Analyse de champs browniens fractionnaires anisotropes

Abstract : In this communication, we present the Directional Averages Method (DAM) to analyse Anisotropic Fractional Brownian Fields (AFBF) defined in the spectral domain by a Hurst parameter H( θ) depending on the direction θ. For a given direction ϕ on the image, the average is formed in that direction and the regularity R( ϕ) is estimated. We show that for θ = ϕ + π/2, the function H( θ) is equal to R( ϕ) -1/2 and can be thus recovered. We have tested DAM on isotropic fractal images as well as on AFBF generated by the inverse Fourier method. Results are fair even if difficulties arise linked to the synthesis of true AFBF, to the analysis of signals which Hölder exponent is greater than one, and to the digitisation of images. Interesting perspectives can be developed concerning the analysis of fractal porous volumes only known from a 2D projection as it is the case for radiographs.
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Submitted on : Thursday, July 27, 2006 - 11:17:35 AM
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  • HAL Id : hal-00087851, version 1



Aline Bonami, Anne Estrade, Rachid Harba, Rachid Jennane, Emmanuel Perrin. Analyse de champs browniens fractionnaires anisotropes. 18eme colloque du GRETSI (Groupe de Recherche et d'Etudes de Traitement du Signal et des Images), 2001, Toulouse, France. pp.99-102. ⟨hal-00087851⟩



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