MS-COOT: Comparing Morse-Smale Complexes with Co-Optimal Transport

Abstract:Understanding and comparing structures in scalar fields is a central challenge in scientific visualization, with applications ranging from feature analysis to temporal and structural comparison. The Morse-Smale (MS) complex provides a natural representation by decomposing a scalar field into regions induced by gradient flow. However, existing approaches typically rely on graph-based representations, capturing relationships between critical points while discarding region-level structure. In this work, we represent the MS complex as a hypergraph, where critical points form nodes and regions define hyperedges. We introduce MS-COOT, a co-optimal transport distance that jointly computes correspondences between critical points and regions. This formulation enables explicit region-to-region matching within a distance-based framework, allowing identification of region-level events such as splitting and merging. We instantiate this framework with domain-specific components, including a hypernetwork function encoding critical point-region relationships, persistence-based probability measures that emphasize topologically significant features, and a sample cost term that incorporates critical point attributes. We evaluate MS-COOT on five datasets spanning 2D simulations, 3D surface meshes, and volumetric data. Our results show that MS-COOT captures region-level structural changes that are not reflected by graph-based distances, while achieving strong performance in downstream tasks such as classification and resolution discrimination.

Graphics (cs.GR); Computer Vision and Pattern Recognition (cs.CV); Machine Learning (cs.LG)

arXiv:2606.08258 [cs.GR]

(or arXiv:2606.08258v1 [cs.GR] for this version)

https://doi.org/10.48550/arXiv.2606.08258 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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