2026-07-25T02:44:19Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:12176 2024-03-06T10:49:37Z ddc:004 open_access

Relative Persistent Homology Blaser, Nello Brun, Morten topological data analysis relative homology Delaunay-Čech complex alpha complex The alpha complex efficiently computes persistent homology of a point cloud X in Euclidean space when the dimension d is low. Given a subset A of X, relative persistent homology can be computed as the persistent homology of the relative Čech complex Č(X, A). But this is not computationally feasible for larger point clouds X. 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-Čech complex DelČ(X, A) whose homology is the relative persistent homology. It is constructed from the Delaunay complex of an embedding of X in (d+1)-dimensional Euclidean space. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Nello Blaser and Morten Brun 2020 Is Part Of LIPIcs, Volume 164, 36th International Symposium on Computational Geometry (SoCG 2020) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.SoCG.2020.18 urn:nbn:de:0030-drops-121762 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2020.18 eng https://creativecommons.org/licenses/by/3.0/legalcode