  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
