The Experts below are selected from a list of 327 Experts worldwide ranked by ideXlab platform
E. S. Gelsema - One of the best experts on this subject based on the ideXlab platform.
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Estimation of Fractal Dimension in radiographs
Medical physics, 1996Co-Authors: Jifke F. Veenland, J. L. Grashuis, Fb Van Der Meer, A. L. D. Beckers, E. S. GelsemaAbstract:In the last decade, the Fractal Dimension has become a popular parameter to characterize image textures. Also in radiographs, various procedures have been used to estimate the Fractal Dimension. However, certain characteristics of the radiographic process, e.g., noise and blurring, interfere with the straightforward application of these estimation methods. In this study, the influence of quantum noise and image blur on several estimation methods was quantified by simulating the effect of quantum noise and the effect of modulation transfer functions, corresponding with different screen-film combinations, on computer generated Fractal images. The results are extrapolated to explain the effect of film-grain noise on Fractal Dimension estimation. The effect of noise is that, irrespective of the noise source, the Fractal Dimension is overestimated, especially for lower Fractal Dimensions. On the other hand, blurring results in an underestimation of the Dimensions. The effect of blurring is dependent on the estimation method used; the Dimension estimates by the power spectrum method are lowered with a constant value, whereas the underestimation by the methods working in the spatial domain is dependent on the given Dimension. The influence of the MTF and noise on Fractal Dimension estimation seriously limits the comparability of Fractal Dimensions estimated from radiographs which differ in noise content or MTF. Only when the power spectrum method is used, it is possible to correct for the influence of different MTFs of screen-film combinations. It is concluded that only when using the same object-focus distance, the same exposure conditions, the same digitizer at the same resolution, can Fractal Dimensions as estimated in radiographs be reliably compared.
Rephael Wenger - One of the best experts on this subject based on the ideXlab platform.
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The Nature of the Isosurface Fractal Dimension
2012Co-Authors: Marc Khoury, Tamal K. Dey, Yusu Wang, Rephael WengerAbstract:A 3D scalar grid is a grid of vertices where each vertex is associated with some scalar value. The grid covers some rectilinear region and partitions that region into cubes. An isosurface for a given isovalue is a triangular mesh which approximates the level set for the isovalue. The size of an isosurface is the number of triangles in the isosurfaces mesh, while the size of a scalar grid is the number of cubes. The relationship between these two quantities describes the complexity of the isosurface. We introduce the Fractal Dimension of an isosurface and show that it is a powerful metric for describing the complexity of an isosurface. Computing the isosurface Fractal Dimension for 60 benchmark data sets, we determine the average growth rate of an isosurface mesh. The number of connected components in an isosurface mesh gives a measure of the topological noise in the data set. We show that there is a high correlation between the Fractal Dimension and topological noise present in isosurface meshes. To better describe the relationship between noise and Fractal Dimension, we employ probabilistic methods to derive a formula for the Fractal Dimension as a function of uniform noise present in a data set. We can restrict our definition of isosurface Fractal Dimension to a small local region and compute the Fractal Dimension for a local region around each vertex. The local isosurface Fractal Dimension gives a measure of the complexity of the isosurface in small regions of the grid. This method can be used for identification of noisy regions in an isosurface mesh. Noise filtering techniques can take advantage of this identification technique to more effectively remove noise from scalar data. Lastly we present an isosurface construction algorithm that moves the isosurface away from noisy regions in the grid to produce a smooth mesh.
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On the Fractal Dimension of Isosurfaces
IEEE transactions on visualization and computer graphics, 2010Co-Authors: Marc Khoury, Rephael WengerAbstract:A (3D) scalar grid is a regular n1 × n2 × n3 grid of vertices where each vertex v is associated with some scalar value sv. Applying trilinear interpolation, the scalar grid determines a scalar function g where g(v) = sv for each grid vertex v. An isosurface with isovalue σ is a triangular mesh which approximates the level set g-1 (σ). The Fractal Dimension of an isosurface represents the growth in the isosurface as the number of grid cubes increases. We define and discuss the Fractal isosurface Dimension. Plotting the Fractal Dimension as a function of the isovalues in a data set provides information about the isosurfaces determined by the data set. We present statistics on the average Fractal Dimension of 60 publicly available benchmark data sets. We also show the Fractal Dimension is highly correlated with topological noise in the benchmark data sets, measuring the topological noise by the number of connected components in the isosurface. Lastly, we present a formula predicting the Fractal Dimension as a function of noise and validate the formula with experimental results.
Yong Deng - One of the best experts on this subject based on the ideXlab platform.
