2026-08-18T02:31:18Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:17864 2024-03-06T11:00:33Z ddc:004 open_access

Efficient Computation of Image Persistence Bauer, Ulrich Schmahl, Maximilian Persistent homology image persistence barcode computation We present an algorithm for computing the barcode of the image of a morphism in persistent homology induced by an inclusion of filtered finite-dimensional chain complexes. The algorithm makes use of the clearing optimization and can be applied to inclusion-induced maps in persistent absolute homology and persistent relative cohomology for filtrations of pairs of simplicial complexes. The clearing optimization works particularly well in the context of relative cohomology, and using previous duality results we can translate the barcodes of images in relative cohomology to those in absolute homology. This forms the basis for an implementation of image persistence computations for inclusions of filtrations of Vietoris-Rips complexes in the framework of the software Ripser. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Ulrich Bauer and Maximilian Schmahl 2023 Is Part Of LIPIcs, Volume 258, 39th International Symposium on Computational Geometry (SoCG 2023) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.SoCG.2023.14 urn:nbn:de:0030-drops-178643 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2023.14 eng https://creativecommons.org/licenses/by/4.0/legalcode