Article

Discrete & Computational Geometry

, Volume 50, Issue 2, pp 330-353

Morse Theory for Filtrations and Efficient Computation of Persistent Homology

  • Konstantin MischaikowAffiliated withDepartment of Mathematics and BioMaPS, Rutgers, The State University of New Jersey
  • , Vidit NandaAffiliated withDepartment of Mathematics, The University of Pennsylvania Email author 

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Abstract

We introduce an efficient preprocessing algorithm to reduce the number of cells in a filtered cell complex while preserving its persistent homology groups. The technique is based on an extension of combinatorial Morse theory from complexes to filtrations.

Keywords

Computational topology Discrete Morse theory Persistent homology