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Geodesic Methods for Shape and Surface Processing

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Date
2009
Link to item file
https://hal.archives-ouvertes.fr/hal-00365899
Dewey
Probabilités et mathématiques appliquées
Sujet
Fast Marching; surface; medical image processing; Geodesics; remeshing; snakes; active contours; segmentation
DOI
http://dx.doi.org/10.1007/978-1-4020-9086-8_2
Book title
Advances in Computational Vision and Medical Image Processing: Methods and Applications
Author
Tavares, João Manuel R.S.; Jorge, R.M. Natal
Publisher
Computational Methods in Applied Sciences
Year
2009
ISBN
978-1-4020-9085-1
Book URL
10.1007/978-1-4020-9086-8
URI
https://basepub.dauphine.fr/handle/123456789/420
Collections
  • CEREMADE : Publications
Metadata
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Author
Peyré, Gabriel
Cohen, Laurent D.
Type
Chapitre d'ouvrage
Item number of pages
29-56
Abstract (EN)
This paper reviews both the theory and practice of the numerical computation of geodesic distances on Riemannian manifolds. The notion of Riemannian manifold allows 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 path 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.

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