Nonlocal Discrete Regularization on Weighted Graphs: A Framework for Image and Manifold Processing

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-Laplace operator, and an approximation one. This formulation leads to a family of simple and fast nonlinear processing methods, parameterized by the degree p of smoothness and by the graph weight function. This is a discrete analogue of recent well-known continuous nonlocal regularization. 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 ...

• Type: Journal
• Year: 2008
• Where: TIP
• Authors: Abderrahim Elmoataz, Olivier Lezoray, Sébastien Bougleux
• Keywords: Continuous Nonlocal Regularization, Discrete Weighted P-Laplace, Nonlocal Discrete Regularization, TIP 2008