Relative persistent homology
Algebraic Topology
2019-11-19 v1
Abstract
The alpha complex efficiently computes persistent homology of a point cloud in Euclidean space when the dimension is low. Given a subset of , relative persistent homology can be computed as the persistent homology of the relative \v{C}ech complex. But this is not computationally feasible for larger point clouds. The aim of this note is to present a method for efficient computation of relative persistent homology in low dimensional Euclidean space. We introduce the relative Delaunay \v{C}ech complex whose homology is the relative persistent homology. It can be constructed from the Delaunay complex of an embedding of the point clouds in -dimensional Euclidean space.
Cite
@article{arxiv.1911.07484,
title = {Relative persistent homology},
author = {Nello Blaser and Morten Brun},
journal= {arXiv preprint arXiv:1911.07484},
year = {2019}
}