Closed Contour Fractal Dimension Estimation by the Fourier Transform

Details Closed Contour Fractal Dimension Estimation by the Fourier Transform Closed Contour Fractal Dimension Estimation by the Fourier Transform

2012-01-15

arxiv.org/abs/1201.3097v1

Chaos, Solitons and Fractals, Volume 44, Issue 10, October 2011, Pages 851--861

Physics

Data Analysis, Statistics and Probability

Scientific paper

10.1016/j.chaos.2011.07.008

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, it is obtained the fractal dimension. The method is compared to other classical fractal dimension estimation methods in the literature, e. g., Bouligand-Minkowski, box-couting 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.

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