4 papers
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…
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…
Computing the Matching Distance of 2-Parameter Persistence Modules from Critical Values
Asilata Bapat, Robyn Brooks, Celia Hacker +3
The exact computation of the matching distance for multi-parameter persistence modules is an active area of research in computational topology. Achieving an easily obtainable exact…
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,…