发表机构
Auburn University; Michigan State University; Rensselaer Polytechnic Institute; University of Georgia（奥本大学; 密歇根州立大学; 伦斯勒理工学院; 佐治亚大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对医学图像分析中几何与拓扑结构建模难题，提出CNMTDL框架，结合Hodge分解与组合注意力机制，在MedMNIST v2六个数据集上验证了其有效性。
AI 中文摘要
医学图像分析由于医学数据中存在的复杂几何和拓扑结构而仍然具有根本性的挑战。传统的卷积神经网络将图像建模为规则的欧几里得网格，限制了其保持几何关系和更高阶结构信息的能力。近年来，流形拓扑深度学习（MTDL）已成为一种有前景的范式，它将深度学习与几何和拓扑表示相结合。然而，现有方法尚未充分利用组合复神经网络中的离散流形结构。为了弥合这一差距，我们引入了CNMTDL，一个将Hodge分解与组合注意力机制相结合的MTDL框架。在我们的方法中，医学图像被表示为离散流形，并分解为三个Hodge分量。从这些分量中提取的特征被拼接并嵌入到组合复架构中，通过基于注意力的块实现$0$-胞腔和$2$-胞腔之间增强的高阶消息传递。我们在MedMNIST v2基准的六个二维和三维数据集上评估了CNMTDL，证明了其在医学图像分析中的有效性。
英文摘要
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.
