The persistence diagram of a real-valued function on a topological space is a multiset of points in the extended plane. We prove that under mild assumptions on the function, the p...
David Cohen-Steiner, Herbert Edelsbrunner, John Ha...
Topological persistence has proven to be a key concept for the study of real-valued functions defined over topological spaces. Its validity relies on the fundamental property tha...
Persistent homology is the mathematical core of recent work on shape, including reconstruction, recognition, and matching. Its pertinent information is encapsulated by a pairing o...
David Cohen-Steiner, Herbert Edelsbrunner, Dmitriy...
Using ideas from persistent homology, the robustness of a level set of a real-valued function is defined in terms of the magnitude of the perturbation necessary to kill the classe...
Paul Bendich, Herbert Edelsbrunner, Michael Kerber...
In this paper, we bound the difference between the total mean curvatures of two closed surfaces in R3 in terms of their total absolute curvatures and the Fr´echet distance betwee...