Nonlocal anisotropic discrete regularization for image, data filtering and clustering

Abstract

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 is proposed. This regulariza-tion 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 different types of data living on differ-ent graph topologies (image, data). In particular we investigate the cases of p = 2, p = 1 and p < 1, this latter being very few considered in literature. Key words: anisotropic discrete regularization; nonlocal operators; graph p-Laplacian; filtering; clustering 1