Discrete regularization on weighted graphs for image and mesh filtering

Authors:
Sébastien Bougleux;Abderrahim Elmoataz;Mahmoud Melkemi
Affiliations:
GREYC, CNRS, UMR, Image, ENSICAEN, Caen Cedex, France;LUSAC, Cherbourg-Octeville, France;LMIA, MAGE, Mulhouse Cedex, France
Venue:
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
Year:
2007

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Abstract

We propose a discrete regularization framework on weighted graphs of arbitrary topology, which unifies image and mesh filtering. 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 the discrete p-Laplace operator, and an approximation one. This formulation leads to a family of simple nonlinear filters, parameterized by the degree p of smoothness and by the graph weight function. Some of these filters provide a graph-based version of well-known filters used in image and mesh processing, such as the bilateral filter, the TV digital filter or the nonlocal mean filter.