Closed contour fractal dimension estimation by the Fourier transform

Autor(es)

Florindo, J. B. ^[1] ; Bruno, O. M. ^[1]

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, IFSC, BR-13560970 Sao Carlos, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: CHAOS SOLITONS & FRACTALS; v. 44, n. 10, p. 851-861, OCT 2011.
• Citações Web of Science: 11

Resumo

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. (C) 2011 Published by Elsevier Ltd. (AU)

• Processo FAPESP: 11/01523-1 - Métodos de visão computacional aplicados à identificação e análise de plantas
• Beneficiário: Odemir Martinez Bruno
• Modalidade de apoio: Auxílio à Pesquisa - Regular