The present lack of a stable method to compare persistent homology groups with torsion is a relevant problem in current research about Persistent Homology and its applications in P...
We solve the problem of minimizing the number of critical points among all functions on a surface within a prescribed distance from a given input function. The result is achieved...
In this paper, we initiate a study of shape description and classification via the application of persistent homology to tangential constructions on geometric objects. Our techniq...
Gunnar Carlsson, Afra Zomorodian, Anne D. Collins,...
Abstract. This paper presents a new hybrid split-and-merge image segmentation method based on computational geometry and topology using persistent homology. The algorithm uses edge...
The persistent homology provides a mathematical tool to describe “features” in a principled manner. The persistence algorithm proposed by Edelsbrunner et al. [9] can compute n...
We show that the persistent homology of a filtered ddimensional simplicial complex is simply the standard homology of a particular graded module over a polynomial ring. Our analy...
In order to better understand human and animal mobility and its potential effects on Mobile Ad-Hoc networks and Delay-Tolerant Networks, many researchers have conducted experiment...