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On calculation of fractal dimension of images

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TLDR
A lower bound of the box size is found and the reason for having it is provided and indicates the need for limiting the box sizes within certain bounds.
About
This article is published in Pattern Recognition Letters.The article was published on 2001-05-01. It has received 122 citations till now. The article focuses on the topics: Fractal dimension on networks & Fractal analysis.

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Citations
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Utilization of Haar wavelet collocation technique for fractal-fractional order problem

TL;DR: In this article , the authors established adequate results for qualitative theory as well as approximate solution of Fractal-fractional order differential equations (F-FDEs) using Haar wavelet collocation.
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Fractal Analysis of the Optimal Hydraulic Gradient Surface in Water Distribution Networks

TL;DR: In this paper , the authors examined the fractal properties of the optimal hydraulic gradient surface (OHGS), a geometrical body that describes the way in which the available energy should be spent within a water distribution network to ensure the calculation of a minimum capital cost design.
References
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Book

The Fractal Geometry of Nature

TL;DR: This book is a blend of erudition, popularization, and exposition, and the illustrations include many superb examples of computer graphics that are works of art in their own right.
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Fractal-Based Description of Natural Scenes

TL;DR: The3-D fractal model provides a characterization of 3-D surfaces and their images for which the appropriateness of the model is verifiable and this characterization is stable over transformations of scale and linear transforms of intensity.
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An efficient differential box-counting approach to compute fractal dimension of image

TL;DR: An efficient differential box-counting approach to estimate fractal dimension is proposed and by comparison with four other methods, it has been shown that the method is both efficient and accurate.
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Texture segmentation using fractal dimension

TL;DR: A modified box-counting approach is proposed to estimate the FD, in combination with feature smoothing in order to reduce spurious regions and to segment a scene into the desired number of classes, an unsupervised K-means like clustering approach is used.