G-LoG Bi-filtration for Medical Image Classification

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 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.

Deep learning has shown strong potential in medical image analysis, but most existing methods rely on large-scale annotations and a closed-world assumption that rarely holds in clinical practice. Although Generalized Category Discovery (GCD) has advanced rapidly on natural images, it remains underexplored in medical imaging. To address this issue, we propose MedXplore, a unified framework for reliable and unbiased medical GCD, optimizing from both perceptual and decision levels. Specifically, at the perceptual level, taking a frequency domain perspective, Frequency-SNR Adaptive Attention and Consistency (FAAC) performs learnable full-spectrum filtering and global-local energy contrast activation to not only highlight local abnormal signals relative to the global context, but also provide reliable semantic anchors for patch consistency learning. At the decision level, Adaptive Cosine-Angular Margin (ACAM) adjusts angular margins using semantic difficulty and feature confidence to balance intra-class compactness and inter-class separability. Together, the two modules improve lesion-sensitive representation learning and mitigate old-class bias. Experiments on multiple benchmarks show an average 8.5% gain in All accuracy over the strongest competing methods. On Kvasir, MedXplore reduces false-old errors from 14.50% to 0.80%, demonstrating strong robustness under severe old-new ambiguity.

Contrastive learning (CL) has become a powerful approach for learning representations from unlabeled images. However, existing CL methods focus predominantly on visual appearance features while neglecting topological characteristics (e.g., connectivity patterns, boundary configurations, cavity formations) that provide valuable cues for medical image analysis. To address this limitation, we propose a new topological CL framework (TopoCL) that explicitly exploits topological structures during contrastive learning for medical imaging. Specifically, we first introduce topology-aware augmentations that control topological perturbations using a relative bottleneck distance between persistence diagrams, preserving medically relevant topological properties while enabling controlled structural variations. We then design a Hierarchical Topology Encoder that captures topological features through self-attention and cross-attention mechanisms. Finally, we develop an adaptive mixture-of-experts (MoE) module to dynamically integrate visual and topological representations. TopoCL can be seamlessly integrated with existing CL methods. We evaluate TopoCL on five representative CL methods (SimCLR, MoCo-v3, BYOL, DINO, and Barlow Twins) and five diverse medical image classification datasets. The experimental results show that TopoCL achieves consistent improvements: an average gain of +3.26% in linear probe classification accuracy with strong statistical significance, verifying its effectiveness.