On calculation of fractal dimension of images
TL;DR: 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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TL;DR: The aim of this review is to explain and to categorize the various algorithms into groups and their application in the field of medical signal analysis.
839 citations
Cites background from "On calculation of fractal dimension..."
...Also Bisoi and Mishra (2001) established a lower bound of the box size to ensure accurate results....
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TL;DR: Almost 130 million forest fragments in three continents are identified that show surprisingly similar power-law size and perimeter distributions as well as fractal dimensions, suggesting that forest fragmentation is close to the critical point of percolation.
Abstract: Remote sensing enables the quantification of tropical deforestation with high spatial resolution. This in-depth mapping has led to substantial advances in the analysis of continent-wide fragmentation of tropical forests. Here we identified approximately 130 million forest fragments in three continents that show surprisingly similar power-law size and perimeter distributions as well as fractal dimensions. Power-law distributions have been observed in many natural phenomena such as wildfires, landslides and earthquakes. The principles of percolation theory provide one explanation for the observed patterns, and suggest that forest fragmentation is close to the critical point of percolation; simulation modelling also supports this hypothesis. The observed patterns emerge not only from random deforestation, which can be described by percolation theory, but also from a wide range of deforestation and forest-recovery regimes. Our models predict that additional forest loss will result in a large increase in the total number of forest fragments-at maximum by a factor of 33 over 50 years-as well as a decrease in their size, and that these consequences could be partly mitigated by reforestation and forest protection.
352 citations
TL;DR: In this article, the fractal dimension calculated by box-counting method based on fractal theory was applied to characterize the pore structure of artificial cores, and three classical fractals and one sand packed bed model were selected as the experimental material to investigate the influence of box sizes, threshold value, and the image resolution when performing fractal analysis.
108 citations
TL;DR: An improved DBC method based on the original one for improvement of the accuracy can solve the two kinds of problems which the DBC has: over-counting boxes along z direction and under- Counting boxes just at the border of two neighboring box blocks where there is a sharp gray-level abruption exits.
107 citations
TL;DR: In this article, the surface morphology of pyrolysis chars was evaluated using scanning electron microscopy technology (SEM) and fractal theory, and it was found that the fractal dimension of residual chars from PAW/PP blends increased from 1.75 to 1.84 as increasing the ratio of PP from 25% to 75%, indicating that PP addition promoted the nonuniformity of the co-pyrolyisation chars.
101 citations
References
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Book•
01 Jan 1982
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.
Abstract: "...a blend of erudition (fascinating and sometimes obscure historical minutiae abound), popularization (mathematical rigor is relegated to appendices) and exposition (the reader need have little knowledge of the fields involved) ...and the illustrations include many superb examples of computer graphics that are works of art in their own right." Nature
24,199 citations
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.
Abstract: This paper addresses the problems of 1) representing natural shapes such as mountains, trees, and clouds, and 2) computing their description from image data. To solve these problems, we must be able to relate natural surfaces to their images; this requires a good model of natural surface shapes. Fractal functions are a good choice for modeling 3-D natural surfaces because 1) many physical processes produce a fractal surface shape, 2) fractals are widely used as a graphics tool for generating natural-looking shapes, and 3) a survey of natural imagery has shown that the 3-D fractal surface model, transformed by the image formation process, furnishes an accurate description of both textured and shaded image regions. The 3-D fractal model provides a characterization of 3-D surfaces and their images for which the appropriateness of the model is verifiable. Furthermore, this characterization is stable over transformations of scale and linear transforms of intensity. The 3-D fractal model has been successfully applied to the problems of 1) texture segmentation and classification, 2) estimation of 3-D shape information, and 3) distinguishing between perceptually ``smooth'' and perceptually ``textured'' surfaces in the scene.
1,919 citations
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.
Abstract: Fractal dimension is an interesting feature proposed to characterize roughness and self-similarity in a picture. This feature has been used in texture segmentation and classification, shape analysis and other problems. An efficient differential box-counting approach to estimate fractal dimension is proposed in this note. By comparison with four other methods, it has been shown that the authors, method is both efficient and accurate. Practical results on artificial and natural textured images are presented. >
767 citations
01 Feb 1985
760 citations
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.
Abstract: This paper deals with the problem of recognizing and segmenting textures in images. For this purpose the authors employ a technique based on the fractal dimension (FD) and the multi-fractal concept. Six FD features are based on the original image, the above average/high gray level image, the below average/low gray level image, the horizontally smoothed image, the vertically smoothed image, and the multi-fractal dimension of order two. A modified box-counting approach is proposed to estimate the FD, in combination with feature smoothing in order to reduce spurious regions. To segment a scene into the desired number of classes, an unsupervised K-means like clustering approach is used. Mosaics of various natural textures from the Brodatz album as well as microphotographs of thin sections of natural rocks are considered, and the segmentation results to show the efficiency of the technique. Supervised techniques such as minimum-distance and k-nearest neighbor classification are also considered. The results are compared with other techniques. >
650 citations