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cs.CG2025
The Mid-sphere Cousin of the Medial Axis Transform
Herbert Edelsbrunner, Elizabeth Stephenson, Martin Hafskjold Thoresen
The medial axis of a smoothly embedded surface in consists of all points for which the Euclidean distance function on the surface has at least two minima. We general…
cs.CG2023
Switch Points of Bi-Persistence Matching Distance
Robyn Brooks, Celia Hacker, Claudia Landi +2
In multi-parameter persistence, the matching distance is defined as the supremum of weighted bottleneck distances on the barcodes given by the restriction of persistence modules to…
cs.CG2022
Tight bounds for the learning of homotopy à la Niyogi, Smale, and Weinberger for subsets of Euclidean spaces and of Riemannian manifolds
Dominique Attali, Hana Dal Poz Kouřimská, Christopher Fillmore +4
In this article we extend and strengthen the seminal work by Niyogi, Smale, and Weinberger on the learning of the homotopy type from a sample of an underlying space. In their work,…