a system is largely independent of scale. Self-similarity is defined as a property of curves or surfaces where each part is indistinguishable from the whole, or where the form of the curve or surface is invariant with respect to scale. An ideal fractal (or monofractal) curve or surface has a constant dimension over all scales, although it may not be an integer value. This is in contrast to Euclidean or topological dimensions, where discrete one, two, and three dimensions describe curves, planes, and volumes. Theoretically, if the digital numbers of a remotely sensed image resemble an ideal fractal surface, then due to the self-similarity property, the fractal dimension of the image will not vary with scale and resolution. However, most geographical phenomena are not strictly self-similar at all scales, but they can often be modeled by a stochastic fractal in which the scaling and self-similarity properties of the fractal have inexact patterns that can be described by statistics. Stochastic fractal sets relax the monofractal self-similarity assumption and measure many scales and resolutions in order to represent the varying form of a phenomenon as a function of local variables across space. In image interpretation, pattern is defined as the overall spatial form of related features, and the repetition of certain forms is a characteristic pattern found in many cultural objects and some natural features. Texture is the visual impression of coarseness or smoothness caused by the variability or uniformity of image tone or color. A potential use of fractals concerns the analysis of image texture. In these situations it is commonly observed that the degree of roughness or inexactness in an image or surface is a function of scale and not of experimental technique. The fractal dimension of remote sensing data could yield quantitative insight on the spatial complexity and
Fractal Image Informatics: from SEM to DEM
NASA Astrophysics Data System (ADS)
Oleschko, K.; Parrot, J.-F.; Korvin, G.; Esteves, M.; Vauclin, M.; Torres-Argüelles, V.; Salado, C. Gaona; Cherkasov, S.
2008-05-01
In this paper, we introduce a new branch of Fractal Geometry: Fractal Image Informatics, devoted to the systematic and standardized fractal analysis of images of natural systems. The methods of this discipline are based on the properties of multiscale images of selfaffine fractal surfaces. As proved in the paper, the image inherits the scaling and lacunarity of the surface and of its reflectance distribution [Korvin, 2005]. We claim that the fractal analysis of these images must be done without any smoothing, thresholding or binarization. Two new tools of Fractal Image Informatics, firmagram analysis (FA) and generalized lacunarity (GL), are presented and discussed in details. These techniques are applicable to any kind of image or to any observed positive-valued physical field, and can be used to correlate between images. It will be shown, by a modified Grassberger-Hentschel-Procaccia approach [Phys. Lett. 97A, 227 (1983); Physica 8D, 435 (1983)] that GL obeys the same scaling law as the Allain-Cloitre lacunarity [Phys. Rev. A 44, 3552 (1991)] but is free of the problems associated with gliding boxes. Several applications are shown from Soil Physics, Surface Science, and other fields.
Pre-Service Teachers' Concept Images on Fractal Dimension
ERIC Educational Resources Information Center
Karakus, Fatih
2016-01-01
The analysis of pre-service teachers' concept images can provide information about their mental schema of fractal dimension. There is limited research on students' understanding of fractal and fractal dimension. Therefore, this study aimed to investigate the pre-service teachers' understandings of fractal dimension based on concept image. The…
MRI Image Processing Based on Fractal Analysis
Marusina, Mariya Y; Mochalina, Alexandra P; Frolova, Ekaterina P; Satikov, Valentin I; Barchuk, Anton A; Kuznetcov, Vladimir I; Gaidukov, Vadim S; Tarakanov, Segrey A
2017-01-01
Background: Cancer is one of the most common causes of human mortality, with about 14 million new cases and 8.2 million deaths reported in in 2012. Early diagnosis of cancer through screening allows interventions to reduce mortality. Fractal analysis of medical images may be useful for this purpose. Materials and Methods: In this study, we examined magnetic resonance (MR) images of healthy livers and livers containing metastases from colorectal cancer. The fractal dimension and the Hurst exponent were chosen as diagnostic features for tomographic imaging using Image J software package for image processings FracLac for applied for fractal analysis with a 120x150 pixel area. Calculations of the fractal dimensions of pathological and healthy tissue samples were performed using the box-counting method. Results: In pathological cases (foci formation), the Hurst exponent was less than 0.5 (the region of unstable statistical characteristics). For healthy tissue, the Hurst index is greater than 0.5 (the zone of stable characteristics). Conclusions: The study indicated the possibility of employing fractal rapid analysis for the detection of focal lesions of the liver. The Hurst exponent can be used as an important diagnostic characteristic for analysis of medical images.
Image Segmentation via Fractal Dimension
1987-12-01
statistical expectation K = a proportionality constant H = the Hurst exponent , in interval [0,1] (14:249) Eq (4) is a mathematical generalization of...ease, negatively correlated (24:16). The Hurst exponent is directly related to the fractal diment.ion of the process being modelled by the relation (24...24) DzE.I -H (5) where D = the fractal dimension E m the Euclidean dimension H = the Hurst exponent The effect of N1 on a typical trace can be seen
Pyramidal fractal dimension for high resolution images.
Mayrhofer-Reinhartshuber, Michael; Ahammer, Helmut
2016-07-01
Fractal analysis (FA) should be able to yield reliable and fast results for high-resolution digital images to be applicable in fields that require immediate outcomes. Triggered by an efficient implementation of FA for binary images, we present three new approaches for fractal dimension (D) estimation of images that utilize image pyramids, namely, the pyramid triangular prism, the pyramid gradient, and the pyramid differences method (PTPM, PGM, PDM). We evaluated the performance of the three new and five standard techniques when applied to images with sizes up to 8192 × 8192 pixels. By using artificial fractal images created by three different generator models as ground truth, we determined the scale ranges with minimum deviations between estimation and theory. All pyramidal methods (PM) resulted in reasonable D values for images of all generator models. Especially, for images with sizes ≥1024×1024 pixels, the PMs are superior to the investigated standard approaches in terms of accuracy and computation time. A measure for the possibility to differentiate images with different intrinsic D values did show not only that the PMs are well suited for all investigated image sizes, and preferable to standard methods especially for larger images, but also that results of standard D estimation techniques are strongly influenced by the image size. Fastest results were obtained with the PDM and PGM, followed by the PTPM. In terms of absolute D values best performing standard methods were magnitudes slower than the PMs. Concluding, the new PMs yield high quality results in short computation times and are therefore eligible methods for fast FA of high-resolution images.
Fresnel diffraction of fractal grating and self-imaging effect.
Wang, Junhong; Zhang, Wei; Cui, Yuwei; Teng, Shuyun
2014-04-01
Based on the self-similarity property of fractal, two types of fractal gratings are produced according to the production and addition operations of multiple periodic gratings. Fresnel diffractions of fractal grating are analyzed theoretically, and the general mathematic expressions of the diffraction intensity distributions of fractal grating are deduced. The gray-scale patterns of the 2D diffraction distributions of fractal grating are provided through numerical calculations. The diffraction patterns take on the periodicity along the longitude and transverse directions. The 1D diffraction distribution at some certain distances shows the same structure as the fractal grating. This indicates that the self-image of fractal grating is really formed in the Fresnel diffraction region. The experimental measurement of the diffraction intensity distribution of fractal grating with different fractal dimensions and different fractal levels is performed, and the self-images of fractal grating are obtained successfully in experiments. The conclusions of this paper are helpful for the development of the application of fractal grating.
Fractal image compression: A resolution independent representation for imagery
NASA Technical Reports Server (NTRS)
Sloan, Alan D.
1993-01-01
A deterministic fractal is an image which has low information content and no inherent scale. Because of their low information content, deterministic fractals can be described with small data sets. They can be displayed at high resolution since they are not bound by an inherent scale. A remarkable consequence follows. Fractal images can be encoded at very high compression ratios. This fern, for example is encoded in less than 50 bytes and yet can be displayed at resolutions with increasing levels of detail appearing. The Fractal Transform was discovered in 1988 by Michael F. Barnsley. It is the basis for a new image compression scheme which was initially developed by myself and Michael Barnsley at Iterated Systems. The Fractal Transform effectively solves the problem of finding a fractal which approximates a digital 'real world image'.
Multi-Scale Fractal Analysis of Image Texture and Pattern
NASA Technical Reports Server (NTRS)
Emerson, Charles W.; Lam, Nina Siu-Ngan; Quattrochi, Dale A.
1999-01-01
Analyses of the fractal dimension of Normalized Difference Vegetation Index (NDVI) images of homogeneous land covers near Huntsville, Alabama revealed that the fractal dimension of an image of an agricultural land cover indicates greater complexity as pixel size increases, a forested land cover gradually grows smoother, and an urban image remains roughly self-similar over the range of pixel sizes analyzed (10 to 80 meters). A similar analysis of Landsat Thematic Mapper images of the East Humboldt Range in Nevada taken four months apart show a more complex relation between pixel size and fractal dimension. The major visible difference between the spring and late summer NDVI images is the absence of high elevation snow cover in the summer image. This change significantly alters the relation between fractal dimension and pixel size. The slope of the fractal dimension-resolution relation provides indications of how image classification or feature identification will be affected by changes in sensor spatial resolution.
Multi-Scale Fractal Analysis of Image Texture and Pattern
NASA Technical Reports Server (NTRS)
Emerson, Charles W.; Lam, Nina Siu-Ngan; Quattrochi, Dale A.
1999-01-01
Analyses of the fractal dimension of Normalized Difference Vegetation Index (NDVI) images of homogeneous land covers near Huntsville, Alabama revealed that the fractal dimension of an image of an agricultural land cover indicates greater complexity as pixel size increases, a forested land cover gradually grows smoother, and an urban image remains roughly self-similar over the range of pixel sizes analyzed (10 to 80 meters). A similar analysis of Landsat Thematic Mapper images of the East Humboldt Range in Nevada taken four months apart show a more complex relation between pixel size and fractal dimension. The major visible difference between the spring and late summer NDVI images of the absence of high elevation snow cover in the summer image. This change significantly alters the relation between fractal dimension and pixel size. The slope of the fractal dimensional-resolution relation provides indications of how image classification or feature identification will be affected by changes in sensor spatial resolution.
Smitha, K A; Gupta, A K; Jayasree, R S
2015-09-07
Glioma, the heterogeneous tumors originating from glial cells, generally exhibit varied grades and are difficult to differentiate using conventional MR imaging techniques. When this differentiation is crucial in the disease prognosis and treatment, even the advanced MR imaging techniques fail to provide a higher discriminative power for the differentiation of malignant tumor from benign ones. A powerful image processing technique applied to the imaging techniques is expected to provide a better differentiation. The present study focuses on the fractal analysis of fluid attenuation inversion recovery MR images, for the differentiation of glioma. For this, we have considered the most important parameters of fractal analysis, fractal dimension and lacunarity. While fractal analysis assesses the malignancy and complexity of a fractal object, lacunarity gives an indication on the empty space and the degree of inhomogeneity in the fractal objects. Box counting method with the preprocessing steps namely binarization, dilation and outlining was used to obtain the fractal dimension and lacunarity in glioma. Statistical analysis such as one-way analysis of variance and receiver operating characteristic (ROC) curve analysis helped to compare the mean and to find discriminative sensitivity of the results. It was found that the lacunarity of low and high grade gliomas vary significantly. ROC curve analysis between low and high grade glioma for fractal dimension and lacunarity yielded 70.3% sensitivity and 66.7% specificity and 70.3% sensitivity and 88.9% specificity, respectively. The study observes that fractal dimension and lacunarity increases with an increase in the grade of glioma and lacunarity is helpful in identifying most malignant grades.
Beyond maximum entropy: Fractal Pixon-based image reconstruction
NASA Technical Reports Server (NTRS)
Puetter, Richard C.; Pina, R. K.
1994-01-01
We have developed a new Bayesian image reconstruction method that has been shown to be superior to the best implementations of other competing methods, including Goodness-of-Fit methods such as Least-Squares fitting and Lucy-Richardson reconstruction, as well as Maximum Entropy (ME) methods such as those embodied in the MEMSYS algorithms. Our new method is based on the concept of the pixon, the fundamental, indivisible unit of picture information. Use of the pixon concept provides an improved image model, resulting in an image prior which is superior to that of standard ME. Our past work has shown how uniform information content pixons can be used to develop a 'Super-ME' method in which entropy is maximized exactly. Recently, however, we have developed a superior pixon basis for the image, the Fractal Pixon Basis (FPB). Unlike the Uniform Pixon Basis (UPB) of our 'Super-ME' method, the FPB basis is selected by employing fractal dimensional concepts to assess the inherent structure in the image. The Fractal Pixon Basis results in the best image reconstructions to date, superior to both UPB and the best ME reconstructions. In this paper, we review the theory of the UPB and FPB pixon and apply our methodology to the reconstruction of far-infrared imaging of the galaxy M51. The results of our reconstruction are compared to published reconstructions of the same data using the Lucy-Richardson algorithm, the Maximum Correlation Method developed at IPAC, and the MEMSYS ME algorithms. The results show that our reconstructed image has a spatial resolution a factor of two better than best previous methods (and a factor of 20 finer than the width of the point response function), and detects sources two orders of magnitude fainter than other methods.
Fractal analysis of palmar electronographic images. Medical anthropological perspectives.
Guja, Cornelia; Voinea, V; Baciu, Adina; Ciuhuţa, M; Crişan, Daniela A
2008-01-01
The present paper brings to the medical specialists' attention a possibility of multivalent imagistic investigation--the palmar electrographic method submitted to a totally new analysis by the fractal method. Its support for information recording is the radiosensitive film. This makes it resemble the radiological investigation, which opened the way of correlating the shape of certain structures of the organism with their function. By the specific electromagnetic impressing of the ultra photosensitive film, palmar electrography has the advantage of catching the shape of certain radiative phenomena, generated by certain structures in their functional dynamics--at the level of the human palmar tegument. This makes it resemble the EEG, EKG and EMG investigations. The purpose of this presentation is to highlight a new modality of studying the states of the human organism in its permanent adaptation to the living environment, using a new anthropological, informational vision--by fractal processing and by the couple of concepts system / interface--much closer to reality than the present systemic thinking. The human palm, which has a special medial-anthropological relevance, is analysed as a complex adaptive biological and socio-cultural interface between the internal and external environment. The fractal phenomena recorded on the image are ubicuitary in nature and especially in the living world and their shapes may he described mathematically and used for decoding their informational laws. They may have very useful implications in the medical act. The paper presents a few introductory elements to the fractal theory, and, in the final part, the pursued objectives are concretely shown by grouping the EG images according to certain more important medical-anthropological themes.
Fractal image coding based on replaced domain pools
NASA Astrophysics Data System (ADS)
Harada, Masaki; Fujii, Toshiaki; Kimoto, Tadahiko; Tanimoto, Masayuki
1998-01-01
Fractal image coding based on iterated function system has been attracting much interest because of the possibilities of drastic data compression. It performs compression by using the self-similarity included in an image. In the conventional schemes, under the assumption of the self- similarity in the image, each block is mapped from that larger block which is considered as the most suitable block to approximate the range block. However, even if the exact self-similarity of an image is found at the encoder, it hardly holds at the decoder because a domain pool of the encoder is different from that of the decoder. In this paper, we prose a fractal image coding scheme by using domain pools replaced with decoded or transformed values to reduce the difference between the domain pools of the encoder and that of the decoder. The proposed scheme performs two-stage encoding. The domain pool is replaced with decoded non-contractive blocks first and then with transformed values for contractive blocks. It is expected that the proposed scheme reduces errors of contractive blocks in the reconstructed image while those of non- contractive blocks are kept unchanged. The experimental result show the effectiveness of the proposed scheme.
Fractal dimension of cerebral surfaces using magnetic resonance images
Majumdar, S.; Prasad, R.R.
1988-11-01
The calculation of the fractal dimension of the surface bounded by the grey matter in the normal human brain using axial, sagittal, and coronal cross-sectional magnetic resonance (MR) images is presented. The fractal dimension in this case is a measure of the convolutedness of this cerebral surface. It is proposed that the fractal dimension, a feature that may be extracted from MR images, may potentially be used for image analysis, quantitative tissue characterization, and as a feature to monitor and identify cerebral abnormalities and developmental changes.
Fractal structures and fractal functions as disease indicators
Escos, J.M; Alados, C.L.; Emlen, J.M.
1995-01-01
Developmental instability is an early indicator of stress, and has been used to monitor the impacts of human disturbance on natural ecosystems. Here we investigate the use of different measures of developmental instability on two species, green peppers (Capsicum annuum), a plant, and Spanish ibex (Capra pyrenaica), an animal. For green peppers we compared the variance in allometric relationship between control plants, and a treatment group infected with the tomato spotted wilt virus. The results show that infected plants have a greater variance about the allometric regression line than the control plants. We also observed a reduction in complexity of branch structure in green pepper with a viral infection. Box-counting fractal dimension of branch architecture declined under stress infection. We also tested the reduction in complexity of behavioral patterns under stress situations in Spanish ibex (Capra pyrenaica). Fractal dimension of head-lift frequency distribution measures predator detection efficiency. This dimension decreased under stressful conditions, such as advanced pregnancy and parasitic infection. Feeding distribution activities reflect food searching efficiency. Power spectral analysis proves to be the most powerful tool for character- izing fractal behavior, revealing a reduction in complexity of time distribution activity under parasitic infection.
MR imaging and osteoporosis: fractal lacunarity analysis of trabecular bone.
Zaia, Annamaria; Eleonori, Roberta; Maponi, Pierluigi; Rossi, Roberto; Murri, Roberto
2006-07-01
We develop a method of magnetic resonance (MR) image analysis able to provide parameter(s) sensitive to bone microarchitecture changes in aging, and to osteoporosis onset and progression. The method has been built taking into account fractal properties of many anatomic and physiologic structures. Fractal lacunarity analysis has been used to determine relevant parameter(s) to differentiate among three types of trabecular bone structure (healthy young, healthy perimenopausal, and osteoporotic patients) from lumbar vertebra MR images. In particular, we propose to approximate the lacunarity function by a hyperbola model function that depends on three coefficients, alpha, beta, and gamma, and to compute these coefficients as the solution of a least squares problem. This triplet of coefficients provides a model function that better represents the variation of mass density of pixels in the image considered. Clinical application of this preliminary version of our method suggests that one of the three coefficients, beta, may represent a standard for the evaluation of trabecular bone architecture and a potentially useful parametric index for the early diagnosis of osteoporosis.
Evaluation of Two Fractal Methods for Magnetogram Image Analysis
NASA Technical Reports Server (NTRS)
Stark, B.; Adams, M.; Hathaway, D. H.; Hagyard, M. J.
1997-01-01
Fractal and multifractal techniques have been applied to various types of solar data to study the fractal properties of sunspots as well as the distribution of photospheric magnetic fields and the role of random motions on the solar surface in this distribution. Other research includes the investigation of changes in the fractal dimension as an indicator for solar flares. Here we evaluate the efficacy of two methods for determining the fractal dimension of an image data set: the Differential Box Counting scheme and a new method, the Jaenisch scheme. To determine the sensitivity of the techniques to changes in image complexity, various types of constructed images are analyzed. In addition, we apply this method to solar magnetogram data from Marshall Space Flight Centers vector magnetograph.
Imai, K; Ikeda, M; Enchi, Y; Niimi, T
2009-12-01
The purposes of our studies are to examine whether or not fractal-feature distance deduced from virtual volume method can simulate observer performance indices and to investigate the physical meaning of pseudo fractal dimension and complexity. Contrast-detail (C-D) phantom radiographs were obtained at various mAs values (0.5 - 4.0 mAs) and 140 kVp with a computed radiography system, and the reference image was acquired at 13 mAs. For all C-D images, fractal analysis was conducted using the virtual volume method that was devised with a fractional Brownian motion model. The fractal-feature distances between the considered and reference images were calculated using pseudo fractal dimension and complexity. Further, we have performed the C-D analysis in which ten radiologists participated, and compared the fractal-feature distances with the image quality figures (IQF). To clarify the physical meaning of the pseudo fractal dimension and complexity, contrast-to-noise ratio (CNR) and standard deviation (SD) of images noise were calculated for each mAs and compared with the pseudo fractal dimension and complexity, respectively. A strong linear correlation was found between the fractal-feature distance and IQF. The pseudo fractal dimensions became large as CNR increased. Further, a linear correlation was found between the exponential complexity and image noise SD.
Person identification using fractal analysis of retina images
NASA Astrophysics Data System (ADS)
Ungureanu, Constantin; Corniencu, Felicia
2004-10-01
Biometric is automated method of recognizing a person based on physiological or behavior characteristics. Among the features measured are retina scan, voice, and fingerprint. A retina-based biometric involves the analysis of the blood vessels situated at the back of the eye. In this paper we present a method, which uses the fractal analysis to characterize the retina images. The Fractal Dimension (FD) of retina vessels was measured for a number of 20 images and have been obtained different values of FD for each image. This algorithm provides a good accuracy is cheap and easy to implement.
Fractal-based image texture analysis of trabecular bone architecture.
Jiang, C; Pitt, R E; Bertram, J E; Aneshansley, D J
1999-07-01
Fractal-based image analysis methods are investigated to extract textural features related to the anisotropic structure of trabecular bone from the X-ray images of cubic bone specimens. Three methods are used to quantify image textural features: power spectrum, Minkowski dimension and mean intercept length. The global fractal dimension is used to describe the overall roughness of the image texture. The anisotropic features formed by the trabeculae are characterised by a fabric ellipse, whose orientation and eccentricity reflect the textural anisotropy of the image. Tests of these methods with synthetic images of known fractal dimension show that the Minkowski dimension provides a more accurate and consistent estimation of global fractal dimension. Tests on bone x-ray (eccentricity range 0.25-0.80) images indicate that the Minkowski dimension is more sensitive to the changes in textural orientation. The results suggest that the Minkowski dimension is a better measure for characterising trabecular bone anisotropy in the x-ray images of thick specimens.
Trabecular architecture analysis in femur radiographic images using fractals.
Udhayakumar, G; Sujatha, C M; Ramakrishnan, S
2013-04-01
Trabecular bone is a highly complex anisotropic material that exhibits varying magnitudes of strength in compression and tension. Analysis of the trabecular architectural alteration that manifest as loss of trabecular plates and connection has been shown to yield better estimation of bone strength. In this work, an attempt has been made toward the development of an automated system for investigation of trabecular femur bone architecture using fractal analysis. Conventional radiographic femur bone images recorded using standard protocols are used in this study. The compressive and tensile regions in the images are delineated using preprocessing procedures. The delineated images are analyzed using Higuchi's fractal method to quantify pattern heterogeneity and anisotropy of trabecular bone structure. The results show that the extracted fractal features are distinct for compressive and tensile regions of normal and abnormal human femur bone. As the strength of the bone depends on architectural variation in addition to bone mass, this study seems to be clinically useful.
Liver ultrasound image classification by using fractal dimension of edge
NASA Astrophysics Data System (ADS)
Moldovanu, Simona; Bibicu, Dorin; Moraru, Luminita
2012-08-01
Medical ultrasound image edge detection is an important component in increasing the number of application of segmentation, and hence it has been subject of many studies in the literature. In this study, we have classified the liver ultrasound images (US) combining Canny and Sobel edge detectors with fractal analysis in order to provide an indicator about of the US images roughness. We intend to provide a classification rule of the focal liver lesions as: cirrhotic liver, liver hemangioma and healthy liver. For edges detection the Canny and Sobel operators were used. Fractal analyses have been applied for texture analysis and classification of focal liver lesions according to fractal dimension (FD) determined by using the Box Counting method. To assess the performance and accuracy rate of the proposed method the contrast-to-noise (CNR) is analyzed.
Fractal image perception provides novel insights into hierarchical cognition.
Martins, M J; Fischmeister, F P; Puig-Waldmüller, E; Oh, J; Geissler, A; Robinson, S; Fitch, W T; Beisteiner, R
2014-08-01
Hierarchical structures play a central role in many aspects of human cognition, prominently including both language and music. In this study we addressed hierarchy in the visual domain, using a novel paradigm based on fractal images. Fractals are self-similar patterns generated by repeating the same simple rule at multiple hierarchical levels. Our hypothesis was that the brain uses different resources for processing hierarchies depending on whether it applies a "fractal" or a "non-fractal" cognitive strategy. We analyzed the neural circuits activated by these complex hierarchical patterns in an event-related fMRI study of 40 healthy subjects. Brain activation was compared across three different tasks: a similarity task, and two hierarchical tasks in which subjects were asked to recognize the repetition of a rule operating transformations either within an existing hierarchical level, or generating new hierarchical levels. Similar hierarchical images were generated by both rules and target images were identical. We found that when processing visual hierarchies, engagement in both hierarchical tasks activated the visual dorsal stream (occipito-parietal cortex, intraparietal sulcus and dorsolateral prefrontal cortex). In addition, the level-generating task specifically activated circuits related to the integration of spatial and categorical information, and with the integration of items in contexts (posterior cingulate cortex, retrosplenial cortex, and medial, ventral and anterior regions of temporal cortex). These findings provide interesting new clues about the cognitive mechanisms involved in the generation of new hierarchical levels as required for fractals.
Wideband fractal antennas for holographic imaging and rectenna applications
NASA Astrophysics Data System (ADS)
Bunch, Kyle J.; McMakin, Douglas L.; Sheen, David M.
2008-04-01
At Pacific Northwest National Laboratory, wideband antenna arrays have been successfully used to reconstruct three-dimensional images at microwave and millimeter-wave frequencies. Applications of this technology have included portal monitoring, through-wall imaging, and weapons detection. Fractal antennas have been shown to have wideband characteristics due to their self-similar nature (that is, their geometry is replicated at different scales). They further have advantages in providing good characteristics in a compact configuration. We discuss the application of fractal antennas for holographic imaging. Simulation results will be presented. Rectennas are a specific class of antennas in which a received signal drives a nonlinear junction and is retransmitted at either a harmonic frequency or a demodulated frequency. Applications include tagging and tracking objects with a uniquely-responding antenna. It is of interest to consider fractal rectenna because the self-similarity of fractal antennas tends to make them have similar resonance behavior at multiples of the primary resonance. Thus, fractal antennas can be suited for applications in which a signal is reradiated at a harmonic frequency. Simulations will be discussed with this application in mind.
Wideband Fractal Antennas for Holographic Imaging and Rectenna Applications
Bunch, Kyle J.; McMakin, Douglas L.; Sheen, David M.
2008-04-18
At Pacific Northwest National Laboratory, wideband antenna arrays have been successfully used to reconstruct three-dimensional images at microwave and millimeter-wave frequencies. Applications of this technology have included portal monitoring, through-wall imaging, and weapons detection. Fractal antennas have been shown to have wideband characteristics due to their self-similar nature (that is, their geometry is replicated at different scales). They further have advantages in providing good characteristics in a compact configuration. We discuss the application of fractal antennas for holographic imaging. Simulation results will be presented. Rectennas are a specific class of antennas in which a received signal drives a nonlinear junction and is retransmitted at either a harmonic frequency or a demodulated frequency. Applications include tagging and tracking objects with a uniquely-responding antenna. It is of interest to consider fractal rectenna because the self-similarity of fractal antennas tends to make them have similar resonance behavior at multiples of the primary resonance. Thus, fractal antennas can be suited for applications in which a signal is reradiated at a harmonic frequency. Simulations will be discussed with this application in mind.
Fractal Analysis of Laplacian Pyramidal Filters Applied to Segmentation of Soil Images
de Castro, J.; Méndez, A.; Tarquis, A. M.
2014-01-01
The laplacian pyramid is a well-known technique for image processing in which local operators of many scales, but identical shape, serve as the basis functions. The required properties to the pyramidal filter produce a family of filters, which is unipara metrical in the case of the classical problem, when the length of the filter is 5. We pay attention to gaussian and fractal behaviour of these basis functions (or filters), and we determine the gaussian and fractal ranges in the case of single parameter a. These fractal filters loose less energy in every step of the laplacian pyramid, and we apply this property to get threshold values for segmenting soil images, and then evaluate their porosity. Also, we evaluate our results by comparing them with the Otsu algorithm threshold values, and conclude that our algorithm produce reliable test results. PMID:25114957
Fractal analysis for reduced reference image quality assessment.
Xu, Yong; Liu, Delei; Quan, Yuhui; Le Callet, Patrick
2015-07-01
In this paper, multifractal analysis is adapted to reduced-reference image quality assessment (RR-IQA). A novel RR-QA approach is proposed, which measures the difference of spatial arrangement between the reference image and the distorted image in terms of spatial regularity measured by fractal dimension. An image is first expressed in Log-Gabor domain. Then, fractal dimensions are computed on each Log-Gabor subband and concatenated as a feature vector. Finally, the extracted features are pooled as the quality score of the distorted image using l1 distance. Compared with existing approaches, the proposed method measures image quality from the perspective of the spatial distribution of image patterns. The proposed method was evaluated on seven public benchmark data sets. Experimental results have demonstrated the excellent performance of the proposed method in comparison with state-of-the-art approaches.
Fractal Dimension of Certain Continuous Functions of Unbounded Variation
NASA Astrophysics Data System (ADS)
Liang, Y. S.; Su, W. Y.
Continuous functions on closed intervals are composed of bounded variation functions and unbounded variation functions. Fractal dimension of continuous functions with bounded variation must be one-dimensional (1D). While fractal dimension of continuous functions with unbounded variation may be 1 or not. Certain continuous functions of unbounded variation whose fractal dimensions are 1 have been mainly investigated in the paper. A continuous function on a closed interval with finite unbounded variation points has been proved to be 1D. Furthermore, we deal with continuous functions which have infinite unbounded variation points and part of them have been proved to be 1D. Certain examples of 1D continuous functions which have uncountable unbounded variation points have been given in the present paper.
Multi-Scale Fractal Analysis of Image Texture and Pattern
NASA Technical Reports Server (NTRS)
Emerson, Charles W.; Quattrochi, Dale A.; Luvall, Jeffrey C.
1997-01-01
Fractals embody important ideas of self-similarity, in which the spatial behavior or appearance of a system is largely scale-independent. Self-similarity is a property of curves or surfaces where each part is indistinguishable from the whole. The fractal dimension D of remote sensing data yields quantitative insight on the spatial complexity and information content contained within these data. Analyses of Normalized Difference Vegetation Index (NDVI) images of homogeneous land covers near Huntsville, Alabama revealed that the fractal dimension of an image of an agricultural land cover indicates greater complexity as pixel size increases, a forested land cover gradually grows smoother, and an urban image remains roughly self-similar over the range of pixel sizes analyzed(l0 to 80 meters). The forested scene behaves as one would expect-larger pixel sizes decrease the complexity of the image as individual clumps of trees are averaged into larger blocks. The increased complexity of the agricultural image with increasing pixel size results from the loss of homogeneous groups of pixels in the large fields to mixed pixels composed of varying combinations of NDVI values that correspond to roads and vegetation. The same process occur's in the urban image to some extent, but the lack of large, homogeneous areas in the high resolution NDVI image means the initially high D value is maintained as pixel size increases. The slope of the fractal dimension-resolution relationship provides indications of how image classification or feature identification will be affected by changes in sensor resolution.
ERIC Educational Resources Information Center
Jurgens, Hartmut; And Others
1990-01-01
The production and application of images based on fractal geometry are described. Discussed are fractal language groups, fractal image coding, and fractal dialects. Implications for these applications of geometry to mathematics education are suggested. (CW)
Fractal descriptors for discrimination of microscopy images of plant leaves
NASA Astrophysics Data System (ADS)
Silva, N. R.; Florindo, J. B.; Gómez, M. C.; Kolb, R. M.; Bruno, O. M.
2014-03-01
This study proposes the application of fractal descriptors method to the discrimination of microscopy images of plant leaves. Fractal descriptors have demonstrated to be a powerful discriminative method in image analysis, mainly for the discrimination of natural objects. In fact, these descriptors express the spatial arrangement of pixels inside the texture under different scales and such arrangements are directly related to physical properties inherent to the material depicted in the image. Here, we employ the Bouligand-Minkowski descriptors. These are obtained by the dilation of a surface mapping the gray-level texture. The classification of the microscopy images is performed by the well-known Support Vector Machine (SVM) method and we compare the success rate with other literature texture analysis methods. The proposed method achieved a correctness rate of 89%, while the second best solution, the Co-occurrence descriptors, yielded only 78%. This clear advantage of fractal descriptors demonstrates the potential of such approach in the analysis of the plant microscopy images.
Fractal Image Filters for Specialized Image Recognition Tasks
2010-02-11
Mendoza , Cambridge University Press, Cambridge, 1995. [20] J . Kigami, Harmonic Calculus on p.c.f. Self-similar Sets, Trans. Amer. Math. Soc. 335 (1993) 721...Transformations between fractals, Progress in Probability, 61 (2009) 227-250. [4] M. F. Barnsley, J . Hutchinson, Ö. Sten�o, V-variable fractals: fractals with...convex body K R2 such that F (K) K. The associated Hilbert metric dH is de�ned on K by dH(x; y) = ln jR (x; y; a; b) j for all x; y 2 K with x 6
Fractal analysis of high-resolution CT images as a tool for quantification of lung diseases
Uppaluri, R.; Mitsa, T.; Galvin, J.R.
1995-12-31
Fractal geometry is increasingly being used to model complex naturally occurring phenomena. There are two types of fractals in nature-geometric fractals and stochastic fractals. The pulmonary branching structure is a geometric fractal and the intensity of its grey scale image is a stochastic fractal. In this paper, the authors attempt to quantify the texture of CT lung images using properties of both types of fractals. A simple algorithm for detecting of abnormality in human lungs, based on 2-D and 3-D fractal dimensions, is presented. This method involves calculating the local fractal dimensions, based on intensities, in the 2-D slice to air edge enhancement. Following this, grey level thresholding is performed and a global fractal dimension, based on structure, for the entire data is estimated in 2-D and 3-D. High Resolution CT images of normal and abnormal lungs were analyzed. Preliminary results showed that classification of normal and abnormal images could be obtained based on the differences between their global fractal dimensions.
A Digital Image Steganography using Sierpinski Gasket Fractal and PLSB
NASA Astrophysics Data System (ADS)
Rupa, Ch.
2013-09-01
Information attacks are caused due to the weaknesses in the information security. These attacks affect the non-repudiation and integrity of the security services. In this paper, a novel security approach that can defend the message from information attacks is proposed. In this new approach the original message is encrypted by Fractal Sierpinski Gasket (FSG) cryptographic algorithm, that result is hidden into an image using penultimate and least significant bit (PLSB) embedding method. This method makes the security more robust than conventional approach. Important properties of fractals are sensitivity and self similarity. These can be exploited to produce avalanche effect. Stegoanalysis of the proposed method shows that it is resistant to various attacks and stronger than the existed steganographic approaches.
SAR image post-processing for the estimation of fractal parameters
NASA Astrophysics Data System (ADS)
Di Martino, Gerardo; Riccio, Daniele; Ruello, Giuseppe; Zinno, Ivana
2011-11-01
In this paper a fractal based processing for the analysis of SAR images of natural surfaces is presented. Its definition is based on a complete direct imaging model developed by the authors. The application of this innovative algorithm to SAR images makes possible to obtain complete maps of the two key parameters of a fractal scene: the fractal dimension and the increment standard deviation. The fractal parameters extraction is based on the estimation of the power spectral density of the SAR amplitude image. From a theoretic point of view, the attention is focused on the retrieving procedure of the increment standard deviation, here presented for the first time. In the last section of the paper, the application of the introduced processing to high resolution SAR images is presented, with the relevant maps of the fractal dimension and of the increment standard deviation.
Wavelets, Fractals, and Radial Basis Functions
2007-11-02
of Signal Processing. San Diego, CA: Aca- demic, 1998. [13] G. Strang and T. Q. Nguyen, Wavelets and Filter Banks . Cambridge, MA: Wellesley-Cambridge...localization, multiresolution, radial basis functions, re- finement filter , scaling functions, self-similarity, splines, tempered distributions, two-scale...one linear constraint per basis function, and the corresponding linear system of equations is invertible under relatively mild conditions [11]. The
Log-periodic route to fractal functions.
Gluzman, S; Sornette, D
2002-03-01
Log-periodic oscillations have been found to decorate the usual power-law behavior found to describe the approach to a critical point, when the continuous scale-invariance symmetry is partially broken into a discrete-scale invariance symmetry. For Ising or Potts spins with ferromagnetic interactions on hierarchical systems, the relative magnitude of the log-periodic corrections are usually very small, of order 10(-5). In growth processes [diffusion limited aggregation (DLA)], rupture, earthquake, and financial crashes, log-periodic oscillations with amplitudes of the order of 10% have been reported. We suggest a "technical" explanation for this 4 order-of-magnitude difference based on the property of the "regular function" g(x) embodying the effect of the microscopic degrees of freedom summed over in a renormalization group (RG) approach F(x)=g(x)+mu(-1)F(gamma x) of an observable F as a function of a control parameter x. For systems for which the RG equation has not been derived, the previous equation can be understood as a Jackson q integral, which is the natural tool for describing discrete-scale invariance. We classify the "Weierstrass-type" solutions of the RG into two classes characterized by the amplitudes A(n) of the power-law series expansion. These two classes are separated by a novel "critical" point. Growth processes (DLA), rupture, earthquake, and financial crashes thus seem to be characterized by oscillatory or bounded regular microscopic functions that lead to a slow power-law decay of A(n), giving strong log-periodic amplitudes. If in addition, the phases of A(n) are ergodic and mixing, the observable presents self-affine nondifferentiable properties. In contrast, the regular function of statistical physics models with "ferromagnetic"-type interactions at equilibrium involves unbound logarithms of polynomials of the control variable that lead to a fast exponential decay of A(n) giving weak log-periodic amplitudes and smoothed observables.
ERIC Educational Resources Information Center
Osler, Thomas J.
1999-01-01
Because fractal images are by nature very complex, it can be inspiring and instructive to create the code in the classroom and watch the fractal image evolve as the user slowly changes some important parameter or zooms in and out of the image. Uses programming language that permits the user to store and retrieve a graphics image as a disk file.…
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
Zaia, Annamaria
2015-03-18
Osteoporosis represents one major health condition for our growing elderly population. It accounts for severe morbidity and increased mortality in postmenopausal women and it is becoming an emerging health concern even in aging men. Screening of the population at risk for bone degeneration and treatment assessment of osteoporotic patients to prevent bone fragility fractures represent useful tools to improve quality of life in the elderly and to lighten the related socio-economic impact. Bone mineral density (BMD) estimate by means of dual-energy X-ray absorptiometry is normally used in clinical practice for osteoporosis diagnosis. Nevertheless, BMD alone does not represent a good predictor of fracture risk. From a clinical point of view, bone microarchitecture seems to be an intriguing aspect to characterize bone alteration patterns in aging and pathology. The widening into clinical practice of medical imaging techniques and the impressive advances in information technologies together with enhanced capacity of power calculation have promoted proliferation of new methods to assess changes of trabecular bone architecture (TBA) during aging and osteoporosis. Magnetic resonance imaging (MRI) has recently arisen as a useful tool to measure bone structure in vivo. In particular, high-resolution MRI techniques have introduced new perspectives for TBA characterization by non-invasive non-ionizing methods. However, texture analysis methods have not found favor with clinicians as they produce quite a few parameters whose interpretation is difficult. The introduction in biomedical field of paradigms, such as theory of complexity, chaos, and fractals, suggests new approaches and provides innovative tools to develop computerized methods that, by producing a limited number of parameters sensitive to pathology onset and progression, would speed up their application into clinical practice. Complexity of living beings and fractality of several physio-anatomic structures suggest
Border extrapolation using fractal attributes in remote sensing images
NASA Astrophysics Data System (ADS)
Cipolletti, M. P.; Delrieux, C. A.; Perillo, G. M. E.; Piccolo, M. C.
2014-01-01
In management, monitoring and rational use of natural resources the knowledge of precise and updated information is essential. Satellite images have become an attractive option for quantitative data extraction and morphologic studies, assuring a wide coverage without exerting negative environmental influence over the study area. However, the precision of such practice is limited by the spatial resolution of the sensors and the additional processing algorithms. The use of high resolution imagery (i.e., Ikonos) is very expensive for studies involving large geographic areas or requiring long term monitoring, while the use of less expensive or freely available imagery poses a limit in the geographic accuracy and physical precision that may be obtained. We developed a methodology for accurate border estimation that can be used for establishing high quality measurements with low resolution imagery. The method is based on the original theory by Richardson, taking advantage of the fractal nature of geographic features. The area of interest is downsampled at different scales and, at each scale, the border is segmented and measured. Finally, a regression of the dependence of the measured length with respect to scale is computed, which then allows for a precise extrapolation of the expected length at scales much finer than the originally available. The method is tested with both synthetic and satellite imagery, producing accurate results in both cases.
NASA Astrophysics Data System (ADS)
Boychuk, T. M.; Bodnar, B. M.; Vatamanesku, L. I.
