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arXiv · 2210.16718

Geometry of the matching distance for 2D filtering functions

Marc Ethier·Patrizio Frosini·Nicola Quercioli·Francesca Tombari
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Abstract

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.

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Marc Ethier, Patrizio Frosini, Nicola Quercioli, Francesca Tombari. 2022-10-30. Geometry of the matching distance for 2D filtering functions. https://doi.org/10.1007/s41468-023-00128-7

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