Euler integration of Gaussian random fields and persistent homology

Omer Bobrowski, Matthew Strom Borman

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper we extend the notion of the Euler characteristic to persistent homology and give the relationship between the Euler integral of a function and the Euler characteristic of the function's persistent homology. We then proceed to compute the expected Euler integral of a Gaussian random field using the Gaussian kinematic formula and obtain a simple closed form expression. This results in the first explicitly computable mean of a quantitative descriptor for the persistent homology of a Gaussian random field.

Original languageEnglish (US)
Pages (from-to)49-70
Number of pages22
JournalJournal of Topology and Analysis
Volume4
Issue number1
DOIs
StatePublished - Mar 2012
Externally publishedYes

Keywords

  • Betti numbers
  • Euler characteristic
  • Gaussian kinematic formula
  • Gaussian processes
  • Persistent homology
  • barcodes
  • random fields

ASJC Scopus subject areas

  • Analysis
  • Geometry and Topology

Fingerprint Dive into the research topics of 'Euler integration of Gaussian random fields and persistent homology'. Together they form a unique fingerprint.

Cite this