2011-09-01
For the first time the complex correlation and fractal analysis was used for the investigation of microscopic images of both tissue images and hemangioma liquids. It was proposed a physical model of description of phase distributions formation of coherent radiation, which was transformed by optical anisotropic biological structures. The phase maps of laser radiation in the boundary diffraction zone were used as the main information parameter. The results of investigating the interrelation between the values of correlation (correlation area, asymmetry coefficient and autocorrelation function excess) and fractal (dispersion of logarithmic dependencies of power spectra) parameters are presented. They characterize the coordinate distributions of phase shifts in the points of laser images of histological sections of hemangioma, hemangioma blood smears and blood plasma with vascular system pathologies. The diagnostic criteria of hemangioma nascency are determined.
NASA Astrophysics Data System (ADS)
Boychuk, T. M.; Bodnar, B. M.; Vatamanesku, L. I.
2012-01-01
For the first time the complex correlation and fractal analysis was used for the investigation of microscopic images of both tissue images and hemangioma liquids. It was proposed a physical model of description of phase distributions formation of coherent radiation, which was transformed by optical anisotropic biological structures. The phase maps of laser radiation in the boundary diffraction zone were used as the main information parameter. The results of investigating the interrelation between the values of correlation (correlation area, asymmetry coefficient and autocorrelation function excess) and fractal (dispersion of logarithmic dependencies of power spectra) parameters are presented. They characterize the coordinate distributions of phase shifts in the points of laser images of histological sections of hemangioma, hemangioma blood smears and blood plasma with vascular system pathologies. The diagnostic criteria of hemangioma nascency are determined.
Simple fractal method of assessment of histological images for application in medical diagnostics
2010-01-01
We propose new method of assessment of histological images for medical diagnostics. 2-D image is preprocessed to form 1-D landscapes or 1-D signature of the image contour and then their complexity is analyzed using Higuchi's fractal dimension method. The method may have broad medical application, from choosing implant materials to differentiation between benign masses and malignant breast tumors. PMID:21134258
Local fuzzy fractal dimension and its application in medical image processing.
Zhuang, Xiaodong; Meng, Qingchun
2004-09-01
The local fuzzy fractal dimension (LFFD) is proposed to extract local fractal feature of medical images. The definition of LFFD is an extension of the pixel-covering method by incorporating the fuzzy set. Multi-feature edge detection is implemented with the LFFD and the Sobel operator. The LFFD can also serve as a characteristic of motion in medical image sequences. The experimental results show that the LFFD is an important feature of edge areas in medical images and can provide information for segmentation of echocardiogram image sequences.
A Lossless hybrid wavelet-fractal compression for welding radiographic images.
Mekhalfa, Faiza; Avanaki, Mohammad R N; Berkani, Daoud
2016-01-01
In this work a lossless wavelet-fractal image coder is proposed. The process starts by compressing and decompressing the original image using wavelet transformation and fractal coding algorithm. The decompressed image is removed from the original one to obtain a residual image which is coded by using Huffman algorithm. Simulation results show that with the proposed scheme, we achieve an infinite peak signal to noise ratio (PSNR) with higher compression ratio compared to typical lossless method. Moreover, the use of wavelet transform speeds up the fractal compression algorithm by reducing the size of the domain pool. The compression results of several welding radiographic images using the proposed scheme are evaluated quantitatively and compared with the results of Huffman coding algorithm.
NASA Astrophysics Data System (ADS)
Lahmiri, Salim
2016-08-01
The main purpose of this work is to explore the usefulness of fractal descriptors estimated in multi-resolution domains to characterize biomedical digital image texture. In this regard, three multi-resolution techniques are considered: the well-known discrete wavelet transform (DWT) and the empirical mode decomposition (EMD), and; the newly introduced; variational mode decomposition mode (VMD). The original image is decomposed by the DWT, EMD, and VMD into different scales. Then, Fourier spectrum based fractal descriptors is estimated at specific scales and directions to characterize the image. The support vector machine (SVM) was used to perform supervised classification. The empirical study was applied to the problem of distinguishing between normal and abnormal brain magnetic resonance images (MRI) affected with Alzheimer disease (AD). Our results demonstrate that fractal descriptors estimated in VMD domain outperform those estimated in DWT and EMD domains; and also those directly estimated from the original image.
Fractal scaling of apparent soil moisture estimated from vertical planes of Vertisol pit images
NASA Astrophysics Data System (ADS)
Cumbrera, Ramiro; Tarquis, Ana M.; Gascó, Gabriel; Millán, Humberto
2012-07-01
SummaryImage analysis could be a useful tool for investigating the spatial patterns of apparent soil moisture at multiple resolutions. The objectives of the present work were (i) to define apparent soil moisture patterns from vertical planes of Vertisol pit images and (ii) to describe the scaling of apparent soil moisture distribution using fractal parameters. Twelve soil pits (0.70 m long × 0.60 m width × 0.30 m depth) were excavated on a bare Mazic Pellic Vertisol. Six of them were excavated in April/2011 and six pits were established in May/2011 after 3 days of a moderate rainfall event. Digital photographs were taken from each Vertisol pit using a Kodak™ digital camera. The mean image size was 1600 × 945 pixels with one physical pixel ≈373 μm of the photographed soil pit. Each soil image was analyzed using two fractal scaling exponents, box counting (capacity) dimension (DBC) and interface fractal dimension (Di), and three prefractal scaling coefficients, the total number of boxes intercepting the foreground pattern at a unit scale (A), fractal lacunarity at the unit scale (Λ1) and Shannon entropy at the unit scale (S1). All the scaling parameters identified significant differences between both sets of spatial patterns. Fractal lacunarity was the best discriminator between apparent soil moisture patterns. Soil image interpretation with fractal exponents and prefractal coefficients can be incorporated within a site-specific agriculture toolbox. While fractal exponents convey information on space filling characteristics of the pattern, prefractal coefficients represent the investigated soil property as seen through a higher resolution microscope. In spite of some computational and practical limitations, image analysis of apparent soil moisture patterns could be used in connection with traditional soil moisture sampling, which always renders punctual estimates.
Fast Basins and Branched Fractal Manifolds of Attractors of Iterated Function Systems
NASA Astrophysics Data System (ADS)
Barnsley, Michael F.; Vince, Andrew
2015-10-01
The fast basin of an attractor of an iterated function system (IFS) is the set of points in the domain of the IFS whose orbits under the associated semigroup intersect the attractor. Fast basins can have non-integer dimension and comprise a class of deterministic fractal sets. The relationship between the basin and the fast basin of a point-fibred attractor is analyzed. To better understand the topology and geometry of fast basins, and because of analogies with analytic continuation, branched fractal manifolds are introduced. A branched fractal manifold is a metric space constructed from the extended code space of a point-fibred attractor, by identifying some addresses. Typically, a branched fractal manifold is a union of a nondenumerable collection of nonhomeomorphic objects, isometric copies of generalized fractal blowups of the attractor.
NASA Technical Reports Server (NTRS)
Emerson, Charles W.; Sig-NganLam, Nina; Quattrochi, Dale A.
2004-01-01
The accuracy of traditional multispectral maximum-likelihood image classification is limited by the skewed statistical distributions of reflectances from the complex heterogenous mixture of land cover types in urban areas. This work examines the utility of local variance, fractal dimension and Moran's I index of spatial autocorrelation in segmenting multispectral satellite imagery. Tools available in the Image Characterization and Modeling System (ICAMS) were used to analyze Landsat 7 imagery of Atlanta, Georgia. Although segmentation of panchromatic images is possible using indicators of spatial complexity, different land covers often yield similar values of these indices. Better results are obtained when a surface of local fractal dimension or spatial autocorrelation is combined as an additional layer in a supervised maximum-likelihood multispectral classification. The addition of fractal dimension measures is particularly effective at resolving land cover classes within urbanized areas, as compared to per-pixel spectral classification techniques.
Morphology and functions of astrocytes cultured on water-repellent fractal tripalmitin surfaces.
Hu, Wei-wei; Wang, Zhe; Zhang, Shan-shan; Jiang, Lei; Zhang, Jing; Zhang, Xiangnan; Lei, Qun-fang; Park, Hyun-Joo; Fang, Wen-jun; Chen, Zhong
2014-08-01
In the brain, astrocytes play an essential role with their multiple functions and sophisticated structure, as surrounded by a fractal environment which has not been available in our traditional cell culture. Water-repellent fractal tripalmitin (PPP) surfaces can imitate the fractal environment in vivo, so the morphology and biochemical characterization of astrocytes on these surfaces are examined. Water-repellent fractal PPP surface can induce astrocytes to display sophisticated morphology with smaller size of cell area, longer and finer filopodium-like processes, and higher morphological complexity. The super water-repellent fractal PPP surface with water contact angle of 150°∼160° produces the maximal effects compared with other surfaces at lower water contact angles. The trends of characteristic protein expression, including that of nestin, vimentin, GFAP and glutamine synthetase, for astrocytes cultured on super water-repellent fractal PPP surfaces approximate more to in vivo pattern. The super water-repellent PPP surface also render astrocytes to perform more pronounced promotion of neurogenesis by increasing the release of nerve growth factor in a co-culture system. Altogether, our results suggest that the super water-repellent fractal PPP surface facilitates the astrocytes to mimic their in vivo performance, thus provides a closer-to-natural culture environment for experimental assessment of glial structure and functions.
NASA Astrophysics Data System (ADS)
Tremberger, George, Jr.; Flamholz, A.; Cheung, E.; Sullivan, R.; Subramaniam, R.; Schneider, P.; Brathwaite, G.; Boteju, J.; Marchese, P.; Lieberman, D.; Cheung, T.; Holden, Todd
2007-09-01
The absorption effect of the back surface boundary of a diffuse layer was studied via laser generated reflection speckle pattern. The spatial speckle intensity provided by a laser beam was measured. The speckle data were analyzed in terms of fractal dimension (computed by NIH ImageJ software via the box counting fractal method) and weak localization theory based on Mie scattering. Bar code imaging was modeled as binary absorption contrast and scanning resolution in millimeter range was achieved for diffusive layers up to thirty transport mean free path thick. Samples included alumina, porous glass and chicken tissue. Computer simulation was used to study the effect of speckle spatial distribution and observed fractal dimension differences were ascribed to variance controlled speckle sizes. Fractal dimension suppressions were observed in samples that had thickness dimensions around ten transport mean free path. Computer simulation suggested a maximum fractal dimension of about 2 and that subtracting information could lower fractal dimension. The fractal dimension was shown to be sensitive to sample thickness up to about fifteen transport mean free paths, and embedded objects which modified 20% or more of the effective thickness was shown to be detectable. The box counting fractal method was supplemented with the Higuchi data series fractal method and application to architectural distortion mammograms was demonstrated. The use of fractals in diffusive analysis would provide a simple language for a dialog between optics experts and mammography radiologists, facilitating the applications of laser diagnostics in tissues.
Improved triangular prism methods for fractal analysis of remotely sensed images
NASA Astrophysics Data System (ADS)
Zhou, Yu; Fung, Tung; Leung, Yee
2016-05-01
Feature extraction has been a major area of research in remote sensing, and fractal feature is a natural characterization of complex objects across scales. Extending on the modified triangular prism (MTP) method, we systematically discuss three factors closely related to the estimation of fractal dimensions of remotely sensed images. They are namely the (F1) number of steps, (F2) step size, and (F3) estimation accuracy of the facets' areas of the triangular prisms. Differing from the existing improved algorithms that separately consider these factors, we simultaneously take all factors to construct three new algorithms, namely the modification of the eight-pixel algorithm, the four corner and the moving-average MTP. Numerical experiments based on 4000 generated images show their superior performances over existing algorithms: our algorithms not only overcome the limitation of image size suffered by existing algorithms but also obtain similar average fractal dimension with smaller standard deviation, only 50% for images with high fractal dimensions. In the case of real-life application, our algorithms more likely obtain fractal dimensions within the theoretical range. Thus, the fractal nature uncovered by our algorithms is more reasonable in quantifying the complexity of remotely sensed images. Despite the similar performance of these three new algorithms, the moving-average MTP can mitigate the sensitivity of the MTP to noise and extreme values. Based on the numerical and real-life case study, we check the effect of the three factors, (F1)-(F3), and demonstrate that these three factors can be simultaneously considered for improving the performance of the MTP method.
Buried mine detection using fractal geometry analysis to the LWIR successive line scan data image
NASA Astrophysics Data System (ADS)
Araki, Kan
2012-06-01
We have engaged in research on buried mine/IED detection by remote sensing method using LWIR camera. A IR image of a ground, containing buried objects can be assumed as a superimposed pattern including thermal scattering which may depend on the ground surface roughness, vegetation canopy, and effect of the sun light, and radiation due to various heat interaction caused by differences in specific heat, size, and buried depth of the objects and local temperature of their surrounding environment. In this cumbersome environment, we introduce fractal geometry for analyzing from an IR image. Clutter patterns due to these complex elements have oftentimes low ordered fractal dimension of Hausdorff Dimension. On the other hand, the target patterns have its tendency of obtaining higher ordered fractal dimension in terms of Information Dimension. Random Shuffle Surrogate method or Fourier Transform Surrogate method is used to evaluate fractional statistics by applying shuffle of time sequence data or phase of spectrum. Fractal interpolation to each line scan was also applied to improve the signal processing performance in order to evade zero division and enhance information of data. Some results of target extraction by using relationship between low and high ordered fractal dimension are to be presented.
ERIC Educational Resources Information Center
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)
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)
On the fractal geometry of DNA by the binary image analysis.
Cattani, Carlo; Pierro, Gaetano
2013-09-01
The multifractal analysis of binary images of DNA is studied in order to define a methodological approach to the classification of DNA sequences. This method is based on the computation of some multifractality parameters on a suitable binary image of DNA, which takes into account the nucleotide distribution. The binary image of DNA is obtained by a dot-plot (recurrence plot) of the indicator matrix. The fractal geometry of these images is characterized by fractal dimension (FD), lacunarity, and succolarity. These parameters are compared with some other coefficients such as complexity and Shannon information entropy. It will be shown that the complexity parameters are more or less equivalent to FD, while the parameters of multifractality have different values in the sense that sequences with higher FD might have lower lacunarity and/or succolarity. In particular, the genome of Drosophila melanogaster has been considered by focusing on the chromosome 3r, which shows the highest fractality with a corresponding higher level of complexity. We will single out some results on the nucleotide distribution in 3r with respect to complexity and fractality. In particular, we will show that sequences with higher FD also have a higher frequency distribution of guanine, while low FD is characterized by the higher presence of adenine.
NASA Astrophysics Data System (ADS)
Sau Fa, Kwok
2017-03-01
Recently, fractal and generalized Fokker–Planck equations have been the subject of considerable interest. In this work, the fractal and generalized Fokker–Planck equations connected with the Langevin equation and continuous time random walk model are considered. Descriptions and applications of these models to the fixed samples of the mouse brain using magnetic resonance imaging (MRI) are discussed.
Plant Identification Based on Leaf Midrib Cross-Section Images Using Fractal Descriptors.
da Silva, Núbia Rosa; Florindo, João Batista; Gómez, María Cecilia; Rossatto, Davi Rodrigo; Kolb, Rosana Marta; Bruno, Odemir Martinez
2015-01-01
The correct identification of plants is a common necessity not only to researchers but also to the lay public. Recently, computational methods have been employed to facilitate this task, however, there are few studies front of the wide diversity of plants occurring in the world. This study proposes to analyse images obtained from cross-sections of leaf midrib using fractal descriptors. These descriptors are obtained from the fractal dimension of the object computed at a range of scales. In this way, they provide rich information regarding the spatial distribution of the analysed structure and, as a consequence, they measure the multiscale morphology of the object of interest. In Biology, such morphology is of great importance because it is related to evolutionary aspects and is successfully employed to characterize and discriminate among different biological structures. Here, the fractal descriptors are used to identify the species of plants based on the image of their leaves. A large number of samples are examined, being 606 leaf samples of 50 species from Brazilian flora. The results are compared to other imaging methods in the literature and demonstrate that fractal descriptors are precise and reliable in the taxonomic process of plant species identification.
Plant Identification Based on Leaf Midrib Cross-Section Images Using Fractal Descriptors
da Silva, Núbia Rosa; Florindo, João Batista; Gómez, María Cecilia; Rossatto, Davi Rodrigo; Kolb, Rosana Marta; Bruno, Odemir Martinez
2015-01-01
The correct identification of plants is a common necessity not only to researchers but also to the lay public. Recently, computational methods have been employed to facilitate this task, however, there are few studies front of the wide diversity of plants occurring in the world. This study proposes to analyse images obtained from cross-sections of leaf midrib using fractal descriptors. These descriptors are obtained from the fractal dimension of the object computed at a range of scales. In this way, they provide rich information regarding the spatial distribution of the analysed structure and, as a consequence, they measure the multiscale morphology of the object of interest. In Biology, such morphology is of great importance because it is related to evolutionary aspects and is successfully employed to characterize and discriminate among different biological structures. Here, the fractal descriptors are used to identify the species of plants based on the image of their leaves. A large number of samples are examined, being 606 leaf samples of 50 species from Brazilian flora. The results are compared to other imaging methods in the literature and demonstrate that fractal descriptors are precise and reliable in the taxonomic process of plant species identification. PMID:26091501
Stadnitski, Tatjana
2012-01-01
WHEN INVESTIGATING FRACTAL PHENOMENA, THE FOLLOWING QUESTIONS ARE FUNDAMENTAL FOR THE APPLIED RESEARCHER: (1) What are essential statistical properties of 1/f noise? (2) Which estimators are available for measuring fractality? (3) Which measurement instruments are appropriate and how are they applied? The purpose of this article is to give clear and comprehensible answers to these questions. First, theoretical characteristics of a fractal pattern (self-similarity, long memory, power law) and the related fractal parameters (the Hurst coefficient, the scaling exponent α, the fractional differencing parameter d of the autoregressive fractionally integrated moving average methodology, the power exponent β of the spectral analysis) are discussed. Then, estimators of fractal parameters from different software packages commonly used by applied researchers (R, SAS, SPSS) are introduced and evaluated. Advantages, disadvantages, and constrains of the popular estimators ([Formula: see text] power spectral density, detrended fluctuation analysis, signal summation conversion) are illustrated by elaborate examples. Finally, crucial steps of fractal analysis (plotting time series data, autocorrelation, and spectral functions; performing stationarity tests; choosing an adequate estimator; estimating fractal parameters; distinguishing fractal processes from short-memory patterns) are demonstrated with empirical time series.
Stadnitski, Tatjana
2012-01-01
When investigating fractal phenomena, the following questions are fundamental for the applied researcher: (1) What are essential statistical properties of 1/f noise? (2) Which estimators are available for measuring fractality? (3) Which measurement instruments are appropriate and how are they applied? The purpose of this article is to give clear and comprehensible answers to these questions. First, theoretical characteristics of a fractal pattern (self-similarity, long memory, power law) and the related fractal parameters (the Hurst coefficient, the scaling exponent α, the fractional differencing parameter d of the autoregressive fractionally integrated moving average methodology, the power exponent β of the spectral analysis) are discussed. Then, estimators of fractal parameters from different software packages commonly used by applied researchers (R, SAS, SPSS) are introduced and evaluated. Advantages, disadvantages, and constrains of the popular estimators (d^ML, power spectral density, detrended fluctuation analysis, signal summation conversion) are illustrated by elaborate examples. Finally, crucial steps of fractal analysis (plotting time series data, autocorrelation, and spectral functions; performing stationarity tests; choosing an adequate estimator; estimating fractal parameters; distinguishing fractal processes from short-memory patterns) are demonstrated with empirical time series. PMID:22586408
Detecting abrupt dynamic change based on changes in the fractal properties of spatial images
NASA Astrophysics Data System (ADS)
Liu, Qunqun; He, Wenping; Gu, Bin; Jiang, Yundi
2016-08-01
Many abrupt climate change events often cannot be detected timely by conventional abrupt detection methods until a few years after these events have occurred. The reason for this lag in detection is that abundant and long-term observational data are required for accurate abrupt change detection by these methods, especially for the detection of a regime shift. So, these methods cannot help us understand and forecast the evolution of the climate system in a timely manner. Obviously, spatial images, generated by a coupled spatiotemporal dynamical model, contain more information about a dynamic system than a single time series, and we find that spatial images show the fractal properties. The fractal properties of spatial images can be quantitatively characterized by the Hurst exponent, which can be estimated by two-dimensional detrended fluctuation analysis (TD-DFA). Based on this, TD-DFA is used to detect an abrupt dynamic change of a coupled spatiotemporal model. The results show that the TD-DFA method can effectively detect abrupt parameter changes in the coupled model by monitoring the changing in the fractal properties of spatial images. The present method provides a new way for abrupt dynamic change detection, which can achieve timely and efficient abrupt change detection results.
Zheng, Xiuqing; Liao, Zhiwu; Hu, Shaoxiang; Li, Ming; Zhou, Jiliu
2013-01-01
NLMs is a state-of-art image denoising method; however, it sometimes oversmoothes anatomical features in low-dose CT (LDCT) imaging. In this paper, we propose a simple way to improve the spatial adaptivity (SA) of NLMs using pointwise fractal dimension (PWFD). Unlike existing fractal image dimensions that are computed on the whole images or blocks of images, the new PWFD, named pointwise box-counting dimension (PWBCD), is computed for each image pixel. PWBCD uses a fixed size local window centered at the considered image pixel to fit the different local structures of images. Then based on PWBCD, a new method that uses PWBCD to improve SA of NLMs directly is proposed. That is, PWBCD is combined with the weight of the difference between local comparison windows for NLMs. Smoothing results for test images and real sinograms show that PWBCD-NLMs with well-chosen parameters can preserve anatomical features better while suppressing the noises efficiently. In addition, PWBCD-NLMs also has better performance both in visual quality and peak signal to noise ratio (PSNR) than NLMs in LDCT imaging.
Foulsham, Tom; Kingstone, Alan
2010-04-07
The direction in which people tend to move their eyes when inspecting images can reveal the different influences on eye guidance in scene perception, and their time course. We investigated biases in saccade direction during a memory-encoding task with natural scenes and computer-generated fractals. Images were rotated to disentangle egocentric and image-based guidance. Saccades in fractals were more likely to be horizontal, regardless of orientation. In scenes, the first saccade often moved down and subsequent eye movements were predominantly vertical, relative to the scene. These biases were modulated by the distribution of visual features (saliency and clutter) in the scene. The results suggest that image orientation, visual features and the scene frame-of-reference have a rapid effect on eye guidance.
Alzheimer's Disease Detection in Brain Magnetic Resonance Images Using Multiscale Fractal Analysis
Lahmiri, Salim; Boukadoum, Mounir
2013-01-01
We present a new automated system for the detection of brain magnetic resonance images (MRI) affected by Alzheimer's disease (AD). The MRI is analyzed by means of multiscale analysis (MSA) to obtain its fractals at six different scales. The extracted fractals are used as features to differentiate healthy brain MRI from those of AD by a support vector machine (SVM) classifier. The result of classifying 93 brain MRIs consisting of 51 images of healthy brains and 42 of brains affected by AD, using leave-one-out cross-validation method, yielded 99.18% ± 0.01 classification accuracy, 100% sensitivity, and 98.20% ± 0.02 specificity. These results and a processing time of 5.64 seconds indicate that the proposed approach may be an efficient diagnostic aid for radiologists in the screening for AD. PMID:24967286
A novel fractal monocular and stereo video codec with object-based functionality
NASA Astrophysics Data System (ADS)
Zhu, Shiping; Li, Liyun; Wang, Zaikuo
2012-12-01
Based on the classical fractal video compression method, an improved monocular fractal compression method is proposed which includes using more effective macroblock partition scheme instead of classical quadtree partition scheme; using improved fast motion estimation to increase the calculation speed; using homo-I-frame like in H.264, etc. The monocular codec uses the motion compensated prediction (MCP) structure. And stereo fractal video coding is proposed which matches the macroblock with two reference frames in left and right views, and it results in increasing compression ratio and reducing bit rate/bandwidth when transmitting compressed video data. The stereo codec combines MCP and disparity compensated prediction. And a new method of object-based fractal video coding is proposed in which each object can be encoded and decoded independently with higher compression ratio and speed and less bit rate/bandwidth when transmitting compressed stereo video data greatly. Experimental results indicate that the proposed monocular method can raise compression ratio 3.6 to 7.5 times, speed up compression time 5.3 to 22.3 times, and improve the image quality 3.81 to 9.24 dB in comparison with circular prediction mapping and non-contractive interframe mapping. The PSNR of the proposed stereo video coding is about 0.17 dB higher than that of the proposed monocular video coding, and 0.69 dB higher than that of JMVC 4.0 on average. Comparing with the bit rate resulted by the proposed monocular video coding and JMVC 4.0, the proposed stereo video coding achieves, on average, 2.53 and 21.14 Kbps bit rate saving, respectively. The proposed object-based fractal monocular and stereo video coding methods are simple and effective, and they make the applications of fractal monocular and stereo video coding more flexible and practicable.
NASA Astrophysics Data System (ADS)
Ahammer, Helmut; DeVaney, Trevor T. J.
2004-03-01
The boundary of a fractal object, represented in a two-dimensional space, is theoretically a line with an infinitely small width. In digital images this boundary or contour is limited to the pixel resolution of the image and the width of the line commonly depends on the edge detection algorithm used. The Minkowski dimension was evaluated by using three different edge detection algorithms (Sobel, Roberts, and Laplace operator). These three operators were investigated because they are very widely used and because their edge detection result is very distinct concerning the line width. Very common fractals (Sierpinski carpet and Koch islands) were investigated as well as the binary images from a cancer invasion assay taken with a confocal laser scanning microscope. The fractal dimension is directly proportional to the width of the contour line and the fact, that in practice very often the investigated objects are fractals only within a limited resolution range is considered too.
Ahammer, Helmut; DeVaney, Trevor T J
2004-03-01
The boundary of a fractal object, represented in a two-dimensional space, is theoretically a line with an infinitely small width. In digital images this boundary or contour is limited to the pixel resolution of the image and the width of the line commonly depends on the edge detection algorithm used. The Minkowski dimension was evaluated by using three different edge detection algorithms (Sobel, Roberts, and Laplace operator). These three operators were investigated because they are very widely used and because their edge detection result is very distinct concerning the line width. Very common fractals (Sierpinski carpet and Koch islands) were investigated as well as the binary images from a cancer invasion assay taken with a confocal laser scanning microscope. The fractal dimension is directly proportional to the width of the contour line and the fact, that in practice very often the investigated objects are fractals only within a limited resolution range is considered too.
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.
Fractal evaluation of drug amorphicity from optical and scanning electron microscope images
NASA Astrophysics Data System (ADS)
Gavriloaia, Bogdan-Mihai G.; Vizireanu, Radu C.; Neamtu, Catalin I.; Gavriloaia, Gheorghe V.
2013-09-01
Amorphous materials are metastable, more reactive than the crystalline ones, and have to be evaluated before pharmaceutical compound formulation. Amorphicity is interpreted as a spatial chaos, and patterns of molecular aggregates of dexamethasone, D, were investigated in this paper by using fractal dimension, FD. Images having three magnifications of D were taken from an optical microscope, OM, and with eight magnifications, from a scanning electron microscope, SEM, were analyzed. The average FD for pattern irregularities of OM images was 1.538, and about 1.692 for SEM images. The FDs of the two kinds of images are less sensitive of threshold level. 3D images were shown to illustrate dependence of FD of threshold and magnification level. As a result, optical image of single scale is enough to characterize the drug amorphicity. As a result, the OM image at a single scale is enough to characterize the amorphicity of D.
Fractal coding of wavelet image based on human vision contrast-masking effect
NASA Astrophysics Data System (ADS)
Wei, Hai; Shen, Lansun
2000-06-01
In this paper, a fractal-based compression approach of wavelet image is presented. The scheme tries to make full use of the sensitivity features of the human visual system. With the wavelet-based multi-resolution representation of image, detail vectors of each high frequency sub-image are constructed in accordance with its spatial orientation in order to grasp the edge information to which human observer is sensitive. Then a multi-level selection algorithm based on human vision's contrast masking effect is proposed to make the decision whether a detail vector is coded or not. Those vectors below the contrast threshold are discarded without introducing visual artifacts because of the ignorance of human vision. As for the redundancy of the retained vectors, different fractal- based methods are employed to decrease the correlation in single sub-image and between the different resolution sub- images with the same orientation. Experimental results suggest the efficiency of the proposed scheme. With the standard test image, our approach outperforms the EZW algorithm and the JPEG method.
Badea, Alexandru Florin; Lupsor Platon, Monica; Crisan, Maria; Cattani, Carlo; Badea, Iulia; Pierro, Gaetano; Sannino, Gianpaolo; Baciut, Grigore
2013-01-01
The geometry of some medical images of tissues, obtained by elastography and ultrasonography, is characterized in terms of complexity parameters such as the fractal dimension (FD). It is well known that in any image there are very subtle details that are not easily detectable by the human eye. However, in many cases like medical imaging diagnosis, these details are very important since they might contain some hidden information about the possible existence of certain pathological lesions like tissue degeneration, inflammation, or tumors. Therefore, an automatic method of analysis could be an expedient tool for physicians to give a faultless diagnosis. The fractal analysis is of great importance in relation to a quantitative evaluation of “real-time” elastography, a procedure considered to be operator dependent in the current clinical practice. Mathematical analysis reveals significant discrepancies among normal and pathological image patterns. The main objective of our work is to demonstrate the clinical utility of this procedure on an ultrasound image corresponding to a submandibular diffuse pathology. PMID:23762183
Badea, Alexandru Florin; Lupsor Platon, Monica; Crisan, Maria; Cattani, Carlo; Badea, Iulia; Pierro, Gaetano; Sannino, Gianpaolo; Baciut, Grigore
2013-01-01
The geometry of some medical images of tissues, obtained by elastography and ultrasonography, is characterized in terms of complexity parameters such as the fractal dimension (FD). It is well known that in any image there are very subtle details that are not easily detectable by the human eye. However, in many cases like medical imaging diagnosis, these details are very important since they might contain some hidden information about the possible existence of certain pathological lesions like tissue degeneration, inflammation, or tumors. Therefore, an automatic method of analysis could be an expedient tool for physicians to give a faultless diagnosis. The fractal analysis is of great importance in relation to a quantitative evaluation of "real-time" elastography, a procedure considered to be operator dependent in the current clinical practice. Mathematical analysis reveals significant discrepancies among normal and pathological image patterns. The main objective of our work is to demonstrate the clinical utility of this procedure on an ultrasound image corresponding to a submandibular diffuse pathology.
Tomomitsu, Tatsushi; Mimura, Hiroaki; Murase, Kenya; Tamada, Tsutomu; Sone, Teruki; Fukunaga, Masao
2005-06-20
Many analyses of bone microarchitecture using three-dimensional images of micro CT (microCT) have been reported recently. However, as extirpated bone is the subject of measurement on microCT, various kinds of information are not available clinically. Our aim is to evaluate usefulness of fractal dimension as an index of bone strength different from bone mineral density in in-vivo, to which microCT could not be applied. In this fundamental study, the relation between pixel size and the slice thickness of images was examined when fractal analysis was applied to clinical images. We examined 40 lumbar spine specimens extirpated from 16 male cadavers (30-88 years; mean age, 60.8 years). Three-dimensional images of the trabeculae of 150 slices were obtained by a microCT system under the following conditions: matrix size, 512 x 512; slice thickness, 23.2 em; and pixel size, 18.6 em. Based on images of 150 slices, images of four different matrix sizes and nine different slice thicknesses were made using public domain software (NIH Image). The threshold value for image binarization, and the relation between pixel size and the slice thickness of an image used for two-dimensional and three-dimensional fractal analyses were studied. In addition, the box counting method was used for fractal analysis. One hundred forty-five in box counting was most suitable as the threshold value for image binarization on the 256 gray levels. The correlation coefficients between two-dimensional fractal dimensions of processed images and three-dimensional fractal dimensions of original images were more than 0.9 for pixel sizes < or =148.8 microm at a slice thickness of 1 mm, and < or =74.4 microm at one of 2 mm. In terms of the relation between the three-dimensional fractal dimension of processed images and three-dimensional fractal dimension of original images, when pixel size was less than 74.4 microm, a correlation coefficient of more than 0.9 was obtained even for the maximal slice thickness
Fractal and digital image processing to determine the degree of dispersion of carbon nanotubes
NASA Astrophysics Data System (ADS)
Liang, Xiao-ning; Li, Wei
2016-05-01
The degree of dispersion is an important parameter to quantitatively study properties of carbon nanotube composites. Among the many methods for studying dispersion, scanning electron microscopy, transmission electron microscopy, and atomic force microscopy are the most commonly used, intuitive, and convincing methods. However, they have the disadvantage of not being quantitative. To overcome this disadvantage, the fractal theory and digital image processing method can be used to provide a quantitative analysis of the morphology and properties of carbon nanotube composites. In this paper, the dispersion degree of carbon nanotubes was investigated using two fractal methods, namely, the box-counting method and the differential box-counting method. On the basis of the results, we propose a new method for the quantitative characterization of the degree of dispersion of carbon nanotubes. This hierarchical grid method can be used as a supplementary method, and can be combined with the fractal calculation method. Thus, the accuracy and effectiveness of the quantitative characterization of the dispersion degree of carbon nanotubes can be improved. (The outer diameter of the carbon nanotubes is about 50 nm; the length of the carbon nanotubes is 10-20 μm.)
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.
Fractal dimension of sparkles in automotive metallic coatings by multispectral imaging measurements.
Medina, José M; Díaz, José A; Vignolo, Carlos
2014-07-23
Sparkle in surface coatings is a property of mirror-like pigment particles that consists of remarkable bright spots over a darker surround under unidirectional illumination. We developed a novel nondestructive method to characterize sparkles based on the multispectral imaging technique, and we focused on automotive metallic coatings containing aluminum flake pigments. Multispectral imaging was done in the visible spectrum at different illumination angles around the test sample. Reflectance spectra at different spatial positions were mapped to color coordinates and visualized in different color spaces. Spectral analysis shows that sparkles exhibit higher reflectance spectra and narrower bandwidths. Colorimetric analysis indicates that sparkles present higher lightness values and are far apart from the bulk of color coordinates spanned by the surround. A box-counting procedure was applied to examine the fractal organization of color coordinates in the CIE 1976 L*a*b* color space. A characteristic noninteger exponent was found at each illumination position. The exponent was independent of the illuminant spectra. Together, these results demonstrate that sparkles are extreme deviations relative to the surround and that their spectral properties can be described as fractal patterns within the color space. Multispectral reflectance imaging provides a powerful, noninvasive method for spectral identification and classification of sparkles from metal flake pigments on the micron scale.
Radial distribution function for hard spheres in fractal dimensions: A heuristic approximation.
Santos, Andrés; de Haro, Mariano López
2016-06-01
Analytic approximations for the radial distribution function, the structure factor, and the equation of state of hard-core fluids in fractal dimension d (1≤d≤3) are developed as heuristic interpolations from the knowledge of the exact and Percus-Yevick results for the hard-rod and hard-sphere fluids, respectively. In order to assess their value, such approximate results are compared with those of recent Monte Carlo simulations and numerical solutions of the Percus-Yevick equation for a fractal dimension [M. Heinen et al., Phys. Rev. Lett. 115, 097801 (2015)PRLTAO0031-900710.1103/PhysRevLett.115.097801], a good agreement being observed.
Angle closure glaucoma detection using fractal dimension index on SS-OCT images.
Ni, Soe Ni; Marzilianol, Pina; Wong, Hon-Tym
2014-01-01
Optical coherence tomography (OCT) is a high resolution, rapid and non-invasive screening tool for angle closure glaucoma. In this paper, we propose a new strategy for automatic and landmark invariant quantification of the anterior chamber angle of the eye using swept source optical coherence tomography (SS-OCT) images. Seven hundred and eight swept source optical coherence tomography SS-OCT images from 148 patients with average age of (59.48 ± 8.97) were analyzed in this study. The angle structure is measured by fractal dimension (FD) analysis to quantify the complexity or changes of angle recess. We evaluated the FD index with biometric parameters for classification of open angle and angle closure glaucoma. The proposed fractal dimension index gives a better representation of the angle configuration for capturing the nature of the angle dynamics involved in different forms of open and closed angle glaucoma (average FD (standard deviation): 1.944 (0.045) for open and 1.894 (0.043) for closed angle). It showed that the proposed approach has promising potential to become a computer aided diagnostic tool for angle closure glaucoma (ACG) disease.
NASA Technical Reports Server (NTRS)
Quattrochi, Dale A.; Emerson, Charles W.; Lam, Nina Siu-Ngan; Laymon, Charles A.
1997-01-01
The Image Characterization And Modeling System (ICAMS) is a public domain software package that is designed to provide scientists with innovative spatial analytical tools to visualize, measure, and characterize landscape patterns so that environmental conditions or processes can be assessed and monitored more effectively. In this study ICAMS has been used to evaluate how changes in fractal dimension, as a landscape characterization index, and resolution, are related to differences in Landsat images collected at different dates for the same area. Landsat Thematic Mapper (TM) data obtained in May and August 1993 over a portion of the Great Basin Desert in eastern Nevada were used for analysis. These data represent contrasting periods of peak "green-up" and "dry-down" for the study area. The TM data sets were converted into Normalized Difference Vegetation Index (NDVI) images to expedite analysis of differences in fractal dimension between the two dates. These NDVI images were also resampled to resolutions of 60, 120, 240, 480, and 960 meters from the original 30 meter pixel size, to permit an assessment of how fractal dimension varies with spatial resolution. Tests of fractal dimension for two dates at various pixel resolutions show that the D values in the August image become increasingly more complex as pixel size increases to 480 meters. The D values in the May image show an even more complex relationship to pixel size than that expressed in the August image. Fractal dimension for a difference image computed for the May and August dates increase with pixel size up to a resolution of 120 meters, and then decline with increasing pixel size. This means that the greatest complexity in the difference images occur around a resolution of 120 meters, which is analogous to the operational domain of changes in vegetation and snow cover that constitute differences between the two dates.
Wang, Jianji; Zheng, Nanning
2013-09-01
Fractal image compression (FIC) is an image coding technology based on the local similarity of image structure. It is widely used in many fields such as image retrieval, image denoising, image authentication, and encryption. FIC, however, suffers from the high computational complexity in encoding. Although many schemes are published to speed up encoding, they do not easily satisfy the encoding time or the reconstructed image quality requirements. In this paper, a new FIC scheme is proposed based on the fact that the affine similarity between two blocks in FIC is equivalent to the absolute value of Pearson's correlation coefficient (APCC) between them. First, all blocks in the range and domain pools are chosen and classified using an APCC-based block classification method to increase the matching probability. Second, by sorting the domain blocks with respect to APCCs between these domain blocks and a preset block in each class, the matching domain block for a range block can be searched in the selected domain set in which these APCCs are closer to APCC between the range block and the preset block. Experimental results show that the proposed scheme can significantly speed up the encoding process in FIC while preserving the reconstructed image quality well.
Dim target detection in IR image sequences based on fractal and rough set theory
NASA Astrophysics Data System (ADS)
Yan, Xiaoke; Shi, Caicheng; He, Peikun
2005-11-01
This paper addresses the problem of detecting small, moving, low amplitude in image sequences that also contain moving nuisance objects and background noise. Rough sets (RS) theory is applied in similarity relation instead of equivalence relation to solve clustering issue. We propose fractal-based texture analysis to describe texture coarseness and locally adaptive threshold technique to seek latent object point. Finally, according to temporal and spatial correlations between different frames, the singular points can be filtered. We demonstrate the effectiveness of the technique by applying it to real infrared image sequences containing targets of opportunity and evolving cloud clutter. The experimental results show that the algorithm can effectively increase detection probability and has robustness.
NASA Astrophysics Data System (ADS)
Yang, Y.; Li, H. T.; Han, Y. S.; Gu, H. Y.
2015-06-01
Image segmentation is the foundation of further object-oriented image analysis, understanding and recognition. It is one of the key technologies in high resolution remote sensing applications. In this paper, a new fast image segmentation algorithm for high resolution remote sensing imagery is proposed, which is based on graph theory and fractal net evolution approach (FNEA). Firstly, an image is modelled as a weighted undirected graph, where nodes correspond to pixels, and edges connect adjacent pixels. An initial object layer can be obtained efficiently from graph-based segmentation, which runs in time nearly linear in the number of image pixels. Then FNEA starts with the initial object layer and a pairwise merge of its neighbour object with the aim to minimize the resulting summed heterogeneity. Furthermore, according to the character of different features in high resolution remote sensing image, three different merging criterions for image objects based on spectral and spatial information are adopted. Finally, compared with the commercial remote sensing software eCognition, the experimental results demonstrate that the efficiency of the algorithm has significantly improved, and the result can maintain good feature boundaries.
NASA Astrophysics Data System (ADS)
Alonso, Carmelo; Tarquis, Ana M.; Zúñiga, Ignacio; Benito, Rosa M.
