Stability of persistence diagrams

被引：746

作者：

Cohen-Steiner, David

Edelsbrunner, Herbert

Harer, John

机构：

[1] INRIA, F-06904 Sophia Antipolis, France

[2] Duke Univ, Dept Comp Sci, Durham, NC 27708 USA

[3] Geomagic, Res Triangle Pk, NC 27709 USA

[4] Duke Univ, Dept Math, Durham, NC 27708 USA

来源：

DISCRETE & COMPUTATIONAL GEOMETRY | 2007年 / 37卷 / 01期

关键词：

Topological Space; Simplicial Complex; Homology Group; Hausdorff Distance; Rigid Motion;

D O I：

10.1007/s00454-006-1276-5

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 [计算机软件与理论];

摘要：

The persistence diagram of a real-valued function on a topological space is a multiset of points in the extended plane. We prove that under mild assumptions on the function, the persistence diagram is stable: small changes in the function imply only small changes in the diagram. We apply this result to estimating the homology of sets in a metric space and to comparing and classifying geometric shapes.

引用

页码：103 / 120

页数：18

共 23 条

[1]

Surface reconstruction by Voronoi filtering [J].