Parallel Computation of Piecewise Linear Morse-Smale Segmentations

Robin G. C. Maack, Jonas Lukasczyk, Julien Tierny, Hans Hagen, Ross Maciejewski, Christoph Garth

Room: 106

2023-10-26T03:12:00ZGMT-0600Change your timezone on the schedule page
Exemplar figure, described by caption below
The image shows the region boundaries of the Morse-Smale Segmentation computed on the Viscous Fingering dataset, simplified with an absolute persistence threshold of 0.1. The boundary interface of viscous fingers is shown as contours of the salt concentration density scalar field, colored by the density from yellow (high concentration) to purple (low concentration). The Morse-Smale segmentation region boundaries can extract the region-separating geometries that separate single viscous fingers without cluttering the visualization. Many Morse-Smale complex implementations would clutter the visualization with additional geometry from the saddle-saddle separatices.
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Morse-Smale complex;segmentation;topology;visualization;watershed transformation


This paper presents a well-scaling parallel algorithm for the computation of Morse-Smale (MS) segmentations, including the region separators and region boundaries. The segmentation of the domain into ascending and descending manifolds, solely defined on the vertices, improves the computational time using path compression and fully segments the border region. Region boundaries and region separators are generated using a multi-label marching tetrahedra algorithm. This enables a fast and simple solution to find optimal parameter settings in preliminary exploration steps by generating an MS complex preview. It also poses a rapid option to generate a fast visual representation of the region geometries for immediate utilization. Two experiments demonstrate the performance of our approach with speedups of over an order of magnitude in comparison to two publicly available implementations. The example section shows the similarity to the MS complex, the useability of the approach, and the benefits of this method with respect to the presented datasets. We provide our implementation with the paper.