Abstract—Multifractal analysis has been recognized as a
powerful tool in characterizing textures. Several studies have
shown the possibilities offered by multifractal analysis in image
processing, in particular in classification of complex textures.
Indeed, in most cases, the mode of multifractal spectrum is used
for classification; in this study, we propose two different
methods to estimate this spectrum. This paper focuses on the
classification of Brodatz textures using multifractal analysis.
Two methods are considered: The first method is based on the
multifractal formalism of Frish and Parisi through the
Legendre transform, the second one is a direct method based on
the box-counting algorithm. For both approaches, we used the
multiresolution coefficients of the wavelet transform, with the
Gaussian first order derivative to find singularity exponents in
the direct method, and the leaders coefficients for the
multifractal formalism. The Legendre transform was used to
estimate the multifractal spectrum, while the box-counting
method was used to compute the Hausdorff dimension of sets of
the same degree of singularity. Results demonstrate that it is
more interesting in some cases to use the box-counting method
than the Legendre transform to obtain a more accurate
spectrum, as in the bimodal spectrum case.
Index Terms—Box-counting method, multifractal formalism,
multifractal spectrum, texture classification.
Khaled Harrar is with the Engineering Faculty, University of M'Hamed
Bougara Boumerdes, Avenue de l'indépendance, 35000, Boumerdes, Algeria
(e-mail: harrar_k@umbb.dz)
Mohamed Khider is with the LTIR laboratory, Electrical engineering
faculty, University of Science and Technology Houari Boumediene, BP 32,
Bab Ezzouar, Algeria (e-mail: mohamed.khider@ieee.org)
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Cite: Khaled Harrar and Mohamed Khider, "Texture Analysis Using Multifractal Spectrum," International Journal of Modeling and Optimization vol. 4, no. 4, pp. 336-341, 2014.
