2026-07-20T11:45:55Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:19989 2024-06-06T06:21:15Z ddc:004 open_access

Stability and Approximations for Decorated Reeb Spaces Curry, Justin Mio, Washington Needham, Tom Okutan, Osman Berat Russold, Florian Reeb spaces Gromov-Hausdorff distance Persistent homology Given a map f:X → M from a topological space X to a metric space M, a decorated Reeb space consists of the Reeb space, together with an attribution function whose values recover geometric information lost during the construction of the Reeb space. For example, when M = ℝ is the real line, the Reeb space is the well-known Reeb graph, and the attributions may consist of persistence diagrams summarizing the level set topology of f. In this paper, we introduce decorated Reeb spaces in various flavors and prove that our constructions are Gromov-Hausdorff stable. We also provide results on approximating decorated Reeb spaces from finite samples and leverage these to develop a computational framework for applying these constructions to point cloud data. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Justin Curry and Washington Mio and Tom Needham and Osman Berat Okutan and Florian Russold 2024 Is Part Of LIPIcs, Volume 293, 40th International Symposium on Computational Geometry (SoCG 2024) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.SoCG.2024.44 urn:nbn:de:0030-drops-199891 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2024.44 eng https://creativecommons.org/licenses/by/4.0/legalcode