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Efficient Algorithms for Image and High Dimensional Data Processing Using Eikonal Equation on Graphs

  • Xavier Desquesnes
  • Abderrahim Elmoataz
  • Olivier Lézoray
  • Vinh-Thong Ta
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6454)

Abstract

In this paper we propose an adaptation of the static eikonal equation over weighted graphs of arbitrary structure using a framework of discrete operators. Based on this formulation, we provide explicit solutions for the \(\mathcal{L}_1, \mathcal{L}_2\) and \(\mathcal{L}_\infty\) norms. Efficient algorithms to compute the explicit solution of the eikonal equation on graphs are also described. We then present several applications of our methodology for image processing such as superpixels decomposition, region based segmentation or patch-based segmentation using non-local configurations. By working on graphs, our formulation provides an unified approach for the processing of any data that can be represented by a graph such as high-dimensional data.

Keywords

Weighted Graph Eikonal Equation Arbitrary Graph Discrete Operator Region Base Segmentation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Xavier Desquesnes
    • 1
  • Abderrahim Elmoataz
    • 1
  • Olivier Lézoray
    • 1
  • Vinh-Thong Ta
    • 2
  1. 1.GREYC Image TeamUniversité de Caen Basse-Normandie, ENSICAEN, CNRSFrance
  2. 2.LaBRI(Université de Bordeaux CNRS) IPBFrance

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