Multifractal-based texture segmentation using variational procedure

Jordan Frecon (1) , Nelly Pustelnik (1) , Herwig Wendt (2, 3) , Laurent Condat (4) , 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
4 GIPSA-AGPIG - GIPSA - Architecture, Géométrie, Perception, Images, Gestes

The present contribution aims at segmenting a scale-free texture into different regions, characterized by an a priori (unknown) multifractal spectrum. The multifractal properties are quantified using multiscale quantities C 1,j and C 2,j that quantify the evolution along the analysis scales 2 j of the empirical mean and variance of a nonlinear transform of wavelet coefficients. The segmentation is performed jointly across all the scales j on the concatenation of both C 1,j and C 2,j by an efficient vectorial extension of a convex relaxation of the piecewise constant Potts segmentation problem. We provide comparisons with the scalar segmentation of the Hölder exponent as well as independent vectorial segmentations over C 1 and C 2 .

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

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

Jordan Frecon, Nelly Pustelnik, Herwig Wendt, Laurent Condat, Patrice Abry. Multifractal-based texture segmentation using variational procedure. IVMSP 2016 - IEEE 12th Image, Video, and Multidimensional Signal Processing Workshop (IVMSP 2016), Jul 2016, Bordeaux, France. pp.1 - 5, ⟨10.1109/IVMSPW.2016.7528187⟩. ⟨hal-01398865⟩