Adaptation of Eikonal Equation over Weighted Graph

Authors:
Vinh-Thong Ta;Abderrahim Elmoataz;Olivier Lézoray
Affiliations:
Université de Caen Basse-Normandie, GREYC CNRS UMR 6072, Image Team,;Université de Caen Basse-Normandie, GREYC CNRS UMR 6072, Image Team,;Université de Caen Basse-Normandie, GREYC CNRS UMR 6072, Image Team,
Venue:
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
Year:
2009

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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.