`%0 Conference Proceedings`

`%4 sid.inpe.br/sibgrapi/2011/07.07.18.15`

`%2 sid.inpe.br/sibgrapi/2011/07.07.18.15.05`

`%A Günther, David,`

`%A Reininghaus, Jan,`

`%A Wagner, Hubert,`

`%A Hotz, Ingrid,`

`%@affiliation Zuse Institute Berlin`

`%@affiliation Zuse Institute Berlin`

`%@affiliation Institute of Computer Science, Jagiellonian University`

`%@affiliation Zuse Institute Berlin`

`%T Memory-Efficient Computation of Persistent Homology for 3D Images using Discrete Morse Theory`

`%B Conference on Graphics, Patterns and Images, 24 (SIBGRAPI)`

`%D 2011`

`%E Lewiner, Thomas,`

`%E Torres, Ricardo,`

`%S Proceedings`

`%8 Aug. 28 - 31, 2011`

`%J Los Alamitos`

`%I IEEE Computer Society Conference Publishing Services`

`%C Maceió`

`%K persistent homology, Morse-Smale complex, discrete Morse theory, large data.`

`%X We 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.`

`%@language en`

`%3 persistenceLargeData.pdf`