2017-03-01
Several studies have shown that vegetation indexes can be used to estimate root zone soil moisture. Earth surface images, obtained by high-resolution satellites, presently give a lot of information on these indexes, based on the data of several wavelengths. Because of the potential capacity for systematic observations at various scales, remote sensing technology extends the possible data archives from the present time to several decades back. Because of this advantage, enormous efforts have been made by researchers and application specialists to delineate vegetation indexes from local scale to global scale by applying remote sensing imagery. In this work, four band images have been considered, which are involved in these vegetation indexes, and were taken by satellites Ikonos-2 and Landsat-7 of the same geographic location, to study the effect of both spatial (pixel size) and radiometric (number of bits coding the image) resolution on these wavelength bands as well as two vegetation indexes: the Normalized Difference Vegetation Index (NDVI) and the Enhanced Vegetation Index (EVI). In order to do so, a multi-fractal analysis of these multi-spectral images was applied in each of these bands and the two indexes derived. The results showed that spatial resolution has a similar scaling effect in the four bands, but radiometric resolution has a larger influence in blue and green bands than in red and near-infrared bands. The NDVI showed a higher sensitivity to the radiometric resolution than EVI. Both were equally affected by the spatial resolution. From both factors, the spatial resolution has a major impact in the multi-fractal spectrum for all the bands and the vegetation indexes. This information should be taken in to account when vegetation indexes based on different satellite sensors are obtained.
LETTER TO THE EDITOR: Fractal diffusion coefficient from dynamical zeta functions
NASA Astrophysics Data System (ADS)
Cristadoro, Giampaolo
2006-03-01
Dynamical zeta functions provide a powerful method to analyse low-dimensional dynamical systems when the underlying symbolic dynamics is under control. On the other hand, even simple one-dimensional maps can show an intricate structure of the grammar rules that may lead to a non-smooth dependence of global observables on parameters changes. A paradigmatic example is the fractal diffusion coefficient arising in a simple piecewise linear one-dimensional map of the real line. Using the Baladi-Ruelle generalization of the Milnor-Thurnston kneading determinant, we provide the exact dynamical zeta function for such a map and compute the diffusion coefficient from its smallest zero.
N'Diaye, Mambaye; Degeratu, Cristinel; Bouler, Jean-Michel; Chappard, Daniel
2013-05-01
Porous structures are becoming more and more important in biology and material science because they help in reducing the density of the grafted material. For biomaterials, porosity also increases the accessibility of cells and vessels inside the grafted area. However, descriptors of porosity are scanty. We have used a series of biomaterials with different types of porosity (created by various porogens: fibers, beads …). Blocks were studied by microcomputed tomography for the measurement of 3D porosity. 2D sections were re-sliced to analyze the microarchitecture of the pores and were transferred to image analysis programs: star volumes, interconnectivity index, Minkowski-Bouligand and Kolmogorov fractal dimensions were determined. Lacunarity and succolarity, two recently described fractal dimensions, were also computed. These parameters provided a precise description of porosity and pores' characteristics. Non-linear relationships were found between several descriptors e.g. succolarity and star volume of the material. A linear correlation was found between lacunarity and succolarity. These techniques appear suitable in the study of biomaterials usable as bone substitutes.
Mossotti, Victor G.; Eldeeb, A. Raouf
2000-01-01
Turcotte, 1997, and Barton and La Pointe, 1995, have identified many potential uses for the fractal dimension in physicochemical models of surface properties. The image-analysis program described in this report is an extension of the program set MORPH-I (Mossotti and others, 1998), which provided the fractal analysis of electron-microscope images of pore profiles (Mossotti and Eldeeb, 1992). MORPH-II, an integration of the modified kernel of the program MORPH-I with image calibration and editing facilities, was designed to measure the fractal dimension of the exposed surfaces of stone specimens as imaged in cross section in an electron microscope.
Characterizing Hyperspectral Imagery (AVIRIS) Using Fractal Technique
NASA Technical Reports Server (NTRS)
Qiu, Hong-Lie; Lam, Nina Siu-Ngan; Quattrochi, Dale
1997-01-01
With the rapid increase in hyperspectral data acquired by various experimental hyperspectral imaging sensors, it is necessary to develop efficient and innovative tools to handle and analyze these data. The objective of this study is to seek effective spatial analytical tools for summarizing the spatial patterns of hyperspectral imaging data. In this paper, we (1) examine how fractal dimension D changes across spectral bands of hyperspectral imaging data and (2) determine the relationships between fractal dimension and image content. It has been documented that fractal dimension changes across spectral bands for the Landsat-TM data and its value [(D)] is largely a function of the complexity of the landscape under study. The newly available hyperspectral imaging data such as that from the Airborne Visible Infrared Imaging Spectrometer (AVIRIS) which has 224 bands, covers a wider spectral range with a much finer spectral resolution. Our preliminary result shows that fractal dimension values of AVIRIS scenes from the Santa Monica Mountains in California vary between 2.25 and 2.99. However, high fractal dimension values (D > 2.8) are found only from spectral bands with high noise level and bands with good image quality have a fairly stable dimension value (D = 2.5 - 2.6). This suggests that D can also be used as a summary statistics to represent the image quality or content of spectral bands.
ERIC Educational Resources Information Center
Esbenshade, Donald H., Jr.
1991-01-01
Develops the idea of fractals through a laboratory activity that calculates the fractal dimension of ordinary white bread. Extends use of the fractal dimension to compare other complex structures as other breads and sponges. (MDH)
Fractal dimensions of wave functions and local spectral measures on the Fibonacci chain
NASA Astrophysics Data System (ADS)
Macé, Nicolas; Jagannathan, Anuradha; Piéchon, Frédéric
2016-05-01
We present a theoretical framework for understanding the wave functions and spectrum of an extensively studied paradigm for quasiperiodic systems, namely the Fibonacci chain. Our analytical results, which are obtained in the limit of strong modulation of the hopping amplitudes, are in good agreement with published numerical data. In the perturbative limit, we show a symmetry of wave functions under permutation of site and energy indices. We compute the wave-function renormalization factors and from them deduce analytical expressions for the fractal exponents corresponding to individual wave functions, as well as their global averages. The multifractality of wave functions is seen to appear at next-to-leading order in ρ . Exponents for the local spectral density are given, in extremely good accord with numerical calculations. Interestingly, our analytical results for exponents are observed to describe the system rather well even for values of ρ well outside the domain of applicability of perturbation theory.
Jitaree, Sirinapa; Phinyomark, Angkoon; Boonyaphiphat, Pleumjit; Phukpattaranont, Pornchai
2015-01-01
Having a classifier of cell types in a breast cancer microscopic image (BCMI), obtained with immunohistochemical staining, is required as part of a computer-aided system that counts the cancer cells in such BCMI. Such quantitation by cell counting is very useful in supporting decisions and planning of the medical treatment of breast cancer. This study proposes and evaluates features based on texture analysis by fractal dimension (FD), for the classification of histological structures in a BCMI into either cancer cells or non-cancer cells. The cancer cells include positive cells (PC) and negative cells (NC), while the normal cells comprise stromal cells (SC) and lymphocyte cells (LC). The FD feature values were calculated with the box-counting method from binarized images, obtained by automatic thresholding with Otsu's method of the grayscale images for various color channels. A total of 12 color channels from four color spaces (RGB, CIE-L*a*b*, HSV, and YCbCr) were investigated, and the FD feature values from them were used with decision tree classifiers. The BCMI data consisted of 1,400, 1,200, and 800 images with pixel resolutions 128 × 128, 192 × 192, and 256 × 256, respectively. The best cross-validated classification accuracy was 93.87%, for distinguishing between cancer and non-cancer cells, obtained using the Cr color channel with window size 256. The results indicate that the proposed algorithm, based on fractal dimension features extracted from a color channel, performs well in the automatic classification of the histology in a BCMI. This might support accurate automatic cell counting in a computer-assisted system for breast cancer diagnosis.
Generalized functional formulation for multi-fractal representation of basin hydraulic geometry
NASA Astrophysics Data System (ADS)
Kim, JongChun; Paik, Kyungrock
2015-04-01
Natural rivers exhibit power-functional variability in their width, depth, and velocity with flow discharge (Leopold and Maddock, 1953). This relation named hydraulic geometry has been empirically supported by many field studies across the world (e.g., Leopold et al., 1964; Stall and Fok, 1968). The relationship appears either at a fixed cross-section, showing temporal variability, or along a downstream direction across an entire basin, showing spatial variability, the latter named downstream or basin hydraulic geometry. Theoretical studies that attempt to explain the power-law phenomenon (fractal), have assumed that the watershed is homogeneous hydrologically and geologically. Nevertheless, real watersheds are often subject to spatially heterogeneous conditions, due to various reasons including partial area storm coverage (Sólyom and Tucker, 2004) and transmission losses on bed and banks (Lane et al., 1997). In this setting, hydraulic geometry relationships are likely to deviate from monotonic power-law relationship and to follow rather more complex multi-fractal characteristics. In fact, deviation from single power-law was reported for at-a-station relationship of midwest rivers in US (Dodov and Foufoula-Georgiou, 2004). In the case of downstream variation, we identify significant multi-fractal characteristics over the Colorado River basin where strong heterogeneity in geological and hydrological settings presents. Conventional power-law hydraulic geometry relationships cannot express the functional variability for these cases. Motivated by this fact, we generalize the hydraulic geometry functional formulation in this study to express multi-fractal relationships. To do so, we couple the formulation of Paik and Kumar (2004), which generalized at-a-station and downstream relationships, with the formulation of Dodov and Foufoula-Georgiou (2004) which was proposed for multi-scaling in at-a-station relationship. The proposed formulation is successfully evaluated with
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…
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.
Adaptive reconfiguration of fractal small-world human brain functional networks.
Bassett, Danielle S; Meyer-Lindenberg, Andreas; Achard, Sophie; Duke, Thomas; Bullmore, Edward
2006-12-19
Brain function depends on adaptive self-organization of large-scale neural assemblies, but little is known about quantitative network parameters governing these processes in humans. Here, we describe the topology and synchronizability of frequency-specific brain functional networks using wavelet decomposition of magnetoencephalographic time series, followed by construction and analysis of undirected graphs. Magnetoencephalographic data were acquired from 22 subjects, half of whom performed a finger-tapping task, whereas the other half were studied at rest. We found that brain functional networks were characterized by small-world properties at all six wavelet scales considered, corresponding approximately to classical delta (low and high), , alpha, beta, and gamma frequency bands. Global topological parameters (path length, clustering) were conserved across scales, most consistently in the frequency range 2-37 Hz, implying a scale-invariant or fractal small-world organization. Dynamical analysis showed that networks were located close to the threshold of order/disorder transition in all frequency bands. The highest-frequency gamma network had greater synchronizability, greater clustering of connections, and shorter path length than networks in the scaling regime of (lower) frequencies. Behavioral state did not strongly influence global topology or synchronizability; however, motor task performance was associated with emergence of long-range connections in both beta and gamma networks. Long-range connectivity, e.g., between frontal and parietal cortex, at high frequencies during a motor task may facilitate sensorimotor binding. Human brain functional networks demonstrate a fractal small-world architecture that supports critical dynamics and task-related spatial reconfiguration while preserving global topological parameters.
NASA Astrophysics Data System (ADS)
Jaroniec, Mietek; Kruk, Michal; Olivier, James
1995-11-01
Methods of calculating the fractal dimension (D) on the basis of single adsorption isotherms were critically tested by using argon composite adsorption isotherms for fractally porous solids. These isotherms were obtained from adsorption data for homogeneous slit-like pores calculated by employing the density functional theory (DFT). The composite adsorption isotherms were used to test the validity of the method based on the Frenkel-Halsey-Hill equation and so called "thermodynamic method" proposed by Neimark. The applicability of these methods was confirmed. However, our studies reveal new aspects of practical usage of both approaches, which need to be taken into consideration in analysis of experimental data.
NASA Astrophysics Data System (ADS)
Pepe, S.; Di Martino, G.; Iodice, A.; Manzo, M.; Pepe, A.; Riccio, D.; Ruello, G.; Sansosti, E.; Tizzani, P.; Zinno, I.
2012-04-01
In the last two decades several aspects relevant to volcanic activity have been analyzed in terms of fractal parameters that effectively describe natural objects geometry. More specifically, these researches have been aimed at the identification of (1) the power laws that governed the magma fragmentation processes, (2) the energy of explosive eruptions, and (3) the distribution of the associated earthquakes. In this paper, the study of volcano morphology via satellite images is dealt with; in particular, we use the complete forward model developed by some of the authors (Di Martino et al., 2012) that links the stochastic characterization of amplitude Synthetic Aperture Radar (SAR) images to the fractal dimension of the imaged surfaces, modelled via fractional Brownian motion (fBm) processes. Based on the inversion of such a model, a SAR image post-processing has been implemented (Di Martino et al., 2010), that allows retrieving the fractal dimension of the observed surfaces, dictating the distribution of the roughness over different spatial scales. The fractal dimension of volcanic structures has been related to the specific nature of materials and to the effects of active geodynamic processes. Hence, the possibility to estimate the fractal dimension from a single amplitude-only SAR image is of fundamental importance for the characterization of volcano structures and, moreover, can be very helpful for monitoring and crisis management activities in case of eruptions and other similar natural hazards. The implemented SAR image processing performs the extraction of the point-by-point fractal dimension of the scene observed by the sensor, providing - as an output product - the map of the fractal dimension of the area of interest. In this work, such an analysis is performed on Cosmo-SkyMed, ERS-1/2 and ENVISAT images relevant to active stratovolcanoes in different geodynamic contexts, such as Mt. Somma-Vesuvio, Mt. Etna, Vulcano and Stromboli in Southern Italy, Shinmoe
FRACTAL DIMENSION OF GALAXY ISOPHOTES
Thanki, Sandip; Rhee, George; Lepp, Stephen E-mail: grhee@physics.unlv.edu
2009-09-15
In this paper we investigate the use of the fractal dimension of galaxy isophotes in galaxy classification. We have applied two different methods for determining fractal dimensions to the isophotes of elliptical and spiral galaxies derived from CCD images. We conclude that fractal dimension alone is not a reliable tool but that combined with other parameters in a neural net algorithm the fractal dimension could be of use. In particular, we have used three parameters to segregate the ellipticals and lenticulars from the spiral galaxies in our sample. These three parameters are the correlation fractal dimension D {sub corr}, the difference between the correlation fractal dimension and the capacity fractal dimension D {sub corr} - D {sub cap}, and, thirdly, the B - V color of the galaxy.
Imaging basal ganglia function
BROOKS, DAVID J.
2000-01-01
In this review, the value of functional imaging for providing insight into the role of the basal ganglia in motor control is reviewed. Brain activation findings in normal subjects and Parkinson's disease patients are examined and evidence supporting the existence for functionally independent distributed basal ganglia-frontal loops is presented. It is argued that the basal ganglia probably act to focus and filter cortical output, optimising the running of motor programs. PMID:10923986
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.)
Radlinski, A.P.; Radlinska, E.Z.; Agamalian, M.; Wignall, G.D.; Lindner, P.; Randl, O.G.
1999-04-01
The analysis of small- and ultra-small-angle neutron scattering data for sedimentary rocks shows that the pore-rock fabric interface is a surface fractal (D{sub s}=2.82) over 3 orders of magnitude of the length scale and 10 orders of magnitude in intensity. The fractal dimension and scatterer size obtained from scanning electron microscopy image processing are consistent with neutron scattering data. {copyright} {ital 1999} {ital The American Physical Society}
NASA Astrophysics Data System (ADS)
Strichartz, Robert S.; Usher, Michael
2000-09-01
A general theory of piecewise multiharmonic splines is constructed for a class of fractals (post-critically finite) that includes the familiar Sierpinski gasket, based on Kigami's theory of Laplacians on these fractals. The spline spaces are the analogues of the spaces of piecewise Cj polynomials of degree 2j + 1 on an interval, with nodes at dyadic rational points. We give explicit algorithms for effectively computing multiharmonic functions (solutions of [Delta]j+1u = 0) and for constructing bases for the spline spaces (for general fractals we need to assume that j is odd), and also for computing inner products of these functions. This enables us to give a finite element method for the approximate solution of fractal differential equations. We give the analogue of Simpson's method for numerical integration on the Sierpinski gasket. We use splines to approximate functions vanishing on the boundary by functions vanishing in a neighbourhood of the boundary.
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.
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.
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.
NASA Astrophysics Data System (ADS)
West, Bruce J.
The proper methodology for describing the dynamics of certain complex phenomena and fractal time series is the fractional calculus through the fractional Langevin equation discussed herein and applied in a biomedical context. We show that a fractional operator (derivative or integral) acting on a fractal function, yields another fractal function, allowing us to construct a fractional Langevin equation to describe the evolution of a fractal statistical process, for example, human gait and cerebral blood flow. The goal of this talk is to make clear how certain complex phenomena, such as those that are abundantly present in human physiology, can be faithfully described using dynamical models involving fractional differential stochastic equations. These models are tested against existing data sets and shown to describe time series from complex physiologic phenomena quite well.
[Power-law species richness accumulation as manifestation of the fractal community structure].
Gelashvili, D B; Iudin, D I; Rozenberg, G S; Iakimov, N V
2007-01-01
Applications of the fractal to describing the species structure of communities are discussed. Fundamental notions of fractal geometry are explained in the first part. The problem of applying the concept of fractal to describe the spatial allocation of particular species and of community as a whole is reviewed in the second part. In the final part, the usage of the selfsimirity principle for analyzing community organization is substantiated, and evidence of the fractal structure of biocenoses is presented according to Whittaker's concept of alpha diversity. It is shown that community is characterized, as a fractal object, by scale invariance, by power function relationship between the number of structural elements of the community (individuals, populations, species) and the scale (sampling effort), and, finally, by fractional value of the power (fractal dimension). Power function is the formula the takes into account the share of rare species, or species represented by a single individual. providing for no saturation of the function f(x). This formula also does not contradict the A.P. Levich's "rule of ecological non-additivity" and, lastly, allows the application of fractal formalism to characterize the species structure of a community. It is concluded that the mathematical image of species richness is a monofractal, i.e., a set characterised by only one parameter, fractal dimension. Thus, the species structure of a community (as well as the pattern of its spatial allocation) displays self-similarity and is a fractal.
Fractal characterization of wear-erosion surfaces
Rawers, J.; Tylczak, J.
1999-12-01
Wear erosion is a complex phenomenon resulting in highly distorted and deformed surface morphologies. Most wear surface features have been described only qualitatively. In this study wear surfaces features were quantified using fractal analysis. The ability to assign numerical values to wear-erosion surfaces makes possible mathematical expressions that will enable wear mechanisms to be predicted and understood. Surface characterization came from wear-erosion experiments that included varying the erosive materials, the impact velocity, and the impact angle. Seven fractal analytical techniques were applied to micrograph images of wear-erosion surfaces. Fourier analysis was the most promising. Fractal values obtained were consistent with visual observations and provided a unique wear-erosion parameter unrelated to wear rate. In this study stainless steel was evaluated as a function of wear erosion conditions.
Fractal design concepts for stretchable electronics.
Fan, Jonathan A; Yeo, Woon-Hong; Su, Yewang; Hattori, Yoshiaki; Lee, Woosik; Jung, Sung-Young; Zhang, Yihui; Liu, Zhuangjian; Cheng, Huanyu; Falgout, Leo; Bajema, Mike; Coleman, Todd; Gregoire, Dan; Larsen, Ryan J; Huang, Yonggang; Rogers, John A
2014-01-01
Stretchable electronics provide a foundation for applications that exceed the scope of conventional wafer and circuit board technologies due to their unique capacity to integrate with soft materials and curvilinear surfaces. The range of possibilities is predicated on the development of device architectures that simultaneously offer advanced electronic function and compliant mechanics. Here we report that thin films of hard electronic materials patterned in deterministic fractal motifs and bonded to elastomers enable unusual mechanics with important implications in stretchable device design. In particular, we demonstrate the utility of Peano, Greek cross, Vicsek and other fractal constructs to yield space-filling structures of electronic materials, including monocrystalline silicon, for electrophysiological sensors, precision monitors and actuators, and radio frequency antennas. These devices support conformal mounting on the skin and have unique properties such as invisibility under magnetic resonance imaging. The results suggest that fractal-based layouts represent important strategies for hard-soft materials integration.
Fractal design concepts for stretchable electronics
NASA Astrophysics Data System (ADS)
Fan, Jonathan A.; Yeo, Woon-Hong; Su, Yewang; Hattori, Yoshiaki; Lee, Woosik; Jung, Sung-Young; Zhang, Yihui; Liu, Zhuangjian; Cheng, Huanyu; Falgout, Leo; Bajema, Mike; Coleman, Todd; Gregoire, Dan; Larsen, Ryan J.; Huang, Yonggang; Rogers, John A.
2014-02-01
Stretchable electronics provide a foundation for applications that exceed the scope of conventional wafer and circuit board technologies due to their unique capacity to integrate with soft materials and curvilinear surfaces. The range of possibilities is predicated on the development of device architectures that simultaneously offer advanced electronic function and compliant mechanics. Here we report that thin films of hard electronic materials patterned in deterministic fractal motifs and bonded to elastomers enable unusual mechanics with important implications in stretchable device design. In particular, we demonstrate the utility of Peano, Greek cross, Vicsek and other fractal constructs to yield space-filling structures of electronic materials, including monocrystalline silicon, for electrophysiological sensors, precision monitors and actuators, and radio frequency antennas. These devices support conformal mounting on the skin and have unique properties such as invisibility under magnetic resonance imaging. The results suggest that fractal-based layouts represent important strategies for hard-soft materials integration.
Fractal characterization and wettability of ion treated silicon surfaces
NASA Astrophysics Data System (ADS)
Yadav, R. P.; Kumar, Tanuj; Baranwal, V.; Vandana, Kumar, Manvendra; Priya, P. K.; Pandey, S. N.; Mittal, A. K.
2017-02-01
Fractal characterization of surface morphology can be useful as a tool for tailoring the wetting properties of solid surfaces. In this work, rippled surfaces of Si (100) are grown using 200 keV Ar+ ion beam irradiation at different ion doses. Relationship between fractal and wetting properties of these surfaces are explored. The height-height correlation function extracted from atomic force microscopic images, demonstrates an increase in roughness exponent with an increase in ion doses. A steep variation in contact angle values is found for low fractal dimensions. Roughness exponent and fractal dimensions are found correlated with the static water contact angle measurement. It is observed that after a crossover of the roughness exponent, the surface morphology has a rippled structure. Larger values of interface width indicate the larger ripples on the surface. The contact angle of water drops on such surfaces is observed to be lowest. Autocorrelation function is used for the measurement of ripple wavelength.
NASA Astrophysics Data System (ADS)
Beech, M.
1989-02-01
The author discusses some of the more recent research on fractal astronomy and results presented in several astronomical studies. First, the large-scale structure of the universe is considered, while in another section one drops in scale to examine some of the smallest bodies in our solar system; the comets and meteoroids. The final section presents some thoughts on what influence the fractal ideology might have on astronomy, focusing particularly on the question recently raised by Kadanoff, "Fractals: where's the physics?"
Ingvar, M
1999-01-01
Functional neuroimaging has fundamentally changed our knowledge about the cerebral representation of pain. For the first time it has been possible to delineate the functional anatomy of different aspects of pain in the medial and lateral pain systems in the brain. The rapid developments in imaging methods over the past years have led to a consensus in the description of the central pain responses between different studies and also to a definition of a central pain matrix with specialized subfunctions in man. In the near future we will see studies where a systems perspective allows for a better understanding of the regulatory mechanisms in the higher-order frontal and parietal cortices. Also, pending the development of experimental paradigms, the functional anatomy of the emotional aspects of pain will become better known. PMID:10466155
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.
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.
Fractal metrology for biogeosystems analysis
NASA Astrophysics Data System (ADS)
Torres-Argüelles, V.; Oleschko, K.; Tarquis, A. M.; Korvin, G.; Gaona, C.; Parrot, J.-F.; Ventura-Ramos, E.
2010-06-01
The solid-pore distribution pattern plays an important role in soil functioning being related with the main physical, chemical and biological multiscale and multitemporal processes. In the present research, this pattern is extracted from the digital images of three soils (Chernozem, Solonetz and "Chocolate'' Clay) and compared in terms of roughness of the gray-intensity distribution (the measurand) quantified by several measurement techniques. Special attention was paid to the uncertainty of each of them and to the measurement function which best fits to the experimental results. Some of the applied techniques are known as classical in the fractal context (box-counting, rescaling-range and wavelets analyses, etc.) while the others have been recently developed by our Group. The combination of all these techniques, coming from Fractal Geometry, Metrology, Informatics, Probability Theory and Statistics is termed in this paper Fractal Metrology (FM). We show the usefulness of FM through a case study of soil physical and chemical degradation applying the selected toolbox to describe and compare the main structural attributes of three porous media with contrasting structure but similar clay mineralogy dominated by montmorillonites.
ERIC Educational Resources Information Center
Gray, Shirley B.
1992-01-01
This article traces the historical development of fractal geometry from early in the twentieth century and offers an explanation of the mathematics behind the recursion formulas and their representations within computer graphics. Also included are the fundamentals behind programing for fractal graphics in the C Language with appropriate…
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 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.
Functional magnetic resonance imaging.
Buchbinder, Bradley R
2016-01-01
Functional magnetic resonance imaging (fMRI) maps the spatiotemporal distribution of neural activity in the brain under varying cognitive conditions. Since its inception in 1991, blood oxygen level-dependent (BOLD) fMRI has rapidly become a vital methodology in basic and applied neuroscience research. In the clinical realm, it has become an established tool for presurgical functional brain mapping. This chapter has three principal aims. First, we review key physiologic, biophysical, and methodologic principles that underlie BOLD fMRI, regardless of its particular area of application. These principles inform a nuanced interpretation of the BOLD fMRI signal, along with its neurophysiologic significance and pitfalls. Second, we illustrate the clinical application of task-based fMRI to presurgical motor, language, and memory mapping in patients with lesions near eloquent brain areas. Integration of BOLD fMRI and diffusion tensor white-matter tractography provides a road map for presurgical planning and intraoperative navigation that helps to maximize the extent of lesion resection while minimizing the risk of postoperative neurologic deficits. Finally, we highlight several basic principles of resting-state fMRI and its emerging translational clinical applications. Resting-state fMRI represents an important paradigm shift, focusing attention on functional connectivity within intrinsic cognitive networks.
Fractal 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.
Li, Heheng; Luo, Liangping; Huang, Li
2011-02-01
The present paper is aimed to study the fractal spectrum of the cerebral computerized tomography in 158 normal infants of different age groups, based on the calculation of chaotic theory. The distribution range of neonatal period was 1.88-1.90 (mean = 1.8913 +/- 0.0064); It reached a stable condition at the level of 1.89-1.90 during 1-12 months old (mean = 1.8927 +/- 0.0045); The normal range of 1-2 years old infants was 1.86-1.90 (mean = 1.8863 +/- 4 0.0085); It kept the invariance of the quantitative value among 1.88-1.91(mean = 1.8958 +/- 0.0083) during 2-3 years of age. ANOVA indicated there's no significant difference between boys and girls (F = 0.243, P > 0.05), but the difference of age groups was significant (F = 8.947, P < 0.001). The fractal dimension of cerebral computerized tomography in normal infants computed by box methods was maintained at an efficient stability from 1.86 to 1.91. It indicated that there exit some attractor modes in pediatric brain development.
Fractal processes in soil water retention
Tyler, S.W.; Wheatcraft, S.W. )
1990-05-01
The authors propose a physical conceptual model for soil texture and pore structure that is based on the concept of fractal geometry. The motivation for a fractal model of soil texture is that some particle size distributions in granular soils have already been shown to display self-similar scaling that is typical of fractal objects. Hence it is reasonable to expect that pore size distributions may also display fractal scaling properties. The paradigm that they used for the soil pore size distribution is the Sierpinski carpet, which is a fractal that contains self similar holes (or pores) over a wide range of scales. The authors evaluate the water retention properties of regular and random Sierpinski carpets and relate these properties directly to the Brooks and Corey (or Campbell) empirical water retention model. They relate the water retention curves directly to the fractal dimension of the Sierpinski carpet and show that the fractal dimension strongly controls the water retention properties of the Sierpinski carpet soil. Higher fractal dimensions are shown to mimic clay-type soils, with very slow dewatering characteristics and relatively low fractal dimensions are shown to mimic a sandy soil with relatively rapid dewatering characteristics. Their fractal model of soil water retention removes the empirical fitting parameters from the soil water retention models and provides paramters which are intrinsic to the nature of the fractal porous structure. The relative permeability functions of Burdine and Mualem are also shown to be fractal directly from fractal water retention results.
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.
[Therapeutic function of images].
Aisenson Kogan, A
1986-03-01
The aim here searched is to explore the reasons why some systems of psychotherapy choose images as a means for attaining the cure. In one case at least (Roger Desoille's "awake dream"--the production and interpretation of images constitutes the basic procedure. The question arises: which sort of images? It is not dealt here with the oniric ones, but with the consciously created and must be called symbolic images. Almost every image that appears during a therapy session reveals a symbolic nature, but the very concept of symbol is not free from ambiguity some positions originated in different areas of investigation are mentioned, ending with a description of the traits that, according to the writer, bestow a symbolic character to images. These can be sensible ones or linguistic, as they appear in literary productions. Their importance as a factor of the psychotherapeutic change resides in the fact that symbolic images thus created are felt as not real events and at the same time containing subjective meaning. These two traits combine to lessen the anxiety before the confrontation with one's own impulses or feelings and at same time to stimulate towards new ways of behavior, until then desired -perhaps unconsciously- but too frightening to materialize in the real world.
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
Fractal dynamics of earthquakes
Bak, P.; Chen, K.
1995-05-01
Many objects in nature, from mountain landscapes to electrical breakdown and turbulence, have a self-similar fractal spatial structure. It seems obvious that to understand the origin of self-similar structures, one must understand the nature of the dynamical processes that created them: temporal and spatial properties must necessarily be completely interwoven. This is particularly true for earthquakes, which have a variety of fractal aspects. The distribution of energy released during earthquakes is given by the Gutenberg-Richter power law. The distribution of epicenters appears to be fractal with dimension D {approx} 1--1.3. The number of after shocks decay as a function of time according to the Omori power law. There have been several attempts to explain the Gutenberg-Richter law by starting from a fractal distribution of faults or stresses. But this is a hen-and-egg approach: to explain the Gutenberg-Richter law, one assumes the existence of another power-law--the fractal distribution. The authors present results of a simple stick slip model of earthquakes, which evolves to a self-organized critical state. Emphasis is on demonstrating that empirical power laws for earthquakes indicate that the Earth`s crust is at the critical state, with no typical time, space, or energy scale. Of course the model is tremendously oversimplified; however in analogy with equilibrium phenomena they do not expect criticality to depend on details of the model (universality).
Terahertz spectroscopy of plasmonic fractals.
Agrawal, A; Matsui, T; Zhu, W; Nahata, A; Vardeny, Z V
2009-03-20
We use terahertz time-domain spectroscopy to study the transmission properties of metallic films perforated with aperture arrays having deterministic or stochastic fractal morphologies ("plasmonic fractals"), and compare them with random aperture arrays. All of the measured plasmonic fractals show transmission resonances and antiresonances at frequencies that correspond to prominent features in their structure factors in k space. However, in sharp contrast to periodic aperture arrays, the resonant transmission enhancement decreases with increasing array size. This property is explained using a density-density correlation function, and is utilized for determining the underlying fractal dimensionality, D(<2). Furthermore, a sum rule for the transmission resonances and antiresonances in plasmonic fractals relative to the transmission of the corresponding random aperture arrays is obtained, and is shown to be universal.
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
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
Fractal Trigonometric Polynomials for Restricted Range Approximation
NASA Astrophysics Data System (ADS)
Chand, A. K. B.; Navascués, M. A.; Viswanathan, P.; Katiyar, S. K.
2016-05-01
One-sided approximation tackles the problem of approximation of a prescribed function by simple traditional functions such as polynomials or trigonometric functions that lie completely above or below it. In this paper, we use the concept of fractal interpolation function (FIF), precisely of fractal trigonometric polynomials, to construct one-sided uniform approximants for some classes of continuous functions.
Investigation into How 8th Grade Students Define Fractals
ERIC Educational Resources Information Center
Karakus, Fatih
2015-01-01
The analysis of 8th grade students' concept definitions and concept images can provide information about their mental schema of fractals. There is limited research on students' understanding and definitions of fractals. Therefore, this study aimed to investigate the elementary students' definitions of fractals based on concept image and concept…
Applications of fractals in ecology.
Sugihara, G; M May, R
1990-03-01
Fractal models describe the geometry of a wide variety of natural objects such as coastlines, island chains, coral reefs, satellite ocean-color images and patches of vegetation. Cast in the form of modified diffusion models, they can mimic natural and artificial landscapes having different types of complexity of shape. This article provides a brief introduction to fractals and reports on how they can be used by ecologists to answer a variety of basic questions, about scale, measurement and hierarchy in, ecological systems.
Fractal structure of asphaltene aggregates.
Rahmani, Nazmul H G; Dabros, Tadeusz; Masliyah, Jacob H
2005-05-15
A photographic technique coupled with image analysis was used to measure the size and fractal dimension of asphaltene aggregates formed in toluene-heptane solvent mixtures. First, asphaltene aggregates were examined in a Couette device and the fractal-like aggregate structures were quantified using boundary fractal dimension. The evolution of the floc structure with time was monitored. The relative rates of shear-induced aggregation and fragmentation/restructuring determine the steady-state floc structure. The average floc structure became more compact or more organized as the floc size distribution attained steady state. Moreover, the higher the shear rate is, the more compact the floc structure is at steady state. Second, the fractal dimensions of asphaltene aggregates were also determined in a free-settling test. The experimentally determined terminal settling velocities and characteristic lengths of the aggregates were utilized to estimate the 2D and 3D fractal dimensions. The size-density fractal dimension (D(3)) of the asphaltene aggregates was estimated to be in the range from 1.06 to 1.41. This relatively low fractal dimension suggests that the asphaltene aggregates are highly porous and very tenuous. The aggregates have a structure with extremely low space-filling capacity.
Quantitative imaging of lymph function.
Sharma, Ruchi; Wang, Wei; Rasmussen, John C; Joshi, Amit; Houston, Jessica P; Adams, Kristen E; Cameron, Arlin; Ke, Shi; Kwon, Sunkuk; Mawad, Michel E; Sevick-Muraca, Eva M
2007-06-01
Functional lymphatic imaging was demonstrated in the abdomen and anterior hindlimb of anesthetized, intact Yorkshire swine by using near-infrared (NIR) fluorescence imaging following intradermal administration of 100-200 microl of 32 microM indocyanine green (ICG) and 64 microM hyaluronan NIR imaging conjugate to target the lymph vascular endothelial receptor (LYVE)-1 on the lymph endothelium. NIR fluorescence imaging employed illumination of 780 nm excitation light ( approximately 2 mW/cm(2)) and collection of 830 nm fluorescence generated from the imaging agents. Our results show the ability to image the immediate trafficking of ICG from the plexus, through the vessels and lymphangions, and to the superficial mammary, subiliac, and middle iliac lymph nodes, which were located as deep as 3 cm beneath the tissue surface. "Packets" of ICG-transited lymph vessels of 2-16 cm length propelled at frequencies of 0.5-3.3 pulses/min and velocities of 0.23-0.75 cm/s. Lymph propulsion was independent of respiration rate. In the case of the hyaluronan imaging agent, lymph propulsion was absent as the dye progressed immediately through the plexus and stained the lymph vessels and nodes. Lymph imaging required 5.0 and 11.9 microg of ICG and hyaluronan conjugate, respectively. Our results suggest that microgram quantities of NIR optical imaging agents and their conjugates have a potential to image lymph function in patients suffering from lymph-related disorders.
Losa, Gabriele A
2009-01-01
The extension of the concepts of Fractal Geometry (Mandelbrot [1983]) toward the life sciences has led to significant progress in understanding complex functional properties and architectural / morphological / structural features characterising cells and tissues during ontogenesis and both normal and pathological development processes. It has even been argued that fractal geometry could provide a coherent description of the design principles underlying living organisms (Weibel [1991]). Fractals fulfil a certain number of theoretical and methodological criteria including a high level of organization, shape irregularity, functional and morphological self-similarity, scale invariance, iterative pathways and a peculiar non-integer fractal dimension [FD]. Whereas mathematical objects are deterministic invariant or self-similar over an unlimited range of scales, biological components are statistically self-similar only within a fractal domain defined by upper and lower limits, called scaling window, in which the relationship between the scale of observation and the measured size or length of the object can be established (Losa and Nonnenmacher [1996]). Selected examples will contribute to depict complex biological shapes and structures as fractal entities, and also to show why the application of the fractal principle is valuable for measuring dimensional, geometrical and functional parameters of cells, tissues and organs occurring within the vegetal and animal realms. If the criteria for a strict description of natural fractals are met, then it follows that a Fractal Geometry of Life may be envisaged and all natural objects and biological systems exhibiting self-similar patterns and scaling properties may be considered as belonging to the new subdiscipline of "fractalomics".
NASA Astrophysics Data System (ADS)
Aushev, A. A.; Barinov, S. P.; Vasin, M. G.; Drozdov, Yu M.; Ignat'ev, Yu V.; Izgorodin, V. M.; Kovshov, D. K.; Lakhtikov, A. E.; Lukovkina, D. D.; Markelov, V. V.; Morovov, A. P.; Shishlov, V. V.
2015-06-01
We present the results of employing the alpha-spectrometry method to determine the characteristics of porous materials used in targets for laser plasma experiments. It is shown that the energy spectrum of alpha-particles, after their passage through porous samples, allows one to determine the distribution of their path length in the foam skeleton. We describe the procedure of deriving such a distribution, excluding both the distribution broadening due to statistical nature of the alpha-particle interaction with an atomic structure (straggling) and hardware effects. The fractal analysis of micro-images is applied to the same porous surface samples that have been studied by alpha-spectrometry. The fractal dimension and size distribution of the number of the foam skeleton grains are obtained. Using the data obtained, a distribution of the total foam skeleton thickness along a chosen direction is constructed. It roughly coincides with the path length distribution of alpha-particles within a range of larger path lengths. It is concluded that the combined use of the alpha-spectrometry method and fractal analysis of images will make it possible to determine the size distribution of foam skeleton grains (or pores). The results can be used as initial data in theoretical studies on propagation of the laser and X-ray radiation in specific porous samples.
Aushev, A A; Barinov, S P; Vasin, M G; Drozdov, Yu M; Ignat'ev, Yu V; Izgorodin, V M; Kovshov, D K; Lakhtikov, A E; Lukovkina, D D; Markelov, V V; Morovov, A P; Shishlov, V V
2015-06-30
We present the results of employing the alpha-spectrometry method to determine the characteristics of porous materials used in targets for laser plasma experiments. It is shown that the energy spectrum of alpha-particles, after their passage through porous samples, allows one to determine the distribution of their path length in the foam skeleton. We describe the procedure of deriving such a distribution, excluding both the distribution broadening due to statistical nature of the alpha-particle interaction with an atomic structure (straggling) and hardware effects. The fractal analysis of micro-images is applied to the same porous surface samples that have been studied by alpha-spectrometry. The fractal dimension and size distribution of the number of the foam skeleton grains are obtained. Using the data obtained, a distribution of the total foam skeleton thickness along a chosen direction is constructed. It roughly coincides with the path length distribution of alpha-particles within a range of larger path lengths. It is concluded that the combined use of the alpha-spectrometry method and fractal analysis of images will make it possible to determine the size distribution of foam skeleton grains (or pores). The results can be used as initial data in theoretical studies on propagation of the laser and X-ray radiation in specific porous samples. (laser plasma)
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…
Pippa, Natassa; Pispas, Stergios; Demetzos, Costas
2014-09-01
The major advance of mixed liposomes (the so-called chimeric systems) is to control the size, structure, and morphology of these nanoassemblies, and therefore, system colloidal properties, with the aid of a large variety of parameters, such as chemical architecture and composition. The goal of this study is to investigate the alterations of the physicochemical and morphological characteristics of chimeric dipalmitoylphosphatidylcholine (DPPC) liposomes, caused by the incorporation of block and gradient copolymers (different macromolecular architecture) with different chemical compositions (different amounts of hydrophobic component). Light scattering techniques were utilized in order to characterize physicochemically and to delineate the fractal morphology of chimeric liposomes. In this study, we also investigated the structural differences between the prepared chimeric liposomes as are visualized by scanning electron microscopy (SEM). It could be concluded that all the chimeric liposomes have regular structure, as SEM images revealed, while their fractal dimensionality was found to be dependent on the macromolecular architecture of the polymeric guest.
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.
Fractal features of seismic noise
NASA Astrophysics Data System (ADS)
Caserta, A.; Consolini, G.; Michelis, P. De
2003-04-01
We present experimental observations and data analysis concerning the fractal features of seismic noise in the frequency range from 1 Hz to 40 Hz. In detail, we investigate the 3D average squared soil displacement and the distribution function of its fluctuations for different near-surface geological structures. We found that the seismic noise is consistent with a persistent fractal brownian motion characterized by a Hurst exponent grather than 1/2. Moreover, a clear dependence of the fractal nature of the seismic noise on the near-surface local geology has been found.
