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Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.SoCG.2023.14
URN: urn:nbn:de:0030-drops-178643
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/17864/
Bauer, Ulrich ;
Schmahl, Maximilian
Efficient Computation of Image Persistence
Abstract
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.
BibTeX - Entry
@InProceedings{bauer_et_al:LIPIcs.SoCG.2023.14,
author = {Bauer, Ulrich and Schmahl, Maximilian},
title = {{Efficient Computation of Image Persistence}},
booktitle = {39th International Symposium on Computational Geometry (SoCG 2023)},
pages = {14:1--14:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-273-0},
ISSN = {1868-8969},
year = {2023},
volume = {258},
editor = {Chambers, Erin W. and Gudmundsson, Joachim},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2023/17864},
URN = {urn:nbn:de:0030-drops-178643},
doi = {10.4230/LIPIcs.SoCG.2023.14},
annote = {Keywords: Persistent homology, image persistence, barcode computation}
}
