Morse complexes and Morse-Smale complexes are topological descriptors popular in topology-based visualization. Comparing these complexes plays an important role in their applications in feature correspondences, feature tracking, symmetry detection, and uncertainty visualization. Leveraging recent advances in optimal transport, we apply a class of optimal transport distances to the comparative analysis of Morse complexes. Contrasting with existing comparative measures, such distances are easy and efficient to compute, and naturally provide structural matching between Morse complexes. We perform an experimental study involving scientific simulation datasets and discuss the effectiveness of these distances as comparative measures for Morse complexes. We also provide an initial guideline for choosing the optimal transport distances under various data assumptions.

翻译：莫尔斯复形和莫尔斯-斯梅尔复形是拓扑可视化领域常用的拓扑描述子。比较这些复形在特征对应、特征追踪、对称性检测和不确定性可视化等应用中具有重要作用。借助最优传输领域的最新进展，我们将一类最优传输距离应用于莫尔斯复形的比较分析。与现有比较度量相比，这类距离计算简便高效，并能自然提供莫尔斯复形之间的结构匹配。我们基于科学模拟数据集开展实验研究，探讨了这些距离作为莫尔斯复形比较度量的有效性，同时针对不同数据假设条件提供了选择最优传输距离的初步指南。