Localized homology

Proceedings - IEEE International Conference on Shape Modeling and Applications 2007, SMI'07

Volumn , Issue , 2007, Pages 189-198

  Zomorodian, Afra ^a   Carlsson, Gunnar ^b  

^a Dartmouth Department of Computer Science_Dartmouth College   (United States)

^b STANFORD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTATIONAL GEOMETRY; TOPOLOGY; VOID FRACTION;

ARBITRARY-DIMENSIONAL ATTRIBUTES; TOPOLOGICAL ATTRIBUTES;

COMPUTATION THEORY;

EID: 38649108808     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/SMI.2007.25     Document Type: Conference Paper

References (21)

1. M. S. Apaydin, D. L. Brutlag, C. Guestrin, D. Hsu, J.-C. Latombe, and C. Varma. Stochastic roadmap simulation: An efficient representation and algorithm for analyzing molecular motion. Journal of Computational Biology, 10:257-281, 2003.
2. J. L. Bentley. Multidimensional search trees used for associative searching. Comm. ACM, 18:509-517, 1975.
3. G. Carlsson, T. Ishkhanov, V. de Silva, and A. Zomorodian. On the local behavior of spaces of natural images. International Journal of Computer Vision, 2007. To appear.
4. G. Carlsson, A. Zomorodian, A. Collins, and L. J. Guibas. Persistence barcodes for shapes. International Journal of Shape Modeling, 11(2): 149-187, 2005.
5. E. Colin de Verdière and F. Lazarus. Optimal system of loops on an orientable surface. Discrete and Computational Geometry, 33(3):507-534, 2005.
6. H. Edelsbrunner, D. Letscher, and A. Zomorodian. Topological persistence and simplification. Discrete and Computational Geometry, 28:511-533, 2002.
7. J. Erickson. Personal communication.
8. J. Erickson and S. Har-Peled. Optimally cutting a surface into a disk. Discrete and Computational Geometry, 31(l):37-59, 2004.
9. J. Erickson and K. Whittlesey. Greedy optimal homotopy and homology generators. In Proc. 16th. Annual ACM-SIAM Symposium on Discrete Algorithms, pages 1038-
10. 1046, 2005.
11. I. Guskov and Z. Wood. Topological noise removal. In Graphics Interface, pages 19-26, 2001.
12. A. Hatcher. Algebraic Topology. Cambridge University i Press, Cambridge, UK, 2001.
13. F. Lazarus, M. Pocchiola, G. Vegter, and A. Verroust. Computing a canonical polygonal schema of an orientable triangulated surface. In Proc. 17th Annu. ACM Sympos. Comput. Geom., pages 80-89, 2001.
14. M. Levoy, K. Pulli, B. Curless, S. Rusinkiewicz, D. Koller, L. Pereira, M. Ginzton, S. Anderson, J. Davis, J. Ginsberg, J. Shade, and D. Fulk. The digital Michelangelo project: 3D scanning of large statues. In SIGGRAPH 00 Conference Proceedings, pages 131-144, 2000.
15. J. R. Munkres. Elements of Algebraic Topology. Addison-Wesley, Reading, MA, 1984.
16. B. Naylor, J. Amanatides, and W. Thibault. Merging BSP trees yield polyhedral modeling results. In SIGGRAPH 90 Conference Proceedings, pages 115-124, 1990.
17. G. Segal. Classifying spaces and spectral sequences. Inst. Hautes Études Sci. Publ. Math., 34:105-112, 1968.
18. G. Vegter and C. K. Yap. Computational complexity of combinatorial surfaces. In Proc. 6th Annu. ACM Sympos. Comput. Geom., pages 102-111, 1990.
19. Z. Wood, H. Hoppe, M. Desbrun, and P. Schröder. Removing excess topology from isosurfaces. ACM Transactions on Graphics, 23(2): 190-208, Apr. 2004.
20. A. Zomorodian. Topology for Computing. Cambridge University Press, New York, NY, 2005.
21. A. Zomorodian and G. Carlsson. Computing persistent homology. Discrete and Computational Geometry, 33(2):249-274, 2005.