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Memory-Efficient Computation of Persistent Homology for 3D Images using Discrete Morse Theory
Zuse Institute Berlin.
Zuse Institue Berlin.
Jagiellonian University,Krakow, Poland.
Zuse Institue Berlin.ORCID iD: 0000-0001-7285-0483
2011 (English)Conference paper (Refereed)
Abstract [en]

We propose a memory-efficient method that computes persistent homology for 3D gray-scale images. The basic idea is to compute the persistence of the induced Morse-Smale complex. Since in practice this complex is much smaller than the input data, significantly less memory is required for the subsequent computations. We propose a novel algorithm that efficiently extracts the Morse-Smale complex based on algorithms from discrete Morse theory. The proposed algorithm is thereby optimal with a computational complexity of O(n2). The persistence is then computed using the Morse-Smale complex by applying an existing algorithm with a good practical running time. We demonstrate that our method allows for the computation of persistent homology for large data on commodity hardware.

Place, publisher, year, edition, pages
2011. 25-32 p.
Keyword [en]
computational topology, algorithm
National Category
Computer Vision and Robotics (Autonomous Systems)
Identifiers
URN: urn:nbn:se:liu:diva-127677DOI: 10.1109/SIBGRAPI.2011.24ISBN: 978-1-4577-1674-4OAI: oai:DiVA.org:liu-127677DiVA: diva2:926368
Conference
2011 24th SIBGRAPI Conference on Graphics, Patterns and Images. 28-31 Aug. 2011 Maceio, Alagoas
Available from: 2016-05-06 Created: 2016-05-06 Last updated: 2016-05-11

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Hotz, Ingrid
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ReferencesLink to record
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