  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.
