Eikonal Equation Adaptation on Weighted Graphs: Fast Geometric Diffusion Process for Local and Non-local Image and Data Processing |
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Authors: | Xavier Desquesnes Abderrahim Elmoataz Olivier Lézoray |
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Affiliation: | 1. GREYC, UMR CNRS 6972, Image Team, ENSICAEN, Université de Caen Basse-Normandie, 6. Bvd Marechal Juin, 14050, Caen, France
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Abstract: | In this paper we propose an adaptation of the Eikonal equation on weighted graphs, using the framework of Partial difference Equations, and with the motivation of extending this equation’s applications to any discrete data that can be represented by graphs. This adaptation leads to a finite difference equation defined on weighted graphs and a new efficient algorithm for multiple labels simultaneous propagation on graphs, based on such equation. We will show that such approach enables the resolution of many applications in image and high dimensional data processing using a unique framework. |
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