The Localized Union-of-Balls Bifiltration

arXiv2303.07002MaRDI QIDQ6429341

Author name not available (Why is that?)

Publication date: 13 March 2023

Abstract: We propose an extension of the classical union-of-balls filtration of persistent homology: fixing a point $q$, we focus our attention to a ball centered at $q$ whose radius is controlled by a second scale parameter. We discuss an absolute variant, where the union is just restricted to the $q$-ball, and a relative variant where the homology of the $q$-ball relative to its boundary is considered. Interestingly, these natural constructions lead to bifiltered simplicial complexes which are not $k$-critical for any finite $k$. Nevertheless, we demonstrate that these bifiltrations can be computed exactly and efficiently, and we provide a prototypical implementation using the CGAL library. We also argue that some of the recent algorithmic advances for $2$-parameter persistence (which usually assume $k$-criticality for some finite $k$) carry over to the $infty$-critical case.

Has companion code repository: https://bitbucket.org/mkerber/demo_absolute_2d

This page was built for publication: The Localized Union-of-Balls Bifiltration

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6429341)