Multivariate optimization for multifractal-based texture segmentation

Jordan Frecon (1) , Nelly Pustelnik (1) , Herwig Wendt (2, 3) , Patrice Abry (1)

1 Phys-ENS - Laboratoire de Physique de l'ENS Lyon
2 IRIT-SC - Signal et Communications
3 CNRS - Centre National de la Recherche Scientifique

This work aims at segmenting a texture into different regions, each characterized by a priori unknown multifractal properties. The multifractal properties are quantified using the multiscale function C 1,j that quantifies the evolution along analysis scales 2 j of the empirical mean of the log of the wavelet leaders. The segmentation procedure, applied on (C 1,j) 1≤j≤J , involves a multivariate Mumford-Shah relaxation formulated as a convex optimization problem involving a structure tensor penalization and an efficient algorithmic solution based on primal-dual proximal algorithm. The performances are evaluated over simulated data.

Mots clés: Local regularity; multifractal spectrum; segmentation; convex optimization; wavelet Leaders

Domaines: Traitement du signal et de l'image [eess.SP]

Jordan Frecon, Nelly Pustelnik, Herwig Wendt, Patrice Abry. Multivariate optimization for multifractal-based texture segmentation. IEEE ICIP 2015, Sep 2015, Québec, Canada. ⟨10.1109/ICIP.2015.7351750⟩. ⟨hal-01252108⟩