Nonlocal Anisotropic Discrete Regularization for Image, Data Filtering and Clustering

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 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 pTV 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! erent types of data living on di! erent 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.

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