TopoAgent: An Agentic Framework for Automated Topology Learning in Medical Imaging

Topological data analysis (TDA), particularly persistent homology (PH), captures geometric structural properties in medical images (e.g., connected components, loops, shape characteristics), which conventional pixel-level deep learning approaches often neglect. While many topological descriptors are known for converting persistence diagrams (PDs) or raw images into topological feature vectors, existing methods mostly default to a single fixed descriptor (e.g., persistence images), leaving the diversity of topological representations largely unexplored. To the best of our knowledge, there is no known large language model (LLM)-based agentic framework that can automatically determine the most suitable topological descriptors for a given image dataset and produce the corresponding topological feature vectors for downstream tasks. To fill this gap, we propose \textbf{TopoAgent}, an LLM-based agentic framework that automates topology learning for medical image analysis.TopoAgent operates through a Perception--Reasoning--Action--Reflection loop supported by 21 domain-specific tools and dual memory that accumulates experience across runs. Its skill set is distilled from systematic evaluation of 15 topological descriptors across 26 datasets with six classifiers. TopoAgent analyzes input images and their topological characteristics, reasons about which topological descriptors best suit the input, and determines the optimal descriptor and its configuration, all without task-specific training.

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

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.