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.

翻译：本文提出一种可良好扩展的并行算法，用于计算Morse-Smale（MS）分割结果，包括区域分隔符与区域边界。该方法将定义于顶点上的升流形与降流形进行域分割，通过路径压缩技术提升计算效率，并实现边界区域的完整分割。采用多标签行进四面体算法生成区域边界与区域分隔符。该方案能在初步探索阶段快速生成MS复合体预览，从而高效简便地确定最优参数设置；同时为区域几何结构的即时可视化提供快速实现途径。两个实验表明，与两种公开实现相比，本方法加速比超过一个数量级。示例部分展示了该方法与MS复合体的相似性、可操作性及其在测试数据集上的优势。本文将随附实现代码。