Euler Integration of Gaussian Random Fields and Persistent Homology

Details Euler Integration of Gaussian Random Fields and Persistent Homology Euler Integration of Gaussian Random Fields and Persistent Homology

2010-03-26

arxiv.org/abs/1003.5175v3

Mathematics

Probability

21 pages, 1 figure

Scientific paper

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.

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