Comparing Morse Complexes Using Optimal Transport: An Experimental Study

TL;DR

This paper explores the use of optimal transport distances to compare Morse complexes efficiently, providing structural matching and practical guidelines for their application in visualization tasks.

Contribution

It introduces a novel application of optimal transport distances for comparing Morse complexes, emphasizing efficiency and structural matching capabilities.

Findings

Optimal transport distances are effective for Morse complex comparison.

The proposed method is computationally efficient.

Guidelines are provided for selecting distances based on data assumptions.

Abstract

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.