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Closed contour fractal dimension estimation by the Fourier transform

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  • Florindo, J.B.
  • Bruno, O.M.

Abstract

This work proposes a novel technique for the numerical calculus of the fractal dimension of fractal objects which can be represented as a closed contour. The proposed method maps the fractal contour onto a complex signal and calculates its fractal dimension using the Fourier transform. The Fourier power spectrum is obtained and an exponential relation is verified between the power and the frequency. From the parameter (exponent) of the relation, is obtained the fractal dimension. The method is compared to other classical fractal dimension estimation methods in the literature, e.g., Bouligand–Minkowski, box-counting and classical Fourier. The comparison is achieved by the calculus of the fractal dimension of fractal contours whose dimensions are well-known analytically. The results showed the high precision and robustness of the proposed technique.

Suggested Citation

  • Florindo, J.B. & Bruno, O.M., 2011. "Closed contour fractal dimension estimation by the Fourier transform," Chaos, Solitons & Fractals, Elsevier, vol. 44(10), pages 851-861.
    • Handle: RePEc:eee:chsofr:v:44:y:2011:i:10:p:851-861
    DOI: 10.1016/j.chaos.2011.07.008
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    Cited by:

    1. Oliveira, Marcos William da S. & Casanova, Dalcimar & Florindo, João B. & Bruno, Odemir M., 2014. "Enhancing fractal descriptors on images by combining boundary and interior of Minkowski dilation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 416(C), pages 41-48.
    2. Klonowski, W. & Pierzchalski, M. & Stepien, P. & Stepien, R. & Sedivy, R. & Ahammer, H., 2013. "Application of Higuchi’s fractal dimension in analysis of images of Anal Intraepithelial Neoplasia," Chaos, Solitons & Fractals, Elsevier, vol. 48(C), pages 54-60.

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