Gromov-Hausdorff distances in Euclidean spaces

2008 IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops, CVPR Workshops

Volumn , Issue , 2008, Pages

  Mémoli, Facundo ^a  

^a STANFORD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EUCLIDEAN; EUCLIDEAN DISTANCE MATRICES; EUCLIDEAN SPACES; EXPLICIT CONSTRUCTIONS; HAUSDORFF DISTANCE; HAUSDORFF DISTANCES;

ARTIFICIAL INTELLIGENCE; COMPUTER VISION; FEATURE EXTRACTION; IMAGE PROCESSING; PATTERN RECOGNITION;

MATRIX ALGEBRA;

EID: 51849139425     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/CVPRW.2008.4563074     Document Type: Conference Paper

References (24)

1. S. Al-Homidan and H. Wolkowicz. Approximate and exact completion problems for Euclidean distance matrices using semidefinite programming. Linear Algebra Appl., 406:109-141, 2005.
2. P. Alestalo, D. A. Trotsenko, and J. Väisälä. Isometric approximation. Israel J. Math., 125:61-82, 2001.
3. A. Y. Alfakih, A. Khandani, and H. Wolkowicz. Solving Euclidean distance matrix completion problems via semidefinite programming. Comput. Optim. Appl., 12(1-3):13-30, 1999. Computational optimization-a tribute to Olvi Mangasarian, Part I.
4. L. M. Blumenthal. Theory and applications of distance geometry. Second edition. Chelsea Publishing Co., New York, 1970.
5. M. Boutin and G. Kemper. On reconstructing n-point configurations from the distribution of distances or areas. Adv. in Appl. Math., 32(4):709-735, 2004.
6. S. Boyd and L. Vandenberghe. Convex optimization. Cambridge University Press, Cambridge, 2004.
7. A. M. Bronstein, M. M. Bronstein, and R. Kimmel. Generalized multidimensional scaling: a framework for isometry-invariant partial surface matching. Proc. Natl. Acad. Sci. USA, 103(5):1168-1172 (electronic), 2006.
8. D. Burago, Y. Burago, and S. Ivanov. A Course in Metric Geometry, volume 33 of AMS Graduate Studies in Math. American Mathematical Society, 2001.
9. S. D. Cohen and L. J. Guibas. The earth mover's distance under transformation sets. In ICCV (2), pages 1076-1083, 1999.
10. A. E. (Elbaz) and R. Kimmel. On bending invariant signatures for surfaces. IEEE Trans. Pattern Anal. Mach. Intell., 25(10):1285-1295, 2003.
11. J. W. Fickett. Approximate isometries on bounded sets with an application to measure theory. Studia Math., 72(1):37-46, 1982.
12. N. Gelfand, N. J. Mitra, L. J. Guibas, and H. Pottmann. Robust global registration. In Symposium on Geometry Processing, pages 197-206, 2005.
13. M. Goodrich, J. Mitchell, and M. Orletsky. Approximate geometric pattern matching under rigid motions. IEEE Transactions on Pattern Analysis and Machine Intelligence, 21(4):371-376, 1999.
14. M. Gromov. Metric structures for Riemannian and non-Riemannian spaces, volume 152 of Progress in Mathematics. Birkhauser Boston Inc., Boston, MA, 1999.
15. D. P. Huttenlocher, G. A. Klanderman, and W. J. Rucklidge. Comparing images using the hausdorff distance. IEEE Transactions on Pattern Analysis and Machine Intelligence, 15:9, 1993.
16. N. J. Kalton and M. I. Ostrovskii. Distances between banach spaces. Forum Math., 11:1:17-48, 1999.
17. F. Mémoli. On the use of gromov-hausdorff distances for shape comparison. In Proceedings of PBG 2007, Prague, Czech Republic, 2007.
18. F. Mémoli and G. Sapiro. Comparing point clouds. In SGP'04: Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing, pages 32-40, New York, NY, USA, 2004. ACM.
19. F. Mémoli and G. Sapiro. A theoretical and computational framework for isometry invariant recognition of point cloud data. Found. Comput. Math., 5(3):313-347, 2005.
20. N. J. Mitra, N. Gelfand, H. Pottmann, and L. Guibas. Registration of point cloud data from a geometric optimization perspective. In Symposium on Geometry Processing, pages 23-31, 2004.
21. H. Pottmann, Q.-X. Huang, Y.-L. Yang, and S.-M. Hu. Geometry and convergence analysis of algorithms for registration of 3D shapes. Int. J. Computer Vision, 67(3):277-296, 2006.
22. Y. Rubner, C. Tomasi, and L. J. Guibas. The earth mover's distance as a metric for image retrieval. Int. J. Comput. Vision, 40(2):99-121, 2000.
23. S. Rusinkiewicz and M. Levoy. Efficient variants of the icp algorithm. In 3DIM, pages 145-152. IEEE Computer Society, 2001.
24. K.-T. Sturm. On the geometry of metric measure spaces. I. Acta Math., 196(1):65-131, 2006.