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Partial Difference Equations on Graphs for Mathematical Morphology Operators overs Images and Manifolds

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 : The main tools of Mathematical Morphology are a broad class of nonlinear image operators. They can be defined in terms of algebraic set operators or as Partial Differential Equations (PDEs). We propose a framework of partial difference equations on arbitrary graphs for introducing and analyzing morphological operators in local and non local configurations. The proposed framework unifies the classical local PDEsbased morphology for image processing, generalizes them for non local configurations and extends them to the processing of any discrete data living on graphs.
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Vinh Thong Ta, Abderrahim Elmoataz, Olivier Lézoray. Partial Difference Equations on Graphs for Mathematical Morphology Operators overs Images and Manifolds. 15th IEEE International Conference on Image Processing (ICIP), Oct 2008, San Diego, United States. pp.801-804, ⟨10.1109/ICIP.2008.4711876⟩. ⟨hal-00333382⟩

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