Gamma-convergence of discrete functionals with non convex perturbation for image classification

Gilles Aubert (1) , Laure Blanc-Féraud , Riccardo March

1 ARIANA - Inverse problems in earth monitoring

The purpose of this report is to show the theoretical soundness of a variation- al method proposed in image processing for supervised classification. Based on works developed for phase transitions in fluid mechanics, the classification is obtained by minimizing a sequence of functionals. The method provides an image composed of homogeneous regions with regular boundaries, a region being defined as a set of pixels belonging to the same class. In this paper, we show the gamma-convergence of the sequence of functionals which differ from the ones proposed in fluid mechanics in the sense that the perturbation term is not quadratic but has a finite asymptote at infinity, corresponding to an edge preserving regularization term in image processing.

Mots clés: GAMMA-CONVERGENCE; IMAGE CLASSIFICATION; EDGE-PRESERVING REGULARIZATION

Domaines: Autre [cs.OH]

Gilles Aubert, Laure Blanc-Féraud, Riccardo March. Gamma-convergence of discrete functionals with non convex perturbation for image classification. RR-4560, INRIA. 2002. ⟨inria-00072028⟩