Adaptation of Eikonal Equation over Weighted Graph

  • Vinh-Thong Ta
  • Abderrahim Elmoataz
  • Olivier Lézoray
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5567)


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.


Image Segmentation Weighted Graph Initial Seed Weighted Distance Eikonal Equation 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Vinh-Thong Ta
    • 1
  • Abderrahim Elmoataz
    • 1
  • Olivier Lézoray
    • 1
  1. 1.Université de Caen Basse-Normandie, GREYC CNRS UMR 6072, Image TeamFrance

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