Résumé (EN)

Fronts propagation can be efficiently carried out through solutions to the Eikonal partial differential equation (PDE). It has been widely applied to image analysis thanks to its solid mathematical background and the wellestablished Eikonal solvers such as the fast marching method [1]. There exist two popular schemes which can be used for image segmentation. The first one is an interactive scheme which requires user-provided scribes to indicate foreground and background (see [2] for a review of the existing related literature), while the second one is the dual-front scheme [3] for active contours evolution. Both image segmentation schemes are based on the Voronoi diagram and Voronoi regions, for which the common objective is to seek the boundary of two adjacent Voronoi regions. In the context of geodesic framework, the Voronoi regions can be identified from the geodesic distance map which is the solution to the Eikonal PDE.