Anatomically plausible segmentations: Explicitly preserving topology through prior deformations

Since the rise of deep learning, new medical segmentation methods have rapidly been proposed with extremely promising results, often reporting marginal improvements on the previous state-of-the-art (SOTA) method. However, on visual inspection errors are often revealed, such as topological mistakes (e.g. holes or folds), that are not detected using traditional evaluation metrics. Incorrect topology can often lead to errors in clinically required downstream image processing tasks. Therefore, there is a need for new methods to focus on ensuring segmentations are topologically correct. In this work, we present TEDS-Net: a segmentation network that preserves anatomical topology whilst maintaining segmentation performance that is competitive with SOTA baselines. Further, we show how current SOTA segmentation methods can introduce problematic topological errors. TEDS-Net achieves anatomically plausible segmentation by using learnt topology-preserving fields to deform a prior. Traditionally, topology-preserving fields are described in the continuous domain and begin to break down when working in the discrete domain. Here, we introduce additional modifications that more strictly enforce topology preservation. We illustrate our method on an open-source medical heart dataset, performing both single and multi-structure segmentation, and show that the generated fields contain no folding voxels, which corresponds to full topology preservation on individual structures whilst vastly outperforming the other baselines on overall scene topology. The code is available at: https://github.com/mwyburd/TEDS-Net.