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

2026-06-06 · Source: Machine Learning · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Computer Vision & Pattern Recognition, Data Science & Analytics · Depth: Expert, quick

Summary

MS-COOT is a novel co-optimal transport distance method designed to compare structures within scalar fields, a key challenge in scientific visualization. Unlike traditional Morse-Smale (MS) complex approaches that use graph-based representations and overlook region-level structure, MS-COOT represents the MS complex as a hypergraph, where critical points are nodes and regions define hyperedges. This formulation jointly computes correspondences between critical points and regions, enabling explicit region-to-region matching and identifying events like splitting and merging. The framework integrates a hypernetwork function encoding critical point-region relationships, persistence-based probability measures for topologically significant features, and a sample cost term for critical point attributes. Evaluated on five datasets, including 2D simulations, 3D surface meshes, and volumetric data, MS-COOT demonstrates superior capture of region-level structural changes compared to graph-based distances, achieving strong performance in classification and resolution discrimination tasks.

Key takeaway

For Research Scientists or Computer Vision Engineers analyzing complex scalar field structures, traditional graph-based Morse-Smale complex comparisons may overlook critical region-level changes. You should consider MS-COOT's hypergraph representation and co-optimal transport distance to achieve more granular and accurate structural comparisons. This approach enables explicit region-to-region matching, allowing you to identify subtle splitting and merging events and improve classification and resolution discrimination in your scientific visualization tasks.

Key insights

MS-COOT leverages hypergraphs and co-optimal transport to enable explicit region-to-region matching in Morse-Smale complexes.

Principles

• Hypergraphs capture region-level structure.
• Co-optimal transport matches interdependent entities.
• Persistence measures emphasize topological features.

Method

Represent the Morse-Smale complex as a hypergraph, then apply co-optimal transport to jointly compute critical point and region correspondences, integrating hypernetwork functions and persistence-based measures.

In practice

• Identify region splitting and merging events.
• Improve classification of scalar field structures.
• Discriminate resolution in scientific data.

Topics

• Morse-Smale Complex
• Co-Optimal Transport
• Hypergraph Representation
• Scientific Visualization
• Scalar Field Analysis
• Topological Data Analysis

Best for: AI Scientist, Research Scientist, Computer Vision Engineer

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Editorial summary, takeaway, and curation by AIssential. Original article published by Machine Learning.