In computational pathology, segmenting densely distributed objects like glands and nuclei is crucial for downstream analysis. To alleviate the burden of obtaining pixel-wise annotations, semi-supervised learning methods learn from large amounts of unlabeled data. Nevertheless, existing semi-supervised methods overlook the topological information hidden in the unlabeled images and are thus prone to topological errors, e.g., missing or incorrectly merged/separated glands or nuclei. To address this issue, we propose TopoSemiSeg, the first semi-supervised method that learns the topological representation from unlabeled data. In particular, we propose a topology-aware teacher-student approach in which the teacher and student networks learn shared topological representations. To achieve this, we introduce topological consistency loss, which contains signal consistency and noise removal losses to ensure the learned representation is robust and focuses on true topological signals. Extensive experiments on public pathology image datasets show the superiority of our method, especially on topology-wise evaluation metrics. Code is available at https://github.com/Melon-Xu/TopoSemiSeg.
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