Region-based fractal video coding
NASA Astrophysics Data System (ADS)
Zhu, Shiping; Belloulata, Kamel
2008-10-01
A novel video sequence compression scheme is proposed in order to realize the efficient and economical transmission of video sequence, and also the region-based functionality of MPEG-4. The CPM and NCIM fractal coding scheme is applied on each region independently by a prior image segmentation map (alpha plane) which is exactly the same as defined in MPEG-4. The first n frames of video sequence are encoded as a "set" using the Circular Prediction Mapping (CPM) and encode the remaining frames using the Non Contractive Interframe Mapping (NCIM). The CPM and NCIM accomplish the motion estimation and compensation, which can exploit the high temporal correlations between the adjacent frames of video sequence. The experimental results with the monocular video sequences provide promising performances at low bit rate coding, such as the application in video conference. We believe the proposed fractal video codec will be a powerful and efficient technique for the region-based video sequence coding.
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
NASA Astrophysics Data System (ADS)
Wuorinen, Charles
2015-03-01
Any of the arts may produce exemplars that have fractal characteristics. There may be fractal painting, fractal poetry, and the like. But these will always be specific instances, not necessarily displaying intrinsic properties of the art-medium itself. Only music, I believe, of all the arts possesses an intrinsically fractal character, so that its very nature is fractally determined. Thus, it is reasonable to assert that any instance of music is fractal...
Fractal analysis of complex microstructure in castings
Lu, S.Z.; Lipp, D.C.; Hellawell, A.
1995-12-31
Complex microstructures in castings are usually characterized descriptively which often raises ambiguity and makes it difficult to relate the microstructure to the growth kinetics or mechanical properties in processing modeling. Combining the principle of fractal geometry and computer image processing techniques, it is feasible to characterize the complex microstructures numerically by the parameters of fractal dimension, D, and shape factor, a, without ambiguity. Procedures of fractal measurement and analysis are described, and a test case of its application to cast irons is provided. The results show that the irregular cast structures may all be characterized numerically by fractal analysis.
Fractal signatures in the aperiodic Fibonacci grating.
Verma, Rupesh; Banerjee, Varsha; Senthilkumaran, Paramasivam
2014-05-01
The Fibonacci grating (FbG) is an archetypal example of aperiodicity and self-similarity. While aperiodicity distinguishes it from a fractal, self-similarity identifies it with a fractal. Our paper investigates the outcome of these complementary features on the FbG diffraction profile (FbGDP). We find that the FbGDP has unique characteristics (e.g., no reduction in intensity with increasing generations), in addition to fractal signatures (e.g., a non-integer fractal dimension). These make the Fibonacci architecture potentially useful in image forming devices and other emerging technologies.
NASA Astrophysics Data System (ADS)
Banerjee, Amit; Banerjee, S. S.
2016-10-01
We investigate the formation of fractal like nano-structures on free standing gold films grown via surfactant mediated thin film growth process. We determine these structures to be confined within the first few monolayers of the thin film. Their chemical composition is identical to that of the Au film, although their density is different from the surrounding film. We observe changes in the morphology of these fractal structures by controlling the film growth rate, which spans across three orders of magnitude. From our study, we quantify the morphological changes in the fractal structure via a roundness parameter and we suggest an empirical relation between the roundness parameter and the growth rate. The study shows an inverse relationship between the roundness parameter and the growth rate and also that the fractal to compact morphological transition is continuous.
Microbialites on Mars: a fractal analysis of the Athena's microscopic images
NASA Astrophysics Data System (ADS)
Bianciardi, G.; Rizzo, V.; Cantasano, N.
2015-10-01
The Mars Exploration Rovers investigated Martian plains where laminated sedimentary rocks are present. The Athena morphological investigation [1] showed microstructures organized in intertwined filaments of microspherules: a texture we have also found on samples of terrestrial (biogenic) stromatolites and other microbialites and not on pseudo-abiogenicstromatolites. We performed a quantitative image analysis in order to compare 50 microbialites images with 50 rovers (Opportunity and Spirit) ones (approximately 30,000/30,000 microstructures). Contours were extracted and morphometric indexes obtained: geometric and algorithmic complexities, entropy, tortuosity, minimum and maximum diameters. Terrestrial and Martian textures resulted multifractals. Mean values and confidence intervals from the Martian images overlapped perfectly with those from terrestrial samples. The probability of this occurring by chance was less than 1/28, p<0.004. Our work show the evidence of a widespread presence of microbialites in the Martian outcroppings: i.e., the presence of unicellular life on the ancient Mars, when without any doubt, liquid water flowed on the Red Planet.
Comparison of two fractal interpolation methods
NASA Astrophysics Data System (ADS)
Fu, Yang; Zheng, Zeyu; Xiao, Rui; Shi, Haibo
2017-03-01
As a tool for studying complex shapes and structures in nature, fractal theory plays a critical role in revealing the organizational structure of the complex phenomenon. Numerous fractal interpolation methods have been proposed over the past few decades, but they differ substantially in the form features and statistical properties. In this study, we simulated one- and two-dimensional fractal surfaces by using the midpoint displacement method and the Weierstrass-Mandelbrot fractal function method, and observed great differences between the two methods in the statistical characteristics and autocorrelation features. From the aspect of form features, the simulations of the midpoint displacement method showed a relatively flat surface which appears to have peaks with different height as the fractal dimension increases. While the simulations of the Weierstrass-Mandelbrot fractal function method showed a rough surface which appears to have dense and highly similar peaks as the fractal dimension increases. From the aspect of statistical properties, the peak heights from the Weierstrass-Mandelbrot simulations are greater than those of the middle point displacement method with the same fractal dimension, and the variances are approximately two times larger. When the fractal dimension equals to 1.2, 1.4, 1.6, and 1.8, the skewness is positive with the midpoint displacement method and the peaks are all convex, but for the Weierstrass-Mandelbrot fractal function method the skewness is both positive and negative with values fluctuating in the vicinity of zero. The kurtosis is less than one with the midpoint displacement method, and generally less than that of the Weierstrass-Mandelbrot fractal function method. The autocorrelation analysis indicated that the simulation of the midpoint displacement method is not periodic with prominent randomness, which is suitable for simulating aperiodic surface. While the simulation of the Weierstrass-Mandelbrot fractal function method has
Functional imaging for regenerative medicine.
Leahy, Martin; Thompson, Kerry; Zafar, Haroon; Alexandrov, Sergey; Foley, Mark; O'Flatharta, Cathal; Dockery, Peter
2016-04-19
In vivo imaging is a platform technology with the power to put function in its natural structural context. With the drive to translate stem cell therapies into pre-clinical and clinical trials, early selection of the right imaging techniques is paramount to success. There are many instances in regenerative medicine where the biological, biochemical, and biomechanical mechanisms behind the proposed function of stem cell therapies can be elucidated by appropriate imaging. Imaging techniques can be divided according to whether labels are used and as to whether the imaging can be done in vivo. In vivo human imaging places additional restrictions on the imaging tools that can be used. Microscopies and nanoscopies, especially those requiring fluorescent markers, have made an extraordinary impact on discovery at the molecular and cellular level, but due to their very limited ability to focus in the scattering tissues encountered for in vivo applications they are largely confined to superficial imaging applications in research laboratories. Nanoscopy, which has tremendous benefits in resolution, is limited to the near-field (e.g. near-field scanning optical microscope (NSNOM)) or to very high light intensity (e.g. stimulated emission depletion (STED)) or to slow stochastic events (photo-activated localization microscopy (PALM) and stochastic optical reconstruction microscopy (STORM)). In all cases, nanoscopy is limited to very superficial applications. Imaging depth may be increased using multiphoton or coherence gating tricks. Scattering dominates the limitation on imaging depth in most tissues and this can be mitigated by the application of optical clearing techniques that can impose mild (e.g. topical application of glycerol) or severe (e.g. CLARITY) changes to the tissue to be imaged. Progression of therapies through to clinical trials requires some thought as to the imaging and sensing modalities that should be used. Smoother progression is facilitated by the use of
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.
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 near-infrared imager
NASA Astrophysics Data System (ADS)
Luo, Qingming; Nioka, Shoko; Chance, Britton
1997-08-01
We developed a continuous wave (cw) light imaging probe which includes 9 light sources and four pairs detectors (each pair has one 850 nm filtered detector and one 760 nm filtered detector). The light sources are controlled by a computer and the signals from the detectors are converted and processed in the computer. There are 16 measurement sections and total detection area is 9 cm multiplied by 4 cm which can be scanned every 8 seconds. The detector-source uses 2.5 cm spacing. In this study, we present the noise, drift, detectivity and spatial resolution test results of the imager. Changes of oxygenation and blood volume in about 2 cm depth from the surface of brain model can be detected. The temporal resolution is 8 seconds and spatial resolution is about 2 cm. The detectivity of OD changes can reach 0.008. With this cw imaging probe, we measured motor function in motor cortex area, visual function in occipital area, and cognitive activity in frontal forehead area of the human brian when the subjects are stimulated by moving fingers, viewing a flashing light and doing an analogy test, respectively. The experimental results show that the cw imaging probe can be used for functional images of brain activity, base upon changes of oxygenation and blood volume due to the stimulus.
NASA 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.
[Presurgical functional magnetic resonance imaging].
Stippich, C
2010-02-01
Functional magnetic resonance imaging (fMRI) is an important and novel neuroimaging modality for patients with brain tumors. By non-invasive measurement, localization and lateralization of brain activiation, most importantly of motor and speech function, fMRI facilitates the selection of the most appropriate and sparing treatment and function-preserving surgery. Prerequisites for the diagnostic use of fMRI are the application of dedicated clinical imaging protocols and standardization of the respective imaging procedures. The combination with diffusion tensor imaging (DTI) also enables tracking and visualization of important fiber bundles such as the pyramidal tract and the arcuate fascicle. These multimodal MR data can be implemented in computer systems for functional neuronavigation or radiation treatment. The practicability, accuracy and reliability of presurgical fMRI have been validated by large numbers of published data. However, fMRI cannot be considered as a fully established modality of diagnostic neuroimaging due to the lack of guidelines of the responsible medical associations as well as the lack of medical certification of important hardware and software components. This article reviews the current research in the field and provides practical information relevant for presurgical fMRI.
Texture analysis of diagnostic x-ray images by use of fractals
NASA Astrophysics Data System (ADS)
Lundahl, T.; Ohley, W. J.; Kay, S. M.; White, H.; Williams, D. O.; Most, A. S.
1986-11-01
In this work a discrete fractional Brownian motion (FBM) model is applied to xray images as a measure of the regional texture. FBM is a generalization of ordinary Wiener-Levy Brownian motion. A Parameter H is introduced which describes the roughness of the realizations. Using generated realizations, a Cramer-Rao bound for the variance of an estimate of Hwas evaluated using asymptotic statistics. The results show that the accuracy of the estimate is independent of the true H. A maximum likelihood estimator is derived for H and applied to the data sets The results were close to the C-R bound. The MLE is then applied to sequences of digital coronary angiograms. The results show that the H parameter is a useful index by which to segment vessels from background noise.
Speckle interferometry from fiber-reinforced materials:A fractal geometry approach
NASA Astrophysics Data System (ADS)
Horta, J. M.; Castano, V. M.
Speckle field studies were performed on fiber-modified Portland cement-based microconcrete beam models subjected to flexural loading. The resulting speckle fields were analyzed in terms of their associated mass fractal dimension by using digital image processing techniques. The experiments showed a change in the fractal dimension of the speckle fields as a function both of the loading and the structure of the microconcrete beams. A study was also conducted on the free-damped frequencies of the beams, which allowed to draw a fractal dimension vs. frequency plot on each loading cycle. These results allow to foresee the use of fractal geometry as a promising tool for better understanding the mechanical behavior of structures.
Segmentation of histological structures for fractal analysis
NASA Astrophysics Data System (ADS)
Dixon, Vanessa; Kouznetsov, Alexei; Tambasco, Mauro
2009-02-01
Pathologists examine histology sections to make diagnostic and prognostic assessments regarding cancer based on deviations in cellular and/or glandular structures. However, these assessments are subjective and exhibit some degree of observer variability. Recent studies have shown that fractal dimension (a quantitative measure of structural complexity) has proven useful for characterizing structural deviations and exhibits great potential for automated cancer diagnosis and prognosis. Computing fractal dimension relies on accurate image segmentation to capture the architectural complexity of the histology specimen. For this purpose, previous studies have used techniques such as intensity histogram analysis and edge detection algorithms. However, care must be taken when segmenting pathologically relevant structures since improper edge detection can result in an inaccurate estimation of fractal dimension. In this study, we established a reliable method for segmenting edges from grayscale images. We used a Koch snowflake, an object of known fractal dimension, to investigate the accuracy of various edge detection algorithms and selected the most appropriate algorithm to extract the outline structures. Next, we created validation objects ranging in fractal dimension from 1.3 to 1.9 imitating the size, structural complexity, and spatial pixel intensity distribution of stained histology section images. We applied increasing intensity thresholds to the validation objects to extract the outline structures and observe the effects on the corresponding segmentation and fractal dimension. The intensity threshold yielding the maximum fractal dimension provided the most accurate fractal dimension and segmentation, indicating that this quantitative method could be used in an automated classification system for histology specimens.
NASA Astrophysics Data System (ADS)
Kunze, Herb; La Torre, Davide; Lin, Jianyi
2017-01-01
We consider the inverse problem associated with IFSM: Given a target function f , find an IFSM, such that its fixed point f ¯ is sufficiently close to f in the Lp distance. Forte and Vrscay [1] showed how to reduce this problem to a quadratic optimization model. In this paper, we extend the collage-based method developed by Kunze, La Torre and Vrscay ([2][3][4]), by proposing the minimization of the 1-norm instead of the 0-norm. In fact, optimization problems involving the 0-norm are combinatorial in nature, and hence in general NP-hard. To overcome these difficulties, we introduce the 1-norm and propose a Sequential Quadratic Programming algorithm to solve the corresponding inverse problem. As in Kunze, La Torre and Vrscay [3] in our formulation, the minimization of collage error is treated as a multi-criteria problem that includes three different and conflicting criteria i.e., collage error, entropy and sparsity. This multi-criteria program is solved by means of a scalarization technique which reduces the model to a single-criterion program by combining all objective functions with different trade-off weights. The results of some numerical computations are presented.
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.
Isherwood, Zoey J; Schira, Mark M; Spehar, Branka
2017-02-01
Natural scenes share a consistent distribution of energy across spatial frequencies (SF) known as the 1/f(α) amplitude spectrum (α≈0.8-1.5, mean 1.2). This distribution is scale-invariant, which is a fractal characteristic of natural scenes with statistically similar structure at different spatial scales. While the sensitivity of the visual system to the 1/f properties of natural scenes has been studied extensively using psychophysics, relatively little is known about the tuning of cortical responses to these properties. Here, we use fMRI and retinotopic mapping techniques to measure and analyze BOLD responses in early visual cortex (V1, V2, and V3) to synthetic noise images that vary in their 1/f(α) amplitude spectra (α=0.25 to 2.25, step size: 0.50) and contrast levels (10% and 30%) (Experiment 1). To compare the dependence of the BOLD response between the photometric (intensity based) and geometric (fractal) properties of our stimuli, in Experiment 2 we compared grayscale noise images to their binary (thresholded) counterparts, which contain only black and white regions. In both experiments, early visual cortex responded maximally to stimuli generated to have an input 1/f slope corresponding to natural 1/f(α) amplitude spectra, and lower BOLD responses were found for steeper or shallower 1/f slopes (peak modulation: 0.59% for 1.25 vs. 0.31% for 2.25). To control for changing receptive field sizes, responses were also analyzed across multiple eccentricity bands in cortical surface space. For most eccentricity bands, BOLD responses were maximal for natural 1/f(α) amplitude spectra, but importantly there was no difference in the BOLD response to grayscale stimuli and their corresponding thresholded counterparts. Since the thresholding of an image changes its measured 1/f slope (α) but not its fractal characteristics, this suggests that neuronal responses in early visual cortex are not strictly driven by spectral slope values (photometric properties) but
Church, E.L.
1988-04-15
Surface finish measurements are usually fitted to models of the finish correlation function which are parametrized in terms of root-mean-square roughnesses, sigma, and correlation lengths, l. Highly finished optical surfaces, however, are frequently better described by fractal models, which involve inverse power-law spectra and are parametrized by spectral strengths, K/sub n/, and spectral indices, n. Analyzing measurements of fractal surfaces in terms of sigma and l gives results which are not intrinsic surface parameters but which depend on the bandwidth parameters of the measurement process used. This paper derives expressions for these pseudoparameters and discusses the errors involved in using them for the characterization and specification of surface finish.
Church, E.L.
1988-01-01
Surface finish measurements are usually fitted to models of the finish correlation function which are parameterized in terms of root-mean-square roughness, sigma, and correlation lengths, l. Highly-finished optical surfaces, however, are frequently better described by fractal models, which involve inverse-power-law spectra and are parameterized by spectral strengths, K/sub n/, and spectral indices, n. Analyzing measurements of fractal surfaces in terms of sigma and l gives results which are not intrinsic surface parameters but which depend on the bandwidth parameters of the measurement process used. This paper derives expressions for these pseudo parameters and discusses the errors involved in using them for the characterization and specification of surface finish. 30 refs., 5 figs., 1 tab.
Application of Fractal Dimension on Palsar Data
NASA Astrophysics Data System (ADS)
Singh, Dharmendra; Pant, Triloki
Study of land cover is the primal task of remote sensing where microwave imaging plays an important role. As an alternate of optical imaging, microwave, in particular, Synthetic Aperture Radar (SAR) imaging is very popular. With the advancement of technology, multi-polarized images are now available, e.g., ALOS-PALSAR (Phased Array type L-band SAR), which are beneficial because each of the polarization channel shows different sensitivity to various land features. Further, using the textural features, various land classes can be classified on the basis of the textural measures. One of the textural measure is fractal dimension. It is noteworthy that fractal dimension is a measure of roughness and thus various land classes can be distinguished on the basis of their roughness. The value of fractal dimension for the surfaces lies between 2.0 and 3.0 where 2.0 represents a smooth surface while 3.0 represents drastically rough surface. The study area covers subset images lying between 2956'53"N, 7750'32"E and 2950'40"N, 7757'19"E. The PALSAR images of the year 2007 and 2009 are considered for the study. In present paper a fractal based classification of PALSAR images has been performed for identification of Water, Urban and Agricultural Area. Since fractals represent the image texture, hence the present study attempts to find the fractal properties of land covers to distinguish them from one another. For the purpose a context has been defined on the basis of a moving window, which is used to estimate the local fractal dimension and then moved over the whole image. The size of the window is an important issue for estimation of textural measures which is considered to be 55 in present study. This procedure, in response, produces a textural map called fractal map. The fractal map is constituted with the help of local fractal dimension values and can be used for contextual classification. In order to study the fractal properties of PALSAR images, the three polarization images
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.
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.
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.
Dik, O E; Sviatogor, I A; Ishinova, V A; Nozdrachev, A D
2012-01-01
The task of estimation of the functional state of the human brain during psychotherapeutic treatment of psychogenic pain in patients with anxious phobic disorders is examined. For solving the task the methods of spectral and multifractal analyses of EEG fragments are applied during the perception of psychogenic pain and its removal by the psychorelaxation technique. Contrary to power spectra singularity spectra allow to distinguish EEGs quanitatively in the examined functional states of the human brain. The pain suppression in patients with anxious phobic disorders during psychorelaxation is accompanied by changing the width of the singularity spectrum and approximation of this multifractal partameter to the value corresponding to a healthy subject.
Feltrin, Gian Pietro; Stramare, Roberto; Miotto, Diego; Giacomini, Dario; Saccavini, Claudio
2004-06-01
Fractal analysis is a quantitative method used to evaluate complex anatomic findings in their elementary component. Its application to biologic images, particularly to cancellous bones, has been well practiced within the past few years. The aims of these applications are to assess changes in bone and the loss of spongious architecture, indicate bone fragility, and to show the increased risk for fracture in primary or secondary osteoporosis. The applications are very promising to help complete the studies that can define bone density (bone mineral density by dual energy x-ray absorptiometry or quantitative computed tomography), and also have the capacity to distinguish the patients with a high or low risk for fracture. Their extension to the clinical fields, to define a test for fracture risk, is still limited by difficult application to the medical quantitative imaging of bones, between correct application at superficial bones and unreliable application to deep bones. The future evolution and validity do not depend upon fractal methods but upon well-detailed imaging of the bones in clinical conditions.
NASA Astrophysics Data System (ADS)
Orbach, R.
1986-02-01
Random structures often exhibit fractal geometry, defined in terms of the mass scaling exponent, D, the fractal dimension. The vibrational dynamics of fractal networks are expressed in terms of the exponent d double bar, the fracton dimensionality. The eigenstates on a fractal network are spatially localized for d double bar less than or equal to 2. The implications of fractal geometry are discussed for thermal transport on fractal networks. The electron-fracton interaction is developed, with a brief outline given for the time dependence of the electronic relaxation on fractal networks. It is suggested that amorphous or glassy materials may exhibit fractal properties at short length scales or, equivalently, at high energies. The calculations of physical properties can be used to test the fractal character of the vibrational excitations in these materials.
Observing the Twinkling Fractal Nature of the Glass Transition
NASA Astrophysics Data System (ADS)
Stanzione, Joseph, III; Wool, Richard; Strawhecker, Kenneth
2010-03-01
The main idea underlying the Twinkling Fractal Theory (TFT) of the glass transition is the development of dynamic percolating solid fractal structures near Tg, which are in dynamic equilibrium with the surrounding liquid. Solid and liquid clusters interchange at a frequency φTF, which is controlled by the population of intermolecular oscillators in excited energy levels in accord with the Orbach vibrational density of states for a particular fractal cluster g(φ) ˜ φ^df-1, where the fracton dimension df = 4/3. To an observer, these clusters would appear to be ``twinkling.'' A time-lapse tapping-mode atomic force microscopy (AFM) technique has been developed in order to experimentally confirm such phenomena. The twinkling behavior of amorphous, atactic polystyrene with MW = 194,000 g/mol, PDI = 1.07 (GPC) and Tg = 375 K (DSC-heating rate of 3 K/min) has been captured above (383 K), below (358 K), and well below (298 K) its Tg. Two-dimensional space images reveal fractal dimensions consistent with the TFT. The twinkling behavior was analyzed using a statistical autocorrelation function in conjunction with the apparent stretched exponential Kohlrausch-Williams-Watts relaxation function.
Quantitating the subtleties of microglial morphology with fractal analysis
Karperien, Audrey; Ahammer, Helmut; Jelinek, Herbert F.
2013-01-01
It is well established that microglial form and function are inextricably linked. In recent years, the traditional view that microglial form ranges between “ramified resting” and “activated amoeboid” has been emphasized through advancing imaging techniques that point to microglial form being highly dynamic even within the currently accepted morphological categories. Moreover, microglia adopt meaningful intermediate forms between categories, with considerable crossover in function and varying morphologies as they cycle, migrate, wave, phagocytose, and extend and retract fine and gross processes. From a quantitative perspective, it is problematic to measure such variability using traditional methods, but one way of quantitating such detail is through fractal analysis. The techniques of fractal analysis have been used for quantitating microglial morphology, to categorize gross differences but also to differentiate subtle differences (e.g., amongst ramified cells). Multifractal analysis in particular is one technique of fractal analysis that may be useful for identifying intermediate forms. Here we review current trends and methods of fractal analysis, focusing on box counting analysis, including lacunarity and multifractal analysis, as applied to microglial morphology. PMID:23386810
NASA Astrophysics Data System (ADS)
Raupov, Dmitry S.; Myakinin, Oleg O.; Bratchenko, Ivan A.; Zakharov, Valery P.; Khramov, Alexander G.
2016-10-01
In this paper, we propose a report about our examining of the validity of OCT in identifying changes using a skin cancer texture analysis compiled from Haralick texture features, fractal dimension, Markov random field method and the complex directional features from different tissues. Described features have been used to detect specific spatial characteristics, which can differentiate healthy tissue from diverse skin cancers in cross-section OCT images (B- and/or C-scans). In this work, we used an interval type-II fuzzy anisotropic diffusion algorithm for speckle noise reduction in OCT images. The Haralick texture features as contrast, correlation, energy, and homogeneity have been calculated in various directions. A box-counting method is performed to evaluate fractal dimension of skin probes. Markov random field have been used for the quality enhancing of the classifying. Additionally, we used the complex directional field calculated by the local gradient methodology to increase of the assessment quality of the diagnosis method. Our results demonstrate that these texture features may present helpful information to discriminate tumor from healthy tissue. The experimental data set contains 488 OCT-images with normal skin and tumors as Basal Cell Carcinoma (BCC), Malignant Melanoma (MM) and Nevus. All images were acquired from our laboratory SD-OCT setup based on broadband light source, delivering an output power of 20 mW at the central wavelength of 840 nm with a bandwidth of 25 nm. We obtained sensitivity about 97% and specificity about 73% for a task of discrimination between MM and Nevus.
Functional imaging in chronic migraine.
Maniyar, Farooq H; Goadsby, Peter J
2013-05-01
Chronic migraine is a relatively common disorder in neurological terms that causes very significant disability at a high cost. The precise mechanisms behind the progression of episodic migraine to chronic migraine are not well understood. Functional neuro-imaging works on the basis that neuronal activations are associated with changes in regional cerebral blood flow, and it can help us answer some of these questions. In this review, we discuss important recent studies in chronic migraine or studies relating to increasing frequency of migraine attacks. The findings show that increasing frequency of migraine attacks is associated with changes in key brainstem areas, basal ganglia and various cortical areas involved in pain.
Fractal antenna and fractal resonator primer
NASA Astrophysics Data System (ADS)
Cohen, Nathan
2015-03-01
Self-similarity and fractals have opened new and important avenues for antenna and electronic solutions over the last 25 years. This primer provides an introduction to the benefits provided by fractal geometry in antennas, resonators, and related structures. Such benefits include, among many, wider bandwidths, smaller sizes, part-less electronic components, and better performance. Fractals also provide a new generation of optimized design tools, first used successfully in antennas but applicable in a general fashion.
Functional brain imaging across development.
Rubia, Katya
2013-12-01
The developmental cognitive neuroscience literature has grown exponentially over the last decade. This paper reviews the functional magnetic resonance imaging (fMRI) literature on brain function development of typically late developing functions of cognitive and motivation control, timing and attention as well as of resting state neural networks. Evidence shows that between childhood and adulthood, concomitant with cognitive maturation, there is progressively increased functional activation in task-relevant lateral and medial frontal, striatal and parieto-temporal brain regions that mediate these higher level control functions. This is accompanied by progressively stronger functional inter-regional connectivity within task-relevant fronto-striatal and fronto-parieto-temporal networks. Negative age associations are observed in earlier developing posterior and limbic regions, suggesting a shift with age from the recruitment of "bottom-up" processing regions towards "top-down" fronto-cortical and fronto-subcortical connections, leading to a more mature, supervised cognition. The resting state fMRI literature further complements this evidence by showing progressively stronger deactivation with age in anti-correlated task-negative resting state networks, which is associated with better task performance. Furthermore, connectivity analyses during the resting state show that with development increasingly stronger long-range connections are being formed, for example, between fronto-parietal and fronto-cerebellar connections, in both task-positive networks and in task-negative default mode networks, together with progressively lesser short-range connections, suggesting progressive functional integration and segregation with age. Overall, evidence suggests that throughout development between childhood and adulthood, there is progressive refinement and integration of both task-positive fronto-cortical and fronto-subcortical activation and task-negative deactivation, leading to
Fractality in the neuron axonal topography of the human brain based on 3-D diffusion MRI
NASA Astrophysics Data System (ADS)
Katsaloulis, P.; Ghosh, A.; Philippe, A. C.; Provata, A.; Deriche, R.
2012-05-01
In this work the fractal architecture of the neuron axonal topography of the human brain is evaluated, as derived from 3-D diffusion MRI (dMRI) acquisitions. This is a 3D extension of work performed previously in 2D regions of interest (ROIs), where the fractal dimension of the neuron axonal topography was computed from dMRI data. A group study with 18 subjects is here conducted and the fractal dimensions D f of the entire 3-D volume of the brains is estimated via the box counting, the correlation dimension and the fractal mass dimension methods. The neuron axon data is obtained using tractography algorithms on diffusion tensor imaging of the brain. We find that all three calculations of D f give consistent results across subjects, namely, they demonstrate fractal characteristics in the short and medium length scales: different fractal exponents prevail at different length scales, an indication of multifractality. We surmise that this complexity stems as a collective property emerging when many local brain units, performing different functional tasks and having different local topologies, are recorded together.
Hashemi, S. M.; Jagodič, U.; Mozaffari, M. R.; Ejtehadi, M. R.; Muševič, I.; Ravnik, M.
2017-01-01
Fractals are remarkable examples of self-similarity where a structure or dynamic pattern is repeated over multiple spatial or time scales. However, little is known about how fractal stimuli such as fractal surfaces interact with their local environment if it exhibits order. Here we show geometry-induced formation of fractal defect states in Koch nematic colloids, exhibiting fractal self-similarity better than 90% over three orders of magnitude in the length scales, from micrometers to nanometres. We produce polymer Koch-shaped hollow colloidal prisms of three successive fractal iterations by direct laser writing, and characterize their coupling with the nematic by polarization microscopy and numerical modelling. Explicit generation of topological defect pairs is found, with the number of defects following exponential-law dependence and reaching few 100 already at fractal iteration four. This work demonstrates a route for generation of fractal topological defect states in responsive soft matter. PMID:28117325
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)
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.
NASA Astrophysics Data System (ADS)
Hashemi, S. M.; Jagodič, U.; Mozaffari, M. R.; Ejtehadi, M. R.; Muševič, I.; Ravnik, M.
2017-01-01
Fractals are remarkable examples of self-similarity where a structure or dynamic pattern is repeated over multiple spatial or time scales. However, little is known about how fractal stimuli such as fractal surfaces interact with their local environment if it exhibits order. Here we show geometry-induced formation of fractal defect states in Koch nematic colloids, exhibiting fractal self-similarity better than 90% over three orders of magnitude in the length scales, from micrometers to nanometres. We produce polymer Koch-shaped hollow colloidal prisms of three successive fractal iterations by direct laser writing, and characterize their coupling with the nematic by polarization microscopy and numerical modelling. Explicit generation of topological defect pairs is found, with the number of defects following exponential-law dependence and reaching few 100 already at fractal iteration four. This work demonstrates a route for generation of fractal topological defect states in responsive soft matter.
Hashemi, S M; Jagodič, U; Mozaffari, M R; Ejtehadi, M R; Muševič, I; Ravnik, M
2017-01-24
Fractals are remarkable examples of self-similarity where a structure or dynamic pattern is repeated over multiple spatial or time scales. However, little is known about how fractal stimuli such as fractal surfaces interact with their local environment if it exhibits order. Here we show geometry-induced formation of fractal defect states in Koch nematic colloids, exhibiting fractal self-similarity better than 90% over three orders of magnitude in the length scales, from micrometers to nanometres. We produce polymer Koch-shaped hollow colloidal prisms of three successive fractal iterations by direct laser writing, and characterize their coupling with the nematic by polarization microscopy and numerical modelling. Explicit generation of topological defect pairs is found, with the number of defects following exponential-law dependence and reaching few 100 already at fractal iteration four. This work demonstrates a route for generation of fractal topological defect states in responsive soft matter.
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
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.
Chamot, Stéphane; Migacheva, Elena; Seydoux, Olivier; Marquet, Pierre; Depeursinge, Christian
2010-11-08
The optical properties within limited volumes of diffusive media can be probed by carrying spatially-resolved measurements of diffused light at short source-detector separation (typically one scattering mean free path). At such distance, analytical models only relying on the absorption and reduced scattering coefficients fail at correctly predicting reflectance and it was demonstrated that adding a third optical coefficient γ improves the description of light propagation conditions near the source. In an attempt to relate the γ coefficient to physical properties of turbid media, this paper uses a fractal distribution law for modeling scatterers' sizes distributions and investigates numerically and experimentally how γ is related to the fractal power α. The results indicate that within the range of γ typically encountered in biological samples, this coefficient is approximately linearly correlated with α.
Fractal aggregates in Titan's atmosphere
NASA Astrophysics Data System (ADS)
Cabane, M.; Rannou, P.; Chassefiere, E.; Israel, G.
1993-04-01
The cluster structure of Titan's atmosphere was modeled by using an Eulerian microphysical model with the specific formulation of microphysical laws applying to fractal particles. The growth of aggregates in the settling phase was treated by introducing the fractal dimension as a parameter of the model. The model was used to obtain a vertical distribution of size and number density of the aggregates for different production altitudes. Results confirm previous estimates of the formation altitude of photochemical aerosols. The vertical profile of the effective radius of aggregates was calculated as a function of the visible optical depth.
Hydrodynamic behavior of fractal aggregates
NASA Astrophysics Data System (ADS)
Wiltzius, Pierre
1987-02-01
Measurements of the radius of gyration RG and the hydrodynamic radius RH of colloidal silica aggregates are reported. These aggregates have fractal geometry and RH is proportional to RG for 500 Å<=RH<=7000 Å, with a ratio RH/RG=0.72+/-0.02. The results are compared with predictions for macromolecules of various shapes. The proportionality of the two radii can be understood with use of the pair correlation function of fractal objects and hydrodynamic interactions on the Oseen level. The value of the ratio remains to be explained.
ERIC Educational Resources Information Center
Fraboni, Michael; Moller, Trisha
2008-01-01
Fractal geometry offers teachers great flexibility: It can be adapted to the level of the audience or to time constraints. Although easily explained, fractal geometry leads to rich and interesting mathematical complexities. In this article, the authors describe fractal geometry, explain the process of iteration, and provide a sample exercise.…
Fractal interpretation of intermittency
Hwa, R.C.
1991-12-01
Implication of intermittency in high-energy collisions is first discussed. Then follows a description of the fractal interpretation of intermittency. A basic quantity with asymptotic fractal behavior is introduced. It is then shown how the factorial moments and the G moments can be expressed in terms of it. The relationship between the intermittency indices and the fractal indices is made explicit.
Functional Magnetic Resonance Imaging Methods
Chen, Jingyuan E.; Glover, Gary H.
2015-01-01
Since its inception in 1992, Functional Magnetic Resonance Imaging (fMRI) has become an indispensible tool for studying cognition in both the healthy and dysfunctional brain. FMRI monitors changes in the oxygenation of brain tissue resulting from altered metabolism consequent to a task-based evoked neural response or from spontaneous fluctuations in neural activity in the absence of conscious mentation (the “resting state”). Task-based studies have revealed neural correlates of a large number of important cognitive processes, while fMRI studies performed in the resting state have demonstrated brain-wide networks that result from brain regions with synchronized, apparently spontaneous activity. In this article, we review the methods used to acquire and analyze fMRI signals. PMID:26248581
ERIC Educational Resources Information Center
Marks-Tarlow, Terry
2010-01-01
In this article, the author draws on contemporary science to illuminate the relationship between early play experiences, processes of self-development, and the later emergence of the fractal self. She argues that orientation within social space is a primary function of early play and developmentally a two-step process. With other people and with…
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.
Hyperspectral image classification using functional data analysis.
Li, Hong; Xiao, Guangrun; Xia, Tian; Tang, Y Y; Li, Luoqing
2014-09-01
The large number of spectral bands acquired by hyperspectral imaging sensors allows us to better distinguish many subtle objects and materials. Unlike other classical hyperspectral image classification methods in the multivariate analysis framework, in this paper, a novel method using functional data analysis (FDA) for accurate classification of hyperspectral images has been proposed. The central idea of FDA is to treat multivariate data as continuous functions. From this perspective, the spectral curve of each pixel in the hyperspectral images is naturally viewed as a function. This can be beneficial for making full use of the abundant spectral information. The relevance between adjacent pixel elements in the hyperspectral images can also be utilized reasonably. Functional principal component analysis is applied to solve the classification problem of these functions. Experimental results on three hyperspectral images show that the proposed method can achieve higher classification accuracies in comparison to some state-of-the-art hyperspectral image classification methods.
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
[Fractal analysis in the diagnosis of breast tumors].
Crişan, D A; Lesaru, M; Dobrescu, R; Vasilescu, C
2007-01-01
Last years studies made by researchers from over the world show that fractal geometry is a viable alternative for image analysis. Fractal features of natural forms give to fractal analysis new valences in various fields, medical imaging being a very important one. This paper intend to prove that fractal dimension, as a way to characterize the complexity of a form, can be used for diagnosis of mammographic lesions classified BI-RADS 4, further investigations being not necessary. The experiments made on 30 cases classified BI-RADS 4 confirmed that 89% of benign lesions have an average fractal dimension under the threshold 1.4, meanwhile malign lesions are characterized, in a similar percentage, by an average fractal dimension over that threshold.
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.
Oliveira, Naiara C; Silva, João H; Barros, Olga A; Pinheiro, Allysson P; Santana, William; Saraiva, Antônio A F; Ferreira, Odair P; Freire, Paulo T C; Paula, Amauri J
2015-10-06
We used here a scanning electron microscopy approach that detected backscattered electrons (BSEs) and X-rays (from ionization processes) along a large-field (LF) scan, applied on a Cretaceous fossil of a shrimp (area ∼280 mm(2)) from the Araripe Sedimentary Basin. High-definition LF images from BSEs and X-rays were essentially generated by assembling thousands of magnified images that covered the whole area of the fossil, thus unveiling morphological and compositional aspects at length scales from micrometers to centimeters. Morphological features of the shrimp such as pleopods, pereopods, and antennae located at near-surface layers (undetected by photography techniques) were unveiled in detail by LF BSE images and in calcium and phosphorus elemental maps (mineralized as hydroxyapatite). LF elemental maps for zinc and sulfur indicated a rare fossilization event observed for the first time in fossils from the Araripe Sedimentary Basin: the mineralization of zinc sulfide interfacing to hydroxyapatite in the fossil. Finally, a dimensional analysis of the phosphorus map led to an important finding: the existence of a fractal characteristic (D = 1.63) for the hydroxyapatite-matrix interface, a result of physical-geological events occurring with spatial scale invariance on the specimen, over millions of years.
Multi-resolution processing for fractal analysis of airborne remotely sensed data
NASA Technical Reports Server (NTRS)
Jaggi, S.; Quattrochi, D.; Lam, N.
1992-01-01
Fractal geometry is increasingly becoming a useful tool for modeling natural phenomenon. As an alternative to Euclidean concepts, fractals allow for a more accurate representation of the nature of complexity in natural boundaries and surfaces. Since they are characterized by self-similarity, an ideal fractal surface is scale-independent; i.e. at different scales a fractal surface looks the same. This is not exactly true for natural surfaces. When viewed at different spatial resolutions parts of natural surfaces look alike in a statistical manner and only for a limited range of scales. Images acquired by NASA's Thermal Infrared Multispectral Scanner are used to compute the fractal dimension as a function of spatial resolution. Three methods are used to determine the fractal dimension - Schelberg's line-divider method, the variogram method, and the triangular prism method. A description of these methods and the results of applying these methods to a remotely-sensed image is also presented. Five flights were flown in succession at altitudes of 2 km (low), 6 km (mid), 12 km (high), and then back again at 6 km and 2 km. The area selected was the Ross Barnett reservoir near Jackson, Mississippi. The mission was flown during the predawn hours of 1 Feb. 1992. Radiosonde data was collected for that duration to profile the characteristics of the atmosphere. This corresponds to 3 different pixel sizes - 5m, 15m, and 30m. After, simulating different spatial sampling intervals within the same image for each of the 3 image sets, the results are cross-correlated to compare the extent of detail and complexity that is obtained when data is taken at lower spatial intervals.
Edges of Saturn's rings are fractal.
Li, Jun; Ostoja-Starzewski, Martin
2015-01-01
The images recently sent by the Cassini spacecraft mission (on the NASA website http://saturn.jpl.nasa.gov/photos/halloffame/) show the complex and beautiful rings of Saturn. Over the past few decades, various conjectures were advanced that Saturn's rings are Cantor-like sets, although no convincing fractal analysis of actual images has ever appeared. Here we focus on four images sent by the Cassini spacecraft mission (slide #42 "Mapping Clumps in Saturn's Rings", slide #54 "Scattered Sunshine", slide #66 taken two weeks before the planet's Augus't 200'9 equinox, and slide #68 showing edge waves raised by Daphnis on the Keeler Gap) and one image from the Voyager 2' mission in 1981. Using three box-counting methods, we determine the fractal dimension of edges of rings seen here to be consistently about 1.63 ~ 1.78. This clarifies in what sense Saturn's rings are fractal.
Functional data analysis in brain imaging studies.
