2026-07-23T22:38:03Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:17910 2024-03-06T11:00:41Z ddc:004 open_access

Slice, Simplify and Stitch: Topology-Preserving Simplification Scheme for Massive Voxel Data Wagner, Hubert Computational topology topological data analysis topological image analysis persistent homology persistence diagram discrete Morse theory algorithm engineering implementation voxel data volume data image data We focus on efficient computations of topological descriptors for voxel data. This type of data includes 2D greyscale images, 3D medical scans, but also higher-dimensional scalar fields arising from physical simulations. In recent years we have seen an increase in applications of topological methods for such data. However, computational issues remain an obstacle. We therefore propose a streaming scheme which simplifies large 3-dimensional voxel data - while provably retaining its persistent homology. We combine this scheme with an efficient boundary matrix reduction implementation, obtaining an end-to-end tool for persistent homology of large data. Computational experiments show its state-of-the-art performance. In particular, we are now able to robustly handle complex datasets with several billions voxels on a regular laptop. A software implementation called Cubicle is available as open-source: https://bitbucket.org/hubwag/cubicle. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Hubert Wagner 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.2023.60 urn:nbn:de:0030-drops-179107 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2023.60 eng https://creativecommons.org/licenses/by/4.0/legalcode