Fractal Measures and Dimensions
Diagnosis of Breast Cancer from Mammograms by Using Fractal Measures
... of fractal geometry to describe the texture of histopathological images can be found in [14, ...The fractal dimension of an object is a non-integer exponent that can be used to describe the complexity of a ...
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AN INTRODUCTION TO DIMENSION THEORY AND FRACTAL GEOMETRY: FRACTAL DIMENSIONS AND MEASURES
... Why is the study of dimension important or useful? Dimension is at the heart of all fractal geometry, and provides a reasonable basis for an invariant between different fractal objects. There are also ...
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Entanglement Entropy of Highly Degenerate States and Fractal Dimensions
... Linear combinations can in general involve infinitely many directions ~v, with appropriate integration measures on the unit sphere. Such linear combinations may occur in quite natural ways: for instance, when a ...
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Mixed moments and local dimensions of measures
... nature of the absolute moments M q (μ) was utilised implicitly in the proofs in [Ols] reducing the arguments in [Ols] to a careful analysis (of the fractal geometric properties) of the set of points x with | x | = ...
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Entanglement in permutation symmetric states, fractal dimensions, and geometric quantum mechanics
... ◦ Department of Mathematics, King’s College London, Strand, London WC2R 2LS, UK We study the von Neumann and R´ enyi bipartite entanglement entropies in the thermodynamic limit of many-body quantum states with spin-s ...
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Using fractal dimensions for characterizing intra-urban diversity. The example of Brussels
... the fractal method used (Johnsen and Brown, ...the fractal dimensions vary differently and fractal characterization may hence lead to false results when applying only one ...equal. ...
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Dimensions of equilibrium measures on a class of planar self affine sets
... 1.3 Entropy and Lyapunov exponents Let m be any shift ergodic Borel probability measure on Σ and let µ = m ◦ Π −1 be the push forward of m onto the fractal F . The support of µ is contained in F , although in ...
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TEXTURAL IMAGES REPRESENTATION USING FRACTAL GEOMETRY MEASURES Kamal Hadi Sager
... the fractal geometry expands the applications of the image processing to many problems of: a) Representing natural shapes such as mountains, trees, and clouds, and b) Computing their description from image ...
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On The Lq dimensions of measures on Heuter Lalley type self affine sets
... 1 Introduction Self-affine sets are natural objects of interest in fractal geometry, and have been intensively studied since the early 1980s. While the dimension theory of non- overlapping self-similar sets is ...
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Packing measures, packing dimensions, and the existence of sets of positive finite measure
... In Chapter 3 we provide a negative result for the diameter-based packing measure that is, for each Hausdorff function we provide a construction of a (compact) metric space of infinite diameter-based packing measure which ...
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Entropies and fractal dimensions
... the fractal dimension of the ...the fractal dimension of the rim of the canyon, defined as the boundary between flat soil and steep terrain, is a number between 1 and ...a fractal dimension (a more ...
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Fractal dimensions of wildfire spreading
... such fractal structures without knowing the details of effects from ecology, climate, ...the fractal dimensions and scaling behaviors of the corresponding empirical data, and show good agreement ...
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FONT DISCRIMINATIO USING FRACTAL DIMENSIONS
... using Fractal Dimensions ...various fractal dimensions. First, some predefined fractal dimensions were combined with directional methods to enhance font ...novel fractal ...
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Theory of Distance Relativity of Fractal Dimensions
... of fractal dimension is that the concept itself is a “relative concept”, that is, the same object can have different fractal dimensions relative to the context in which the fractal dimension ...
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LOCAL DISTRIBUTION OF FRACTAL SETS AND MEASURES
... In particular, Besicovitch studied the distribution of the above sets A on certain cones. These results have since then been used and also generalised by various authors, but mostly only for the Hausdorff ...
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Classification of mangrove species based on leaf fractal dimensions
... the fractal dimensions of the leaves of mangrove species locally found in the City of Tangub to determine if the same can be used for classification ...that fractal dimensions can be used to ...
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Bifurcation Analysis and Fractal Dimensions of a Non- Linear Map
... various fractal dimensions like Correlation dimension, Box-counting and Information dimension have been calculated to verify the geometry of the strange ...
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Moments and associated measures of copulas with fractal support
... On the other hand, integral calculus for functions is required to study association measures for copulas. Again, computations are complicated when the support of the copula is a fractal set. In this paper ...
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Evaluation of fractal dimensions from bitmap image (Part: Algorithms)
... The work assembled the complex application for evaluation of main fractal characteristics from input image. New simple modifications of evaluation of positive cells according to appropriate scale were implemented. ...
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Fractality in hadron interactions: a conservation law and quantization of fractal dimensions
... corresponding fractal dimensions and is a simple function of the respective momentum frac- ...the fractal dimensions possess quantum ...
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