Deep learning methods have achieved impressive performance for multi-class medical image segmentation. However, they are limited in their ability to encode topological interactions among different classes (e.g., containment and exclusion). These constraints naturally arise in biomedical images and can be crucial in improving segmentation quality. In this paper, we introduce a novel topological interaction module to encode the topological interactions into a deep neural network. The implementation is completely convolution-based and thus can be very efficient. This empowers us to incorporate the constraints into end-to-end training and enrich the feature representation of neural networks. The efficacy of the proposed method is validated on different types of interactions. We also demonstrate the generalizability of the method on both proprietary and public challenge datasets, in both 2D and 3D settings, as well as across different modalities such as CT and Ultrasound. Code is available at: https://github.com/TopoXLab/TopoInteraction

本文提出了一种新的拓扑交互模块，可以将拓扑交互编码到深度神经网络中，从而改善医学图像分割的质量。该模块使用完全基于卷积，有助于在端到端的训练中将约束融入到神经网络的特征表示中。该方法在不同类型的交互中得到验证，并在不同的模态上实现了方法的普适性。

多类医学图像分割的拓扑交互学习