# Topology-Preserving Segmentation Network: A Deep Learning Segmentation Framework for Connected Component

arXiv: https://arxiv.org/abs/2202.13331 · HTML: https://mlsanity.com/paper/2202.13331/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 41 references that are in the map.
- First posted on arXiv 27 Feb 2022.

## Builds on (most cited first, 22 of 22)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [V-Net: Fully Convolutional Neural Networks for Volumetric Medical Image Segmentation](https://mlsanity.com/paper/1606.04797/) (2016)
- [UNet++: A Nested U-Net Architecture for Medical Image Segmentation](https://mlsanity.com/paper/1807.10165/) (2018)
- [3D U-Net: Learning Dense Volumetric Segmentation from Sparse Annotation](https://mlsanity.com/paper/1606.06650/) (2016)
- [Spatial Transformer Networks](https://mlsanity.com/paper/1506.02025/) (2015)
- [UNETR: Transformers for 3D Medical Image Segmentation](https://mlsanity.com/paper/2103.10504/) (2021)
- [clDice -- A Novel Topology-Preserving Loss Function for Tubular Structure Segmentation](https://mlsanity.com/paper/2003.07311/) (2020)
- [Topology-Preserving Deep Image Segmentation](https://mlsanity.com/paper/1906.05404/) (2019)
- [The state of the art in kidney and kidney tumor segmentation in contrast-enhanced CT imaging: Results of the KiTS19 Challenge](https://mlsanity.com/paper/1912.01054/) (2019)
- [A Topological Loss Function for Deep-Learning based Image Segmentation using Persistent Homology](https://mlsanity.com/paper/1910.01877/) (2019)
- [DoubleU-Net: A Deep Convolutional Neural Network for Medical Image Segmentation](https://mlsanity.com/paper/2006.04868/) (2020)
- [Anatomically Constrained Neural Networks (ACNN): Application to Cardiac Image Enhancement and Segmentation](https://mlsanity.com/paper/1705.08302/) (2017)
- [Prior-aware Neural Network for Partially-Supervised Multi-Organ Segmentation](https://mlsanity.com/paper/1904.06346/) (2019)
- [Beyond the Pixel-Wise Loss for Topology-Aware Delineation](https://mlsanity.com/paper/1712.02190/) (2017)
- [Unsupervised Learning of Image Segmentation Based on Differentiable Feature Clustering](https://mlsanity.com/paper/2007.09990/) (2020)
- [Autoregressive Unsupervised Image Segmentation](https://mlsanity.com/paper/2007.08247/) (2020)
- [nnDetection: A Self-configuring Method for Medical Object Detection](https://mlsanity.com/paper/2106.00817/) (2021)
- [Efficient Medical Image Segmentation Based on Knowledge Distillation](https://mlsanity.com/paper/2108.09987/) (2021)
- [Topology-Preserving 3D Image Segmentation Based On Hyperelastic Regularization](https://mlsanity.com/paper/2103.16768/) (2021)
- [TEDS-Net: Enforcing Diffeomorphisms in Spatial Transformers to Guarantee Topology Preservation in Segmentations](https://mlsanity.com/paper/2107.13542/) (2021)
- [Harmonic Beltrami Signature: A Novel 2D Shape Representation for Object Classification](https://mlsanity.com/paper/2103.16411/) (2021)

## Built on by (most cited first, 4 of 4)

- [QIS : Interactive Segmentation via Quasi-Conformal Mappings](https://mlsanity.com/paper/2402.14695/) (2024)
- [SDF-TopoNet: A Two-Stage Framework for Tubular Structure Segmentation via SDF Pre-training and Topology-Aware Fine-Tuning](https://mlsanity.com/paper/2503.14523/) (2025)
- [Harmonic Beltrami Signature Network: a Shape Prior Module in Deep Learning Framework](https://mlsanity.com/paper/2603.02907/) (2026)
- [Structure-Guided Masked Autoencoders for Ultra-High Resolution Scientific Image Understanding](https://mlsanity.com/paper/2609.30682/) (2026)

## Abstract (arXiv)

Medical image segmentation, which aims to automatically extract anatomical or pathological structures, plays a key role in computer-aided diagnosis and disease analysis. Despite the problem has been widely studied, existing methods are prone to topological errors. In medical imaging, the topology of the structure, such as the kidney or lung, is usually known. Preserving the topology of the structure in the segmentation process is of utmost importance for accurate image analysis. In this work, a novel learning-based segmentation model is proposed. A it topology-preserving segmentation network (TPSN) is trained to give an accurate segmentation result of an input image that preserves the prescribed topology. TPSN is a deformation-based model that yields a deformation map through a UNet, which takes the medical image and a template mask as inputs. The main idea is to deform a template mask describing the prescribed topology by a diffeomorphism to segment the object in the image. The topology of the shape in the template mask is well preserved under the diffeomorphic map. The diffeomorphic property of the map is controlled by introducing a regularization term related to the Jacobian in the loss function. As such, a topology-preserving segmentation result can be guaranteed. Furthermore, a multi-scale TPSN is developed in this paper that incorporates multi-level information of images to produce more precise segmentation results. To evaluate our method, we applied the 2D TPSN on Ham10000 and 3D TPSN on KiTS21. Experimental results illustrate our method outperforms the baseline UNet segmentation model with/without connected-component analysis (CCA) by both the dice score and IoU score. Besides, results show that our method can produce reliable results even in challenging cases, where pixel-wise segmentation models by UNet and CCA fail to obtain accurate results.