论文信息 - On critical kernels

On critical kernels

We propose a method for collapsing simplicial complexes. For that purpose, we introduce the notion of an essential face, and the one of a core of a cell. Then, we define the critical kernel of a complex. Our main result is that the critical kernel of a given complex X is a collapse of X. We extend this result by giving a necessary and sufficient condition which characterizes a certain class of subcomplexes of X which contain the critical kernel of X. In particular, any complex which belongs to this class is homotopy equivalent to X. To cite this article: G. Bertrand, C. R. Acad. Sci. Paris, Ser. I 345 (2007).

Gilles Bertrand | Gilles Bertrand

[1] P. Giblin. Graphs, surfaces, and homology , 1977 .

[2] T. Yung Kong,et al. Topology-Preserving Deletion of 1's from 2-, 3- and 4-Dimensional Binary Images , 1997, DGCI.

[3] Azriel Rosenfeld,et al. Digital geometry - geometric methods for digital picture analysis , 2004 .

[4] Marshall M. Cohen. A Course in Simple-Homotopy Theory , 1973 .

[5] T. Yung Kong,et al. On Topology Preservation in 2-D and 3-D Thinning , 1995, Int. J. Pattern Recognit. Artif. Intell..

[6] J. Whitehead. Simplicial Spaces, Nuclei and m‐Groups , 1939 .

[7] Gilles Bertrand,et al. On P-simple points , 1995 .

[8] Gilles Bertrand,et al. Two-Dimensional Parallel Thinning Algorithms Based on Critical Kernels , 2008, Journal of Mathematical Imaging and Vision.