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Nonlocal Graph Morphology

Vinh Thong Ta 1 Abderrahim Elmoataz 1 Olivier Lezoray 1
1 Equipe Image - Laboratoire GREYC - UMR6072
GREYC - Groupe de Recherche en Informatique, Image, Automatique et Instrumentation de Caen
Abstract : Mathematical morphology (MM) operators can be defined in terms of algebraic sets or as partial differential equations. In this paper, we introduce a novel formulation of MM over weighted graphs of arbitrary topology. The proposed framework recovers local algebraic and PDEs-based formulations of MM and introduces nonlocal configurations. This enables to PDEs-based methods to process any discrete data that can be described by a graph such as high dimensional data defined on irregular domains.
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https://hal.archives-ouvertes.fr/hal-00403942
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Vinh Thong Ta, Abderrahim Elmoataz, Olivier Lezoray. Nonlocal Graph Morphology. International Symposium on Mathematical Morphology, 2009, Groningen, Netherlands. pp.5-9, ⟨10.1007/978-3-642-03613-2⟩. ⟨hal-00403942⟩

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