  Accurate topology is key when performing meaningful anatomical segmentations,
however, it is often overlooked in traditional deep learning methods. In this
work we propose TEDS-Net: a novel segmentation method that guarantees accurate
topology. Our method is built upon a continuous diffeomorphic framework, which
enforces topology preservation. However, in practice, diffeomorphic fields are
represented using a finite number of parameters and sampled using methods such
as linear interpolation, violating the theoretical guarantees. We therefore
introduce additional modifications to more strictly enforce it. Our network
learns how to warp a binary prior, with the desired topological
characteristics, to complete the segmentation task. We tested our method on
myocardium segmentation from an open-source 2D heart dataset. TEDS-Net
preserved topology in 100% of the cases, compared to 90% from the U-Net,
without sacrificing on Hausdorff Distance or Dice performance. Code will be
made available at: www.github.com/mwyburd/TEDS-Net
