Results 221 to 230 of about 15,404 (265)

Trabecular Bone Texture Characterization Using Regularization Dimension and Box-counting Dimension

TENCON 2019 - 2019 IEEE Region 10 Conference (TENCON), 2019
This paper presents texture characterization techniques for effective diagnosis of osteoporosis cases on bone radiograph images. The automatic classification of osteoporosis and healthy (control) cases with bone radiograph images presents a major challenge as the images show little or no visual difference for both cases.
Dhevendra Alagan Palanivel, Sivakumaran Natarajan, Sainarayanan Gopalakrishnan, Rachid Jennane   +3 more
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Network Box Counting Dimension

2020
In this chapter we begin our detailed study of fractal dimensions of a network \(\mathbb {G}\). There are two approaches to calculating a fractal dimension of \(\mathbb {G}\). One approach, applicable if \(\mathbb {G}\) is a spatially embedded network, is to treat \(\mathbb {G}\) as a geometric object and apply techniques, such as box counting or ...
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Topological and Box Counting Dimensions

2020
A mind once stretched by a new idea never regains its original dimension. Oliver Wendell Holmes, Jr. (1841–1935), American, U.S. Supreme Court justice from 1902 to 1932.
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Computing the Box Counting Dimension

2020
From roughly the late 1980s to the mid-1990s, a very large number of papers studied computational issues in determining fractal dimensions of geometric objects, or provided variants of algorithms for calculating the fractal dimensions, or applied these techniques to real-world problems.
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On the performance of box-counting estimators of fractal dimension

Biometrika, 1993
Summary: Box-counting estimators are popular for estimating fractal dimension. However, very little is known of their stochastic properties, despite increasing statistical interest in their application. We show that, if the irregular curve to which the estimators are applied is modelled by a Gaussian process, concise formulae may be developed for ...
Hall, Peter, Wood, Andrew
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A Modified Box-Counting Method to Estimate the Fractal Dimensions

Applied Mechanics and Materials, 2011
A fractal is a property of self-similarity, each small part of the fractal object is similar to the whole body. The traditional box-counting method (TBCM) to estimate fractal dimension can not reflect the self-similar property of the fractal and leads to two major problems, the border effect and noninteger values of box size.
Xu J., Lacidogna G.
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FRACTAL DIMENSION-BASED GENERALIZED BOX-COUNTING TECHNIQUE WITH APPLICATION TO GRAYSCALE IMAGES

Fractals, 2021
Fractal Dimension (FD) estimation in digital image analysis has received much attention due to its dimensional significance and therefore has become an active area of research over the year. The earlier FD-based techniques often followed traditional box-counting and its different variation of differential box-counting (DBC) paradigms, in which the ...
SOUMYA RANJAN NAYAK, JIBITESH MISHRA
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The box-counting dimension for geometrically finite Kleinian groups

Fundamenta Mathematicae, 1996
Patterson was the first studying the limit set in terms of measure theory and in particular, in terms of fractal dimensions. By constructing a measure, later called Patterson measure, on the limit set, he was able to get the following result for a finitely generated Fuchsian group \(G\): ``The exponent of convergence \(\gamma=\delta(G)\) is equal to \(\
Stratmann, B., Urbański, M.
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IMAGE PYRAMIDS FOR CALCULATION OF THE BOX COUNTING DIMENSION

Fractals, 2012
The fractal dimensions of real world objects are commonly investigated using digital images. Unfortunately, these images are unable to represent an infinitesimal range of scales. In addition, a proper evaluation of the applied methods that encompass the image processing techniques is often missing.
H. AHAMMER, M. MAYRHOFER-REINHARTSHUBER
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Hausdorff dimension method reduces the error of box counting

Theoretical and Natural Science, 2023
The Hausdorff dimension of an object is a topological measure of the size of its covering properties. To compute the Hausdorff dimension of an object, this report reviews the method of box counting, a method of gathering data for analyzing complex patterns by breaking a dataset, object, image, etc.
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