Combinatorial Network-Based Manifold Topological Deep Learning for Image Analysis

2026-09-21

AI Summary

该研究针对医学图像分析中的几何和拓扑结构挑战，提出了一种结合Hodge分解与组合注意力机制的深度学习框架CNMTDL，以更好地处理医学数据中的复杂结构。

Abstract

Medical image analysis remains fundamentally challenging because of the intricate geometric and topological structures present in medical data. Conventional convolutional neural networks model images as regular Euclidean grids, limiting their ability to preserve geometric relationships and higher-order structural information. Recently, manifold topological deep learning (MTDL) has emerged as a promising paradigm that integrates deep learning with geometric and topological representations. Nevertheless, existing methods have not yet fully exploited discrete manifold structures within combinatorial complex neural networks. To bridge this gap, we introduce CNMTDL, a MTDL framework that integrates Hodge decomposition with a combinatorial attention mechanism. In our approach, medical images are represented as discrete manifolds and decomposed into three Hodge components. Features extracted from these components are concatenated and embedded into a combinatorial complex architecture, enabling enhanced higher-order message passing between $0$-cells and $2$-cells through attention-based blocks. We evaluate CNMTDL on six two-dimensional and three-dimensional datasets from the MedMNIST v2 benchmark, demonstrating its effectiveness for medical image analysis.

Problem

• Medical Image Analysis
• Geometric and Topological Structures
• Convolutional Neural Networks
• Manifold Topological Deep Learning

Innovation

• Hodge decomposition
• combinatorial attention mechanism
• discrete manifolds