Geodesic Methods in Computer Vision and Graphics - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Foundations and Trends in Computer Graphics and Vision Année : 2010

Geodesic Methods in Computer Vision and Graphics

Résumé

This paper reviews both the theory and practice of the numerical computation of geodesic distances on Riemannian manifolds. The notion of Riemannian manifold allows one to define a local metric (a symmetric positive tensor field) that encodes the information about the problem one wishes to solve. This takes into account a local isotropic cost (whether some point should be avoided or not) and a local anisotropy (which direction should be preferred). Using this local tensor field, the geodesic distance is used to solve many problems of practical interest such as segmentation using geodesic balls and Voronoi regions, sampling points at regular geodesic distance or meshing a domain with geodesic Delaunay triangles. The shortest paths for this Riemannian distance, the so-called geodesics, are also important because they follow salient curvilinear structures in the domain. We show several applications of the numerical computation of geodesic distances and shortest paths to problems in surface and shape processing, in particular segmentation, sampling, meshing and comparison of shapes.
Fichier principal
Vignette du fichier
fnt-geodesic.pdf (12.47 Mo) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-00528999 , version 1 (23-10-2010)

Identifiants

  • HAL Id : hal-00528999 , version 1

Citer

Gabriel Peyré, Mickaël Péchaud, Renaud Keriven, Laurent D. Cohen. Geodesic Methods in Computer Vision and Graphics. Foundations and Trends in Computer Graphics and Vision, 2010, 5 (3-4), pp.197-397. ⟨hal-00528999⟩
1049 Consultations
1838 Téléchargements

Partager

Gmail Facebook X LinkedIn More