Computation of homology groups and generators

Lecture Notes in Computer Science

Volumn 3429, Issue , 2005, Pages 195-205

  Peltier, Samuel ^a   Alayrangues, Sylvie ^b   Fuchs, Laurent ^a   Lachaud, Jacques Olivier ^b  

^a UNIVERSITÉ DE POITIERS   (France)

^b UNIVERSITÉ BORDEAUX 1   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; IMAGE PROCESSING; TOPOLOGY; TORSIONAL STRESS;

BETTI NUMBERS; GEOMETRIC MODELING; HOMOLOGY; TORSION COEFFICIENTS;

COMPUTATIONAL COMPLEXITY;

EID: 24344434628     PISSN: 03029743     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1007/978-3-540-31965-8_19     Document Type: Conference Paper

References (21)

1. [ACZ04] M. Allili, D. Corriveau, and D. Ziou. Morse homology desriptor for shape characterization. In Proc. ICPR 2004, 2004.
2. [ADFQ03] R. Ayala, E. Dominguez, A.R. Francès, and A. Quintero. Homotopy in digital spaces. DAMATH: Discrete Appl. Math. and Combin. Oper. Research and Comput. Science, 125, 2003.
3. [Ago76] M. K. Agoston. Algebraic Topology, a first course. Marcel Dekker Ed., 1976.
4. [Box99] L. Boxer. A classical construction for the digital fundamental group. J. Math. Imaging Vision, 10:51-62, 1999.
5. [Cai61] S. S. Cairns. Introductory Topology. Ronald Press Company, 1961.
6. [Cur71] E. Curtis. Simplicial homotopy theory. Adv. Math., 6:107-209, 1971.
7. [DE95] C. J. A. Delfinado and H. Edelsbrunner. An incremental algorithm for betti numbers of simplicial complexes on the 3-sphere. Comput. Aided Geom. Design, 12(7):771-784, 1995.
8. [DG03] P. Desbarats and S. Gueorguieva. Topological mainframe for numerical representations of objects. In Proc. Int. Conf. Comput. Science and its Appl., volume 2668 of LNCS, pages 498-507. Springer, 2003.
9. [DSV01] J. G. Dumas, B.D. Saunders, and G. Villard. On efficient sparse integer matrix smith normal form computations. Journal of Symbolic Computation, 2001.
10. [GDR03] R. González-Díaz and P. Real. Toward digital cohomology. In G. Sanniti di Baja, S. Svensson, and I. Nyström, editors, Proc. DGCI'2003, volume 2886 of LNCS, pages 92-101. Springer, 2003.
11. [Gie95] M. Giesbrecht. Nearly optimal-algorithms for canonical matrix-forms. SIAM J. COMPUT., 24(5):948-969, OCT 1995.
12. [Hat02] A. Hatcher. Algebraic Topology. Cambridge University Press, 2002. disponible sur http://www.math.cornell.edu/~hatcher/AT/ATpage.html.
13. [KMS98] T. Kaczynski, M. Mrozek, and M. Slusarek. Homology computation by reduction of chain complexes. Computers & Math. Appl., 34(4):59-70, 1998.
14. [Kon89] T. Y. Kong. A digital fundamental group. Computers and Graphics, 13(2):159-166, 1989.
15. [KR89] T. Y. Kong and A. Rosenfeld. Digital Topology: Introduction and Survey. Comput. Vision, Graphics, and Image Processing, 48(3):357-393, 1989.
16. [LE93] P. Lienhardt and H. Elter. Different combinatorial models based on the map concept for the representation of different types of cellular complexes. In Proceedings of IFIP TC 5/WG II Work. Conf. on Geom. Modeling in Comp. Graphics. Springer, 1993.
17. [LL95] V. Lang and P. Lienhardt. Geometric modeling with simplicial sets. In Proc. of Pacific Graphics'95, Seoul, Korea, 1995.
18. [Mal01] R. Malgouyres. Computing the fundamental group in digital spaces. IJPRAI, 15(7): 1075-1088, 2001.
19. [May67] J. P. May. Simplicial Objects in Algebraic Topology. Van Nostrand, 1967.
20. [Mun84] J. R. Munkres. Elements of algebraic topology. Perseus Books, 1984.
21. [Sto96] A. Storjohann. Near optimal algorithms for computing Smith normal forms of integer matrices. In Y. N. Lakshman, editor, Proceedings of the 1996 International Symposium on Symbolic and Algebraic Computation, pages 267-274. ACM, 1996.