Discrete Regularization on Weighted Graphs for Image and Mesh Filtering

Sébastien Bougleux (1) , Abderrahim Elmoataz (1) , Mahmoud Melkemi (2)

1 Equipe Image - Laboratoire GREYC - UMR6072
2 LMIA - Laboratoire de Mathématiques Informatique et Applications [UHA]

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.

Domaines: Traitement des images [eess.IV]; Mathématique discrète [cs.DM]

Sébastien Bougleux, Abderrahim Elmoataz, Mahmoud Melkemi. Discrete Regularization on Weighted Graphs for Image and Mesh Filtering. 1st International Conference on Scale Space and Variational Methods in Computer Vision (SSVM 2007), May 2007, Ischia, Italy. pp.128-139, ⟨10.1007/978-3-540-72823-8_12⟩. ⟨hal-00333374⟩