2026-07-23T15:20:19Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:17870 2024-03-06T11:00:34Z ddc:004 open_access

Sparse Higher Order Čech Filtrations Buchet, Mickaël B. Dornelas, Bianca Kerber, Michael Sparsification k-fold cover Higher order Čech complexes For a finite set of balls of radius r, the k-fold cover is the space covered by at least k balls. Fixing the ball centers and varying the radius, we obtain a nested sequence of spaces that is called the k-fold filtration of the centers. For k = 1, the construction is the union-of-balls filtration that is popular in topological data analysis. For larger k, it yields a cleaner shape reconstruction in the presence of outliers. We contribute a sparsification algorithm to approximate the topology of the k-fold filtration. Our method is a combination and adaptation of several techniques from the well-studied case k = 1, resulting in a sparsification of linear size that can be computed in expected near-linear time with respect to the number of input points. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Mickaël Buchet and Bianca B. Dornelas and Michael Kerber 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.2023.20 urn:nbn:de:0030-drops-178709 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2023.20 eng https://creativecommons.org/licenses/by/4.0/legalcode