Résumé en anglais

This paper presents a new method to quickly extract geodesic paths on images and 3D meshes. We use a heuristic to drive the front propagation procedure of the classical Fast Marching. This results in a modification of the Fast Marching algorithm that is similar to the A$^*$ algorithm used in artificial intelligence. In order to find very quickly geodesic paths between any given pair of points, two methods are proposed to devise an heuristic that restrict the front propagation. The multiresolition heuristic computes the heuristic using a propagation on a coarse map. For applications where pre-computation is acceptable, the landmark-based heuristic pre-computes distance maps to a sparse set of landmark points. We introduce various distortion metrics in order to quantify the errors introduced by the heuristically driven propagations. We show that both heuristic approaches bring a large speed-up for large scale applications that require the extraction of geodesics on images and 3D meshes.