35 citations · 35 across the 4 of their papers we have counts for
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…
Maximum Persistent Betti Numbers of Čech Complexes
Herbert Edelsbrunner, Matthew Kahle, Shu Kanazawa
This note proves that only a linear number of holes in a Čech complex of points in can persist over an interval of constant length. Specifically, for any fixed d…
Merge Trees of Periodic Filtrations
Herbert Edelsbrunner, Teresa Heiss
Motivated by applications to crystalline materials, we generalize the merge tree and the related barcode of a filtered complex to the periodic setting in Euclidean space. They are…
The Morse theory of Čech and Delaunay complexes
Ulrich Bauer, Herbert Edelsbrunner
Given a finite set of points in and a radius parameter, we study the Čech, Delaunay-Čech, Delaunay (or Alpha), and Wrap complexes in the light of generalized discrete…