Digital topological method for computing genus and the Betti numbers

Topology and its Applications

Volumn 157, Issue 12, 2010, Pages 1931-1936

  Chen, Li ^a   Rong, Yongwu ^b  

^a UNIVERSITY OF THE DISTRICT OF COLUMBIA   (United States)

^b GEORGE WASHINGTON UNIVERSITY   (United States)

Author keywords

Betti numbers; Digital surface points; Gauss Bonnett theorem; Genus; Linear time algorithms

Indexed keywords

EID: 77952952637     PISSN: 01668641     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.topol.2010.04.006     Document Type: Article

References (16)

1. Brimkov V., Klette R. Border and surface tracing. IEEE Transactions on Pattern Analysis and Machine Intelligence 2008, 30(4):577-590.
2. Chen L., Cooley D., Zhang J. Equivalence between two definitions of digital surfaces. Information Sciences 1999, 115:201-220.
3. Chen L. Discrete Surfaces and Manifolds 2004, Sp Computing, Rockville.
4. Damiand G., Peltier S., Fuchs L. Computing homology generators for volumes using minimal generalized maps. LNCS 2008, vol. 4958:63-74.
5. Delfinado C.J.A., Edelsbrunner H. An incremental algorithm for Betti numbers of simplicial complexes on the 3-sphere. Computer Aided Geometric Design 1995, 12:771-784.
6. Dey T.K., Guha S. Computing homology groups of simplicial complexes in R3. Journal of the ACM 1998, 45:266-287.
7. Hatcher A. Algebraic Topology 2002, Cambridge University Press.
8. Kaczynski T., Mischaikow K., Mrozek M. Computing homology. Homology, Homotopy and Applications 2003, 5(2):233-256.
9. Kaczynski T., Mischaikow K., Mrozek M. Computational Homology. Applied Mathematical Sciences 2004, vol. 157. Springer.
10. Kalies W.D., Mischaikow K., Watson G. Cubical Approximation and Computation of Homology. Banach Center Publ. 1999, vol. 47. pp. 115-131.
11. Klette R., Rosenfeld A. Digital Geometry: Geometric Methods for Digital Image Analysis 2004, Morgan Kaufmann.
12. Topological Algorithms for Digital Image Processing 2006, Elsevier. T.Y. Kong, A. Rosenfeld (Eds.).
13. Kot P. Homology calculation of cubical complexes in Rn. Computational Methods in Science and Technology 2006, 12:115-121.
14. Latecki L.J. 3D well-composed pictures. Graphical Models and Image Processing 1997, 59:164-172.
15. Novikov P.S. On the algorithmic unsolvability of the word problem in group theory. Trudy Mat. Inst. Steklov.. Amer. Math. Soc. Transl. 1958, 9:1-122. English transl.:.
16. K. Polthier, Polyhedral surfaces of constant mean curvature, Habilitationsschrift, Technische University, Berlin, 2002.