# Comparing Morse Complexes Using Optimal Transport: An Experimental Study

arXiv: https://arxiv.org/abs/2309.04681 · HTML: https://mlsanity.com/paper/2309.04681/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Sep 2023.

## Built on by (most cited first, 1 of 1)

- [MS-COOT: Comparing Morse-Smale Complexes with Co-Optimal Transport](https://mlsanity.com/paper/2606.08258/) (2026)

## Abstract (arXiv)

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.