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Fuzzy Fractal Dimension of complex networks
Applied Soft Computing, 2014Co-Authors: Haixin Zhang, Sankaran Mahadevan, Xin Lan, Yong DengAbstract:Graphical abstractDisplay Omitted HighlightsA new Fractal Dimensional model based on fuzzy sets theory is proposed.The complexity in our model reduced significantly from NP-hard problems.This model could obtain a deterministic Fractal Dimension for a certain network. Complex networks are widely used to describe the structure of many complex systems in nature and society. The box-covering algorithm is widely applied to calculate the Fractal Dimension, which plays an important role in complex networks. However, there are two open issues in the existing box-covering algorithms. On the one hand, to identify the minimum boxes for any given size belongs to a family of Non-deterministic Polynomial-time hard problems. On the other hand, there exists randomness. In this paper, a fuzzy Fractal Dimension model of complex networks with fuzzy sets is proposed. The results are illustrated to show that the proposed model is efficient and less time consuming.
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box covering algorithm for Fractal Dimension of weighted networks
Scientific Reports, 2013Co-Authors: Daijun Wei, Qi Liu, Haixin Zhang, Yong Deng, Sankaran MahadevanAbstract:Box-covering algorithm is a widely used method to measure the Fractal Dimension of complex networks. Existing researches mainly deal with the Fractal Dimension of unweighted networks. Here, the classical box covering algorithm is modified to deal with the Fractal Dimension of weighted networks. Box size length is obtained by accumulating the distance between two nodes connected directly and graph-coloring algorithm is based on the node strength. The proposed method is applied to calculate the Fractal Dimensions of the “Sierpinski” weighted Fractal networks, the E.coli network, the Scientific collaboration network, the C.elegans network and the USAir97 network. Our results show that the proposed method is efficient when dealing with the Fractal Dimension problem of complex networks. We find that the Fractal property is influenced by the edge-weight in weighted networks. The possible variation of Fractal Dimension due to changes in edge-weights of weighted networks is also discussed.
V. V. Kutarov - One of the best experts on this subject based on the ideXlab platform.
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Fractal Dimension of Polymer Sorbents
Langmuir, 1996Co-Authors: B. M. Kats, V. V. KutarovAbstract:Some methods of defining certain features that characterize polymolecular sorption of water vapor by polymers are discussed : the Fractal Dimension, through the Frenkel-Halsey-Hill formalism ; BET ; the sorption film area, through the Kiselev equation and the differential function of pore surface distribution. In the framework of the BET theory, a new approach is proposed to define the surface Fractal Dimension of polymer sorbents, which is based on finding the number of the polylayers. The proposed method is compared with the existing ones. The proposed definition of the surface Fractal Dimension allowed to derive a three-parameter sorption isotherm equation, which takes into consideration the sorbent Fractal properties in the domain of the relative change of water vapor pressure, is 0.05 ≤ x ≤ 0.95.
Jifke F. Veenland - One of the best experts on this subject based on the ideXlab platform.
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Estimation of Fractal Dimension in radiographs
Medical physics, 1996Co-Authors: Jifke F. Veenland, J. L. Grashuis, Fb Van Der Meer, A. L. D. Beckers, E. S. GelsemaAbstract:In the last decade, the Fractal Dimension has become a popular parameter to characterize image textures. Also in radiographs, various procedures have been used to estimate the Fractal Dimension. However, certain characteristics of the radiographic process, e.g., noise and blurring, interfere with the straightforward application of these estimation methods. In this study, the influence of quantum noise and image blur on several estimation methods was quantified by simulating the effect of quantum noise and the effect of modulation transfer functions, corresponding with different screen-film combinations, on computer generated Fractal images. The results are extrapolated to explain the effect of film-grain noise on Fractal Dimension estimation. The effect of noise is that, irrespective of the noise source, the Fractal Dimension is overestimated, especially for lower Fractal Dimensions. On the other hand, blurring results in an underestimation of the Dimensions. The effect of blurring is dependent on the estimation method used; the Dimension estimates by the power spectrum method are lowered with a constant value, whereas the underestimation by the methods working in the spatial domain is dependent on the given Dimension. The influence of the MTF and noise on Fractal Dimension estimation seriously limits the comparability of Fractal Dimensions estimated from radiographs which differ in noise content or MTF. Only when the power spectrum method is used, it is possible to correct for the influence of different MTFs of screen-film combinations. It is concluded that only when using the same object-focus distance, the same exposure conditions, the same digitizer at the same resolution, can Fractal Dimensions as estimated in radiographs be reliably compared.
