Computational topology in text mining
CTIC'12 Proceedings of the 4th international conference on Computational Topology in Image Context
Extraction of Dominant Extremal Structures in Volumetric Data Using Separatrix Persistence
Computer Graphics Forum
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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.