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Adaptation of Eikonal Equation over Weighted Graphs

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 : In this paper, an adaptation of the eikonal equation is proposed by considering the latter on weighted graphs of arbitrary structure. This novel approach is based on a family of discrete morphological local and nonlocal gradients expressed by partial difference equations (PdEs). Our formulation of the eikonal equation on weighted graphs generalizes local and nonlocal configurations in the context of image processing and extends this equation for the processing of any unorganized high dimensional discrete data that can be represented by a graph. Our approach leads to a unified formulation for image segmentation and high dimensional irregular data processing.
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Vinh Thong Ta, Abderrahim Elmoataz, Olivier Lezoray. Adaptation of Eikonal Equation over Weighted Graphs. 2nd International Conference on Scale Space and Variational Methods in Computer Vision (SSVM 09), 2009, Voss, Norway. pp.187-199, ⟨10.1007/978-3-642-02256-2_16⟩. ⟨hal-00404070⟩

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