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

Vinh Thong Ta 1 Abderrahim Elmoataz 1 Olivier Lézoray 1
1 Equipe Image - Laboratoire GREYC - UMR6072
GREYC - Groupe de Recherche en Informatique, Image, Automatique et Instrumentation de Caen
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.
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Vinh Thong Ta, Abderrahim Elmoataz, Olivier Lézoray. Partial Difference Equations over Graphs: Morphological Processing of Arbitrary Discrete Data. 10th European Conference on Computer Vision (ECCV 2008), Oct 2008, Marseille, France. pp.668-680, ⟨10.1007/978-3-540-88690-7_50⟩. ⟨hal-00333390⟩

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