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Discrete Regularization on Weighted Graphs for Image and Mesh Filtering

  • Sébastien Bougleux
  • Abderrahim Elmoataz
  • Mahmoud Melkemi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4485)

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.

Keywords

Weight Function Weighted Graph Image Denoising Neighborhood Graph Arbitrary Topology 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Sébastien Bougleux
    • 1
  • Abderrahim Elmoataz
    • 2
  • Mahmoud Melkemi
    • 3
  1. 1.GREYC CNRS UMR 6072 - Image, ENSICAEN, 6 BD du Maréchal Juin, 14050 Caen CedexFrance
  2. 2.LUSAC - VAI, Site Universitaire, BP 78, 50130 Cherbourg-OctevilleFrance
  3. 3.LMIA - MAGE, 4 rue des Frères Lumière, 68093 Mulhouse CedexFrance

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