Proceedings of the Annual ACM Symposium on Computational Geometry, pages 127-134, 2006. |

SoCG'06 | |

Official ACM version: | through ACM portal |

We continue the study of topological persistence [5] by investigating the problem of simplifying a function f in a way that removes topological noise as determined by its persistence diagram [2]. To state our results, we call a function g an ε-simplification of another function f if ||f - g||

[2]

David Cohen-Steiner, Herbert Edelsbrunner and John Harer. Stability of persistence diagrams. In "Proc. 21st Ann. Sympos. Comput. Geom., 2005", 263-271.

[3]

Herbert Edelsbrunner, Valerio Pascucci, and Dmitriy Morozov. Persistence-Sensitive Simplification of Functions on 2-Manifolds. Proceedings of the Annual Symposium on Computational Geometry, pages 127-134, New York, New York, June 2006.

[5]

Herbert Edelsbrunner, David Letscher and Afra Zomorodian. Topological persistence and simplification. Discrete Comput. Geom. 28 (2002), 511-533.