Tian, Tian Siva
2010-01-01
Functional data analysis (FDA) considers the continuity of the curves or functions, and is a topic of increasing interest in the statistics community. FDA is commonly applied to time-series and spatial-series studies. The development of functional brain imaging techniques in recent years made it possible to study the relationship between brain and mind over time. Consequently, an enormous amount of functional data is collected and needs to be analyzed. Functional techniques designed for these data are in strong demand. This paper discusses three statistically challenging problems utilizing FDA techniques in functional brain imaging analysis. These problems are dimension reduction (or feature extraction), spatial classification in functional magnetic resonance imaging studies, and the inverse problem in magneto-encephalography studies. The application of FDA to these issues is relatively new but has been shown to be considerably effective. Future efforts can further explore the potential of FDA in functional brain imaging studies.
Compressive optical remote sensing via fractal classification
NASA Astrophysics Data System (ADS)
Sun, Quan-sen; Liu, Ji-xin
2015-11-01
High resolution and large field of view are two major development trends in optical remote sensing imaging. But these trends will cause the difficult problem of mass data processing and remote sensor design under the limitation of conventional sampling method. Therefore, we will propose a novel optical remote sensing imaging method based on compressed sensing theory and fractal feature extraction in this study. We could utilize the result of fractal classification to realize the selectable partitioned image recovery with undersampling measurement. The two experiments illustrate the availability and feasibility of this new method.
Molecular dynamics simulation of fractal aggregate diffusion
NASA Astrophysics Data System (ADS)
Pranami, Gaurav; Lamm, Monica H.; Vigil, R. Dennis
2010-11-01
The diffusion of fractal aggregates constructed with the method by Thouy and Jullien [J. Phys. A 27, 2953 (1994)10.1088/0305-4470/27/9/012] comprised of Np spherical primary particles was studied as a function of the aggregate mass and fractal dimension using molecular dynamics simulations. It is shown that finite-size effects have a strong impact on the apparent value of the diffusion coefficient (D) , but these can be corrected by carrying out simulations using different simulation box sizes. Specifically, the diffusion coefficient is inversely proportional to the length of a cubic simulation box, and the constant of proportionality appears to be independent of the aggregate mass and fractal dimension. Using this result, it is possible to compute infinite dilution diffusion coefficients (Do) for aggregates of arbitrary size and fractal dimension, and it was found that Do∝Np-1/df , as is often assumed by investigators simulating Brownian aggregation of fractal aggregates. The ratio of hydrodynamic radius to radius of gyration is computed and shown to be independent of mass for aggregates of fixed fractal dimension, thus enabling an estimate of the diffusion coefficient for a fractal aggregate based on its radius of gyration.
Advances in noninvasive functional imaging of bone.
Lan, Sheng-Min; Wu, Ya-Na; Wu, Ping-Ching; Sun, Chi-Kuang; Shieh, Dar-Bin; Lin, Ruey-Mo
2014-02-01
The demand for functional imaging in clinical medicine is comprehensive. Although the gold standard for the functional imaging of human bones in clinical settings is still radionuclide-based imaging modalities, nonionizing noninvasive imaging technology in small animals has greatly advanced in recent decades, especially the diffuse optical imaging to which Britton Chance made tremendous contributions. The evolution of imaging probes, instruments, and computation has facilitated exploration in the complicated biomedical research field by allowing longitudinal observation of molecular events in live cells and animals. These research-imaging tools are being used for clinical applications in various specialties, such as oncology, neuroscience, and dermatology. The Bone, a deeply located mineralized tissue, presents a challenge for noninvasive functional imaging in humans. Using nanoparticles (NP) with multiple favorable properties as bioimaging probes has provided orthopedics an opportunity to benefit from these noninvasive bone-imaging techniques. This review highlights the historical evolution of radionuclide-based imaging, computed tomography, positron emission tomography, and magnetic resonance imaging, diffuse optics-enabled in vivo technologies, vibrational spectroscopic imaging, and a greater potential for using NPs for biomedical imaging.
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)
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.…
NASA Astrophysics Data System (ADS)
Knutson, Paul; Dahlberg, E. Dan
2003-10-01
In examples of fractals such as moon craters, rivers,2 cauliflower,3 and bread,4 the actual growth process of the fractal object is missed. In the simple experiment described here, one can observe and record the growth of calcium carbonate crystals — a ubiquitous material found in marble and seashells — in real time. The video frames can be digitized and analyzed to determine the fractal dimension.
Fractal Geometry of Architecture
NASA Astrophysics Data System (ADS)
Lorenz, Wolfgang E.
In Fractals smaller parts and the whole are linked together. Fractals are self-similar, as those parts are, at least approximately, scaled-down copies of the rough whole. In architecture, such a concept has also been known for a long time. Not only architects of the twentieth century called for an overall idea that is mirrored in every single detail, but also Gothic cathedrals and Indian temples offer self-similarity. This study mainly focuses upon the question whether this concept of self-similarity makes architecture with fractal properties more diverse and interesting than Euclidean Modern architecture. The first part gives an introduction and explains Fractal properties in various natural and architectural objects, presenting the underlying structure by computer programmed renderings. In this connection, differences between the fractal, architectural concept and true, mathematical Fractals are worked out to become aware of limits. This is the basis for dealing with the problem whether fractal-like architecture, particularly facades, can be measured so that different designs can be compared with each other under the aspect of fractal properties. Finally the usability of the Box-Counting Method, an easy-to-use measurement method of Fractal Dimension is analyzed with regard to architecture.
GENERATING FRACTAL PATTERNS BY USING p-CIRCLE INVERSION
NASA Astrophysics Data System (ADS)
Ramírez, José L.; Rubiano, Gustavo N.; Zlobec, Borut Jurčič
2015-10-01
In this paper, we introduce the p-circle inversion which generalizes the classical inversion with respect to a circle (p = 2) and the taxicab inversion (p = 1). We study some basic properties and we also show the inversive images of some basic curves. We apply this new transformation to well-known fractals such as Sierpinski triangle, Koch curve, dragon curve, Fibonacci fractal, among others. Then we obtain new fractal patterns. Moreover, we generalize the method called circle inversion fractal be means of the p-circle inversion.
Automatic detection of microcalcifications with multi-fractal spectrum.
Ding, Yong; Dai, Hang; Zhang, Hang
2014-01-01
For improving the detection of micro-calcifications (MCs), this paper proposes an automatic detection of MC system making use of multi-fractal spectrum in digitized mammograms. The approach of automatic detection system is based on the principle that normal tissues possess certain fractal properties which change along with the presence of MCs. In this system, multi-fractal spectrum is applied to reveal such fractal properties. By quantifying the deviations of multi-fractal spectrums between normal tissues and MCs, the system can identify MCs altering the fractal properties and finally locate the position of MCs. The performance of the proposed system is compared with the leading automatic detection systems in a mammographic image database. Experimental results demonstrate that the proposed system is statistically superior to most of the compared systems and delivers a superior performance.
Investigations of human EEG response to viewing fractal patterns.
Hagerhall, Caroline M; Laike, Thorbjörn; Taylor, Richard P; Küller, Marianne; Küller, Rikard; Martin, Theodore P
2008-01-01
Owing to the prevalence of fractal patterns in natural scenery and their growing impact on cultures around the world, fractals constitute a common feature of our daily visual experiences, raising an important question: what responses do fractals induce in the observer? We monitored subjects' EEG while they were viewing fractals with different fractal dimensions, and the results show that significant effects could be found in the EEG even by employing relatively simple silhouette images. Patterns with a fractal dimension of 1.3 elicited the most interesting EEG, with the highest alpha in the frontal lobes but also the highest beta in the parietal area, pointing to a complicated interplay between different parts of the brain when experiencing this pattern.
Functional imaging for prostate cancer: therapeutic implications.
Mari Aparici, Carina; Seo, Youngho
2012-09-01
Functional radionuclide imaging modalities, now commonly combined with anatomical imaging modalities computed tomography (CT) or magnetic resonance imaging (single photon emission computed tomography [SPECT]/CT, positron emission tomography [PET]/CT, and PET/magnetic resonance imaging), are promising tools for the management of prostate cancer, particularly for therapeutic implications. Sensitive detection capability of prostate cancer using these imaging modalities is one issue; however, the treatment of prostate cancer using the information that can be obtained from functional radionuclide imaging techniques is another challenging area. There are not many SPECT or PET radiotracers that can cover the full spectrum of the management of prostate cancer from initial detection to staging, prognosis predictor, and all the way to treatment response assessment. However, when used appropriately, the information from functional radionuclide imaging improves, and sometimes significantly changes, the whole course of the cancer management. The limitations of using SPECT and PET radiotracers with regard to therapeutic implications are not so much different from their limitations solely for the task of detecting prostate cancer; however, the specific imaging target and how this target is reliably imaged by SPECT and PET can potentially make significant impact in the treatment of prostate cancer. Finally, although the localized prostate cancer is considered manageable, there is still significant need for improvement in noninvasive imaging of metastatic prostate cancer, in treatment guidance, and in response assessment from functional imaging, including radionuclide-based techniques. In this review article, we present the rationale of using functional radionuclide imaging and the therapeutic implications for each of radionuclide imaging agent that have been studied in human subjects.
Paradigms of Complexity: Fractals and Structures in the Sciences
NASA Astrophysics Data System (ADS)
Novak, Miroslav M.
The Table of Contents for the book is as follows: * Preface * The Origin of Complexity (invited talk) * On the Existence of Spatially Uniform Scaling Laws in the Climate System * Multispectral Backscattering: A Fractal-Structure Probe * Small-Angle Multiple Scattering on a Fractal System of Point Scatterers * Symmetric Fractals Generated by Cellular Automata * Bispectra and Phase Correlations for Chaotic Dynamical Systems * Self-Organized Criticality Models of Neural Development * Altered Fractal and Irregular Heart Rate Behavior in Sick Fetuses * Extract Multiple Scaling in Long-Term Heart Rate Variability * A Semi-Continous Box Counting Method for Fractal Dimension Measurement of Short Single Dimension Temporal Signals - Preliminary Study * A Fractional Brownian Motion Model of Cracking * Self-Affine Scaling Studies on Fractography * Coarsening of Fractal Interfaces * A Fractal Model of Ocean Surface Superdiffusion * Stochastic Subsurface Flow and Transport in Fractal Fractal Conductivity Fields * Rendering Through Iterated Function Systems * The σ-Hull - The Hull Where Fractals Live - Calculating a Hull Bounded by Log Spirals to Solve the Inverse IFS-Problem by the Detected Orbits * On the Multifractal Properties of Passively Convected Scalar Fields * New Statistical Textural Transforms for Non-Stationary Signals: Application to Generalized Mutlifractal Analysis * Laplacian Growth of Parallel Needles: Their Mullins-Sekerka Instability * Entropy Dynamics Associated with Self-Organization * Fractal Properties in Economics (invited talk) * Fractal Approach to the Regional Seismic Event Discrimination Problem * Fractal and Topological Complexity of Radioactive Contamination * Pattern Selection: Nonsingular Saffman-Taylor Finger and Its Dynamic Evolution with Zero Surface Tension * A Family of Complex Wavelets for the Characterization of Singularities * Stabilization of Chaotic Amplitude Fluctuations in Multimode, Intracavity-Doubled Solid-State Lasers * Chaotic
Clinical applications of functional MR imaging.
Belyaev, Artem S; Peck, Kyung K; Brennan, Nicole M Petrovich; Holodny, Andrei I
2013-05-01
Functional magnetic resonance (fMR) imaging for neurosurgical planning has become the standard of care in centers where it is available. Although paradigms to measure eloquent cortices are not yet standardized, simple tasks elicit reliable maps for planning neurosurgical procedures. A patient-specific paradigm design will refine the usability of fMR imaging for prognostication and recovery of function. Certain pathologic conditions and technical issues limit the interpretation of fMR imaging maps in clinical use and should be considered carefully. However, fMR imaging for neurosurgical planning continues to provide insights into how the brain works and how it responds to pathologic insults.
NASA Astrophysics Data System (ADS)
Uzol, Oguz; Hazaveh, Hooman Amiri
2016-11-01
The 3D flow structure within the near wake of a four-iteration fractal square turbulence grid is obtained by combining data from closely-spaced horizontal and vertical two-dimensional PIV measurement planes. For this purpose, the grid is placed inside the entrance of the test section of a suction type wind tunnel. The experiments are conducted at a freestream velocity of 8 m/s, corresponding to a Reynolds number of 9000 based on effective mesh size. The freestream turbulence intensity is about 0.5%. The measurement volume extends about 7 effective mesh sizes downstream of the grid. Within the measurement volume, 1000 vector maps are obtained on each one of the 220 horizontal and 220 vertical 2D PIV planes that are separated from each other by 500 microns, which is close to the in-plane vector spacing of 600 microns. This dataset allowed us to calculate all components of mean velocity, velocity gradient tensor, and vorticity as well as the Reynolds stress tensor except for (v'w') component. Using the analyzed three-dimensional mean flow field data, we are able to observe the three dimensional structure of the wakes of the largest bars that dominate the flow field and the corresponding turbulence generation characteristics. We focus on how the wake geometry, decay characteristics and stress-strain relations get impacted by the presence of smaller wakes surrounding the largest wake regions. We also investigate how 3D mean flow non-uniformities get generated downstream of the grid such as lateral contraction and bulging of mean wake shapes.
Fractal dimension and architecture of trabecular bone.
Fazzalari, N L; Parkinson, I H
1996-01-01
The fractal dimension of trabecular bone was determined for biopsies from the proximal femur of 25 subjects undergoing hip arthroplasty. The average age was 67.7 years. A binary profile of the trabecular bone in the biopsy was obtained from a digitized image. A program written for the Quantimet 520 performed the fractal analysis. The fractal dimension was calculated for each specimen, using boxes whose sides ranged from 65 to 1000 microns in length. The mean fractal dimension for the 25 subjects was 1.195 +/- 0.064 and shows that in Euclidean terms the surface extent of trabecular bone is indeterminate. The Quantimet 520 was also used to perform bone histomorphometric measurements. These were bone volume/total volume (BV/TV) (per cent) = 11.05 +/- 4.38, bone surface/total volume (BS/TV) (mm2/mm3) = 1.90 +/- 0.51, trabecular thickness (Tb.Th) (mm) = 0.12 +/- 0.03, trabecular spacing (Tb.Sp) (mm) = 1.03 +/- 0.36, and trabecular number (Tb.N) (number/mm) = 0.95 +/- 0.25. Pearsons' correlation coefficients showed a statistically significant relationship between the fractal dimension and all the histomorphometric parameters, with BV/TV (r = 0.85, P < 0.0001), BS/TV (r = 0.74, P < 0.0001), Tb.Th (r = 0.50, P < 0.02), Tb.Sp (r = -0.81, P < 0.0001), and Tb.N (r = 0.76, P < 0.0001). This method for calculating fractal dimension shows that trabecular bone exhibits fractal properties over a defined box size, which is within the dimensions of a structural unit for trabecular bone. Therefore, the fractal dimension of trabecular bone provides a measure which does not rely on Euclidean descriptors in order to describe a complex geometry.
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.
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.
NASA Astrophysics Data System (ADS)
Warchalowski, Wiktor; Krawczyk, Malgorzata J.
2017-03-01
We found the Lindenmayer systems for line graphs built on selected fractals. We show that the fractal dimension of such obtained graphs in all analysed cases is the same as for their original graphs. Both for the original graphs and for their line graphs we identified classes of nodes which reflect symmetry of the graph.
Fractal structures and processes
Bassingthwaighte, J.B.; Beard, D.A.; Percival, D.B.; Raymond, G.M.
1996-06-01
Fractals and chaos are closely related. Many chaotic systems have fractal features. Fractals are self-similar or self-affine structures, which means that they look much of the same when magnified or reduced in scale over a reasonably large range of scales, at least two orders of magnitude and preferably more (Mandelbrot, 1983). The methods for estimating their fractal dimensions or their Hurst coefficients, which summarize the scaling relationships and their correlation structures, are going through a rapid evolutionary phase. Fractal measures can be regarded as providing a useful statistical measure of correlated random processes. They also provide a basis for analyzing recursive processes in biology such as the growth of arborizing networks in the circulatory system, airways, or glandular ducts. {copyright} {ital 1996 American Institute of Physics.}
Molecular and functional imaging of internet addiction.
Zhu, Yunqi; Zhang, Hong; Tian, Mei
2015-01-01
Maladaptive use of the Internet results in Internet addiction (IA), which is associated with various negative consequences. Molecular and functional imaging techniques have been increasingly used for analysis of neurobiological changes and neurochemical correlates of IA. This review summarizes molecular and functional imaging findings on neurobiological mechanisms of IA, focusing on magnetic resonance imaging (MRI) and nuclear imaging modalities including positron emission tomography (PET) and single photon emission computed tomography (SPECT). MRI studies demonstrate that structural changes in frontal cortex are associated with functional abnormalities in Internet addicted subjects. Nuclear imaging findings indicate that IA is associated with dysfunction of the brain dopaminergic systems. Abnormal dopamine regulation of the prefrontal cortex (PFC) could underlie the enhanced motivational value and uncontrolled behavior over Internet overuse in addicted subjects. Further investigations are needed to determine specific changes in the Internet addictive brain, as well as their implications for behavior and cognition.
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 analysis of DNA sequence data
Berthelsen, C.L.
1993-01-01
DNA sequence databases are growing at an almost exponential rate. New analysis methods are needed to extract knowledge about the organization of nucleotides from this vast amount of data. Fractal analysis is a new scientific paradigm that has been used successfully in many domains including the biological and physical sciences. Biological growth is a nonlinear dynamic process and some have suggested that to consider fractal geometry as a biological design principle may be most productive. This research is an exploratory study of the application of fractal analysis to DNA sequence data. A simple random fractal, the random walk, is used to represent DNA sequences. The fractal dimension of these walks is then estimated using the [open quote]sandbox method[close quote]. Analysis of 164 human DNA sequences compared to three types of control sequences (random, base-content matched, and dimer-content matched) reveals that long-range correlations are present in DNA that are not explained by base or dimer frequencies. The study also revealed that the fractal dimension of coding sequences was significantly lower than sequences that were primarily noncoding, indicating the presence of longer-range correlations in functional sequences. The multifractal spectrum is used to analyze fractals that are heterogeneous and have a different fractal dimension for subsets with different scalings. The multifractal spectrum of the random walks of twelve mitochondrial genome sequences was estimated. Eight vertebrate mtDNA sequences had uniformly lower spectra values than did four invertebrate mtDNA sequences. Thus, vertebrate mitochondria show significantly longer-range correlations than to invertebrate mitochondria. The higher multifractal spectra values for invertebrate mitochondria suggest a more random organization of the sequences. This research also includes considerable theoretical work on the effects of finite size, embedding dimension, and scaling ranges.
Functional magnetic resonance imaging 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.
Quantitative Amyloid Imaging Using Image-Derived Arterial Input Function
Su, Yi; Blazey, Tyler M.; Snyder, Abraham Z.; Raichle, Marcus E.; Hornbeck, Russ C.; Aldea, Patricia; Morris, John C.; Benzinger, Tammie L. S.
2015-01-01
Amyloid PET imaging is an indispensable tool widely used in the investigation, diagnosis and monitoring of Alzheimer’s disease (AD). Currently, a reference region based approach is used as the mainstream quantification technique for amyloid imaging. This approach assumes the reference region is amyloid free and has the same tracer influx and washout kinetics as the regions of interest. However, this assumption may not always be valid. The goal of this work is to evaluate an amyloid imaging quantification technique that uses arterial region of interest as the reference to avoid potential bias caused by specific binding in the reference region. 21 participants, age 58 and up, underwent Pittsburgh compound B (PiB) PET imaging and MR imaging including a time-of-flight (TOF) MR angiography (MRA) scan and a structural scan. FreeSurfer based regional analysis was performed to quantify PiB PET data. Arterial input function was estimated based on coregistered TOF MRA using a modeling based technique. Regional distribution volume (VT) was calculated using Logan graphical analysis with estimated arterial input function. Kinetic modeling was also performed using the estimated arterial input function as a way to evaluate PiB binding (DVRkinetic) without a reference region. As a comparison, Logan graphical analysis was also performed with cerebellar cortex as reference to obtain DVRREF. Excellent agreement was observed between the two distribution volume ratio measurements (r>0.89, ICC>0.80). The estimated cerebellum VT was in line with literature reported values and the variability of cerebellum VT in the control group was comparable to reported variability using arterial sampling data. This study suggests that image-based arterial input function is a viable approach to quantify amyloid imaging data, without the need of arterial sampling or a reference region. This technique can be a valuable tool for amyloid imaging, particularly in population where reference normalization
Quantitative amyloid imaging using image-derived arterial input function.
Su, Yi; Blazey, Tyler M; Snyder, Abraham Z; Raichle, Marcus E; Hornbeck, Russ C; Aldea, Patricia; Morris, John C; Benzinger, Tammie L S
2015-01-01
Amyloid PET imaging is an indispensable tool widely used in the investigation, diagnosis and monitoring of Alzheimer's disease (AD). Currently, a reference region based approach is used as the mainstream quantification technique for amyloid imaging. This approach assumes the reference region is amyloid free and has the same tracer influx and washout kinetics as the regions of interest. However, this assumption may not always be valid. The goal of this work is to evaluate an amyloid imaging quantification technique that uses arterial region of interest as the reference to avoid potential bias caused by specific binding in the reference region. 21 participants, age 58 and up, underwent Pittsburgh compound B (PiB) PET imaging and MR imaging including a time-of-flight (TOF) MR angiography (MRA) scan and a structural scan. FreeSurfer based regional analysis was performed to quantify PiB PET data. Arterial input function was estimated based on coregistered TOF MRA using a modeling based technique. Regional distribution volume (VT) was calculated using Logan graphical analysis with estimated arterial input function. Kinetic modeling was also performed using the estimated arterial input function as a way to evaluate PiB binding (DVRkinetic) without a reference region. As a comparison, Logan graphical analysis was also performed with cerebellar cortex as reference to obtain DVRREF. Excellent agreement was observed between the two distribution volume ratio measurements (r>0.89, ICC>0.80). The estimated cerebellum VT was in line with literature reported values and the variability of cerebellum VT in the control group was comparable to reported variability using arterial sampling data. This study suggests that image-based arterial input function is a viable approach to quantify amyloid imaging data, without the need of arterial sampling or a reference region. This technique can be a valuable tool for amyloid imaging, particularly in population where reference normalization may
NASA Astrophysics Data System (ADS)
Subramaniam, Raji; Sullivan, R.; Schneider, P. S.; Flamholz, A.; Cheung, E.; Tremberger, G., Jr.; Wong, P. K.; Lieberman, D. H.; Cheung, T. D.; Garcia, F.; Bewry, N.; Yee, A.
2006-10-01
Images of packaged raw chicken purchased in neighborhood supermarkets were captured via a digital camera in laboratory and home settings. Each image contained the surface reflectivity information of the chicken tissue. The camera's red, green and blue light signals fluctuated and each spectral signal exhibited a random series across the surface. The Higuchi method, where the length of each increment in time (or spatial) lag is plotted against the lag, was used to explore the fractal property of the random series. (Higuchi, T., "Approach to an irregular time series on the basis of fractal theory", Physica D, vol 31, 277-283, 1988). The fractal calculation algorithm was calibrated with the Weierstrass function. The standard deviation and fractal dimension were shown to correlate with the time duration that a package was left at room temperature within a 24-hour period. Comparison to packaged beef results suggested that the time dependence could be due microbial spoilage. The fractal dimension results in this study were consistent with those obtained from yeast cell, mammalian cell and bacterial cell studies. This analysis method can be used to detect the re-refrigeration of a "left-out" package of chicken. The extension to public health issues such as consumer shopping is also discussed.
Functional 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
Functional minimization problems in image processing
NASA Astrophysics Data System (ADS)
Kim, Yunho; Vese, Luminita A.
2008-02-01
In this work we wish to recover an unknown image from a blurry version. We solve this inverse problem by energy minimization and regularization. We seek a solution of the form u + v, where u is a function of bounded variation (cartoon component), while v is an oscillatory component (texture), modeled by a Sobolev function with negative degree of differentiability. Experimental results show that this cartoon + texture model better recovers textured details in natural images, by comparison with the more standard models where the unknown is restricted only to the space of functions of bounded variation.
Multimodal Imaging of Dynamic Functional Connectivity
Tagliazucchi, Enzo; Laufs, Helmut
2015-01-01
The study of large-scale functional interactions in the human brain with functional magnetic resonance imaging (fMRI) extends almost to the first applications of this technology. Due to historical reasons and preconceptions about the limitations of this brain imaging method, most studies have focused on assessing connectivity over extended periods of time. It is now clear that fMRI can resolve the temporal dynamics of functional connectivity, like other faster imaging techniques such as electroencephalography and magnetoencephalography (albeit on a different temporal scale). However, the indirect nature of fMRI measurements can hinder the interpretability of the results. After briefly summarizing recent advances in the field, we discuss how the simultaneous combination of fMRI with electrophysiological activity measurements can contribute to a better understanding of dynamic functional connectivity in humans both during rest and task, wakefulness, and other brain states. PMID:25762977
Advantages in functional imaging of the brain
Mier, Walter; Mier, Daniela
2015-01-01
As neuronal pathologies cause only minor morphological alterations, molecular imaging techniques are a prerequisite for the study of diseases of the brain. The development of molecular probes that specifically bind biochemical markers and the advances of instrumentation have revolutionized the possibilities to gain insight into the human brain organization and beyond this—visualize structure-function and brain-behavior relationships. The review describes the development and current applications of functional brain imaging techniques with a focus on applications in psychiatry. A historical overview of the development of functional imaging is followed by the portrayal of the principles and applications of positron emission tomography (PET) and functional magnetic resonance imaging (fMRI), two key molecular imaging techniques that have revolutionized the ability to image molecular processes in the brain. We conclude that the juxtaposition of PET and fMRI in hybrid PET/MRI scanners enhances the significance of both modalities for research in neurology and psychiatry and might pave the way for a new area of personalized medicine. PMID:26042013
Talbot effect of grating with fractal rough edges
NASA Astrophysics Data System (ADS)
Teng, Shuyun; Cui, Yuwei; Li, Zhong
2016-01-01
Since the random edges of practically manufactured grating can be described by the self-affine fractal model, this paper investigates theoretically Fresnel diffraction of grating with rough edges on the basis of the self-affine fractal theory and discusses the variation of the Talbot image of grating with the rough parameters of edges. The amplitude gratings with different rough edges are produced with the help of the correlation function of the random distribution. Then, simulations of the diffraction intensity distributions of rough gratings are performed, and the modulation effect of speckles on Talbot image are shown. In order to explain the variation of the Talbot image of grating with rough edges, the theoretical analysis of the Talbot effect of grating with rough edges is given according to the statistic optics theory. The presented approximate analytic expression of the average diffraction intensity indicates the relationship between the diffraction and rough parameters of grating edges. The conclusions of this paper are useful for evaluating the Talbot image of practical grating.
Spatial Pattern of Biological Soil Crust with Fractal Geometry
NASA Astrophysics Data System (ADS)
Ospina, Abelardo; Florentino, Adriana; Tarquis, Ana M.
2015-04-01
Soil surface characteristics are subjected to changes driven by several interactions between water, air, biotic and abiotic components. One of the examples of such interactions is provided through biological soil crusts (BSC) in arid and semi-arid environments. BSC are communities composed of cyanobacteria, fungi, mosses, lichens, algae and liverworts covering the soil surface and play an important role in ecosystem functioning. The characteristics and formation of these BSC influence the soil hydrological balance, control the mass of eroded sediment, increase stability of soil surface, and influence plant productivity through the modification of nitrogen and carbon cycle. This study focus on characterize the spatial arrangements of the BSC based on image analysis and fractal concepts. To this end, RGB images of different types of biological soil crust where taken, each image corresponding to an area of 3.6 cm2 with a resolution of 1024x1024 pixels. For each image and channel, mass dimension and entropy were calculated. Preliminary results indicate that fractal methods are useful to describe changes associated to different types of BSC. Further research is necessary to apply these methodologies to several situations.
Fractal frontiers in cardiovascular magnetic resonance: towards clinical implementation.
Captur, Gabriella; Karperien, Audrey L; Li, Chunming; Zemrak, Filip; Tobon-Gomez, Catalina; Gao, Xuexin; Bluemke, David A; Elliott, Perry M; Petersen, Steffen E; Moon, James C
2015-09-07
Many of the structures and parameters that are detected, measured and reported in cardiovascular magnetic resonance (CMR) have at least some properties that are fractal, meaning complex and self-similar at different scales. To date however, there has been little use of fractal geometry in CMR; by comparison, many more applications of fractal analysis have been published in MR imaging of the brain.This review explains the fundamental principles of fractal geometry, places the fractal dimension into a meaningful context within the realms of Euclidean and topological space, and defines its role in digital image processing. It summarises the basic mathematics, highlights strengths and potential limitations of its application to biomedical imaging, shows key current examples and suggests a simple route for its successful clinical implementation by the CMR community.By simplifying some of the more abstract concepts of deterministic fractals, this review invites CMR scientists (clinicians, technologists, physicists) to experiment with fractal analysis as a means of developing the next generation of intelligent quantitative cardiac imaging tools.
The role of the circadian system in fractal neurophysiological control
Pittman-Polletta, Benjamin R.; Scheer, Frank A.J.L.; Butler, Matthew P.; Shea, Steven A.; Hu, Kun
2013-01-01
Many neurophysiological variables such as heart rate, motor activity, and neural activity are known to exhibit intrinsic fractal fluctuations - similar temporal fluctuation patterns at different time scales. These fractal patterns contain information about health, as many pathological conditions are accompanied by their alteration or absence. In physical systems, such fluctuations are characteristic of critical states on the border between randomness and order, frequently arising from nonlinear feedback interactions between mechanisms operating on multiple scales. Thus, the existence of fractal fluctuations in physiology challenges traditional conceptions of health and disease, suggesting that high levels of integrity and adaptability are marked by complex variability, not constancy, and are properties of a neurophysiological network, not individual components. Despite the subject's theoretical and clinical interest, the neurophysiological mechanisms underlying fractal regulation remain largely unknown. The recent discovery that the circadian pacemaker (suprachiasmatic nucleus) plays a crucial role in generating fractal patterns in motor activity and heart rate sheds an entirely new light on both fractal control networks and the function of this master circadian clock, and builds a bridge between the fields of circadian biology and fractal physiology. In this review, we sketch the emerging picture of the developing interdisciplinary field of fractal neurophysiology by examining the circadian system’s role in fractal regulation. PMID:23573942
The role of the circadian system in fractal neurophysiological control.
Pittman-Polletta, Benjamin R; Scheer, Frank A J L; Butler, Matthew P; Shea, Steven A; Hu, Kun
2013-11-01
Many neurophysiological variables such as heart rate, motor activity, and neural activity are known to exhibit intrinsic fractal fluctuations - similar temporal fluctuation patterns at different time scales. These fractal patterns contain information about health, as many pathological conditions are accompanied by their alteration or absence. In physical systems, such fluctuations are characteristic of critical states on the border between randomness and order, frequently arising from nonlinear feedback interactions between mechanisms operating on multiple scales. Thus, the existence of fractal fluctuations in physiology challenges traditional conceptions of health and disease, suggesting that high levels of integrity and adaptability are marked by complex variability, not constancy, and are properties of a neurophysiological network, not individual components. Despite the subject's theoretical and clinical interest, the neurophysiological mechanisms underlying fractal regulation remain largely unknown. The recent discovery that the circadian pacemaker (suprachiasmatic nucleus) plays a crucial role in generating fractal patterns in motor activity and heart rate sheds an entirely new light on both fractal control networks and the function of this master circadian clock, and builds a bridge between the fields of circadian biology and fractal physiology. In this review, we sketch the emerging picture of the developing interdisciplinary field of fractal neurophysiology by examining the circadian system's role in fractal regulation.
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)
ERIC Educational Resources Information Center
Bannon, Thomas J.
1991-01-01
Discussed are several different transformations based on the generation of fractals including self-similar designs, the chaos game, the koch curve, and the Sierpinski Triangle. Three computer programs which illustrate these concepts are provided. (CW)
Milovanovic, Petar; Djuric, Marija; Rakocevic, Zlatko
2012-01-01
There is an increasing interest in bone nano-structure, the ultimate goal being to reveal the basis of age-related bone fragility. In this study, power spectral density (PSD) data and fractal dimensions of the mineralized bone matrix were extracted from atomic force microscope topography images of the femoral neck trabeculae. The aim was to evaluate age-dependent differences in the mineralized matrix of human bone and to consider whether these advanced nano-descriptors might be linked to decreased bone remodeling observed by some authors and age-related decline in bone mechanical competence. The investigated bone specimens belonged to a group of young adult women (n = 5, age: 20–40 years) and a group of elderly women (n = 5, age: 70–95 years) without bone diseases. PSD graphs showed the roughness density distribution in relation to spatial frequency. In all cases, there was a fairly linear decrease in magnitude of the power spectra with increasing spatial frequencies. The PSD slope was steeper in elderly individuals (−2.374 vs. −2.066), suggesting the dominance of larger surface morphological features. Fractal dimension of the mineralized bone matrix showed a significant negative trend with advanced age, declining from 2.467 in young individuals to 2.313 in the elderly (r = 0.65, P = 0.04). Higher fractal dimension in young women reflects domination of smaller mineral grains, which is compatible with the more freshly remodeled structure. In contrast, the surface patterns in elderly individuals were indicative of older tissue age. Lower roughness and reduced structural complexity (decreased fractal dimension) of the interfibrillar bone matrix in the elderly suggest a decline in bone toughness, which explains why aged bone is more brittle and prone to fractures. PMID:22946475
On image analysis in fractography (Methodological Notes)
NASA Astrophysics Data System (ADS)
Shtremel', M. A.
2015-10-01
As other spheres of image analysis, fractography has no universal method for information convolution. An effective characteristic of an image is found by analyzing the essence and origin of every class of objects. As follows from the geometric definition of a fractal curve, its projection onto any straight line covers a certain segment many times; therefore, neither a time series (one-valued function of time) nor an image (one-valued function of plane) can be a fractal. For applications, multidimensional multiscale characteristics of an image are necessary. "Full" wavelet series break the law of conservation of information.
Functional MR Imaging in Chest Malignancies.
Broncano, Jordi; Luna, Antonio; Sánchez-González, Javier; Alvarez-Kindelan, Antonio; Bhalla, Sanjeev
2016-02-01
With recent advances in MR imaging, its application in the thorax has been feasible. The performance of both morphologic and functional techniques in the evaluation of thoracic malignances has improved not only differentiation from benign etiologies but also treatment monitoring based on a multiparametric approach. Several MR imaging-derived parameters have been described as potential biomarkers linked with prognosis and survival. Therefore, an integral approach with a nonradiating and noninvasive technique could be an optimal alternative for evaluating those patients.
NASA Astrophysics Data System (ADS)
Turcotte, Donald L.
Tectonic processes build landforms that are subsequently destroyed by erosional processes. Landforms exhibit fractal statistics in a variety of ways; examples include (1) lengths of coast lines; (2) number-size statistics of lakes and islands; (3) spectral behavior of topography and bathymetry both globally and locally; and (4) branching statistics of drainage networks. Erosional processes are dominant in the development of many landforms on this planet, but similar fractal statistics are also applicable to the surface of Venus where minimal erosion has occurred. A number of dynamical systems models for landforms have been proposed, including (1) cellular automata; (2) diffusion limited aggregation; (3) self-avoiding percolation; and (4) advective-diffusion equations. The fractal statistics and validity of these models will be discussed. Earthquakes also exhibit fractal statistics. The frequency-magnitude statistics of earthquakes satisfy the fractal Gutenberg-Richter relation both globally and locally. Earthquakes are believed to be a classic example of self-organized criticality. One model for earthquakes utilizes interacting slider-blocks. These slider block models have been shown to behave chaotically and to exhibit self-organized criticality. The applicability of these models will be discussed and alternative approaches will be presented. Fragmentation has been demonstrated to produce fractal statistics in many cases. Comminution is one model for fragmentation that yields fractal statistics. It has been proposed that comminution is also responsible for much of the deformation in the earth's crust. The brittle disruption of the crust and the resulting earthquakes present an integrated problem with many fractal aspects.
Baish, J W; Jain, R K
2000-07-15
Recent studies have shown that fractal geometry, a vocabulary of irregular shapes, can be useful for describing the pathological architecture of tumors and, perhaps more surprisingly, for yielding insights into the mechanisms of tumor growth and angiogenesis that complement those obtained by modern molecular methods. This article outlines the basic methods of fractal geometry and discusses the value and limitations of applying this new tool to cancer research.
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.
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.
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.
Fractal characterization of wear-erosion surfaces
Rawers, James C.; Tylczak, Joseph H.
1999-12-01
Wear erosion is a complex phenomenon resulting in highly distorted and deformed surface morphologies. Most wear surface features have been described only qualitatively. In this study wear surfaces features were quantified using fractal analysis. The ability to assign numerical values to wear-erosion surfaces makes possible mathematical expressions that will enable wear mechanisms to be predicted and understood. Surface characterization came from wear-erosion experiments that included varying the erosive materials, the impact velocity, and the impact angle. Seven fractal analytical techniques were applied to micrograph images of wear-erosion surfaces. Fourier analysis was the most promising. Fractal values obtained were consistent with visual observations and provided a unique wear-erosion parameter unrelated to wear rate.
``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.
Trabecular Pattern Analysis Using Fractal Dimension
NASA Astrophysics Data System (ADS)
Ishida, Takayuki; Yamashita, Kazuya; Takigawa, Atsushi; Kariya, Komyo; Itoh, Hiroshi
1993-04-01
Feature extraction from a digitized image is advantageous for the detection of signs of disease. In this work, we attempted to evaluate bone trabecular pattern changes in osteoporosis using the fractal dimension and the root mean square (RMS) values. The relationship between the fractal dimension and the 1st moment of the power spectrum is explored, and we investigated the relationship between the results of this analysis and the bone mineral density (BMD) value which was measured using dual-energy X-ray absorptiometry (DEXA). As a result, we were able to extract useful information, using the fractal dimension and the RMS value of the radiographs (lateral view of the lumbar vertebrae), for the diagnosis of osteoporosis. Abnormal clinical cases were separated from normal cases based on the evaluation values. Negligible correlation between the BMD value and these indexes was observed.
Fractal Dimension in Epileptic EEG Signal Analysis
NASA Astrophysics Data System (ADS)
Uthayakumar, R.
Fractal Analysis is the well developed theory in the data analysis of non-linear time series. Especially Fractal Dimension is a powerful mathematical tool for modeling many physical and biological time signals with high complexity and irregularity. Fractal dimension is a suitable tool for analyzing the nonlinear behaviour and state of the many chaotic systems. Particularly in analysis of chaotic time series such as electroencephalograms (EEG), this feature has been used to identify and distinguish specific states of physiological function.Epilepsy is the main fatal neurological disorder in our brain, which is analyzed by the biomedical signal called Electroencephalogram (EEG). The detection of Epileptic seizures in the EEG Signals is an important tool in the diagnosis of epilepsy. So we made an attempt to analyze the EEG in depth for knowing the mystery of human consciousness. EEG has more fluctuations recorded from the human brain due to the spontaneous electrical activity. Hence EEG Signals are represented as Fractal Time Series.The algorithms of fractal dimension methods have weak ability to the estimation of complexity in the irregular graphs. Divider method is widely used to obtain the fractal dimension of curves embedded into a 2-dimensional space. The major problem is choosing initial and final step length of dividers. We propose a new algorithm based on the size measure relationship (SMR) method, quantifying the dimensional behaviour of irregular rectifiable graphs with minimum time complexity. The evidence for the suitability (equality with the nature of dimension) of the algorithm is illustrated graphically.We would like to demonstrate the criterion for the selection of dividers (minimum and maximum value) in the calculation of fractal dimension of the irregular curves with minimum time complexity. For that we design a new method of computing fractal dimension (FD) of biomedical waveforms. Compared to Higuchi's algorithm, advantages of this method include
Adolescent body image and psychosocial functioning.
Davison, Tanya E; McCabe, Marita P
2006-02-01
Researchers have highlighted the significance of a poor body image in the development of dysfunctional eating but have systematically investigated few other outcomes. The authors examined the relationships between different aspects of body image and psychosocial functioning. Participants were 245 boys and 173 girls from Grades 8 and 9 (M age = 13.92 years, SD = 0.69 years). Respondents completed measures of physical attractiveness, body satisfaction, body image importance, body image behaviors, appearance comparison, social physique anxiety, self-esteem, depression, anxiety, and same-sex and opposite-sex relations. Whereas girls tended to report a more negative body image than did boys, the relevance of body image to self-esteem was similar for boys and girls. Concern about others' evaluation of their bodies was especially important in understanding low female self-esteem, whereas for boys, ratings of general attractiveness most strongly predicted self-esteem. The authors found a negative body image to be unrelated to symptoms of negative affect but to be strongly associated with poor opposite-sex peer relationships, especially among boys. A negative body image also affected same-sex relations among girls.
