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A simple method for estimating the fractal dimension from digital images: The compression dimension

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  • Chamorro-Posada, Pedro

Abstract

The fractal structure of real world objects is often analyzed using digital images. In this context, the compression fractal dimension is put forward. It provides a simple method for the direct estimation of the dimension of fractals stored as digital image files. The computational scheme can be implemented using readily available free software. Its simplicity also makes it very interesting for introductory elaborations of basic concepts of fractal geometry, complexity, and information theory. A test of the computational scheme using limited-quality images of well-defined fractal sets obtained from the Internet and free software has been performed. Also, a systematic evaluation of the proposed method using computer generated images of the Weierstrass cosine function shows an accuracy comparable to those of the methods most commonly used to estimate the dimension of fractal data sequences applied to the same test problem.

Suggested Citation

  • Chamorro-Posada, Pedro, 2016. "A simple method for estimating the fractal dimension from digital images: The compression dimension," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 562-572.
    • Handle: RePEc:eee:chsofr:v:91:y:2016:i:c:p:562-572
    DOI: 10.1016/j.chaos.2016.08.002
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    References listed on IDEAS

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    1. József Berke, 2007. "Measuring Of Spectral Fractal Dimension," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 3(03), pages 409-418.
    2. Ahammer, H. & Kroepfl, J.M. & Hackl, Ch. & Sedivy, R., 2011. "Fractal dimension and image statistics of anal intraepithelial neoplasia," Chaos, Solitons & Fractals, Elsevier, vol. 44(1), pages 86-92.
    3. Spodarev, Evgeny & Straka, Peter & Winter, Steffen, 2015. "Estimation of fractal dimension and fractal curvatures from digital images," Chaos, Solitons & Fractals, Elsevier, vol. 75(C), pages 134-152.
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    Cited by:

    1. Arce, Walker & Pierce, James & Velcsov, Mihaela Teodora, 2021. "A single-scale fractal feature for classification of color images: A virus case study," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    2. Liu, Jingshou & Ding, Wenlong & Dai, Junsheng & Zhao, Gang & Sun, Yaxiong & Yang, Haimeng, 2018. "Unreliable determination of fractal characteristics using the capacity dimension and a new method for computing the information dimension," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 16-24.
    3. Zuo, Xue & Tang, Xiang & Zhou, Yuankai, 2020. "Influence of sampling length on estimated fractal dimension of surface profile," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).

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