Anisotropic geodesics for perceptual grouping and domain meshing

Sébastien Bougleux (1) , Gabriel Peyré (2) , Laurent D. Cohen (2)

1 Image
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

This paper shows how Voronoi diagrams and their dual Delaunay complexes, defined with geodesic distances over 2D Reimannian manifolds, can be used to solve two important problems encountered in computer vision and graphics. The first problem studied is perceptual grouping which is a curve reconstruction problem where one should complete in a meaningful way a sparse set of noisy curves. From this latter curves, our grouping algorithm first designs an anisotropic tensor field that corresponds to a Reimannian metric. Then, according to this metric, the Delaunay graph is constructed and pruned in order to correctly link together salient features. The second problem studied is planar domain meshing, where one should build a good quality triangulation of a given domain. Our meshing algorithm is a geodesic Delaunay refinement method that exploits an anisotropic tensor field in order to locally impose the orientation and aspect ratio of the created triangles.

Domaines: Vision par ordinateur et reconnaissance de formes [cs.CV]; Géométrie algorithmique [cs.CG]; Traitement des images [eess.IV]

Sébastien Bougleux, Gabriel Peyré, Laurent D. Cohen. Anisotropic geodesics for perceptual grouping and domain meshing. 10th European Conference on Computer Vision, Oct 2008, Marseille, France. pp.129-142, ⟨10.1007/978-3-540-88688-4_10⟩. ⟨hal-00333330⟩