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.
Izhaky, David; Nelson, Darin A; Burgansky-Eliash, Zvia; Grinvald, Amiram
2009-07-01
The Retinal Function Imager (RFI; Optical Imaging, Rehovot, Israel) is a unique, noninvasive multiparameter functional imaging instrument that directly measures hemodynamic parameters such as retinal blood-flow velocity, oximetric state, and metabolic responses to photic activation. In addition, it allows capillary perfusion mapping without any contrast agent. These parameters of retinal function are degraded by retinal abnormalities. This review delineates the development of these parameters and demonstrates their clinical applicability for noninvasive detection of retinal function in several modalities. The results suggest multiple clinical applications for early diagnosis of retinal diseases and possible critical guidance of their treatment.
Acoustic noise during functional magnetic resonance imaging.
Ravicz, M E; Melcher, J R; Kiang, N Y
2000-10-01
Functional magnetic resonance imaging (fMRI) enables sites of brain activation to be localized in human subjects. For studies of the auditory system, acoustic noise generated during fMRI can interfere with assessments of this activation by introducing uncontrolled extraneous sounds. As a first step toward reducing the noise during fMRI, this paper describes the temporal and spectral characteristics of the noise present under typical fMRI study conditions for two imagers with different static magnetic field strengths. Peak noise levels were 123 and 138 dB re 20 microPa in a 1.5-tesla (T) and a 3-T imager, respectively. The noise spectrum (calculated over a 10-ms window coinciding with the highest-amplitude noise) showed a prominent maximum at 1 kHz for the 1.5-T imager (115 dB SPL) and at 1.4 kHz for the 3-T imager (131 dB SPL). The frequency content and timing of the most intense noise components indicated that the noise was primarily attributable to the readout gradients in the imaging pulse sequence. The noise persisted above background levels for 300-500 ms after gradient activity ceased, indicating that resonating structures in the imager or noise reverberating in the imager room were also factors. The gradient noise waveform was highly repeatable. In addition, the coolant pump for the imager's permanent magnet and the room air-handling system were sources of ongoing noise lower in both level and frequency than gradient coil noise. Knowledge of the sources and characteristics of the noise enabled the examination of general approaches to noise control that could be applied to reduce the unwanted noise during fMRI sessions.
Fractal 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
Optical imaging device of retinal function
NASA Astrophysics Data System (ADS)
Kardon, Randy H.; Kwon, Young; Truitt, Paul; Nemeth, Sheila C.; T'so, Dan; Soliz, Peter
2002-06-01
An optical imaging device of retina function (OID-RF) has been constructed to record changes in reflected 700-nm light from the fundus caused by retinal activation in response to a visual 535-nm stimulus. The resulting images reveal areas of the retina activated by visual stimulation. This device is a modified fundus camera designed to provide a patterned, moving visual stimulus over a 45-degree field of view to the subject in the green wavelength portion of the visual spectrum while simultaneously imaging the fundus in another, longer wavelength range. Data was collected from 3 normal subjects and recorded for 13 seconds at 4 Hz; 3 seconds were recorded during pre-stimulus baseline, 5 seconds during the stimulus, and 5 seconds post-stimulus. This procedure was repeated several times and, after image registration, the images were averaged to improve signal to noise. The change in reflected intensity from the retina due to the stimulus was then calculated by comparison to the pre-stimulus state. Reflected intensity from areas of stimulated retina began to increase steadily within 1 second after stimulus onset and decayed after stimulus offset. These results indicated that a functional optical signal can be recorded from the human eye.
Random sequential adsorption on fractals.
Ciesla, Michal; Barbasz, Jakub
2012-07-28
Irreversible adsorption of spheres on flat collectors having dimension d < 2 is studied. Molecules are adsorbed on Sierpinski's triangle and carpet-like fractals (1 < d < 2), and on general Cantor set (d < 1). Adsorption process is modeled numerically using random sequential adsorption (RSA) algorithm. The paper concentrates on measurement of fundamental properties of coverages, i.e., maximal random coverage ratio and density autocorrelation function, as well as RSA kinetics. Obtained results allow to improve phenomenological relation between maximal random coverage ratio and collector dimension. Moreover, simulations show that, in general, most of known dimensional properties of adsorbed monolayers are valid for non-integer dimensions.
NASA Astrophysics Data System (ADS)
Marks-Tarlow, Terry
Linear concepts of time plus the modern capacity to track history emerged out of circular conceptions characteristic of ancient and traditional cultures. A fractal concept of time lies implicitly within the analog clock, where each moment is treated as unique. With fractal geometry the best descriptor of nature, qualities of self-similarity and scale invariance easily model her endless variety and recursive patterning, both in time and across space. To better manage temporal aspects of our lives, a fractal concept of time is non-reductive, based more on the fullness of being than on fragments of doing. By using a fractal concept of time, each activity or dimension of life is multiply and vertically nested. Each nested cycle remains simultaneously present, operating according to intrinsic dynamics and time scales. By adding the vertical axis of simultaneity to the horizontal axis of length, time is already full and never needs to be filled. To attend to time's vertical dimension is to tap into the imaginary potential for infinite depth. To switch from linear to fractal time allows us to relax into each moment while keeping in mind the whole.
[Physical and fractal properties of polyaluminum chloride-humic acid (PACl-HA) flocs].
Wang, Yi-Li; Liu, Jie; Du, Bai-Yu
2006-11-01
The powder of polyaluminum chloride-humic acid (PACl-HA) flocs was prepared by cryo-freezing-vacuum-drying method. These flocs were characterized by X-ray diffractometry, FTIR spectroscopy, elementary analysis and surface area determination. The results show that these flocs are amorphous, mainly composed by elements of C, O, Al, and reserve some characteristic functional groups from PACl, HA or Kaolin. The N2 absorption-desorption data determined the microstructure of PACl-HA flocs: 130 - 161 m2 x g(-1) of BET specific surface area, 0.38 - 0.52 cm3 x g(-1) of BJH cumulative absorbed volume and 7.7 - 9.6nm of BJH desorption average pore diameter. The peak values of pore size distribution (PSD) curves were found at 8.4 - 11.2nm of pore diameter. The self-similar and rough surface was observed in SEM images of PACl-HA flocs. The surface fractal dimensions D(s) of the flocs determined from both SEM images method and N2 absorption-desorption one were 2.03 - 2.26 and 2.24 - 2.37, respectively. The correspondent fractal scale for the former method was 23 - 390nm, mainly belonging to exterior surface scales, and the lowest limit of the fractal scale for the latter method was 0.2nm and fell in pore surface scales. This demonstrated that the flocs surface had multi-scale fractal properties. Furthermore, some difference was given between the pore surface fractal dimensions D(s) calculated from N2 absorption data and desorption data. The calculated pore surface D(s) values of much more than three through thermodynamic model had discrepancy from Sahouli et al's results.
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.
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.
A Tutorial Review on Fractal Spacetime and Fractional Calculus
NASA Astrophysics Data System (ADS)
He, Ji-Huan
2014-11-01
This tutorial review of fractal-Cantorian spacetime and fractional calculus begins with Leibniz's notation for derivative without limits which can be generalized to discontinuous media like fractal derivative and q-derivative of quantum calculus. Fractal spacetime is used to elucidate some basic properties of fractal which is the foundation of fractional calculus, and El Naschie's mass-energy equation for the dark energy. The variational iteration method is used to introduce the definition of fractional derivatives. Fractal derivative is explained geometrically and q-derivative is motivated by quantum mechanics. Some effective analytical approaches to fractional differential equations, e.g., the variational iteration method, the homotopy perturbation method, the exp-function method, the fractional complex transform, and Yang-Laplace transform, are outlined and the main solution processes are given.
Determining Effective Thermal Conductivity of Fabrics by Using Fractal Method
NASA Astrophysics Data System (ADS)
Zhu, Fanglong; Li, Kejing
2010-03-01
In this article, a fractal effective thermal conductivity model for woven fabrics with multiple layers is developed. Structural models of yarn and plain woven fabric are derived based on the fractal characteristics of macro-pores (gap or channel) between the yarns and micro-pores inside the yarns. The fractal effective thermal conductivity model can be expressed as a function of the pore structure (fractal dimension) and architectural parameters of the woven fabric. Good agreement is found between the fractal model and the thermal conductivity measurements in the general porosity ranges. It is expected that the model will be helpful in the evaluation of thermal comfort for woven fabric in the whole range of porosity.
A tale of two fractals: The Hofstadter butterfly and the integral Apollonian gaskets
NASA Astrophysics Data System (ADS)
Satija, Indubala I.
2016-11-01
This paper unveils a mapping between a quantum fractal that describes a physical phenomena, and an abstract geometrical fractal. The quantum fractal is the Hofstadter butterfly discovered in 1976 in an iconic condensed matter problem of electrons moving in a two-dimensional lattice in a transverse magnetic field. The geometric fractal is the integer Apollonian gasket characterized in terms of a 300 BC problem of mutually tangent circles. Both of these fractals are made up of integers. In the Hofstadter butterfly, these integers encode the topological quantum numbers of quantum Hall conductivity. In the Apollonian gaskets an infinite number of mutually tangent circles are nested inside each other, where each circle has integer curvature. The mapping between these two fractals reveals a hidden D3 symmetry embedded in the kaleidoscopic images that describe the asymptotic scaling properties of the butterfly. This paper also serves as a mini review of these fractals, emphasizing their hierarchical aspects in terms of Farey fractions.
[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.
Fractal radar scattering from soil.
Oleschko, Klaudia; Korvin, Gabor; Figueroa, Benjamin; Vuelvas, Marco Antonio; Balankin, Alexander S; Flores, Lourdes; Carreón, Dora
2003-04-01
A general technique is developed to retrieve the fractal dimension of self-similar soils through microwave (radar) scattering. The technique is based on a mathematical model relating the fractal dimensions of the georadargram to that of the scattering structure. Clear and different fractal signatures have been observed over four geosystems (soils and sediments) compared in this work.
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.
Image reconstruction with analytical point spread functions
NASA Astrophysics Data System (ADS)
Asensio Ramos, A.; López Ariste, A.
2010-07-01
Context. The image degradation produced by atmospheric turbulence and optical aberrations is usually alleviated using post-facto image reconstruction techniques, even when observing with adaptive optics systems. Aims: These techniques rely on the development of the wavefront using Zernike functions and the non-linear optimization of a certain metric. The resulting optimization procedure is computationally heavy. Our aim is to alleviate this computational burden. Methods: We generalize the extended Zernike-Nijboer theory to carry out the analytical integration of the Fresnel integral and present a natural basis set for the development of the point spread function when the wavefront is described using Zernike functions. Results: We present a linear expansion of the point spread function in terms of analytic functions, which, in addition, takes defocusing into account in a natural way. This expansion is used to develop a very fast phase-diversity reconstruction technique, which is demonstrated in terms of some applications. Conclusions: We propose that the linear expansion of the point spread function can be applied to accelerate other reconstruction techniques in use that are based on blind deconvolution.
Electromagnetic inverse applications for functional brain imaging
Wood, C.C.
1997-10-01
This is the final report of a one-year, Laboratory Directed Research and Development (LDRD) project at Los Alamos National Laboratory (LANL). This project addresses an important mathematical and computational problem in functional brain imaging, namely the electromagnetic {open_quotes}inverse problem.{close_quotes} Electromagnetic brain imaging techniques, magnetoencephalography (MEG) and electroencephalography (EEG), are based on measurements of electrical potentials and magnetic fields at hundreds of locations outside the human head. The inverse problem is the estimation of the locations, magnitudes, and time-sources of electrical currents in the brain from surface measurements. This project extends recent progress on the inverse problem by combining the use of anatomical constraints derived from magnetic resonance imaging (MRI) with Bayesian and other novel algorithmic approaches. The results suggest that we can achieve significant improvements in the accuracy and robustness of inverse solutions by these two approaches.
Functional lung imaging using hyperpolarized gas MRI.
Fain, Sean B; Korosec, Frank R; Holmes, James H; O'Halloran, Rafael; Sorkness, Ronald L; Grist, Thomas M
2007-05-01
The noninvasive assessment of lung function using imaging is increasingly of interest for the study of lung diseases, including chronic obstructive pulmonary disease (COPD) and asthma. Hyperpolarized gas MRI (HP MRI) has demonstrated the ability to detect changes in ventilation, perfusion, and lung microstructure that appear to be associated with both normal lung development and disease progression. The physical characteristics of HP gases and their application to MRI are presented with an emphasis on current applications. Clinical investigations using HP MRI to study asthma, COPD, cystic fibrosis, pediatric chronic lung disease, and lung transplant are reviewed. Recent advances in polarization, pulse sequence development for imaging with Xe-129, and prototype low magnetic field systems dedicated to lung imaging are highlighted as areas of future development for this rapidly evolving technology.
Backbone fractal dimension and fractal hybrid orbital of protein structure
NASA Astrophysics Data System (ADS)
Peng, Xin; Qi, Wei; Wang, Mengfan; Su, Rongxin; He, Zhimin
2013-12-01
Fractal geometry analysis provides a useful and desirable tool to characterize the configuration and structure of proteins. In this paper we examined the fractal properties of 750 folded proteins from four different structural classes, namely (1) the α-class (dominated by α-helices), (2) the β-class (dominated by β-pleated sheets), (3) the (α/β)-class (α-helices and β-sheets alternately mixed) and (4) the (α + β)-class (α-helices and β-sheets largely segregated) by using two fractal dimension methods, i.e. "the local fractal dimension" and "the backbone fractal dimension" (a new and useful quantitative parameter). The results showed that the protein molecules exhibit a fractal behavior in the range of 1 ⩽ N ⩽ 15 (N is the number of the interval between two adjacent amino acid residues), and the value of backbone fractal dimension is distinctly greater than that of local fractal dimension for the same protein. The average value of two fractal dimensions decreased in order of α > α/β > α + β > β. Moreover, the mathematical formula for the hybrid orbital model of protein based on the concept of backbone fractal dimension is in good coincidence with that of the similarity dimension. So it is a very accurate and simple method to analyze the hybrid orbital model of protein by using the backbone fractal dimension.
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)
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.
Effects of Image Contrast on Functional MRI Image Registration
Gonzalez-Castillo, Javier; Duthie, Kristen N.; Saad, Ziad S.; Chu, Carlton; Bandettini, Peter A.; Luh, Wen-Ming
2012-01-01
Lack of tissue contrast and existing inhomogeneous bias fields from multi-channel coils have the potential to degrade the output of registration algorithms; and consequently degrade group analysis and any attempt to accurately localize brain function. Non-invasive ways to improve tissue contrast in fMRI images include the use of low flip angles (FAs) well below the Ernst angle and longer repetition times (TR). Techniques to correct intensity inhomogeneity are also available in most mainstream fMRI data analysis packages; but are not used as part of the pre-processing pipeline in many studies. In this work, we use a combination of real data and simulations to show that simple-to-implement acquisition/pre-processing techniques can significantly improve the outcome of both functional-to-functional and anatomical-to-functional image registrations. We also emphasize the need of tissue contrast on EPI images to be able to appropriately evaluate the quality of the alignment. In particular, we show that the use of low FAs (e.g., θ≤40°), when physiological noise considerations permit such an approach, significantly improves accuracy, consistency and stability of registration for data acquired at relatively short TRs (TR≤2s). Moreover, we also show that the application of bias correction techniques significantly improves alignment both for array-coil data (known to contain high intensity inhomogeneity) as well as birdcage-coil data. Finally, improvements in alignment derived from the use of the first infinite-TR volumes (ITVs) as targets for registration are also demonstrated. For the purpose of quantitatively evaluating the different scenarios, two novel metrics were developed: Mean Voxel Distance (MVD) to evaluate registration consistency, and Deviation of Mean Voxel Distance (dMVD) to evaluate registration stability across successive alignment attempts. PMID:23128074
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
One-stop-shop stroke imaging with functional CT.
Tong, Elizabeth; Komlosi, Peter; Wintermark, Max
2015-12-01
Advanced imaging techniques have extended beyond traditional anatomic imaging and progressed to dynamic, physiologic and functional imaging. Neuroimaging is no longer a mere diagnostic tool. Multimodal functional CT, comprising of NCCT, PCT and CTA, provides a one-stop-shop for rapid stroke imaging. Integrating those imaging findings with pertinent clinical information can help guide subsequent treatment decisions, medical management and follow-up imaging selection. This review article will briefly discuss the indication and utility of each modality in acute stroke imaging.
Pediatric Epilepsy: Neurology, Functional Imaging, and Neurosurgery.
Mountz, James M; Patterson, Christina M; Tamber, Mandeep S
2017-03-01
In this chapter we provide a comprehensive review of the current role that functional imaging can have in the care of the pediatric epilepsy patient from the perspective of the epilepsy neurologist and the epilepsy neurosurgeon. In the neurology section, the diagnosis and classification of epilepsy adapted by the International League Against Epilepsy as well as the etiology and incidence of the disease is presented. The neuroimaging section describes how advanced nuclear medicine imaging methods can be synergized to provide a maximum opportunity to localize an epileptogenic focus. This section described the value of FDG-PET and regional cerebral blood flow SPECT in the identification of an epileptogenic focus. The imaging section also emphasizes the importance on developing a dedicated epilepsy management team, comprised of an epilepsy imaging specialist, epilepsy neurologist and epilepsy neurosurgeon, to provide the maximum benefit to each child with epilepsy. An emphasis is placed on preparation for ictal SPECT injection procedures, including the critical role of an automated injector well as the use of state-of-the-art dedicated nuclear medicine imaging and analysis protocols to correctly localize the epileptogenic focus location. In the final section, surgical options, approaches and expected outcomes for the different classes of epilepsy is presented.
Fast Optical Imaging of Human Brain Function
Gratton, Gabriele; Fabiani, Monica
2010-01-01
Great advancements in brain imaging during the last few decades have opened a large number of new possibilities for neuroscientists. The most dominant methodologies (electrophysiological and magnetic resonance-based methods) emphasize temporal and spatial information, respectively. However, theorizing about brain function has recently emphasized the importance of rapid (within 100 ms or so) interactions between different elements of complex neuronal networks. Fast optical imaging, and in particular the event-related optical signal (EROS, a technology that has emerged over the last 15 years) may provide descriptions of localized (to sub-cm level) brain activity with a temporal resolution of less than 100 ms. The main limitations of EROS are its limited penetration, which allows us to image cortical structures not deeper than 3 cm from the surface of the head, and its low signal-to-noise ratio. Advantages include the fact that EROS is compatible with most other imaging methods, including electrophysiological, magnetic resonance, and trans-cranial magnetic stimulation techniques, with which can be recorded concurrently. In this paper we present a summary of the research that has been conducted so far on fast optical imaging, including evidence for the possibility of recording neuronal signals with this method, the properties of the signals, and various examples of applications to the study of human cognitive neuroscience. Extant issues, controversies, and possible future developments are also discussed. PMID:20631845
Imaging visual function of the human brain
Marg, E.
1988-10-01
Imaging of human brain structure and activity with particular reference to visual function is reviewed along with methods of obtaining the data including computed tomographic (CT) scan, magnetic resonance imaging (MRI), magnetic resonance spectroscopy (MRS), and positron emission tomography (PET). The literature is reviewed and the potential for a new understanding of brain visual function is discussed. PET is reviewed from basic physical principles to the most recent visual brain findings with oxygen-15. It is shown that there is a potential for submillimeter localization of visual functions with sequentially different visual stimuli designed for the temporal separation of the responses. Single photon emission computed tomography (SPECT), a less expensive substitute for PET, is also discussed. MRS is covered from basic physical principles to the current state of the art of in vivo biochemical analysis. Future possible clinical applications are discussed. Improved understanding of the functional neural organization of vision and brain will open a window to maps and circuits of human brain function.119 references.
Electroencephalographic imaging of higher brain function
NASA Technical Reports Server (NTRS)
Gevins, A.; Smith, M. E.; McEvoy, L. K.; Leong, H.; Le, J.
1999-01-01
High temporal resolution is necessary to resolve the rapidly changing patterns of brain activity that underlie mental function. Electroencephalography (EEG) provides temporal resolution in the millisecond range. However, traditional EEG technology and practice provide insufficient spatial detail to identify relationships between brain electrical events and structures and functions visualized by magnetic resonance imaging or positron emission tomography. Recent advances help to overcome this problem by recording EEGs from more electrodes, by registering EEG data with anatomical images, and by correcting the distortion caused by volume conduction of EEG signals through the skull and scalp. In addition, statistical measurements of sub-second interdependences between EEG time-series recorded from different locations can help to generate hypotheses about the instantaneous functional networks that form between different cortical regions during perception, thought and action. Example applications are presented from studies of language, attention and working memory. Along with its unique ability to monitor brain function as people perform everyday activities in the real world, these advances make modern EEG an invaluable complement to other functional neuroimaging modalities.
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
Retinal functional imager (RFI): non-invasive functional imaging of the retina.
Ganekal, S
2013-01-01
Retinal functional imager (RFI) is a unique non-invasive functional imaging system with novel capabilities for visualizing the retina. The objective of this review was to show the utility of non-invasive functional imaging in various disorders. Electronic literature search was carried out using the websites www.pubmed.gov and www.google.com. The search words were retinal functional imager and non-invasive retinal imaging used in combination. The articles published or translated into English were studied. The RFI directly measures hemodynamic parameters such as retinal blood-flow velocity, oximetric state, metabolic responses to photic activation and generates capillary perfusion maps (CPM) that provides retinal vasculature detail similar to flourescein angiography. All of these parameters stand in a direct relationship to the function and therefore the health of the retina, and are known to be degraded in the course of retinal diseases. Detecting changes in retinal function aid early diagnosis and treatment as functional changes often precede structural changes in many retinal disorders.
Fractal Images: Procedure and Theory.
1987-08-01
the group of one-on-one analytic map- pings is the group of Moebius transforms, that is, maps of the form -az + b g(z) cz + d ad - bc * 0cz Moebius ...powerful. Let h(z) = Az2 + 2Bz + C be a general quadratic equation in C. For f(z) as above, it is possible to solve for a Moebius transform g(z) and a...given by g(z) = Az + B I = AC + B -B 2 Since two dynamical systems in C conjugate by a Moebius transform are the same, every quadratic dynamical system
Hsü, K J; Hsü, A J
1990-01-01
Music critics have compared Bach's music to the precision of mathematics. What "mathematics" and what "precision" are the questions for a curious scientist. The purpose of this short note is to suggest that the mathematics is, at least in part, Mandelbrot's fractal geometry and the precision is the deviation from a log-log linear plot. PMID:11607061
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)
Fuzzy membership functions for analysis of high-resolution CT images of diffuse pulmonary diseases.
Almeida, Eliana; Rangayyan, Rangaraj M; Azevedo-Marques, Paulo M
2015-08-01
We propose the use of fuzzy membership functions to analyze images of diffuse pulmonary diseases (DPDs) based on fractal and texture features. The features were extracted from preprocessed regions of interest (ROIs) selected from high-resolution computed tomography images. The ROIs represent five different patterns of DPDs and normal lung tissue. A Gaussian mixture model (GMM) was constructed for each feature, with six Gaussians modeling the six patterns. Feature selection was performed and the GMMs of the five significant features were used. From the GMMs, fuzzy membership functions were obtained by a probability-possibility transformation and further statistical analysis was performed. An average classification accuracy of 63.5% was obtained for the six classes. For four of the six classes, the classification accuracy was superior to 65%, and the best classification accuracy was 75.5% for one class. The use of fuzzy membership functions to assist in pattern classification is an alternative to deterministic approaches to explore strategies for medical diagnosis.
A Fractal Perspective on Scale in Geography
NASA Astrophysics Data System (ADS)
Jiang, Bin; Brandt, S.
2016-06-01
Scale is a fundamental concept that has attracted persistent attention in geography literature over the past several decades. However, it creates enormous confusion and frustration, particularly in the context of geographic information science, because of scale-related issues such as image resolution, and the modifiable areal unit problem (MAUP). This paper argues that the confusion and frustration mainly arise from Euclidean geometric thinking, with which locations, directions, and sizes are considered absolute, and it is time to reverse this conventional thinking. Hence, we review fractal geometry, together with its underlying way of thinking, and compare it to Euclidean geometry. Under the paradigm of Euclidean geometry, everything is measurable, no matter how big or small. However, geographic features, due to their fractal nature, are essentially unmeasurable or their sizes depend on scale. For example, the length of a coastline, the area of a lake, and the slope of a topographic surface are all scale-dependent. Seen from the perspective of fractal geometry, many scale issues, such as the MAUP, are inevitable. They appear unsolvable, but can be dealt with. To effectively deal with scale-related issues, we introduce topological and scaling analyses based on street-related concepts such as natural streets, street blocks, and natural cities. We further contend that spatial heterogeneity, or the fractal nature of geographic features, is the first and foremost effect of two spatial properties, because it is general and universal across all scales. Keywords: Scaling, spatial heterogeneity, conundrum of length, MAUP, topological analysis
Flames in fractal grid generated turbulence
NASA Astrophysics Data System (ADS)
Goh, K. H. H.; Geipel, P.; Hampp, F.; Lindstedt, R. P.
2013-12-01
Twin premixed turbulent opposed jet flames were stabilized for lean mixtures of air with methane and propane in fractal grid generated turbulence. A density segregation method was applied alongside particle image velocimetry to obtain velocity and scalar statistics. It is shown that the current fractal grids increase the turbulence levels by around a factor of 2. Proper orthogonal decomposition (POD) was applied to show that the fractal grids produce slightly larger turbulent structures that decay at a slower rate as compared to conventional perforated plates. Conditional POD (CPOD) was also implemented using the density segregation technique and the results show that CPOD is essential to segregate the relative structures and turbulent kinetic energy distributions in each stream. The Kolmogorov length scales were also estimated providing values ∼0.1 and ∼0.5 mm in the reactants and products, respectively. Resolved profiles of flame surface density indicate that a thin flame assumption leading to bimodal statistics is not perfectly valid under the current conditions and it is expected that the data obtained will be of significant value to the development of computational methods that can provide information on the conditional structure of turbulence. It is concluded that the increase in the turbulent Reynolds number is without any negative impact on other parameters and that fractal grids provide a route towards removing the classical problem of a relatively low ratio of turbulent to bulk strain associated with the opposed jet configuration.
NASA Astrophysics Data System (ADS)
Maslovskaya, A. G.; Barabash, T. K.
2017-01-01
The article presents some results of fractal analysis of ferroelectric domain structure images visualized with scanning electron microscope (SEM) techniques. The fractal and multifractal characteristics were estimated to demonstrate self-similar organization of ferroelectric domain structure registered with static and dynamic contrast modes of SEM. Fractal methods as sensitive analytical tools were used to indicate degree of domain structure and domain boundary imperfections. The electron irradiation-induced erosion effect of ferroelectric domain boundaries in electron beam-stimulated polarization current mode of SEM is characterized by considerable raising of fractal dimension. For dynamic contrast mode of SEM there was revealed that complication of domain structure during its dynamics is specified by increase in fractal dimension of images and slight raising of boundary fractal dimension.
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.
Functional MRI using regularized parallel imaging acquisition.
Lin, Fa-Hsuan; Huang, Teng-Yi; Chen, Nan-Kuei; Wang, Fu-Nien; Stufflebeam, Steven M; Belliveau, John W; Wald, Lawrence L; Kwong, Kenneth K
2005-08-01
Parallel MRI techniques reconstruct full-FOV images from undersampled k-space data by using the uncorrelated information from RF array coil elements. One disadvantage of parallel MRI is that the image signal-to-noise ratio (SNR) is degraded because of the reduced data samples and the spatially correlated nature of multiple RF receivers. Regularization has been proposed to mitigate the SNR loss originating due to the latter reason. Since it is necessary to utilize static prior to regularization, the dynamic contrast-to-noise ratio (CNR) in parallel MRI will be affected. In this paper we investigate the CNR of regularized sensitivity encoding (SENSE) acquisitions. We propose to implement regularized parallel MRI acquisitions in functional MRI (fMRI) experiments by incorporating the prior from combined segmented echo-planar imaging (EPI) acquisition into SENSE reconstructions. We investigated the impact of regularization on the CNR by performing parametric simulations at various BOLD contrasts, acceleration rates, and sizes of the active brain areas. As quantified by receiver operating characteristic (ROC) analysis, the simulations suggest that the detection power of SENSE fMRI can be improved by regularized reconstructions, compared to unregularized reconstructions. Human motor and visual fMRI data acquired at different field strengths and array coils also demonstrate that regularized SENSE improves the detection of functionally active brain regions.
Functional MRI Using Regularized Parallel Imaging Acquisition
Lin, Fa-Hsuan; Huang, Teng-Yi; Chen, Nan-Kuei; Wang, Fu-Nien; Stufflebeam, Steven M.; Belliveau, John W.; Wald, Lawrence L.; Kwong, Kenneth K.
2013-01-01
Parallel MRI techniques reconstruct full-FOV images from undersampled k-space data by using the uncorrelated information from RF array coil elements. One disadvantage of parallel MRI is that the image signal-to-noise ratio (SNR) is degraded because of the reduced data samples and the spatially correlated nature of multiple RF receivers. Regularization has been proposed to mitigate the SNR loss originating due to the latter reason. Since it is necessary to utilize static prior to regularization, the dynamic contrast-to-noise ratio (CNR) in parallel MRI will be affected. In this paper we investigate the CNR of regularized sensitivity encoding (SENSE) acquisitions. We propose to implement regularized parallel MRI acquisitions in functional MRI (fMRI) experiments by incorporating the prior from combined segmented echo-planar imaging (EPI) acquisition into SENSE reconstructions. We investigated the impact of regularization on the CNR by performing parametric simulations at various BOLD contrasts, acceleration rates, and sizes of the active brain areas. As quantified by receiver operating characteristic (ROC) analysis, the simulations suggest that the detection power of SENSE fMRI can be improved by regularized reconstructions, compared to unregularized reconstructions. Human motor and visual fMRI data acquired at different field strengths and array coils also demonstrate that regularized SENSE improves the detection of functionally active brain regions. PMID:16032694
Structural and functional brain imaging in schizophrenia.
Cleghorn, J M; Zipursky, R B; List, S J
1991-01-01
We present an evaluation of the contribution of structural and functional brain imaging to our understanding of schizophrenia. Methodological influences on the validity of the data generated by these new technologies include problems with measurement and clinical and anatomic heterogeneity. These considerations greatly affect the interpretation of the data generated by these technologies. Work in these fields to date, however, has produced strong evidence which suggests that schizophrenia is a disease which involves abnormalities in the structure and function of many brain areas. Structural brain imaging studies of schizophrenia using computed tomography (CT) and magnetic resonance imaging (MRI) are reviewed and their contribution to current theories of the pathogenesis of schizophrenia are discussed. Positron emission tomography (PET) studies of brain metabolic activity and dopamine receptor binding in schizophrenia are summarized and the critical questions raised by these studies are outlined. Future studies in these fields have the potential to yield critical insights into the pathophysiology of schizophrenia; new directions for studies of schizophrenia using these technologies are identified. PMID:1911736
Functional CT imaging of prostate cancer
NASA Astrophysics Data System (ADS)
Henderson, Elizabeth; Milosevic, Michael F.; Haider, Masoom A.; Yeung, Ivan W. T.
2003-09-01
The purpose of this paper is to investigate the distribution of blood flow (F), mean capillary transit time (Tc), capillary permeability (PS) and blood volume (vb) in prostate cancer using contrast-enhanced CT. Nine stage T2-T3 prostate cancer patients were enrolled in the study. Following bolus injection of a contrast agent, a time series of CT images of the prostate was acquired. Functional maps showing the distribution of F, Tc, PS and vb within the prostate were generated using a distributed parameter tracer kinetic model, the adiabatic approximation to the tissue homogeneity model. The precision of the maps was assessed using covariance matrix analysis. Finally, maps were compared to the findings of standard clinical investigations. Eight of the functional maps demonstrated regions of increased F, PS and vb, the locations of which were consistent with the results of standard clinical investigations. However, model parameters other than F could only be measured precisely within regions of high F. In conclusion functional CT images of cancer-containing prostate glands demonstrate regions of elevated F, PS and vb. However, caution should be used when applying a complex tracer kinetic model to the study of prostate cancer since not all parameters can be measured precisely in all areas.
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
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.
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 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.
Fractal analysis of circulating platelets in type 2 diabetic patients.
Bianciardi, G; Tanganelli, I
2015-01-01
This paper investigates the use of computerized fractal analysis for objective characterization by means of transmission electron microscopy of the complexity of circulating platelets collected from healthy individuals and from type 2 diabetic patients, a pathologic condition in which platelet hyperreactivity has been described. Platelet boundaries were extracted by means of automatically image analysis. Local fractal dimension by box counting (measure of geometric complexity) was automatically calculated. The results showed that the platelet boundary observed by electron microscopy is fractal and that the shape of the circulating platelets is significantly more complex in the diabetic patients in comparison to healthy subjects (p < 0.01), with 100% correct classification. In vitro activated platelets from healthy subjects show an analogous increase of geometric complexity. Computerized fractal analysis of platelet shape by transmission electron microscopy can provide accurate, quantitative, data to study platelet activation in diabetes mellitus.
Is fractal geometry useful in medicine and biomedical sciences?
Heymans, O; Fissette, J; Vico, P; Blacher, S; Masset, D; Brouers, F
2000-03-01
Fractal geometry has become very useful in the understanding of many phenomena in various fields such as astrophysics, economy or agriculture and recently in medicine. After a brief intuitive introduction to the basis of fractal geometry, the clue is made about the correlation between Df and the complexity or the irregularity of a structure. However, fractal analysis must be applied with certain caution in natural objects such as bio-medical ones. The cardio-vascular system remains one of the most important fields of application of these kinds of approach. Spectral analysis of the R-R interval, morphology of the distal coronary arteries constitute two examples. Other very interesting applications are founded in bacteriology, medical imaging or ophthalmology. In our institution, we apply fractal analysis in order to quantitate angiogenesis and other vascular processes.
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.
Multilayer adsorption on fractal surfaces.
Vajda, Péter; Felinger, Attila
2014-01-10
Multilayer adsorption is often observed in liquid chromatography. The most frequently employed model for multilayer adsorption is the BET isotherm equation. In this study we introduce an interpretation of multilayer adsorption measured on liquid chromatographic stationary phases based on the fractal theory. The fractal BET isotherm model was successfully used to determine the apparent fractal dimension of the adsorbent surface. The nonlinear fitting of the fractal BET equation gives us the estimation of the adsorption equilibrium constants and the monolayer saturation capacity of the adsorbent as well. In our experiments, aniline and proline were used as test molecules on reversed phase and normal phase columns, respectively. Our results suggest an apparent fractal dimension 2.88-2.99 in the case of reversed phase adsorbents, in the contrast with a bare silica column with a fractal dimension of 2.54.
Applications of fractal geometry to dynamical evolution of sunspots
Milovanov, A.V.; Zelenyi, L.M. )
1993-07-01
A fractal model for sunspot dynamics is presented. Formation of a sunspot in the solar photosphere is considered from the viewpoint of aggregation of magnetic flux tubes on a fractal geometry. Fine structure of the magnetic flux tubes is analyzed for a broad class of non-Maxwellian plasma distribution functions. The sunspot fractal dimension is proved to depend on the parameters of the plasma distribution function, enabling one to investigate intrinsic properties of the solar plasma by means of powerful geometrical methods. Magnetic field dissipation in the tubes is shown to result in effective sunspot decay. Sunspot formation and decay times as well as the diffusion constant [ital K] deduced by using the fractal model, are in a good agreement with observational data. Disappearance of umbras in decaying sunspots is interpreted as a second-order phase transition reminiscent of the transition through the Curie point in ferromagnetics.
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.
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 polyzirconosiloxane cluster coatings
Sugama, T.
1992-08-01
Fractal polyzirconosiloxane (PZS) cluster films were prepared through the hydrolysis-polycondensation-pyrolysis synthesis of two-step HCl acid-NaOH base catalyzed sol precursors consisting of N-[3-(triethoxysilyl)propyl]-4,5-dihydroimidazole, Zr(OC{sub 3}H{sub 7}){sub 4}, methanol, and water. When amorphous PZSs were applied to aluminum as protective coatings against NaCl-induced corrosion, the effective film was that derived from the sol having a pH near the isoelectric point in the positive zeta potential region. The following four factors played an important role in assembling the protective PZS coating films: (1) a proper rate of condensation, (2) a moderate ratio of Si-O-Si to Si-O-Zr linkages formed in the PZS network, (3) hydrophobic characteristics, and (4) a specific microstructural geometry, in which large fractal clusters were linked together.
Fractal polyzirconosiloxane cluster coatings
Sugama, T.
1992-01-01
Fractal polyzirconosiloxane (PZS) cluster films were prepared through the hydrolysis-polycondensation-pyrolysis synthesis of two-step HCl acid-NaOH base catalyzed sol precursors consisting of N-(3-(triethoxysilyl)propyl)-4,5-dihydroimidazole, Zr(OC{sub 3}H{sub 7}){sub 4}, methanol, and water. When amorphous PZSs were applied to aluminum as protective coatings against NaCl-induced corrosion, the effective film was that derived from the sol having a pH near the isoelectric point in the positive zeta potential region. The following four factors played an important role in assembling the protective PZS coating films: (1) a proper rate of condensation, (2) a moderate ratio of Si-O-Si to Si-O-Zr linkages formed in the PZS network, (3) hydrophobic characteristics, and (4) a specific microstructural geometry, in which large fractal clusters were linked together.
Turbulent wakes of fractal objects.
Staicu, Adrian; Mazzi, Biagio; Vassilicos, J C; van de Water, Willem
2003-06-01
Turbulence of a windtunnel flow is stirred using objects that have a fractal structure. The strong turbulent wakes resulting from three such objects which have different fractal dimensions are probed using multiprobe hot-wire anemometry in various configurations. Statistical turbulent quantities are studied within inertial and dissipative range scales in an attempt to relate changes in their self-similar behavior to the scaling of the fractal objects.
Langevin Equation on Fractal Curves
NASA Astrophysics Data System (ADS)
Satin, Seema; Gangal, A. D.
2016-07-01
We analyze random motion of a particle on a fractal curve, using Langevin approach. This involves defining a new velocity in terms of mass of the fractal curve, as defined in recent work. The geometry of the fractal curve, plays an important role in this analysis. A Langevin equation with a particular model of noise is proposed and solved using techniques of the Fα-Calculus.
Fractal multifiber microchannel plates
NASA Technical Reports Server (NTRS)
Cook, Lee M.; Feller, W. B.; Kenter, Almus T.; Chappell, Jon H.
1992-01-01
The construction and performance of microchannel plates (MCPs) made using fractal tiling mehtods are reviewed. MCPs with 40 mm active areas having near-perfect channel ordering were produced. These plates demonstrated electrical performance characteristics equivalent to conventionally constructed MCPs. These apparently are the first MCPs which have a sufficiently high degree of order to permit single channel addressability. Potential applications for these devices and the prospects for further development are discussed.
NASA Astrophysics Data System (ADS)
Martin, Demetri
2015-03-01
Demetri Maritn prepared this palindromic poem as his project for Michael Frame's fractal geometry class at Yale. Notice the first, fourth, and seventh words in the second and next-to-second lines are palindromes, the first two and last two lines are palindromes, the middle line, "Be still if I fill its ebb" minus its last letter is a palindrome, and the entire poem is a palindrome...
Fractal Properties in Economics
2000-01-01
field of science, econophysics , was established recently in 1997 [2, 3]. This is a study of economic phenomena based on the methods and approaches of...physics. Among 244 many topics in econophysics there are three topics that are closely related to the study of fractals. They are price changes in open...prices, J. of Bussiness (Chicago) 36 (1963) pp.3 9 4 -4 19 . 2. J. Kertesz and 1. Kondor (Eds.), Econophysics : an emerging science (Kluwer Academic
NASA Astrophysics Data System (ADS)
Besselink, R.; Stawski, T. M.; Van Driessche, A. E. S.; Benning, L. G.
2016-12-01
Densely packed surface fractal aggregates form in systems with high local volume fractions of particles with very short diffusion lengths, which effectively means that particles have little space to move. However, there are no prior mathematical models, which would describe scattering from such surface fractal aggregates and which would allow the subdivision between inter- and intraparticle interferences of such aggregates. Here, we show that by including a form factor function of the primary particles building the aggregate, a finite size of the surface fractal interfacial sub-surfaces can be derived from a structure factor term. This formalism allows us to define both a finite specific surface area for fractal aggregates and the fraction of particle interfacial sub-surfaces at the perimeter of an aggregate. The derived surface fractal model is validated by comparing it with an ab initio approach that involves the generation of a "brick-in-a-wall" von Koch type contour fractals. Moreover, we show that this approach explains observed scattering intensities from in situ experiments that followed gypsum (CaSO4 ṡ 2H2O) precipitation from highly supersaturated solutions. Our model of densely packed "brick-in-a-wall" surface fractal aggregates may well be the key precursor step in the formation of several types of mosaic- and meso-crystals.
