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Entropy 2017, 19(10), 534; doi:10.3390/e19100534

An Approximated Box Height for Differential-Box-Counting Method to Estimate Fractal Dimensions of Gray-Scale Images

1
PDPM Indian Institute of Information Technology, Design and Manufacturing, Jabalpur 482005, India
2
Center for Biomedical Technology, Universidad Politécnica de Madrid, Campus de Montegancedo, 28233 Pozuelo de Alarcón, Spain
3
Instituto de Oceanografía y Cambio Global, IOCAG, Campus de Tafira, Edificios de Telecomunicaciones, 35017 Las Palmas, Spain
*
Author to whom correspondence should be addressed.
Received: 7 June 2017 / Revised: 30 August 2017 / Accepted: 30 September 2017 / Published: 10 October 2017
(This article belongs to the Special Issue Wavelets, Fractals and Information Theory III)
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Abstract

The Fractal Dimension (FD) of an image defines the roughness using a real number which is highly associated with the human perception of surface roughness. It has been applied successfully for many computer vision applications such as texture analysis, segmentation and classification. Several techniques can be found in literature to estimate FD. One such technique is Differential Box Counting (DBC). Its performance is influenced by many parameters. In particular, the box height is directly related to the gray-level variations over image grid, which badly affects the performance of DBC. In this work, a new method for estimating box height is proposed without changing the other parameters of DBC. The proposed box height has been determined empirically and depends only on the image size. All the experiments have been performed on simulated Fractal Brownian Motion (FBM) Database and Brodatz Database. It has been proved experimentally that the proposed box height allow to improve the performance of DBC, Shifting DBC, Improved DBC and Improved Triangle DBC, which are closer to actual FD values of the simulated FBM images. View Full-Text
Keywords: Fractal Dimension; Dfferential Box Counting; box height; Fractal Brownian Motion; Brodatz Database Fractal Dimension; Dfferential Box Counting; box height; Fractal Brownian Motion; Brodatz Database
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Panigrahy, C.; Garcia-Pedrero, A.; Seal, A.; Rodríguez-Esparragón, D.; Mahato, N.K.; Gonzalo-Martín, C. An Approximated Box Height for Differential-Box-Counting Method to Estimate Fractal Dimensions of Gray-Scale Images. Entropy 2017, 19, 534.

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