  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.