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.
Darwinian Evolution and Fractals
NASA Astrophysics Data System (ADS)
Carr, Paul H.
2009-05-01
Did nature's beauty emerge by chance or was it intelligently designed? Richard Dawkins asserts that evolution is blind aimless chance. Michael Behe believes, on the contrary, that the first cell was intelligently designed. The scientific evidence is that nature's creativity arises from the interplay between chance AND design (laws). Darwin's ``Origin of the Species,'' published 150 years ago in 1859, characterized evolution as the interplay between variations (symbolized by dice) and the natural selection law (design). This is evident in recent discoveries in DNA, Madelbrot's Fractal Geometry of Nature, and the success of the genetic design algorithm. Algorithms for generating fractals have the same interplay between randomness and law as evolution. Fractal statistics, which are not completely random, characterize such phenomena such as fluctuations in the stock market, the Nile River, rainfall, and tree rings. As chaos theorist Joseph Ford put it: God plays dice, but the dice are loaded. Thus Darwin, in discovering the evolutionary interplay between variations and natural selection, was throwing God's dice!
Fractals in 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.
Dimension of fractal basin boundaries
Park, B.S.
1988-01-01
In many dynamical systems, multiple attractors coexist for certain parameter ranges. The set of initial conditions that asymptotically approach each attractor is its basin of attraction. These basins can be intertwined on arbitrary small scales. Basin boundary can be either smooth or fractal. Dynamical systems that have fractal basin boundary show final state sensitivity of the initial conditions. A measure of this sensitivity (uncertainty exponent {alpha}) is related to the dimension of the basin boundary d = D - {alpha}, where D is the dimension of the phase space and d is the dimension of the basin boundary. At metamorphosis values of the parameter, there might happen a conversion from smooth to fractal basin boundary (smooth-fractal metamorphosis) or a conversion from fractal to another fractal basin boundary characteristically different from the previous fractal one (fractal-fractal metamorphosis). The dimension changes continuously with the parameter except at the metamorphosis values where the dimension of the basin boundary jumps discontinuously. We chose the Henon map and the forced damped pendulum to investigate this. Scaling of the basin volumes near the metamorphosis values of the parameter is also being studied for the Henon map. Observations are explained analytically by using low dimensional model map.
Investigating Fractal Geometry Using LOGO.
ERIC Educational Resources Information Center
Thomas, David A.
1989-01-01
Discusses dimensionality in Euclidean geometry. Presents methods to produce fractals using LOGO. Uses the idea of self-similarity. Included are program listings and suggested extension activities. (MVL)
Fractals in 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.
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 properties of macrophage membrane studied by AFM.
Bitler, A; Dover, R; Shai, Y
2012-12-01
Complexity of cell membrane poses difficulties to quantify corresponding morphology changes during cell proliferation and damage. We suggest using fractal dimension of the cell membrane to quantify its complexity and track changes produced by various treatments. Glutaraldehyde fixed mouse RAW 264.7 macrophage membranes were chosen as model system and imaged in PeakForce QNM (quantitative nanomechanics) mode of AFM (atomic force microscope). The morphology of the membranes was characterized by fractal dimension. The parameter was calculated for set of AFM images by three different methods. The same calculations were done for the AFM images of macrophages treated with colchicine, an inhibitor of the microtubule polymerization, and microtubule stabilizing agent taxol. We conclude that fractal dimension can be additional and useful parameter to characterize the cell membrane complexity and track the morphology changes produced by different treatments.
Nanoparticle Functionalization and Its Potentials for Molecular Imaging
Thiruppathi, Rukmani; Mishra, Sachin; Ganapathy, Mathangi
2016-01-01
Functionalization enhances the properties and characteristics of nanoparticles through surface modification, and enables them to play a major role in the field of medicine. In molecular imaging, quality functional images are required with proper differentiation which can be seen with high contrast to obtain viable information. This review article discusses how functionalization enhances molecular imaging and enables multimodal imaging by which images with combination of functions particular to each modality can be obtained. This also explains how nanoparticles interacting at molecular level, when functionalized with molecules can target the cells of interest or substances with high specificity, reducing background signal and allowing simultaneous therapies to be carried out while imaging. Functionalization allows imaging for a prolonged period and enables to track the cells over a period of time. Recent researches and progress in functionalizing the nanoparticles to specifically enhance bioimaging with different modalities and their applications are reviewed in this article. PMID:28331783
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.
NASA Astrophysics Data System (ADS)
Boyko, Anton N.; Pyatilova, Olga V.; Kalmykov, Rustam M.; Gaev, Dahir S.; Timoshenkov, Sergei P.; Gavrilov, Sergei A.
2016-12-01
Study of new materials and composites based on porous silicon is of great interest for electronics and microelectronics industry. Functional characteristics of structured layers are closely associated with their morphology properties and treatment conditions correspondently. In this work a porous silicon layers formed by metal-assisted chemical etching (MACE) with the use of gas adsorption-desorption method, scanning electron microscopy (SEM) and fractal geometry have been examined. Specific surface area given by multi-point BET method was about of 7 m2/g and 13 m2/g for n-Si and p-Si specimens correspondently. Surface fractal dimension Ds was estimated for p-type mesoporous silicon from BET results using Neimark's thermodynamic approach, the value is Ds=2.86. "Slit islands" Mandelbrot's algorithm was applied for analysis of SEM images and calculations of surface fractal dimension Ds, computation gives Ds = 2.52 for n-Si sample and Ds = 2.84 for p-Si sample. The study testified the fractal nature of porous layers formed by MACE and exhibits correlation between different methods of fractal dimension estimation. The results can be applied for improvement of methods of structured solids characterization.
Imaging of the diaphragm: anatomy and function.
Nason, Laura K; Walker, Christopher M; McNeeley, Michael F; Burivong, Wanaporn; Fligner, Corinne L; Godwin, J David
2012-01-01
The diaphragm is the primary muscle of ventilation. Dysfunction of the diaphragm is an underappreciated cause of respiratory difficulties and may be due to a wide variety of entities, including surgery, trauma, tumor, and infection. Diaphragmatic disease usually manifests as elevation at chest radiography. Functional imaging with fluoroscopy (or ultrasonography or magnetic resonance imaging) is a simple and effective method of diagnosing diaphragmatic dysfunction, which can be classified as paralysis, weakness, or eventration. Diaphragmatic paralysis is indicated by absence of orthograde excursion on quiet and deep breathing, with paradoxical motion on sniffing. Diaphragmatic weakness is indicated by reduced or delayed orthograde excursion on deep breathing, with or without paradoxical motion on sniffing. Eventration is congenital thinning of a segment of diaphragmatic muscle and manifests as focal weakness. Treatment of diaphragmatic paralysis depends on the cause of the dysfunction and the severity of the symptoms. Treatment options include plication and phrenic nerve stimulation. Supplemental material available at http://radiographics.rsna.org/lookup/suppl/doi:10.1148/rg.322115127/-/DC1.
Fractal analysis of lumbar vertebral cancellous bone architecture.
Feltrin, G P; Macchi, V; Saccavini, C; Tosi, E; Dus, C; Fassina, A; Parenti, A; De Caro, R
2001-11-01
Osteoporosis is characterized by bone mineral density (BMD) decreasing and spongy bone rearrangement with consequent loss of elasticity and increased bone fragility. Quantitative computed tomography (QCT) quantifies bone mineral content but does not describe spongy architecture. Analysis of trabecular pattern may provide additional information to evaluate osteoporosis. The aim of this study was to determine whether the fractal analysis of the microradiography of lumbar vertebrae provides a reliable assessment of bone texture, which correlates with the BMD. The lumbar segment of the spine was removed from 22 cadavers with no history of back pain and examined with standard x-ray, traditional tomography, and quantitative computed tomography to measure BMD. The fractal dimension, which quantifies the image fractal complexity, was calculated on microradiographs of axial sections of the fourth lumbar vertebra to determine its characteristic spongy network. The relationship between the values of the BMD and those of the fractal dimension was evaluated by linear regression and a statistically significant correlation (R = 0.96) was found. These findings suggest that the application of fractal analysis to radiological analyses can provide valuable information on the trabecular pattern of vertebrae. Thus, fractal dimensions of trabecular bone structure should be considered as a supplement to BMD evaluation in the assessment of osteoporosis.
Fractal analysis: methodologies for biomedical researchers.
Ristanović, Dusan; Milosević, Nebojsa T
2012-01-01
Fractal analysis has become a popular method in all branches of scientific investigations including biology and medicine. Although there is a growing interest in the application of fractal analysis in biological sciences, questions about the methodology of fractal analysis have partly restricted its wider and comprehensible application. It is a notable fact that fractal analysis is derived from fractal geometry, but there are some unresolved issues that need to be addressed. In this respect, we discuss several related underlying principles for fractal analysis and establish the meaningful relationship between fractal analysis and fractal geometry. Since some concepts in fractal analysis are determined descriptively and/or qualitatively, this paper provides their exact mathematical definitions or explanations. Another aim of this study is to show that nowadays fractal analysis is an independent mathematical and experimental method based on Mandelbrot's fractal geometry, Euclidean traditiontal geometry and Richardson's coastline method.
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.
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.
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.
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.
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).
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.
Familial Essential Tremor Studied With Functional Magnetic Resonance Imaging
NASA Astrophysics Data System (ADS)
Hernandez, A.; Salgado, P.; Gil, A.; Barrios, F. A.
2003-09-01
Functional Magnetic Resonance Imaging has become an important analytical tool to study neurodegenerative diseases. We applied the EPI-BOLD functional Magnetic Resonance Imaging technique to acquire functional images of patients with familial essential tremor (FET) disorder and healthy control volunteers, during a motor task activity. Functional and anatomic images were used to produce the brain activation maps of the patients and volunteers. These functional maps of the primary somatosensorial and motor cortexes of patients and control subjects were compared for functional differences per subject. The averaged functional brain images of eight of each case were acquired were, it can be clearly observed the differences in active zones. The results presented in this work show that there are differences in the functional maps during motor task activation between control subjects and FET patients suggesting a cerebral functional reorganization that can be mapped with BOLD-fMRI.
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.
Fractals analysis of cardiac arrhythmias.
Saeed, Mohammed
2005-09-06
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.
Medical imaging 1995: Physiology and function from multidimensional images
Hoffman, E.A.
1995-12-31
This conference was held February 27--28, 1995 in San Diego, California. The purpose of the conference was to provide a forum for exchange of state-of-the art information on physiologic imaging. This meeting is unique in bringing together the physicists, image processors, workstation developers, experts in image perception, and the experts of picture archiving and display. Individual papers have been processed separately for inclusion in the appropriate data bases.
Analysis of Fractional Flow for Transient Two-Phase Flow in Fractal Porous Medium
NASA Astrophysics Data System (ADS)
Lu, Ting; Duan, Yonggang; Fang, Quantang; Dai, Xiaolu; Wu, Jinsui
2016-03-01
Prediction of fractional flow in fractal porous medium is important for reservoir engineering and chemical engineering as well as hydrology. A physical conceptual fractional flow model of transient two-phase flow is developed in fractal porous medium based on the fractal characteristics of pore-size distribution and on the approximation that porous medium consist of a bundle of tortuous capillaries. The analytical expression for fractional flow for wetting phase is presented, and the proposed expression is the function of structural parameters (such as tortuosity fractal dimension, pore fractal dimension, maximum and minimum diameters of capillaries) and fluid properties (such as contact angle, viscosity and interfacial tension) in fractal porous medium. The sensitive parameters that influence fractional flow and its derivative are formulated, and their impacts on fractional flow are discussed.
Imaging the wave functions of adsorbed molecules.
Lüftner, Daniel; Ules, Thomas; Reinisch, Eva Maria; Koller, Georg; Soubatch, Serguei; Tautz, F Stefan; Ramsey, Michael G; Puschnig, Peter
2014-01-14
The basis for a quantum-mechanical description of matter is electron wave functions. For atoms and molecules, their spatial distributions and phases are known as orbitals. Although orbitals are very powerful concepts, experimentally only the electron densities and -energy levels are directly observable. Regardless whether orbitals are observed in real space with scanning probe experiments, or in reciprocal space by photoemission, the phase information of the orbital is lost. Here, we show that the experimental momentum maps of angle-resolved photoemission from molecular orbitals can be transformed to real-space orbitals via an iterative procedure which also retrieves the lost phase information. This is demonstrated with images obtained of a number of orbitals of the molecules pentacene (C22H14) and perylene-3,4,9,10-tetracarboxylic dianhydride (C24H8O6), adsorbed on silver, which are in excellent agreement with ab initio calculations. The procedure requires no a priori knowledge of the orbitals and is shown to be simple and robust.
Tissue as a self-organizing system with fractal dynamics.
Waliszewski, P; Konarski, J
2001-01-01
Cell is a supramolecular dynamic network. Screening of tissue-specific cDNA library and results of Relative RT-PCR indicate that the relationship between genotype, (i.e., dynamic network of genes and their protein regulatory elements) and phenotype is non-bijective, and mendelian inheritance is a special case only. This implies non-linearity, complexity, and quasi-determinism, (i.e., co-existence of deterministic and non-deterministic events) of dynamic cellular network; prerequisite conditions for the existence of fractal structure. Indeed, the box counting method reveals that morphological patterns of the higher order, such as gland-like structures or populations of differentiating cancer cells possess fractal dimension and self-similarity. Since fractal space is not filled out randomly, a variety of morphological patterns of functional states arises. The expansion coefficient characterizes evolution of fractal dynamics. The coefficient indicates what kind of interactions occurs between cells, and how far from the limiting integer dimension of the Euclidean space the expanding population of cells is. We conclude that cellular phenomena occur in the fractal space; aggregation of cells is a supracollective phenomenon (expansion coefficient > 0), and differentiation is a collective one (expansion coefficient < 0). Fractal dimension or self-similarity are lost during tumor progression. The existence of fractal structure in a complex tissue system denotes that dynamic cellular phenomena generate an attractor with the appropriate organization of space-time. And vice versa, this attractor sets up physical limits for cellular phenomena during their interactions with various fields. This relationship can help to understand the emergence of extraterrestial forms of life. Although those forms can be composed of non-carbon molecules, fractal structure appears to be the common feature of all interactive biosystems.
Random-fractal Ansatz for the configurations of two-dimensional critical systems
NASA Astrophysics Data System (ADS)
Lee, Ching Hua; Ozaki, Dai; Matsueda, Hiroaki
2016-12-01
Critical systems have always intrigued physicists and precipitated the development of new techniques. Recently, there has been renewed interest in the information contained in the configurations of classical critical systems, whose computation do not require full knowledge of the wave function. Inspired by holographic duality, we investigated the entanglement properties of the classical configurations (snapshots) of the Potts model by introducing an Ansatz ensemble of random fractal images. By virtue of the central limit theorem, our Ansatz accurately reproduces the entanglement spectra of actual Potts snapshots without any fine tuning of parameters or artificial restrictions on ensemble choice. It provides a microscopic interpretation of the results of previous studies, which established a relation between the scaling behavior of snapshot entropy and the critical exponent. More importantly, it elucidates the role of ensemble disorder in restoring conformal invariance, an aspect previously ignored. Away from criticality, the breakdown of scale invariance leads to a renormalization of the parameter Σ in the random fractal Ansatz, whose variation can be used as an alternative determination of the critical exponent. We conclude by providing a recipe for the explicit construction of fractal unit cells consistent with a given scaling exponent.
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.
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
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.
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 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.
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.
Functional calcium imaging in developing cortical networks.
Dawitz, Julia; Kroon, Tim; Hjorth, J J Johannes; Meredith, Rhiannon M
2011-10-22
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
Landscape roughness analysis of Mt. Etna volcanic complex detected via fractal geometry
NASA Astrophysics Data System (ADS)
De Luca, Claudio; Bonfante, Antonello; Di Martino, Gerardo; Iodice, Antonio; Manzo, Mariarosaria; Pepe, Antonio; Pepe, Susi; Riccio, Daniele; Sansosti, Eugenio; Tizzani, Pietro; Zinno, Ivana
2013-04-01
During the last years several aspects relevant to volcanic activity have been analyzed in fractal context. These studies have been aimed at identifying the power laws that govern the magma fragmentation processes and/or the classification of different geological processes. In this work we exploit the algorithm proposed by Di Martino et al. (2012) that allows retrieving the fractal dimension of a natural surface starting from its corresponding Synthetic Aperture Radar (SAR) image. Such an algorithm is based on an analytical model that links the stochastic characterization of a single SAR amplitude image to the fractal dimension of the observed surface, modeled via a fractional Brownian motion (fBm) process. The considered SAR image processing provides - as an output product - the pixel by pixel map of the fractal dimension of the scene observed by the sensor. Previous works demonstrated that the fractal dimension of lava flows is strictly connected to the natural surface roughness. Moreover, Pepe et al. (2012) showed the possibility of characterizing the single volcanic structures by means of the fractal dimension values retrieved from the corresponding SAR images. In the present work we consider a data-set of Cosmo-SkyMed high resolution images acquired over the Mt. Etna volcanic complex (South Italy), spanning the 2009 - 2011 time period. Starting from the SAR amplitude images of the considered data-set, we generated the corresponding fractal dimension maps that were subsequently co-registered each other, thus retrieving the fractal dimension time-series of the Mt. Etna volcano. Then, by averaging the so-computed fractal dimension maps with respect to time we generated a map of the mean fractal dimension of the investigated area. This procedure allows significantly improving the quality of the final fractal dimension map, as the average operation reduces the noise (due to the speckle effect on SAR images) present on each fractal map. Besides, the so-obtained mean
Fractal behavior of traffic volume on urban expressway through adaptive fractal analysis
NASA Astrophysics Data System (ADS)
He, Hong-di; Wang, Jun-li; Wei, Hai-rui; Ye, Cheng; Ding, Yi
2016-02-01
In this paper, we investigate the fractal behavior of traffic volume in urban expressway based on a newly developed adaptive fractal analysis (AFA), which has a number of advantages over traditional method of detrended fluctuation analysis (DFA). Before fractal analysis, autocorrelation function was first adopted on traffic volume data and the long-range correlation behavior was found to be existed in both on-ramp and off-ramp situations. Then AFA as well as DFA was applied to further examine the fractal behavior. The results showed that the multifractality and the long-range anti-persistent behavior existed on both on-ramp and off-ramp. Additionally, multifractal analysis on weekdays and weekends are performed respectively and the results show that the degree of multifractality on weekdays is higher than that on weekends, implying that long-range correlation behaviors were more obvious on weekdays. Finally, the source of multifractality is examined with randomly shuffled and the surrogated series. Long-range correlation behaviors are identified in both on-ramp and off-ramp situations and fat-tail distributions were found to make little in the contributions of multifractality.
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
Tan, Wanyu; Li, Yongmei; Tan, Kaixuan; Duan, Xianzhe; Liu, Dong; Liu, Zehua
2016-12-01
Radon diffusion and transport through different media is a complex process affected by many factors. In this study, the fractal theories and field covering experiments were used to study the fractal characteristics of particle size distribution (PSD) of six kinds of geotechnical materials (e.g., waste rock, sand, laterite, kaolin, mixture of sand and laterite, and mixture of waste rock and laterite) and their effects on radon diffusion. In addition, the radon diffusion coefficient and diffusion length were calculated. Moreover, new formulas for estimating diffusion coefficient and diffusion length functional of fractal dimension d of PSD were proposed. These results demonstrate the following points: (1) the fractal dimension d of the PSD can be used to characterize the property of soils and rocks in the studies of radon diffusion behavior; (2) the diffusion coefficient and diffusion length decrease with increasing fractal dimension of PSD; and (3) the effectiveness of final covers in reducing radon exhalation of uranium tailings impoundments can be evaluated on the basis of the fractal dimension of PSD of materials.
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.
Thermal collapse of snowflake fractals
NASA Astrophysics Data System (ADS)
Gallo, T.; Jurjiu, A.; Biscarini, F.; Volta, A.; Zerbetto, F.
2012-08-01
Snowflakes are thermodynamically unstable structures that would ultimately become ice balls. To investigate their dynamics, we mapped atomistic molecular dynamics simulations of small ice crystals - built as filled von Koch fractals - onto a discrete-time random walk model. Then the walkers explored the thermal evolution of high fractal generations. The in silico experiments showed that the evolution is not entirely random. The flakes step down one fractal generation before forfeiting their architecture. The effect may be used to trace the thermal history of snow.
Functional anatomy and imaging of the foot.
Ridola, C; Palma, A
2001-01-01
) suspending the arch from a cable above the level of the bridge. In this manner, we obtain a "functional unit" with two important aims: to support the body weight (static foot), and to serve as a lever to propel the bodies forward in walking and running (dinamic foot). Imaging techniques are able to provide further data on functional anatomy of the foot; in particular, these techniques show the bones structures, ligaments, muscles and tendons, taking part to the arch setting. Routine x-ray examinations precise information about the bone-shape and their relationship. The short and long ligaments, the tendons and the suspending the arch from above are instead successfully valuable using ultrasonography, CT and MR.
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.
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.
Dynamic contact interactions of fractal surfaces
NASA Astrophysics Data System (ADS)
Jana, Tamonash; Mitra, Anirban; Sahoo, Prasanta
2017-01-01
Roughness parameters and material properties have significant influence on the static and dynamic properties of a rough surface. In the present paper, fractal surface is generated using the modified two-variable Weierstrass-Mandelbrot function in MATLAB and the same is imported to ANSYS to construct the finite element model of the rough surface. The force-deflection relationship between the deformable rough fractal surface and a contacting rigid flat is studied by finite element analysis. For the dynamic analysis, the contacting system is represented by a single degree of freedom spring mass-damper-system. The static force-normal displacement relationship obtained from FE analysis is used to determine the dynamic characteristics of the rough surface for free, as well as for forced damped vibration using numerical methods. The influence of fractal surface parameters and the material properties on the dynamics of the rough surface is also analyzed. The system exhibits softening property for linear elastic surface and the softening nature increases with rougher topography. The softening nature of the system increases with increase in tangent modulus value. Above a certain value of yield strength the nature of the frequency response curve is observed to change its nature from softening to hardening.
[Modeling continuous scaling of NDVI based on fractal theory].
Luan, Hai-Jun; Tian, Qing-Jiu; Yu, Tao; Hu, Xin-Li; Huang, Yan; Du, Ling-Tong; Zhao, Li-Min; Wei, Xi; Han, Jie; Zhang, Zhou-Wei; Li, Shao-Peng
2013-07-01
Scale effect was one of the very important scientific problems of remote sensing. The scale effect of quantitative remote sensing can be used to study retrievals' relationship between different-resolution images, and its research became an effective way to confront the challenges, such as validation of quantitative remote sensing products et al. Traditional up-scaling methods cannot describe scale changing features of retrievals on entire series of scales; meanwhile, they are faced with serious parameters correction issues because of imaging parameters' variation of different sensors, such as geometrical correction, spectral correction, etc. Utilizing single sensor image, fractal methodology was utilized to solve these problems. Taking NDVI (computed by land surface radiance) as example and based on Enhanced Thematic Mapper Plus (ETM+) image, a scheme was proposed to model continuous scaling of retrievals. Then the experimental results indicated that: (a) For NDVI, scale effect existed, and it could be described by fractal model of continuous scaling; (2) The fractal method was suitable for validation of NDVI. All of these proved that fractal was an effective methodology of studying scaling of quantitative remote sensing.
Use of fractal models in the Earth's remote sensing of the arctic zone
NASA Astrophysics Data System (ADS)
Berg, D. B.; Medvedev, A. N.; Manzhurov, I. L.; Taubaev, A. A.
2016-12-01
The development and practical application of new mathematical methods of processing, image analysis and pattern recognition has significant prospects for mapping the Earth from space. In the paper, it is proposed to use the fractal model of the surface contamination distribution, previously developed by the authors, for the analysis of color multispectral satellite images on the example of the territory of the Polar Urals. The research has shown the following: 1) The brightness distribution on remote sensing snapshot has a fractal character. 2) The values of fractal dimension of the territory images in different spectral ranges significantly differ. 3) The hierarchy of geomorphological structures in the range of 13-1700 m may be considered as self-similar. Thus, the proposed method of calculating the fractal dimension value of the snapshot may become one of the informative attributes for remote sensing images interpretation.
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
Dynamic ultrasound imaging applications to quantify musculoskeletal function.
Sikdar, Siddhartha; Wei, Qi; Cortes, Nelson
2014-07-01
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.
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.
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
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)
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
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.
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.
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
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.
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
Steady laminar flow of fractal fluids
NASA Astrophysics Data System (ADS)
Balankin, Alexander S.; Mena, Baltasar; Susarrey, Orlando; Samayoa, Didier
2017-02-01
We study laminar flow of a fractal fluid in a cylindrical tube. A flow of the fractal fluid is mapped into a homogeneous flow in a fractional dimensional space with metric induced by the fractal topology. The equations of motion for an incompressible Stokes flow of the Newtonian fractal fluid are derived. It is found that the radial distribution for the velocity in a steady Poiseuille flow of a fractal fluid is governed by the fractal metric of the flow, whereas the pressure distribution along the flow direction depends on the fractal topology of flow, as well as on the fractal metric. The radial distribution of the fractal fluid velocity in a steady Couette flow between two concentric cylinders is also derived.
Structural and Functional Imaging in Parkinsonian Syndromes
Hunt, Christopher H.; Johnson, Geoffrey B.; Morreale, Robert F.; Lowe, Val J.; Peller, Patrick J.
2014-01-01
Movement disorders with parkinsonian features are common, and in recent years imaging has assumed a greater role in diagnosis and management. Thus, it is important that radiologists become familiar with the most common imaging patterns of parkinsonism, especially given the significant clinical overlap and diagnostic difficulty associated with these disorders. The authors review the most common magnetic resonance (MR) and molecular imaging patterns of idiopathic Parkinson disease and atypical parkinsonian syndromes. They also discuss the interpretation of clinically available molecular imaging studies, including assessment of cerebral metabolism with 2-[fluorine-18]fluoro-2-deoxy-d-glucose (FDG) positron emission tomography (PET), cortical amyloid deposition with carbon 11 (11C) Pittsburgh compound B and fluorine 18 (18F) florbetapir PET, and dopaminergic activity with iodine 123 (123I) ioflupane single photon emission computed tomography (SPECT). Although no single imaging test is diagnostic, a combination of tests may help narrow the differential diagnosis. Findings at 123I ioflupane SPECT can confirm the loss of dopaminergic neurons in patients with parkinsonism and help distinguish these syndromes from treatable conditions, including essential tremor and drug-induced parkinsonism. FDG PET uptake can demonstrate patterns of neuronal dysfunction that are specific to a particular parkinsonian syndrome. Although MR imaging findings are typically nonspecific in parkinsonian syndromes, classic patterns of T2 signal change can be seen in multiple system atrophy and progressive supranuclear palsy. Finally, positive amyloid-binding PET findings can support the diagnosis of dementia with Lewy bodies. Combined with a thorough clinical evaluation, multimodality imaging information can afford accurate diagnosis, allow selection of appropriate therapy, and provide important prognostic information. ©RSNA, 2014 PMID:25208280
[Lithology feature extraction of CASI hyperspectral data based on fractal signal algorithm].
Tang, Chao; Chen, Jian-Ping; Cui, Jing; Wen, Bo-Tao
2014-05-01
Hyperspectral data is characterized by combination of image and spectrum and large data volume dimension reduction is the main research direction. Band selection and feature extraction is the primary method used for this objective. In the present article, the authors tested methods applied for the lithology feature extraction from hyperspectral data. Based on the self-similarity of hyperspectral data, the authors explored the application of fractal algorithm to lithology feature extraction from CASI hyperspectral data. The "carpet method" was corrected and then applied to calculate the fractal value of every pixel in the hyperspectral data. The results show that fractal information highlights the exposed bedrock lithology better than the original hyperspectral data The fractal signal and characterized scale are influenced by the spectral curve shape, the initial scale selection and iteration step. At present, research on the fractal signal of spectral curve is rare, implying the necessity of further quantitative analysis and investigation of its physical implications.
Analysis of fractal electrodes for efficient neural stimulation
Golestanirad, Laleh; Elahi, Behzad; Molina, Alberto; Mosig, Juan R.; Pollo, Claudio; Chen, Robert; Graham, Simon J.
2013-01-01
Planar electrodes are increasingly used in therapeutic neural stimulation techniques such as functional electrical stimulation, epidural spinal cord stimulation (ESCS), and cortical stimulation. Recently, optimized electrode geometries have been shown to increase the efficiency of neural stimulation by increasing the variation of current density on the electrode surface. In the present work, a new family of modified fractal electrode geometries is developed to enhance the efficiency of neural stimulation. It is shown that a promising approach in increasing the neural activation function is to increase the “edginess” of the electrode surface, a concept that is explained and quantified by fractal mathematics. Rigorous finite element simulations were performed to compute electric potential produced by proposed modified fractal geometries. The activation of 256 model axons positioned around the electrodes was then quantified, showing that modified fractal geometries required a 22% less input power while maintaining the same level of neural activation. Preliminary in vivo experiments investigating muscle evoked potentials due to median nerve stimulation showed encouraging results, supporting the feasibility of increasing neural stimulation efficiency using modified fractal geometries. PMID:23874290
Fractal analysis of bone architecture at distal radius.
Tomomitsu, Tatsushi; Mimura, Hiroaki; Murase, Kenya; Sone, Teruki; Fukunaga, Masao
2005-12-20
Bone strength depends on bone quality (architecture, turnover, damage accumulation, and mineralization) as well as bone mass. In this study, human bone architecture was analyzed using fractal image analysis, and the clinical relevance of this method was evaluated. The subjects were 12 healthy female controls and 16 female patients suspected of having osteoporosis (age range, 22-70 years; mean age, 49.1 years). High-resolution CT images of the distal radius were acquired and analyzed using a peripheral quantitative computed tomography (pQCT) system. On the same day, bone mineral densities of the lumbar spine (L-BMD), proximal femur (F-BMD), and distal radius (R-BMD) were measured by dual-energy X-ray absorptiometry (DXA). We examined the correlation between the fractal dimension and six bone mass indices. Subjects diagnosed with osteopenia or osteoporosis were divided into two groups (with and without vertebral fracture), and we compared measured values between these two groups. The fractal dimension correlated most closely with L-BMD (r=0.744). The coefficient of correlation between the fractal dimension and L-BMD was very similar to the coefficient of correlation between L-BMD and F-BMD (r=0.783) and the coefficient of correlation between L-BMD and R-BMD (r=0.742). The fractal dimension was the only measured value that differed significantly between both the osteopenic and the osteoporotic subjects with and without vertebral fracture. The present results suggest that the fractal dimension of the distal radius can be reliably used as a bone strength index that reflects bone architecture as well as bone mass.
Preliminary evidence for a theory of the fractal city.
Batty, M; Xie, Y
1996-10-01
"In this paper, we argue that the geometry of urban residential development is fractal. Both the degree to which space is filled and the rate at which it is filled follow scaling laws which imply invariance of function, and self-similarity of urban form across scale. These characteristics are captured in population density functions based on inverse power laws whose parameters are fractal dimensions. First we outline the relevant elements of the theory in terms of scaling relations and then we introduce two methods for estimating fractal dimension based on varying the size of cities and the scale at which their form is detected. Exact and statistical estimation techniques are applied to each method respectively generating dimensions which measure the extent and the rate of space filling. These methods are then applied to residential development patterns in six industrial cities in the northeastern United States...."
Synthetic turbulence, fractal interpolation, and large-eddy simulation.
Basu, Sukanta; Foufoula-Georgiou, Efi; Porté-Agel, Fernando
2004-08-01
Fractal interpolation has been proposed in the literature as an efficient way to construct closure models for the numerical solution of coarse-grained Navier-Stokes equations. It is based on synthetically generating a scale-invariant subgrid-scale field and analytically evaluating its effects on large resolved scales. In this paper, we propose an extension of previous work by developing a multiaffine fractal interpolation scheme and demonstrate that it preserves not only the fractal dimension but also the higher-order structure functions and the non-Gaussian probability density function of the velocity increments. Extensive a priori analyses of atmospheric boundary layer measurements further reveal that this multiaffine closure model has the potential for satisfactory performance in large-eddy simulations. The pertinence of this newly proposed methodology in the case of passive scalars is also discussed.
Functional imaging in treatment planning in radiation therapy: a review.
Perez, Carlos A; Bradley, Jeffrey; Chao, Clifford K S; Grigsby, Perry W; Mutic, Sasa; Malyapa, Robert
2002-01-01
The remarkable technical developments obtained in radiation oncology have resulted in an increasing use of image-based treatment planning in radiation therapy for three-dimensional and intensity modulated radiation therapy, stereotactic irradiation and image-guided brachytherapy. There has been increased use of computer-based record and verify systems as well as electronic portal imaging to enhance treatment delivery. From the data presented it is evident that PET scanning and other functional imaging techniques play a major role in the definition of tumor extent and staging of patients with cancer. The recent introduction of a combined CT and PET scanner will substantially simplify image acquisition and treatment planning.
Hyper-Fractal Analysis: A visual tool for estimating the fractal dimension of 4D objects
NASA Astrophysics Data System (ADS)
Grossu, I. V.; Grossu, I.; Felea, D.; Besliu, C.; Jipa, Al.; Esanu, T.; Bordeianu, C. C.; Stan, E.
2013-04-01
This work presents a new version of a Visual Basic 6.0 application for estimating the fractal dimension of images and 3D objects (Grossu et al. (2010) [1]). The program was extended for working with four-dimensional objects stored in comma separated values files. This might be of interest in biomedicine, for analyzing the evolution in time of three-dimensional images. New version program summaryProgram title: Hyper-Fractal Analysis (Fractal Analysis v03) Catalogue identifier: AEEG_v3_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEEG_v3_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC license, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 745761 No. of bytes in distributed program, including test data, etc.: 12544491 Distribution format: tar.gz Programming language: MS Visual Basic 6.0 Computer: PC Operating system: MS Windows 98 or later RAM: 100M Classification: 14 Catalogue identifier of previous version: AEEG_v2_0 Journal reference of previous version: Comput. Phys. Comm. 181 (2010) 831-832 Does the new version supersede the previous version? Yes Nature of problem: Estimating the fractal dimension of 4D images. Solution method: Optimized implementation of the 4D box-counting algorithm. Reasons for new version: Inspired by existing applications of 3D fractals in biomedicine [3], we extended the optimized version of the box-counting algorithm [1, 2] to the four-dimensional case. This might be of interest in analyzing the evolution in time of 3D images. The box-counting algorithm was extended in order to support 4D objects, stored in comma separated values files. A new form was added for generating 2D, 3D, and 4D test data. The application was tested on 4D objects with known dimension, e.g. the Sierpinski hypertetrahedron gasket, Df=ln(5)/ln(2) (Fig. 1). The algorithm could be extended, with minimum effort, to
The impact of functional imaging on radiation medicine.
Sharma, Nidhi; Neumann, Donald; Macklis, Roger
2008-09-15
Radiation medicine has previously utilized planning methods based primarily on anatomic and volumetric imaging technologies such as CT (Computerized Tomography), ultrasound, and MRI (Magnetic Resonance Imaging). In recent years, it has become apparent that a new dimension of non-invasive imaging studies may hold great promise for expanding the utility and effectiveness of the treatment planning process. Functional imaging such as PET (Positron Emission Tomography) studies and other nuclear medicine based assays are beginning to occupy a larger place in the oncology imaging world. Unlike the previously mentioned anatomic imaging methodologies, functional imaging allows differentiation between metabolically dead and dying cells and those which are actively metabolizing. The ability of functional imaging to reproducibly select viable and active cell populations in a non-invasive manner is now undergoing validation for many types of tumor cells. Many histologic subtypes appear amenable to this approach, with impressive sensitivity and selectivity reported. For clinical radiation medicine, the ability to differentiate between different levels and types of metabolic activity allows the possibility of risk based focal treatments in which the radiation doses and fields are more tightly connected to the perceived risk of recurrence or progression at each location. This review will summarize many of the basic principles involved in the field of functional PET imaging for radiation oncology planning and describe some of the major relevant published data behind this expanding trend.
Hu, Kun; Meijer, Johanna H; Shea, Steven A; vanderLeest, Henk Tjebbe; Pittman-Polletta, Benjamin; Houben, Thijs; van Oosterhout, Floor; Deboer, Tom; Scheer, Frank A J L
2012-01-01
The mammalian central circadian pacemaker (the suprachiasmatic nucleus, SCN) contains thousands of neurons that are coupled through a complex network of interactions. In addition to the established role of the SCN in generating rhythms of ~24 hours in many physiological functions, the SCN was recently shown to be necessary for normal self-similar/fractal organization of motor activity and heart rate over a wide range of time scales--from minutes to 24 hours. To test whether the neural network within the SCN is sufficient to generate such fractal patterns, we studied multi-unit neural activity of in vivo and in vitro SCNs in rodents. In vivo SCN-neural activity exhibited fractal patterns that are virtually identical in mice and rats and are similar to those in motor activity at time scales from minutes up to 10 hours. In addition, these patterns remained unchanged when the main afferent signal to the SCN, namely light, was removed. However, the fractal patterns of SCN-neural activity are not autonomous within the SCN as these patterns completely broke down in the isolated in vitro SCN despite persistence of circadian rhythmicity. Thus, SCN-neural activity is fractal in the intact organism and these fractal patterns require network interactions between the SCN and extra-SCN nodes. Such a fractal control network could underlie the fractal regulation observed in many physiological functions that involve the SCN, including motor control and heart rate regulation.
Learning a cost function for microscope image segmentation.
Nilufar, Sharmin; Perkins, Theodore J
2014-01-01
Quantitative analysis of microscopy images is increasingly important in clinical researchers' efforts to unravel the cellular and molecular determinants of disease, and for pathological analysis of tissue samples. Yet, manual segmentation and measurement of cells or other features in images remains the norm in many fields. We report on a new system that aims for robust and accurate semi-automated analysis of microscope images. A user interactively outlines one or more examples of a target object in a training image. We then learn a cost function for detecting more objects of the same type, either in the same or different images. The cost function is incorporated into an active contour model, which can efficiently determine optimal boundaries by dynamic programming. We validate our approach and compare it to some standard alternatives on three different types of microscopic images: light microscopy of blood cells, light microscopy of muscle tissue sections, and electron microscopy cross-sections of axons and their myelin sheaths.
Energy and Laplacian on Hanoi-type fractal quantum graphs
NASA Astrophysics Data System (ADS)
Alonso-Ruiz, Patricia; Kelleher, Daniel J.; Teplyaev, Alexander
2016-04-01
This article studies potential theory and spectral analysis on compact metric spaces, which we refer to as fractal quantum graphs. These spaces can be represented as a (possibly infinite) union of one-dimensional intervals and a totally disconnected (possibly uncountable) compact set, which roughly speaking represents the set of junction points. Classical quantum graphs and fractal spaces such as the Hanoi attractor are included among them. We begin with proving the existence of a resistance form on the Hanoi attractor, and go on to establish heat kernel estimates and upper and lower bounds on the eigenvalue counting function of Laplacians corresponding to weakly self-similar measures on the Hanoi attractor. These estimates and bounds rely heavily on the relation between the length and volume scaling factors of the fractal. We then state and prove a necessary and sufficient condition for the existence of a resistance form on a general fractal quantum graph. Finally, we extend our spectral results to a large class of weakly self-similar fractal quantum graphs.
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.
Fractal study and simulation of fracture roughness
Kumar, S.; Bodvarsson, G.S. )
1990-05-01
This study examines the roughness profiles of the surfaces of fractures and faults by using concepts from fractal geometry. Relationships between fractal characteristics of profiles and isotropic surfaces are analytically developed and a deterministic representation of the roughness is examined.
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.
The fractal aggregation of asphaltenes.
Hoepfner, Michael P; Fávero, Cláudio Vilas Bôas; Haji-Akbari, Nasim; Fogler, H Scott
2013-07-16
This paper discusses time-resolved small-angle neutron scattering results that were used to investigate asphaltene structure and stability with and without a precipitant added in both crude oil and model oil. A novel approach was used to isolate the scattering from asphaltenes that are insoluble and in the process of aggregating from those that are soluble. It was found that both soluble and insoluble asphaltenes form fractal clusters in crude oil and the fractal dimension of the insoluble asphaltene clusters is higher than that of the soluble clusters. Adding heptane also increases the size of soluble asphaltene clusters without modifying the fractal dimension. Understanding the process of insoluble asphaltenes forming fractals with higher fractal dimensions will potentially reveal the microscopic asphaltene destabilization mechanism (i.e., how a precipitant modifies asphaltene-asphaltene interactions). It was concluded that because of the polydisperse nature of asphaltenes, no well-defined asphaltene phase stability envelope exists and small amounts of asphaltenes precipitated even at dilute precipitant concentrations. Asphaltenes that are stable in a crude oil-precipitant mixture are dispersed on the nanometer length scale. An asphaltene precipitation mechanism is proposed that is consistent with the experimental findings. Additionally, it was found that the heptane-insoluble asphaltene fraction is the dominant source of small-angle scattering in crude oil and the previously unobtainable asphaltene solubility at low heptane concentrations was measured.
