论文信息 - Topological Persistence and Simplification

Topological Persistence and Simplification

AbstractWe formalize a notion of topological simplification within the framework of a filtration, which is the history of a growing complex. We classify a topological change that happens during growth as either a feature or noise depending on its lifetime or persistence within the filtration. We give fast algorithms for computing persistence and experimental evidence for their speed and utility.

[1] John McCleary,et al. User's Guide to Spectral Sequences , 1985 .

[2] Herbert Edelsbrunner,et al. An incremental algorithm for Betti numbers of simplicial complexes on the 3-sphere , 1995, Comput. Aided Geom. Des..

[3] Herbert Edelsbrunner,et al. Three-dimensional alpha shapes , 1992, VVS.

[4] James R. Munkres,et al. Elements of algebraic topology , 1984 .

[5] J. Meiss,et al. Computational topology at multiple resolutions: foundations and applications to fractals and dynamics , 2000 .

[6] Herbert Edelsbrunner,et al. An incremental algorithm for Betti numbers of simplicial complexes , 1993, SCG '93.

[7] Stanley Osher,et al. Level Set Methods , 2003 .

[8] Jesse Freeman,et al. in Morse theory, , 1999 .

[9] Jihad El-Sana,et al. Topology Simplification for Polygonal Virtual Environments , 1998, IEEE Trans. Vis. Comput. Graph..