Geodesic methods for shape and surface processing

Computational Methods in Applied Sciences

Volumn 13, Issue , 2009, Pages 29-56

  Peyré, Gabriel ^a   Cohen, Laurent D ^a  

^a UNIVERSITÉ PARIS DAUPHINE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84962844512     PISSN: 18713033     EISSN: None     Source Type: Book Series    
DOI: 10.1007/978-1-4020-9086-8_2     Document Type: Conference Paper

References (27)

1. Cohen, L.D.: Minimal paths and fast marching methods for image analysis. In: Handbook of Mathematical Methods in Computer Vision, N. Paragios and Y. Chen and O. Faugeras Editors, Springer, Berlin (2005)
2. Prados, E., Lenglet, C., Pons, J.P., Wotawa, N., Deriche, R., Faugeras, O.D., Soatto, S.: Control theory and fast marching methods for brain connectivity mapping. In: Proc. CVPR 2006. (2006)
3. Crandall, M.G., Ishii, H., Lions, P.L.: User's guide to viscosity solutions of second order partial differential equations. Bull. Amer. Math. Soc 27(1992) 1
4. Cohen, L.D., Kimmel, R.: Global minimum for active contour models: a minimal path approach. International Journal of Computer Vision 24(1) (Aug. 1997) 57-78
5. Sethian, J.: Level Sets Methods and Fast Marching Methods. 2nd edn. Cambridge University Press, Cambridge (1999)
6. Osher, S.J., Fedkiw, R.: Level Set Methods and Dynamic Implicit Surfaces. Springer, New York (2002)
7. Kimmel, R.: Numerical Geometry of Images: Theory, Algorithms, and Applications. Springer, Berlin New York (2004)
8. Bronstein, A., Bronstein, M., Kimmel, R.: Numerical Geometry of Non-Rigid Shapes. Springer-Verlag New York (2007)
9. Osher, S.J., Paragios, N.: Geometric Level Set Methods in Imaging, Vision, and Graphics. Springer New York (July 2003)
10. Paragios, N., Chen, Y., Faugeras, O.D.: Handbook of Mathematical Models in Computer Vision. Springer-Verlag New York (2005)
11. Kimmel, R., Sethian, J.: Computing geodesic paths on manifolds. Proc. Natl. Acad. Sci. 95(15) (1998) 8431-8435
12. Spira, A., Kimmel, R.: An efficient solution to the eikonal equation. Interfaces Free Boundaries 6(3) (2004) 315-327
13. Bronstein, A.M., Bronstein, M.M., Kimmel, R.: Weighted distance maps computation on parametric three-dimensional manifolds. J. Comput. Phys., accepted (2007)
14. Kimmel, R., Amir, A., Bruckstein, A.M.: Finding shortest paths on surfaces using level sets propagation. IEEE Trans. PAMI 17(6) (1995) 635-640
15. Deschamps, T., Cohen, L.: Fast Extraction of Minimal Paths in 3D Images and Applications to Virtual Endoscopy. Med. Image Anal. 5(4) (December 2001)
16. Kothe, U.: Edge and junction detection with an improved structure tensor. In: Proc. DAGM03. (2003) 25-32
17. Ion, A., Peyré, G., Haxhimusa, Y., Peltier, S., Kropatsch, W.G., Cohen, L.: Shape matching using the geodesic eccentricity transform. In: Proc. OAGM'07. (2007)
18. Ling, H., Jacobs, D.W.: Using the inner-distance for classification of articulated shapes. In: CVPR 2005, 20-26 June 2005, San Diego, CA. (2005) 719-726
19. Nilsson, N.: Problem-solving Methods in Artificial Intelligence. McGraw-Hill, New York (1971)
20. ∗ search meets graph theory. Technical Report MSR-TR-2004-24 (2004)
21. Peyré, G., Cohen, L.: Heuristically driven front propagation for fast geodesic extraction. Int. J. Comput. Vision Biomech. 1(1) (2007)
22. Eldar, Y., Lindenbaum, M., Porat, M., Zeevi, Y.Y.: The farthest point strategy for progressive image sampling. IEEE Trans. Image Process. 6(9) (September 1997) 1305-1315
23. Peyré, G., Cohen, L.D.: Geodesic remeshing using front propagation. Int. J. Comput. Vision 69(1) (2006) 145-156
24. Cohen, L.: Multiple Contour Finding and Perceptual Grouping Using Minimal Paths. J. Math. Imaging Vis. 14(3) (May 2001) 225-236
25. Clarkson, K.L.: Building triangulations using epsilon-nets. In Kleinberg, J.M., ed.: STOC, ACM (2006) 326-335
26. Alliez, P., Ucelli, G., Gotsman, C., Attene, M.: Recent advances in remeshing of surfaces. In: AIM@SHAPE repport. (2005)
27. Leibon, G., Letscher, D.: Delaunay triangulations and voronoi diagrams for riemannian manifolds. In: SCG '00: Proceedings of the sixteenth annual symposium on Computational geometry, New York, NY, ACM (2000) 341-349