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Foundations and Trends in Computer Graphics and Vision 5, 3-4 (2010) 197-397

Geodesic Methods in Computer Vision and Graphics

Gabriel Peyré 1, Mickaël Péchaud 2, 3, Renaud Keriven 2, 3, Laurent D. Cohen 1

(2010)

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.

1 :	CEntre de REcherches en MAthématiques de la DEcision (CEREMADE)
	CNRS : UMR7534 – Université Paris IX - Paris Dauphine
2 :	IMAGINE
	CSTB – Ecole des Ponts ParisTech – Université Paris XII - Paris Est Créteil Val-de-Marne
3 :	Laboratoire d'Informatique Gaspard-Monge (LIGM)
	Université Paris Est Marne-la-Vallée – ESIEE – Ecole des Ponts ParisTech – Fédération de Recherche Bézout – CNRS : UMR8049

Domaine

:

Informatique/Traitement du signal et de l'image Sciences de l'ingénieur/Traitement du signal et de l'image

Mots Clés : Computer vision – computer graphics – geodesic distance – Riemannian manifold – Fast Marching – mesh – image – level set – active contour – shortest path – image segmentation – medical imaging – remeshing – sampling

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Contributeur : Gabriel Peyré <>

Soumis le : Samedi 23 Octobre 2010, 21:23:20

Dernière modification le : Mardi 14 Février 2012, 15:24:51