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Nonlocal Discrete Regularization on Weighted Graphs: a framework for Image and Manifold Processing

Abderrahim Elmoataz 1 Olivier Lezoray 1 Sébastien Bougleux 1
1 Equipe Image - Laboratoire GREYC - UMR6072
GREYC - Groupe de Recherche en Informatique, Image, Automatique et Instrumentation de Caen
Abstract : We introduce a nonlocal discrete regularization framework on weighted graphs of the arbitrary topologies for image and manifold processing. The approach considers the problem as a variational one, which consists in minimizing a weighted sum of two energy terms: a regularization one that uses a discrete weighted p-Dirichlet energy, and an approximation one. This is the discrete analogue of recent continuous Euclidean nonlocal regularization functionals. The proposed formulation leads to a family of simple and fast nonlinear processing methods based on the weighted p-Laplace operator, parameterized by the degree p of regularity, the graph structure and the graph weight function. These discrete processing methods provide a graph-based version of recently proposed semi-local or nonlocal processing methods used in image and mesh processing, such as the bilateral filter, the TV digital filter or the nonlocal means filter. It works with equal ease on regular 2D-3D images, manifolds or any data. We illustrate the abilities of the approach by applying it to various types of images, meshes, manifolds and data represented as graphs
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Submitted on : Friday, December 7, 2007 - 1:43:07 PM
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Abderrahim Elmoataz, Olivier Lezoray, Sébastien Bougleux. Nonlocal Discrete Regularization on Weighted Graphs: a framework for Image and Manifold Processing. IEEE Transactions on Image Processing, Institute of Electrical and Electronics Engineers, 2008, 17 (7), pp.1047-1060. ⟨hal-00163573v2⟩

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