Geometry of the matching distance for 2D filtering functions

Marc Ethier, Patrizio Frosini, Nicola Quercioli, Francesca Tombari

Published 2022-10-30Version 1

In this paper we exploit the concept of extended Pareto grid to study the geometric properties of the matching distance for $\mathbb{R}^2$-valued regular functions defined on a Riemannian closed manifold. In particular, we prove that in this case the matching distance is realised either at special values or at values corresponding to vertical, horizontal or slope 1 lines.