Reference TypeConference Proceedings
Citation KeyGüntherReinWagnHotz:2011:MeCoPe
Author1 Günther, David
2 Reininghaus, Jan
3 Wagner, Hubert
4 Hotz, Ingrid
Affiliation1 Zuse Institute Berlin
2 Zuse Institute Berlin
3 Institute of Computer Science, Jagiellonian University
4 Zuse Institute Berlin
TitleMemory-Efficient Computation of Persistent Homology for 3D Images using Discrete Morse Theory
Conference NameConference on Graphics, Patterns and Images, 24 (SIBGRAPI)
EditorLewiner, Thomas
Torres, Ricardo
Book TitleProceedings
DateAug. 28 - 31, 2011
Publisher CityLos Alamitos
PublisherIEEE Computer Society
Conference LocationMaceió
Keywordspersistent homology, Morse-Smale complex, discrete Morse theory, large data.
AbstractWe propose a memory-efficient method that com- putes 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 per- sistence 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.
Tertiary TypeFull Paper
FormatDVD, On-line.
Size3387 KiB
Number of Files1
Target FilepersistenceLargeData.pdf
Last Update2011:
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History2011-07-23 15:36:12 :: -> administrator :: 2011
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