Efficient algorithms for image and high dimensional data processing using eikonal equation on graphs

Authors:
Xavier Desquesnes;Abderrahim Elmoataz;Olivier Lézoray;Vinh-Thong Ta
Affiliations:
Université de Caen Basse-Normandie, ENSICAEN, CNRS;Université de Caen Basse-Normandie, ENSICAEN, CNRS;Université de Caen Basse-Normandie, ENSICAEN, CNRS;LaBRI, Université de Bordeaux, CNRS, IPB
Venue:
ISVC'10 Proceedings of the 6th international conference on Advances in visual computing - Volume Part II
Year:
2010

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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 L1,L2 and L∞ 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 patchbased 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.