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
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
Synthesis, Analysis, and Processing of Fractal Signals
1991-10-01
fractal dimension of the underlying signal , when defined. Robust estimation of the fractal dimension of 1/f processes is important in a number of...modeling errors. The resulting parameter estimation algorithms, which compute both fractal dimension parameters and the accompanying signal and noise...Synthesis, Analysis, and Processing of Fractal Signals RLE Technical Report No. 566 Gregory W. Wornell October 1991 Research Laboratory of
Qian, A R; Li, D; Han, J; Gao, X; Di, S M; Zhang, W; Hu, L F; Shang, Peng
2012-05-01
Osteoblasts, the bone-forming cells, respond to various mechanical forces, such as stretch and fluid shear force in essentially similar ways. The cytoskeleton, as the load-bearing architecture of the cell, is sensitive to altered inertial forces. Disruption of the cytoskeleton will result in alteration of cellular structure and function. However, it is difficult to quantitatively illustrate cytoskeletal rearrangement because of the complexity of cytoskeletal structure. Usually, the morphological changes in actin organization caused by external stimulus are basically descriptive. In this study, fractal dimensions (D) analysis was used to quantify the morphological changes in the actin cytoskeleton of osteoblast-like cells (MC3T3-E1) under simulated microgravity using 3-D/2-D clinostats. The ImageJ software was used to count the fractal dimension of actin cytoskeleton by box-counting methods. Real-time PCR and immunofluroscent assays were used to further confirm the results obtained by fractal dimension analysis. The results showed significant decreases in D value of actin cytoskeleton, β-actin mRNA expression, and the mean fluorescence intensity of F-actin in osteoblast-like cells after 24 or 48 h of incubation under 3-D/2-D clinorotation condition compared with control. The findings indicate that 3-D/2-D clinorotation affects both actin cytoskeleton architecture and mRNA expression, and fractal may be a promising approach for quantitative analysis of the changes in cytoskeleton in different environments.
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.
Fractal analysis of microvascular networks in malignant brain tumors.
Di Ieva, Antonio
2012-01-01
Brain tumors are characterized by a microvascular network which differs from normal brain vascularity. Different tumors show individual angiogenic patterns. Microvascular heterogeneity can also be observed within a neoplastic histotype. It has been shown that quantification of neoplastic microvascular patterns could be used in combination with the histological grade for tumor characterization and to refine clinical prognoses, even if no objective parameters have yet been validated. To overcome the limits of the Euclidean approach, we employ fractal geometry to analyze the geometric complexity underlying the microangioarchitectural networks in brain tumors. We have developed a computer-aided fractal-based analysis for the quantification of the microvascular patterns in histological specimens and ultra-high-field (7-Tesla) magnetic resonance images. We demonstrate that the fractal parameters are valid estimators of microvascular geometrical complexity. Furthermore, our analysis allows us to demonstrate the high geometrical variability underlying the angioarchitecture of glioblastoma multiforme and to differentiate low-grade from malignant tumors in histological specimens and radiological images. Based on the results of this study, we speculate the existence of a gradient in the geometrical complexity of microvascular networks from those in the normal brain to those in malignant brain tumors. Here, we summarize a new methodology for the application of fractal analysis to the study of the microangioarchitecture of brain tumors; we further suggest this approach as a tool for quantifying and categorizing different neoplastic microvascular patterns and as a potential morphometric biomarker for use in clinical practice.
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.
Power-law hereditariness of hierarchical fractal bones.
Deseri, Luca; Di Paola, Mario; Zingales, Massimiliano; Pollaci, Pietro
2013-12-01
In this paper, the authors introduce a hierarchic fractal model to describe bone hereditariness. Indeed, experimental data of stress relaxation or creep functions obtained by compressive/tensile tests have been proved to be fit by power law with real exponent 0 ⩽ β ⩽1. The rheological behavior of the material has therefore been obtained, using the Boltzmann-Volterra superposition principle, in terms of real order integrals and derivatives (fractional-order calculus). It is shown that the power laws describing creep/relaxation of bone tissue may be obtained by introducing a fractal description of bone cross-section, and the Hausdorff dimension of the fractal geometry is then related to the exponent of the power law.
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.".
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 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.
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 properties of cancellous bone of the iliac crest in vertebral crush fracture.
Fazzalari, N L; Parkinson, I H
1998-07-01
Fractal analysis is a method for describing complex shapes, including the cancellous structure of bone. It describes the surface texture and form of individual trabecular profiles and the overall cancellous structure. Sixty-four postmenopausal women with symptoms of back pain were referred for investigation for osteoporosis. The patients were divided into two groups for comparison: vertebral crush fracture (n = 31, mean age 68.58 +/- 6.47 years), and no vertebral crush fracture (n = 33, mean age 63.36 +/- 7.21 years). Cores of cancellous bone, 3 mm in diameter, were taken from the iliac crest and sectioned. A box-counting method implemented on an image analyzer was used to measure the fractal dimension. Three fractal dimensions describing trabecular surface texture (fractal 1), trabecular shape (fractal 2), and trabecular arrangement (fractal 3) were measured, indicating that cancellous bone has sectional self-similarity. Conventional histomorphometry was also performed on the samples. The results show that fractal 2 is significantly lower in the vertebral crush fracture group than in the nonfracture group (1.15 +/- 0.10 < 1.23 +/- 0.090, p < 0.0013). The histomorphometric analysis shows that bone surface total volume (p < 0.0002), trabecular number (p < 0.0001), and osteoid surface bone surface (p < 0.028) are significantly lower in the fracture group than the nonfracture group. Eroded surface/bone surface (p < 0.056) follows this trend, whereas trabecular separation (p < 0.001) is significantly higher in the fracture group than in the nonfracture group. Fractal 1 and fractal 3 were not significantly different between study groups. The fractal dimension detects changes in the cancellous architecture and gives information about iliac bone transformation in postmenopausal women with vertebral fracture.
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.
Loew, M.H. )
1990-01-01
This book is covered under the following topics: human visual pattern recognition, fractals, rules, and segments, three-dimensional image processing, MRI, MRI and mammography, clinical applications 1, angiography, image processing systems, image processing poster session.
Technical considerations for functional magnetic resonance imaging analysis.
Conklin, Chris J; Faro, Scott H; Mohamed, Feroze B
2014-11-01
Clinical application of functional magnetic resonance imaging (fMRI) based on blood oxygenation level-dependent (BOLD) effect has increased over the past decade because of its ability to map regional blood flow in response to brain stimulation. This mapping is primarily achieved by exploiting the BOLD effect precipitated by changes in the magnetic properties of hemoglobin. BOLD fMRI has utility in neurosurgical planning and mapping neuronal functional connectivity. Conventional echo planar imaging techniques are used to acquire stimulus-driven fMR imaging BOLD data. This article highlights technical aspects of fMRI data analysis to make it more accessible in clinical settings.
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.
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.
Fractal mechanisms of light scattering in biological tissue and cells
NASA Astrophysics Data System (ADS)
Xu, M.; Alfano, R. R.
2005-11-01
We use fractal continuous random media to model visible and near-infrared light scattering by biological tissue and cell suspensions. The power law of the reduced scattering coefficient, the anisotropy factor of scattering, and the phase function are derived with good agreement with experimental results. Implications for spectroscopic tissue diagnosis are discussed.
Functional brain imaging in respiratory medicine.
Pattinson, Kyle
2015-06-01
Discordance of clinical symptoms with markers of disease severity remains a conundrum in a variety of respiratory conditions. The breathlessness of chronic lung disease correlates poorly with spirometry, yet is a better predictor of mortality. In chronic cough, symptoms are often evident without clear physical cause. In asthma, the terms 'over perceivers' and 'under perceivers' are common parlance. In all these examples, aberrant brain mechanisms may explain the mismatch between symptoms and pathology. Functional MRI is a non-invasive method of measuring brain function. It has recently become significantly advanced enough to be useful in clinical research and to address these potential mechanisms. This article explains how FMRI works, current understanding from FMRI in breathlessness, cough and asthma and suggests possibilities for future research.
Regional lung function and mechanics using image registration
NASA Astrophysics Data System (ADS)
Ding, Kai
The main function of the respiratory system is gas exchange. Since many disease or injury conditions can cause biomechanical or material property changes that can alter lung function, there is a great interest in measuring regional lung function and mechanics. In this thesis, we present a technique that uses multiple respiratory-gated CT images of the lung acquired at different levels of inflation with both breath-hold static scans and retrospectively reconstructed 4D dynamic scans, along with non-rigid 3D image registration, to make local estimates of lung tissue function and mechanics. We validate our technique using anatomical landmarks and functional Xe-CT estimated specific ventilation. The major contributions of this thesis include: (1) developing the registration derived regional expansion estimation approach in breath-hold static scans and dynamic 4DCT scans, (2) developing a method to quantify lobar sliding from image registration derived displacement field, (3) developing a method for measurement of radiation-induced pulmonary function change following a course of radiation therapy, (4) developing and validating different ventilation measures in 4DCT. The ability of our technique to estimate regional lung mechanics and function as a surrogate of the Xe-CT ventilation imaging for the entire lung from quickly and easily obtained respiratory-gated images, is a significant contribution to functional lung imaging because of the potential increase in resolution, and large reductions in imaging time, radiation, and contrast agent exposure. Our technique may be useful to detect and follow the progression of lung disease such as COPD, may be useful as a planning tool during RT planning, may be useful for tracking the progression of toxicity to nearby normal tissue during RT, and can be used to evaluate the effectiveness of a treatment post-therapy.
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.
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.
Designing fractal nanostructured biointerfaces for biomedical applications.
Zhang, Pengchao; Wang, Shutao
2014-06-06
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.
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.
Mahajan, A; Goh, V; Basu, S; Vaish, R; Weeks, A J; Thakur, M H; Cook, G J
2015-10-01
Ongoing research on malignant and normal cell biology has substantially enhanced the understanding of the biology of cancer and carcinogenesis. This has led to the development of methods to image the evolution of cancer, target specific biological molecules, and study the anti-tumour effects of novel therapeutic agents. At the same time, there has been a paradigm shift in the field of oncological imaging from purely structural or functional imaging to combined multimodal structure-function approaches that enable the assessment of malignancy from all aspects (including molecular and functional level) in a single examination. The evolving molecular functional imaging using specific molecular targets (especially with combined positron-emission tomography [PET] computed tomography [CT] using 2- [(18)F]-fluoro-2-deoxy-D-glucose [FDG] and other novel PET tracers) has great potential in translational research, giving specific quantitative information with regard to tumour activity, and has been of pivotal importance in diagnoses and therapy tailoring. Furthermore, molecular functional imaging has taken a key place in the present era of translational cancer research, producing an important tool to study and evolve newer receptor-targeted therapies, gene therapies, and in cancer stem cell research, which could form the basis to translate these agents into clinical practice, popularly termed "theranostics". Targeted molecular imaging needs to be developed in close association with biotechnology, information technology, and basic translational scientists for its best utility. This article reviews the current role of molecular functional imaging as one of the main pillars of translational research.
EANM/ESC guidelines for radionuclide imaging of cardiac function.
Hesse, B; Lindhardt, T B; Acampa, W; Anagnostopoulos, C; Ballinger, J; Bax, J J; Edenbrandt, L; Flotats, A; Germano, G; Stopar, T Gmeiner; Franken, P; Kelion, A; Kjaer, A; Le Guludec, D; Ljungberg, M; Maenhout, A F; Marcassa, C; Marving, J; McKiddie, F; Schaefer, W M; Stegger, L; Underwood, R
2008-04-01
Radionuclide imaging of cardiac function represents a number of well-validated techniques for accurate determination of right (RV) and left ventricular (LV) ejection fraction (EF) and LV volumes. These first European guidelines give recommendations for how and when to use first-pass and equilibrium radionuclide ventriculography, gated myocardial perfusion scintigraphy, gated PET, and studies with non-imaging devices for the evaluation of cardiac function. The items covered are presented in 11 sections: clinical indications, radiopharmaceuticals and dosimetry, study acquisition, RV EF, LV EF, LV volumes, LV regional function, LV diastolic function, reports and image display and reference values from the literature of RVEF, LVEF and LV volumes. If specific recommendations given cannot be based on evidence from original, scientific studies, referral is given to "prevailing or general consensus". The guidelines are designed to assist in the practice of referral to, performance, interpretation and reporting of nuclear cardiology studies for the evaluation of cardiac performance.
Dual-modality imaging of function and physiology
NASA Astrophysics Data System (ADS)
Hasegawa, Bruce H.; Iwata, Koji; Wong, Kenneth H.; Wu, Max C.; Da Silva, Angela; Tang, Hamilton R.; Barber, William C.; Hwang, Andrew B.; Sakdinawat, Anne E.
2002-04-01
Dual-modality imaging is a technique where computed tomography or magnetic resonance imaging is combined with positron emission tomography or single-photon computed tomography to acquire structural and functional images with an integrated system. The data are acquired during a single procedure with the patient on a table viewed by both detectors to facilitate correlation between the structural and function images. The resulting data can be useful for localization for more specific diagnosis of disease. In addition, the anatomical information can be used to compensate the correlated radionuclide data for physical perturbations such as photon attenuation, scatter radiation, and partial volume errors. Thus, dual-modality imaging provides a priori information that can be used to improve both the visual quality and the quantitative accuracy of the radionuclide images. Dual-modality imaging systems also are being developed for biological research that involves small animals. The small-animal dual-modality systems offer advantages for measurements that currently are performed invasively using autoradiography and tissue sampling. By acquiring the required data noninvasively, dual-modality imaging has the potential to allow serial studies in a single animal, to perform measurements with fewer animals, and to improve the statistical quality of the data.
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.
Real-time functional near-infrared imager
NASA Astrophysics Data System (ADS)
Luo, Qingming; Zeng, Shaoqun; Chance, Britton; Nioka, Shoko
1998-08-01
A real time functional Near-InfraRed Imager (fNIRI) was presented in this paper. We developed a continuous wave (cw) light imaging probe which includes 9 light sources and 4 pairs detectors (each pair has one 850 nm filtered detector and one 760 nm filtered detector). There are 16 measurement sections and total detection area is 9 cm X 4 cm. The detector- source uses 2.5 cm spacing. The light sources are controlled by a computer and the signals from the detectors are converted and processed in real time by the computer. The user-friendly software was programmed with Visual C++ language. Relative changes of oxy-Hb, Hb, and total blood concentration in 16 channels and the corresponding images combined by 16 channels could be displayed in real time on computer. With this cw imaging probe, we have measured motor function in motor cortex area, visual function in occipital area, and cognitive activity in frontal forehead area of the human brain 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, based upon changes of oxygenation and blood volume due to the stimulus.
Development of contrast-enhanced rodent imaging using functional CT
NASA Astrophysics Data System (ADS)
Liang, Yun; Stantz, Keith M.; Krishnamurthi, Ganapathy; Steinmetz, Rosemary; Hutchins, Gary D.
2003-05-01
Micro-computed tomography (microCT) is capable of obtaining high-resolution images of skeletal tissues. However its image contrast among soft tissues remains inadequate for tumor detection. High speed functional computed tomography will be needed to image tumors by employing x-ray contrast medium. The functional microCT development will not only facilitate the image contrast enhancement among different tissues but also provide information of tumor physiology. To demonstrate the feasibility of functional CT in mouse imaging, sequential computed tomography is performed in mice after contrast material administration using a high-speed clinical CT scanner. Although the resolution of the clinical scanner is not sufficient to dissolve the anatomic details of rodents, bulky physiological parameters in major organs such as liver, kidney, pancreas, and ovaries (testicular) can be examined. For data analysis, a two-compartmental model is employed and implemented to characterize the tissue physiological parameters (regional blood flow, capillary permeability, and relative compartment volumes.) The measured contrast dynamics in kidneys are fitted with the compartmental model to derive the kidney tissue physiology. The study result suggests that it is feasible to extract mouse tissue physiology using functional CT imaging technology.
Astrophysical fractals - An overview and prospects
NASA Technical Reports Server (NTRS)
Perdang, J.
1990-01-01
Different astrophysical circumstances under which fractal structures have been identified so far, or are likely to be identified in the future, are reviewed. The observed fractals can be classified into 2 main groups: (1) fractal configurations in space-time, materializing as fractals defined over the time axis at a given position in space, or over the physical configuration space at a fixed instant in time; and (2) fractals in parameter spaces. The theoretical interpretation of the origin of the spatial fractal geometry of the most conspicuous 'irregular' astronomical bodies is still wanting in the context of standard continuum models. In contrast, the less conventional discrete models (cellular automata) naturally produce such spatially fractal structures.
Emergence of fractal scaling in complex networks.
Wei, Zong-Wen; Wang, Bing-Hong
2016-09-01
Some real-world networks are shown to be fractal or self-similar. It is widespread that such a phenomenon originates from the repulsion between hubs or disassortativity. Here we show that this common belief fails to capture the causality. Our key insight to address it is to pinpoint links critical to fractality. Those links with small edge betweenness centrality (BC) constitute a special architecture called fractal reference system, which gives birth to the fractal structure of those reported networks. In contrast, a small amount of links with high BC enable small-world effects, hiding the intrinsic fractality. With enough of such links removed, fractal scaling spontaneously arises from nonfractal networks. Our results provide a multiple-scale view on the structure and dynamics and place fractality as a generic organizing principle of complex networks on a firmer ground.
Emergence of fractal scaling in complex networks
NASA Astrophysics Data System (ADS)
Wei, Zong-Wen; Wang, Bing-Hong
2016-09-01
Some real-world networks are shown to be fractal or self-similar. It is widespread that such a phenomenon originates from the repulsion between hubs or disassortativity. Here we show that this common belief fails to capture the causality. Our key insight to address it is to pinpoint links critical to fractality. Those links with small edge betweenness centrality (BC) constitute a special architecture called fractal reference system, which gives birth to the fractal structure of those reported networks. In contrast, a small amount of links with high BC enable small-world effects, hiding the intrinsic fractality. With enough of such links removed, fractal scaling spontaneously arises from nonfractal networks. Our results provide a multiple-scale view on the structure and dynamics and place fractality as a generic organizing principle of complex networks on a firmer ground.
NASA Astrophysics Data System (ADS)
Dellino, P.; Liotino, G.
2002-03-01
Image processing analysis is used to check the ability of the fractal dimension for quantitatively describing the shape of volcanic ash particles. Digitized scanning electron microscopy images of fine pyroclasts from the eruptions of Monte Pilato-Rocche Rosse (Lipari, Italy) are investigated to test the efficiency of the fractal dimension to discriminate between particles of different eruptive processes. Multivariate analysis of multiple fractal components allows distinction between magmatic particles and phreatomagmatic particles, which however is less significant than the discrimination obtained in previous studies by the use of simple 'adimensional' shape parameters. Approximation of the actual particle boundary and the not rotation invariant nature of the fractal data frequently result in a significant scatter of data points in the Mandelbrot-Richardson plot. Such behavior obscures in some cases the actual information of particle shape and renders the discriminating power of fractal analysis less effective than classical shape descriptors. Data less affected by scatter reveal that phreatomagmatic particles of the Monte Pilato-Rocche Rosse eruptions are true (mono) fractals, whereas magmatic particles are multifractals. The textural (small-scale) fractal of magmatic particles is similar to the fractal dimension value of phreatomagmatic particles, and is attributed to the rheological behavior of melt upon brittle fragmentation. The structural (large-scale) fractal of magmatic particles refers to the walls of ruptured vesicles that lay on the particle outline. The high difference between the values of the textural and structural fractals of magmatic particles of the Monte Pilato-Rocche Rosse eruptions suggests two distinct and independent processes in the formation of such pyroclasts. At the scales corresponding to the textural fractal, the fragmentation process is independent of vesicles. Magmatic fragmentation is not simply related to growth, expansion
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.
Yanagawa, Fumiki; Onuki, Yoshinori; Morishita, Mariko; Takayama, Kozo
2006-01-10
Fractal geometry was applied to quantify the complexity of an internal structure of porous membranes prepared with poly(2-hydroxyethyl methacrylate) (pHEMA). The porous pHEMA membranes were synthesized by means of free-radical solution polymerization. Boundary lines of the porous structures in the pHEMA membrane were taken by a scanning electron microscope as image data, and these images were fed into a computer to estimate the fractal dimension. The boundary images of porous pHEMA membranes were observed to be a typical fractal and their complexity was quantified as a non-integral fractal dimension. The permeation of fluorescein isothiocyanate-labeled dextran, molecular weight 4400 (FD-4) as a model penetrant through the porous pHEMA membrane was determined using water-jacket type two-chamber diffusion cells. A fairly good negative relationship between the permeability coefficient of FD-4 and the fractal dimension was observed, suggesting the usefulness of the fractal dimension as a novel means for evaluating solute permeation through the porous membranes.
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
2016-02-15
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.
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…
Application of fractal theory in analysis of human electroencephalographic signals.
Paramanathan, P; Uthayakumar, R
2008-03-01
In medical discipline, complexity measure is focused on the analysis of nonlinear patterns in processing waveform signals. The complexity measure of such waveform signals is well performed by fractal dimension technique, which is an index for measuring the complexity of an object. Its applications are found in diverse fields like medical, image and signal processing. Several algorithms have been suggested to compute the fractal dimension of waveforms. We have evaluated the performance of the two famous algorithms namely Higuchi and Katz. They contain some problems of determining the initial and final length of scaling factors and their performance with electroencephalogram (EEG) signals did not give better results. In this paper, fractal dimension is proposed as an effective tool for analyzing and measuring the complexity of nonlinear human EEG signals. We have developed an algorithm based on size measure relationship (SMR) method. The SMR algorithm can be used to detect the brain disorders and it locates the affected brain portions by analyzing the behavior of signals. The efficiency of the algorithm to locate the critical brain sites (recurrent seizure portion) is compared to other fractal dimension algorithms. The K-means clustering algorithm is used for grouping of electrode positions.
[Imaging evaluation of renal function: principles and limitations].
Vivier, P-H; Dolores, M; Le Cloirec, J; Beurdeley, M; Liard, A; Elbaz, F; Roset, J-B; Dacher, J-N
2011-04-01
The kidney performs multiple functions. Glomerular filtration is the most studied of these functions. In clinical practice, the surgical indication for patients with unilateral uropathy is frequently based on the split renal function as demonstrated by scintigraphy. MRI is not yet validated as a technique but nonetheless offers an interesting non-radiating alternative to achieve both morphological and functional renal evaluation. Recent pulse sequences such as diffusion, arterial spin labeling, and blood oxygenation dependent imaging may also provide additional information. CT and US remain of limited value for the evaluation of renal function.
Imaging P-to-S conversions with multichannel receiver functions
NASA Astrophysics Data System (ADS)
Neal, Scott L.; Pavlis, Gary L.
We present a new methodology in the direct imaging of P-to-S converted phases recorded on broadband seismic arrays. Our approach is based on conventional three-component array processing and receiver function techniques with the key addition of a weighted stack based on an aerial smoothing function. This creates synthetic arrays with a specified aperture whose image points vary continuously across the array. With this approach, it is possible to interpolate data from an array of broadband stations onto an arbitrarily fine grid. We have applied this technique to a single deep event recorded by the Lodore broadband array, located in northern Colorado and southern Wyoming. The resulting images show distinct differences in crustal structure across the array, and also image major upper mantle discontinuities.
Functional imaging of tumor vascular network in small animal models
NASA Astrophysics Data System (ADS)
Kalchenko, Vyacheslav; Madar-Balakirski, Noa; Kuznetsov, Yuri; Meglinski, Igor; Harmelin, Alon
2011-07-01
In current report we present synchronized in vivo imaging of tumor vascular network and tumor microenvironment obtained by combined use of Dynamic Light Scattering Imaging, Spectrally Enhanced Microscopy, and Fluorescence Intravital Microscopy. Dynamic Light Scattering Imaging is used for functional imaging of the vascular network and blood microcirculation. Spectrally Enhanced Microscopy provides information regarding blood vessel topography. Fluorescence Intravital Microscopy is used for imaging of tumor microvasculature and tumor microenvironment. These well known modalities have been comprehensively validated in the past and are widely used in various bio-medical applications. As shown here, their combined application has great potential for studies of vascular biology. This multi-modal non-invasive diagnostic technique expands our current capacity to investigate blood microcirculation and tumor angiogenesis in vivo, thereby contributing to the development of cancer research and treatment.
Insights into dendritic cell function using advanced imaging modalities.
Vyas, Jatin M
2012-11-15
The application of advanced imaging techniques to fundamental questions in immunology has provided insight into dendritic cell function and has challenged dogma created using static imaging of lymphoid tissue. The history of dendritic cell biology has a storied past and is tightly linked to imaging. The development of imaging techniques that emphasize live cell imaging in situ has provided not only breath-taking movies, but also novel insights into the importance of spatiotemporal relationships between antigen presenting cells and T cells. This review serves to provide a primer on two-photon microscopy, TIRF microscopy, spinning disk confocal microscopy and optical trapping and provides selective examples of insights gained from these tools on dendritic cell biology.
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.
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.
Emerging concepts in functional and molecular photoacoustic imaging.
Hu, Song
2016-08-01
Providing the specific imaging contrast of optical absorption and excellent spatial scalability across the optical and ultrasonic dimensions, photoacoustic imaging has been rapidly emerging and expanding in the past two decades. In this review, I focus on a few latest advances in this enabling technology that hold the potential to transform in vivo functional and molecular imaging at multiple length scales. Specifically, multi-parametric photoacoustic microscopy enables simultaneous high-resolution mapping of hemoglobin concentration, oxygen saturation and blood flow-opening up the possibility of quantifying the metabolic rate of oxygen at the microscopic level. The pump-probe approach harnesses a variety of photoinduced transient optical absorption as novel contrast mechanisms for high-specificity molecular imaging at depth and as nonlinear excitation strategies for high-resolution volumetric microscopy beyond the conventional limit. Novel magneto-optical and photochromic probes lead to contrast-enhanced molecular photoacoustic imaging through differential detection.
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
Pu, Yang; Wang, Wubao; Al-Rubaiee, Mohammad; Gayen, Swapan Kumar; Xu, Min
2012-07-01
Optical extinction and diffuse reflection spectra of cancerous and normal prostate tissues in the 750 to 860 nm spectral range were measured. Optical extinction measurements using thin ex vivo prostate tissue samples were used to determine the scattering coefficient (μ(s)), while diffuse reflection measurements using thick prostate tissue samples were used to extract the absorption coefficient (μ(a)) and the reduced scattering coefficient (μ'(s)). The anisotropy factor (g) was obtained using the extracted values of μ(s) and μ'(s). The values of fractal dimension (D(f)) of cancerous and normal prostate tissues were obtained by fitting to the wavelength dependence of μ'(s). The number of scattering particles contributing to μ(s) as a function of particle size and the cutoff diameter d(max) as a function of g were investigated using the fractal soft tissue model and Mie theory. Results show that d(max) of the normal tissue is larger than that of the cancerous tissue. The cutoff diameter d(max) is observed to agree with the nuclear size for the normal tissues and the nucleolar size for the cancerous tissues. Transmission spectral polarization imaging measurements were performed that could distinguish the cancerous prostate tissue samples from the normal tissue samples based on the differences between their absorption and scattering parameters.
Fractal scaling and fluid flow in fracture networks in rock
Barton, C.C.
1996-12-31
Recovery of oil and gas resources and injection of toxic waste materials requires quantitative models to describe and predict the movement of fluids in rock. Existing models based on pore-space flow are inappropriate for study of the more rapid process of fluid flow through fracture networks. This type of flow is not a simple function of the fracture characteristics at any particular scale, but rather the integration of fracture contributions at all scales. The mathematical constructs of fractal geometry are well suited to quantify and model relationships within complex systems that are statistically self-similar over a wide range of scales. Analyses show that fracture traces mapped on two-dimensional slices through three-dimensional nature fracture networks in rock follow a fractal scaling law over six orders of magnitude. Detailed measurements of 17 two-dimensional samples of fracture networks (at diverse scales in rocks of dissimilar age, lithology, and tectonic setting) show similar fractal dimensions in the range 1.3-1.7. The range in fractal dimension implies that a single physical process of rock fracturing operates over a wide range of scales, from microscopic cracks to large, regional fault systems. The knowledge that rock-fracture networks are fractal allows the use of data from a one-dimensional drill-hole sample to predict the two- and three-dimensional scaling of the fracture system. The spacing of fractures in drill holes is a fractal Cantor distribution, and the range of fractal dimension is 0.4-0.6, which is an integer dimension less than that of fracture-trace patterns exposed on two-dimensional, planar sections. A reconstruction of the fracture history at the point of initial connectivity across the network (percolation) has a fractal dimension of 1.35 as compared to a dimension of 1.9 for the percolation cluster in a two-dimensional model. Paleo flow was mapped based on the deposition of aqueous minerals on the fracture surface.
Fractal scaling and fluid flow in fracture networks in rock
Barton, C.C. )
1996-01-01
Recovery of oil and gas resources and injection of toxic waste materials requires quantitative models to describe and predict the movement of fluids in rock. Existing models based on pore-space flow are inappropriate for study of the more rapid process of fluid flow through fracture networks. This type of flow is not a simple function of the fracture characteristics at any particular scale, but rather the integration of fracture contributions at all scales. The mathematical constructs of fractal geometry are well suited to quantify and model relationships within complex systems that are statistically self-similar over a wide range of scales. Analyses show that fracture traces mapped on two-dimensional slices through three-dimensional nature fracture networks in rock follow a fractal scaling law over six orders of magnitude. Detailed measurements of 17 two-dimensional samples of fracture networks (at diverse scales in rocks of dissimilar age, lithology, and tectonic setting) show similar fractal dimensions in the range 1.3-1.7. The range in fractal dimension implies that a single physical process of rock fracturing operates over a wide range of scales, from microscopic cracks to large, regional fault systems. The knowledge that rock-fracture networks are fractal allows the use of data from a one-dimensional drill-hole sample to predict the two- and three-dimensional scaling of the fracture system. The spacing of fractures in drill holes is a fractal Cantor distribution, and the range of fractal dimension is 0.4-0.6, which is an integer dimension less than that of fracture-trace patterns exposed on two-dimensional, planar sections. A reconstruction of the fracture history at the point of initial connectivity across the network (percolation) has a fractal dimension of 1.35 as compared to a dimension of 1.9 for the percolation cluster in a two-dimensional model. Paleo flow was mapped based on the deposition of aqueous minerals on the fracture surface.
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.
Sensitivity analysis of near-infrared functional lymphatic imaging
Weiler, Michael; Kassis, Timothy
2012-01-01
Abstract. 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. PMID:22734775
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 renal imaging: new trends in radiology and nuclear medicine.
Durand, Emmanuel; Chaumet-Riffaud, Philippe; Grenier, Nicolas
2011-01-01
The objective of this work is to compare the characteristics of various techniques for functional renal imaging, with a focus on nuclear medicine and magnetic resonance imaging. Even with low spatial resolution and rather poor signal-to-noise ratio, classical nuclear medicine has the advantage of linearity and good sensitivity. It remains the gold standard technique for renal relative functional assessment. Technetium-99m ((99m)Tc)-labeled diethylenetriamine penta-acetate remains the reference glomerular tracer. Tubular tracers have been improved: (123)I- or (131)I-hippuran, (99m)Tc-MAG3 and, recently, (99m)Tc-nitrilotriacetic acid. However, advancement in molecular imaging has not produced a groundbreaking tracer. Renal magnetic resonance imaging with classical gadolinated tracers probably has potential in this domain but has a lack of linearity and, therefore, its value still needs evaluation. Moreover, the advent of nephrogenic systemic fibrosis has delayed its expansion. Other developments, such as diffusion or blood oxygen level-dependent imaging, may have a role in the future. The other modalities have a limited role in clinical practice for functional renal imaging.
Embedding based on function approximation for large scale image search.
Do, Thanh-Toan; Cheung, Ngai-Man
2017-03-23
The objective of this paper is to design an embedding method that maps local features describing an image (e.g. SIFT) to a higher dimensional representation useful for the image retrieval problem. First, motivated by the relationship between the linear approximation of a nonlinear function in high dimensional space and the stateof- the-art feature representation used in image retrieval, i.e., VLAD, we propose a new approach for the approximation. The embedded vectors resulted by the function approximation process are then aggregated to form a single representation for image retrieval. Second, in order to make the proposed embedding method applicable to large scale problem, we further derive its fast version in which the embedded vectors can be efficiently computed, i.e., in the closed-form. We compare the proposed embedding methods with the state of the art in the context of image search under various settings: when the images are represented by medium length vectors, short vectors, or binary vectors. The experimental results show that the proposed embedding methods outperform existing the state of the art on the standard public image retrieval benchmarks.
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.
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.
Predicting beauty: fractal dimension and visual complexity in art.
Forsythe, A; Nadal, M; Sheehy, N; Cela-Conde, C J; Sawey, M
2011-02-01
Visual complexity has been known to be a significant predictor of preference for artistic works for some time. The first study reported here examines the extent to which perceived visual complexity in art can be successfully predicted using automated measures of complexity. Contrary to previous findings the most successful predictor of visual complexity was Gif compression. The second study examined the extent to which fractal dimension could account for judgments of perceived beauty. The fractal dimension measure accounts for more of the variance in judgments of perceived beauty in visual art than measures of visual complexity alone, particularly for abstract and natural images. Results also suggest that when colour is removed from an artistic image observers are unable to make meaningful judgments as to its beauty.
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.
Design and implementation of non-linear image processing functions for CMOS image sensor
NASA Astrophysics Data System (ADS)
Musa, Purnawarman; Sudiro, Sunny A.; Wibowo, Eri P.; Harmanto, Suryadi; Paindavoine, Michel
2012-11-01
Today, solid state image sensors are used in many applications like in mobile phones, video surveillance systems, embedded medical imaging and industrial vision systems. These image sensors require the integration in the focal plane (or near the focal plane) of complex image processing algorithms. Such devices must meet the constraints related to the quality of acquired images, speed and performance of embedded processing, as well as low power consumption. To achieve these objectives, low-level analog processing allows extracting the useful information in the scene directly. For example, edge detection step followed by a local maxima extraction will facilitate the high-level processing like objects pattern recognition in a visual scene. Our goal was to design an intelligent image sensor prototype achieving high-speed image acquisition and non-linear image processing (like local minima and maxima calculations). For this purpose, we present in this article the design and test of a 64×64 pixels image sensor built in a standard CMOS Technology 0.35 μm including non-linear image processing. The architecture of our sensor, named nLiRIC (non-Linear Rapid Image Capture), is based on the implementation of an analog Minima/Maxima Unit. This MMU calculates the minimum and maximum values (non-linear functions), in real time, in a 2×2 pixels neighbourhood. Each MMU needs 52 transistors and the pitch of one pixel is 40×40 mu m. The total area of the 64×64 pixels is 12.5mm2. Our tests have shown the validity of the main functions of our new image sensor like fast image acquisition (10K frames per second), minima/maxima calculations in less then one ms.
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
NASA Astrophysics Data System (ADS)
Arnholt, Jeff C.; Hanson, Dennis P.; Robb, Richard A.
1995-05-01
NIFTY (NeuroImaging Functional Toolkit) is a tool designed to perform quantitative analysis and visualization of neurofunctional magnetic resonance image (fMRI) data sets. NIFTY is an OSF/Motif application which utilizes the AVW (a visualization workshop) imaging library developed in our laboratory and includes algorithms for robust image registration, statistical analysis, and mapping of neurofunctional data sets. Anisotropic diffusion routines can be used to enhance the signal-to-noise- ratio of these images. Tools capable of histogram equalization, thresholding, volume rendering, atlas matching, and a large number of other functions can then be used to visualize the data. NIFTY's development will offer a robust and flexible system of essential functions integrated into an interactive, graphically-oriented program, allowing neuroscientists the means by which to process, visualize, and interpret their data.
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.
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.
Order-fractal transitions in abstract paintings
Calleja, E.M. de la; Cervantes, F.; Calleja, J. de la
2016-08-15
In this study, we determined the degree of order for 22 Jackson Pollock paintings using the Hausdorff–Besicovitch fractal dimension. Based on the maximum value of each multi-fractal spectrum, the artworks were classified according to the year in which they were painted. It has been reported that Pollock’s paintings are fractal and that this feature was more evident in his later works. However, our results show that the fractal dimension of these paintings ranges among values close to two. We characterize this behavior as a fractal-order transition. Based on the study of disorder-order transition in physical systems, we interpreted the fractal-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. -- Highlights: •We determined the degree of order in Jackson Pollock paintings using the Hausdorff–Besicovitch dimension. •We detected a fractal-order transition from Pollock’s paintings between 1947 and 1951. •We suggest that Jackson Pollock could have painted Teri’s Find.
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.
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.
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.
Signal and image processing techniques for functional near-infrared imaging of the human brain
Toronov, Vladislav Y.; Zhang, Xiaofeng; Fabiani, Monica; Gratton, Gabriele; Webb, Andrew G.
2011-01-01
Near-infrared spectro-imaging (NIRSI) is a quickly developing method for the in-vivo imaging of biological tissues. In particular, it is now extensively employed for imaging the human brain. In this non-invasive technique, the information about the brain is obtained from the analysis of spatial light bundles formed by the photons traveling from light sources to detectors placed on the surface of the head. Most significant problems in the functional brain NIRSI are the separation of the brain information from the physiological noise in non-cerebral tissues, and the localization of functional signals. In this paper we describe signal and image processing techniques we developed in order to measure two types of functional cerebral signals: the hemodynamic responses, and neuronal responses. PMID:21738383
Signal and image processing techniques for functional near-infrared imaging of the human brain
NASA Astrophysics Data System (ADS)
Toronov, Vladislav Y.; Zhang, Xiaofeng; Fabiani, Monica; Gratton, Gabriele; Webb, Andrew G.
2005-03-01
Near-infrared spectro-imaging (NIRSI) is a quickly developing method for the in-vivo imaging of biological tissues. In particular, it is now extensively employed for imaging the human brain. In this non-invasive technique, the information about the brain is obtained from the analysis of spatial light bundles formed by the photons traveling from light sources to detectors placed on the surface of the head. Most significant problems in the functional brain NIRSI are the separation of the brain information from the physiological noise in non-cerebral tissues, and the localization of functional signals. In this paper we describe signal and image processing techniques we developed in order to measure two types of functional cerebral signals: the hemodynamic responses, and neuronal responses.
NASA Astrophysics Data System (ADS)
Greynolds, Alan W.
2016-09-01
Previous research on optical surface scatter either assumed for the ACV (Auto-Covariance function) a simple analytical but unrealistic Gaussian form or depended on intensive numerical integrations. Measurements of polished optical surfaces indicate they accurately follow a simple inverse power law for the BSDF (Bi-directional Scatter Distribution Function) and the related PSD (Power Spectral Density) of their random height variations, i.e. they are fractal-like. By applying the appropriate limits to the scale-invariant (no intrinsic correlation length) PSD, a general analytic form for the corresponding ACV and STF (Surface or Scatter Transfer Function) can be derived. Combined with other Fourier-Bessel transform pairs, it's possible to accurately simulate the effect of not only diffraction and aberrations such as defocus (via the system OTF or Optical Transfer Function) but also surface and particulate scatter on the incoherent imaging of highcontrast fine-detail scenes. Simple examples of Gaussian and point objects are first presented followed by application to digital cameras that require integrating the aerial image over each pixel's active area. The needed subsampling for a camera with over ten million pixels (each only few microns in size) requires two-dimensional FFTs (Fast Fourier Transforms) of many gigabytes to accurately perform the detailed imaging calculations.
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
Noninvasive structural, functional, and molecular imaging in drug development.
Rudin, Markus
2009-06-01
Modern drug research is mechanism-based and the development of disease modifying therapies involves the identification of molecular key players in the pathological cascade. Today, noninvasive imaging tools enable the visualization and quantitative assessment of the expression of molecular targets, of their interaction with potential ligands, as well as of the functional consequence of this interaction at a molecular (e.g. activation of signaling cascades), cellular, metabolic, physiological, and morphological level in a temporo-spatially resolved manner. The ability to gather such information from the intact organism with all regulatory processes in place renders imaging highly attractive for the biomedical researcher and for the drug developer in particular. Molecular imaging is potentially capable of providing this information. Today, proof-of-principle has been established that imaging is in fact adding value to the drug discovery and development processes. Numerous studies have used structural and functional imaging readouts to document therapy efficacy, mainly during lead optimization. Similarly, major efforts have been devoted to the development and evaluation of imaging biomarkers that might serve as early readouts for therapy response with the potential of being used in the clinical drug evaluation thereby facilitating translational research. In this contribution, we illustrate the role and potential of imaging in modern drug discovery and development with selected examples. Yet, despite its huge potential the impact of imaging on drug discovery has been modest in the past; potential reasons will be discussed. Nevertheless, noninvasive imaging methods are rapidly evolving and it is beyond doubt that their importance for biomedical research will increase.
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.