Eikonal equation adaptation on weighted graphs: fast geometric diffusion process for local and non-local image and data processing

Xavier Desquesnes (1) , Abderrahim Elmoataz (1) , Olivier Lezoray (1)

1 Equipe Image - Laboratoire GREYC - UMR6072

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.

Mots clés: Eikonal equation; weighted graph; non-local image processing; active contour; PdE; fast marching; high dimensional data

Domaines: Traitement des images [eess.IV]

Xavier Desquesnes, Abderrahim Elmoataz, Olivier Lezoray. Eikonal equation adaptation on weighted graphs: fast geometric diffusion process for local and non-local image and data processing. Journal of Mathematical Imaging and Vision, 2013, 46 (2), pp.238-257. ⟨10.1007/s10851-012-0380-9⟩. ⟨hal-00932510⟩