Unifying Local and Nonlocal Processing with Partial Difference Operators on Weighted Graphs

@inproceedings{Elmoataz2008UnifyingLA,
  title={Unifying Local and Nonlocal Processing with Partial Difference Operators on Weighted Graphs},
  author={Abderrahim Elmoataz and Olivier L{\'e}zoray and S{\'e}bastien Bougleux and Vinh-Thong Ta},
  year={2008}
}
In this paper, local and nonlocal image processing are unified, within the same framework, by defining discrete derivatives on weighted graphs. These discrete derivatives allow to transcribe continuous partial differential equations and energy functionals to partial difference equations and discrete functionals over weighted graphs. With this methodology, we consider two gradient-based problems: regularization and mathematical morphology. The gradient-based regularization framework allows to… CONTINUE READING

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