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

Author Hubert Wagner

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Author Details

Hubert Wagner
  • University of Florida, Gainesville, Fl, USA

Funding

Supported by the 2022 Google Research Scholar Award in Algorithms and Optimization.

Acknowledgements

I would like to thank Herbert Edelsbrunner, Teresa Heiss, Kevin Knudson, Marian Mrozek, Georg Osang and Vanessa Robins for their helpful comments.

Cite As Get BibTex

Hubert Wagner. Slice, Simplify and Stitch: Topology-Preserving Simplification Scheme for Massive Voxel Data. In 39th International Symposium on Computational Geometry (SoCG 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 258, pp. 60:1-60:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.SoCG.2023.60

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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
  • Mathematics of computing → Combinatorial algorithms
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

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Supplementary Materials

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