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Partial Difference Equations over Graphs: Morphological Processing of Arbitrary Discrete Data

  • Vinh-Thong Ta
  • Abderrahim Elmoataz
  • Olivier Lézoray
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5304)

Abstract

Mathematical Morphology (MM) offers a wide range of operators to address various image processing problems. These processing can be defined in terms of algebraic set or as partial differential equations (PDEs). In this paper, a novel approach is formalized as a framework of partial difference equations (PdEs) on weighted graphs. We introduce and analyze morphological operators in local and nonlocal configurations. Our framework recovers classical local algebraic and PDEs-based morphological methods in image processing context; generalizes them for nonlocal configurations and extends them to the treatment of any arbitrary discrete data that can be represented by a graph. It leads to considering a new field of application of MM processing: the case of high-dimensional multivariate unorganized data.

Keywords

Weight Function Texture Image Weighted Graph Mathematical Morphology Graph 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-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Vinh-Thong Ta
    • 1
  • Abderrahim Elmoataz
    • 1
  • Olivier Lézoray
    • 1
  1. 1.University of Caen Basse-Normandie, GREYC CNRS UMR 6072, Image TeamCaen CedexFrance

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