Nonlocal Anisotropic Discrete Regularization for Image, Data Filtering and Clustering

Vinh Thong Ta (1) , Sébastien Bougleux (2) , Abderrahim Elmoataz (2) , Olivier Lézoray (1)

1 GREYC - Groupe de Recherche en Informatique, Image et Instrumentation de Caen
2 Equipe Image - Laboratoire GREYC - UMR6072

In this paper, we propose a nonlocal anisotropic discrete regularization on graphs of arbitrary topologies as a framework for image, data filtering and clustering. Inspired by recent works on nonlocal regularization and on the TV digital filter, a family of discrete anisotropic functional regularization on graphs. This regularization is based on the Lp norm of the nonlocal gradient and the discrete p-Laplacian on graphs. It can be viewed as the discrete analogue on graphs of the continuous p-TV anisotropic functionals regularization formulations. After providing definitions and algorithms to resolve such a discrete nonlocal anisotropic regularization, we show its properties for filtering, clustering on di

Mots clés: anisotropic discrete regularization; nonlocal operators; graph p-Laplacian; filtering; clustering

Domaines: Mathématique discrète [cs.DM]; Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]

Vinh Thong Ta, Sébastien Bougleux, Abderrahim Elmoataz, Olivier Lézoray. Nonlocal Anisotropic Discrete Regularization for Image, Data Filtering and Clustering. 2007. ⟨hal-00187165v1⟩