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Fractal Dimension Estimation for Color Texture Images

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Abstract

As an important feature of image texture, fractal dimension is widely used to index, segment or classify texture images. Previously, many methods have been proposed to estimate fractal dimension. However, most of them are for binary and gray-scale images. Only a few of them are for color images. In this paper, by extending the differential box-counting approach to five-dimensional Euclidean hyper-space, we present a new robust and simple algorithm to estimate fractal dimension for color texture images. By the differential box-counting method, a real empty box not covering any pixel even with ideal resolution is also counted as a box having pixels, resulting in errors of computations. This problem is eliminated by our method based on fractal Brownian surface model. Our experiments demonstrate that our algorithm is able to capture the complexity of color natures, and outperforms other methods in terms of color texture complexity ranking and discrimination, robustness and computational complexity.

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Acknowledgements

The author is very grateful to the editor and the anonymous referees for their careful reading and valuable suggestions, which have notably improved the paper.

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  1. School of information Engineering, Southwestern University of Finance and Economics, Chengdu, 610074, China

    Yurong Li

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  1. Yurong Li
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This work is supported by the Humanities and Social Sciences Foundation of Ministry of Education of China under Grant No. 15YJAZH037 and the Fundamental Research Funds for the Central Universities under Grant No. JBK1902030.

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Li, Y. Fractal Dimension Estimation for Color Texture Images. J Math Imaging Vis 62, 37–53 (2020). https://doi.org/10.1007/s10851-019-00912-0

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