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In digital pathology, the spatial context of cells is important for cell classification, cancer diagnosis and prognosis. To model such complex cell context, however, is challenging. Cells form different mixtures, lineages, clusters and holes. To model such structural patterns in a learnable fashion, we introduce several mathematical tools from spatial statistics and topological data analysis. We incorporate such structural descriptors into a deep generative model as both conditional inputs and a differentiable loss. This way, we are able to generate high quality multi-class cell layouts for the first time. We show that the topology-rich cell layouts can be used for data augmentation and improve the performance of downstream tasks such as cell classification. 

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.