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

arXiv: https://arxiv.org/abs/2107.13542 · HTML: https://mlsanity.com/paper/2107.13542/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 19 references that are in the map.
- First posted on arXiv 28 Jul 2021.

## Builds on (most cited first, 10 of 10)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Spatial Transformer Networks](https://mlsanity.com/paper/1506.02025/) (2015)
- [VoxelMorph: A Learning Framework for Deformable Medical Image Registration](https://mlsanity.com/paper/1809.05231/) (2018)
- [Topology-Preserving Deep Image Segmentation](https://mlsanity.com/paper/1906.05404/) (2019)
- [Unsupervised Learning of Probabilistic Diffeomorphic Registration for Images and Surfaces](https://mlsanity.com/paper/1903.03545/) (2019)
- [A Topological Loss Function for Deep-Learning based Image Segmentation using Persistent Homology](https://mlsanity.com/paper/1910.01877/) (2019)
- [Unsupervised Learning for Fast Probabilistic Diffeomorphic Registration](https://mlsanity.com/paper/1805.04605/) (2018)
- [Beyond the Pixel-Wise Loss for Topology-Aware Delineation](https://mlsanity.com/paper/1712.02190/) (2017)
- [Linear and Deformable Image Registration with 3D Convolutional Neural Networks](https://mlsanity.com/paper/1809.06226/) (2018)
- [Probabilistic Atlases to Enforce Topological Constraints](https://mlsanity.com/paper/1909.08330/) (2019)

## Built on by (most cited first, 7 of 7)

- [Coordinate Translator for Learning Deformable Medical Image Registration](https://mlsanity.com/paper/2203.03626/) (2022)
- [UniBrain: Universal Brain MRI Diagnosis with Hierarchical Knowledge-enhanced Pre-training](https://mlsanity.com/paper/2309.06828/) (2023)
- [A Learning-based Framework for Topology-Preserving Segmentation using Quasiconformal Mappings](https://mlsanity.com/paper/2210.03299/) (2022)
- [Topology-Preserving Segmentation Network: A Deep Learning Segmentation Framework for Connected Component](https://mlsanity.com/paper/2202.13331/) (2022)
- [SCOPE: Structural Continuity Preservation for Medical Image Segmentation](https://mlsanity.com/paper/2304.14572/) (2023)
- [rNCA: Self-Repairing Segmentation Masks](https://mlsanity.com/paper/2512.13397/) (2025)
- [Conformable Convolution for Topologically Aware Learning of Complex Anatomical Structures](https://mlsanity.com/paper/2412.20608/) (2024)

## Abstract (arXiv)

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