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Efficient Computation of 3D Morse-Smale Complexes and Persistent Homology using Discrete Morse Theory
Saarbrücken, Germany.
Zuse Institute Berlin, Germany.
Lojasiewicza 6, Krakow, Poland .
Zuse Institute Berlin, Germany.ORCID iD: 0000-0001-7285-0483
2012 (English)In: The Visual Computer, ISSN 0178-2789, E-ISSN 1432-2315, Vol. 28, no 10, 959-969 p.Article in journal (Refereed) Published
Abstract [en]

We propose an efficient algorithm that computes the Morse–Smale complex for 3D gray-scale images. This complex allows for an efficient computation of persistent homology since it is, in general, much smaller than the input data but still contains all necessary information. Our method improves a recently proposed algorithm to extract the Morse–Smale complex in terms of memory consumption and running time. It also allows for a parallel computation of the complex. The computational complexity of the Morse–Smale complex extraction solely depends on the topological complexity of the input data. 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
2012. Vol. 28, no 10, 959-969 p.
Keyword [en]
Persistent homology – Morse–Smale complex – Discrete Morse theory – Large data
National Category
Media Engineering
Identifiers
URN: urn:nbn:se:liu:diva-127664DOI: 10.1007/s00371-012-0726-8OAI: oai:DiVA.org:liu-127664DiVA: diva2:926355
Available from: 2016-05-06 Created: 2016-05-06 Last updated: 2016-05-12

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ReferencesLink to record
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