TopoImages: Incorporating Local Topology Encoding into Deep Learning Models for Medical Image Classification

2025-08-02

AI Summary

Existing deep learning methods rely predominantly on appearance-based features while neglecting topological structures—such as connected components and holes—thereby limiting performance in medical image classification. To address this, we propose TopoImages: the first framework that encodes local persistent homology into differentiable, vectorized topological images, enabling multi-channel topological representations. We design a multi-view topological fusion mechanism to seamlessly integrate topological features into deep neural networks. Our approach jointly optimizes filter function generation, topological vectorization, and end-to-end training, achieving topology-aware image representation learning. Evaluated on three public medical image datasets, TopoImages consistently achieves significant improvements in classification accuracy. Results demonstrate the effectiveness, differentiability, and cross-dataset generalizability of local topological modeling. This work establishes a novel paradigm for topology-guided medical image analysis.

Technology Category

• Computer Vision: Medical and Biological Imaging
• Machine Learning: Representation Learning
• Search and Optimization: Learning to Search

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

Topological structures in image data, such as connected components and loops, play a crucial role in understanding image content (e.g., biomedical objects). % Despite remarkable successes of numerous image processing methods that rely on appearance information, these methods often lack sensitivity to topological structures when used in general deep learning (DL) frameworks. % In this paper, we introduce a new general approach, called TopoImages (for Topology Images), which computes a new representation of input images by encoding local topology of patches. % In TopoImages, we leverage persistent homology (PH) to encode geometric and topological features inherent in image patches. % Our main objective is to capture topological information in local patches of an input image into a vectorized form. % Specifically, we first compute persistence diagrams (PDs) of the patches, % and then vectorize and arrange these PDs into long vectors for pixels of the patches. % The resulting multi-channel image-form representation is called a TopoImage. % TopoImages offers a new perspective for data analysis. % To garner diverse and significant topological features in image data and ensure a more comprehensive and enriched representation, we further generate multiple TopoImages of the input image using various filtration functions, which we call multi-view TopoImages. % The multi-view TopoImages are fused with the input image for DL-based classification, with considerable improvement. % Our TopoImages approach is highly versatile and can be seamlessly integrated into common DL frameworks. Experiments on three public medical image classification datasets demonstrate noticeably improved accuracy over state-of-the-art methods.

Problem

• Encode local topology in medical images for deep learning
• Improve sensitivity to topological structures in image classification
• Integrate persistent homology features into DL frameworks effectively

Innovation

• Encodes local topology using persistent homology
• Generates multi-view TopoImages with filtrations
• Integrates TopoImages with deep learning frameworks