Efficient computation of 3D Morse-Smale complexes and persistent homology using discrete Morse theory

摘要

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 in put data but still contains all necessary information. Our method improves a recently proposed algorithm to extract the Morse-Smale complex in terms of memory consump tion and running time. It also allows for a parallel com putation 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 apply ing 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 hard ware.