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Efficient construction of the Čech complex

Authors
Journal
Computers & Graphics
0097-8493
Publisher
Elsevier
Volume
36
Issue
6
Identifiers
DOI: 10.1016/j.cag.2012.02.016
Keywords
  • Čech Complex
  • Vietoris–Rips Complex
  • Persistent Topology
  • Topological Data Analysis
Disciplines
  • Computer Science
  • Mathematics

Abstract

Abstract In many applications, the first step into the topological analysis of a discrete point set P sampled from a manifold is the construction of a simplicial complex with vertices on P. In this paper, we present an algorithm for the efficient computation of the Čech complex of P for a given value ε of the radius of the covering balls. Experiments show that the proposed algorithm can generally handle input sets of several thousand points, while for the topologically most interesting small values of ε can handle inputs with tens of thousands of points. We also present an algorithm for the construction of all possible Čech complices on P.

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