Euler integration of Gaussian random fields and persistent homology

Omer Bobrowski, Matthew Strom Borman

Research output: Contribution to journalArticlepeer-review


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
Pages (from-to)49-70
Number of pages22
JournalJournal of Topology and Analysis
Issue number1
StatePublished - Mar 2012


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

All Science Journal Classification (ASJC) codes

  • Analysis
  • Geometry and Topology


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