TEDS-Net: Enforcing Diffeomorphisms in Spatial Transformers to Guarantee Topology Preservation in Segmentations

Accurate topology is key when performing meaningful anatomical segmentations,\nhowever, it is often overlooked in traditional deep learning methods. In this\nwork we propose TEDS-Net: a novel segmentation method that guarantees accurate\ntopology. Our method is built upon a continuous diffeomorphic framework, which\nenforces topology preservation. However, in practice, diffeomorphic fields are\nrepresented using a finite number of parameters and sampled using methods such\nas linear interpolation, violating the theoretical guarantees. We therefore\nintroduce additional modifications to more strictly enforce it. Our network\nlearns how to warp a binary prior, with the desired topological\ncharacteristics, to complete the segmentation task. We tested our method on\nmyocardium segmentation from an open-source 2D heart dataset. TEDS-Net\npreserved topology in 100% of the cases, compared to 90% from the U-Net,\nwithout sacrificing on Hausdorff Distance or Dice performance. Code will be\nmade available at: www.github.com/mwyburd/TEDS-Net\n