A Closed Formula for the Interleaving Distance of Rectangle Persistence Modules

TL;DR

This paper provides explicit formulas for computing the interleaving distance between rectangle persistence modules based on their geometric properties, and extends these results to bottleneck distances for decomposable modules.

Contribution

It introduces a closed-form formula for interleaving distances of rectangle persistence modules, simplifying calculations based on geometric data.

Findings

Formulas depend only on rectangle geometry

Extended results to bottleneck distance for decomposable modules

Simplifies distance calculations in topological data analysis

Abstract

We give formulas for calculating the interleaving distance between rectangle persistence modules that depend solely on the geometry of the underlying rectangles. Moreover, we extend our results to calculate the bottleneck distance for rectangle decomposable persistence modules.