License: 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.2023.60
URN: urn:nbn:de:0030-drops-179107
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/17910/
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Wagner, Hubert

Slice, Simplify and Stitch: Topology-Preserving Simplification Scheme for Massive Voxel Data

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LIPIcs-SoCG-2023-60.pdf (1 MB)

Abstract

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.

BibTeX - Entry

@InProceedings{wagner:LIPIcs.SoCG.2023.60,
  author =	{Wagner, Hubert},
  title =	{{Slice, Simplify and Stitch: Topology-Preserving Simplification Scheme for Massive Voxel Data}},
  booktitle =	{39th International Symposium on Computational Geometry (SoCG 2023)},
  pages =	{60:1--60:16},
  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/2023/17910},
  URN =		{urn:nbn:de:0030-drops-179107},
  doi =		{10.4230/LIPIcs.SoCG.2023.60},
  annote =	{Keywords: Computational topology, topological data analysis, topological image analysis, persistent homology, persistence diagram, discrete Morse theory, algorithm engineering, implementation, voxel data, volume data, image data}
}

Keywords: Computational topology, topological data analysis, topological image analysis, persistent homology, persistence diagram, discrete Morse theory, algorithm engineering, implementation, voxel data, volume data, image data
Collection: 39th International Symposium on Computational Geometry (SoCG 2023)
Issue Date: 2023
Date of publication: 09.06.2023
Supplementary Material: Software: https://bitbucket.org/hubwag/cubicle archived at: https://archive.softwareheritage.org/swh:1:dir:5f25601ea576ea1a004c37d94e2e2f5b94b9c00d

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