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

Xavier Desquesnes (1) , Abderrahim Elmoataz (1) , Olivier Lezoray (1) , Vinh Thong Ta (2)

1 Equipe Image - Laboratoire GREYC - UMR6072
2 LaBRI - Laboratoire Bordelais de Recherche en Informatique

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 solu- tions 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 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.

Domaines: Traitement des images [eess.IV]

Xavier Desquesnes, Abderrahim Elmoataz, Olivier Lezoray, Vinh Thong Ta. Efficient Algorithms for Image and High Dimensional Data Processing Using Eikonal Equation on Graphs. International Symposium on Visual Computing, 2010, Las Vegas, Nevada, United States. pp.647-658, ⟨10.1007/978-3-642-17274-8_63⟩. ⟨hal-00708981⟩