# Topology-Preserving Image Segmentation with Spatial-Aware Persistent Feature Matching

arXiv: https://arxiv.org/abs/2412.02076 · HTML: https://mlsanity.com/paper/2412.02076/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 40 references that are in the map.
- First posted on arXiv 3 Dec 2024.

## Builds on (most cited first, 18 of 18)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Segment Anything](https://mlsanity.com/paper/2304.02643/) (2023)
- [Segment Anything in High Quality](https://mlsanity.com/paper/2306.01567/) (2023)
- [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)
- [A Topological Loss Function for Deep-Learning based Image Segmentation using Persistent Homology](https://mlsanity.com/paper/1910.01877/) (2019)
- [DUNet: A deformable network for retinal vessel segmentation](https://mlsanity.com/paper/1811.01206/) (2018)
- [Dynamic Snake Convolution based on Topological Geometric Constraints for Tubular Structure Segmentation](https://mlsanity.com/paper/2307.08388/) (2023)
- [Beyond the Pixel-Wise Loss for Topology-Aware Delineation](https://mlsanity.com/paper/1712.02190/) (2017)
- [Topology-Aware Segmentation Using Discrete Morse Theory](https://mlsanity.com/paper/2103.09992/) (2021)
- [Topologically faithful image segmentation via induced matching of persistence barcodes](https://mlsanity.com/paper/2211.15272/) (2022)
- [Geometry Helps to Compare Persistence Diagrams](https://mlsanity.com/paper/1606.03357/) (2016)
- [Topology-Aware Uncertainty for Image Segmentation](https://mlsanity.com/paper/2306.05671/) (2023)
- [A persistent homology-based topological loss for CNN-based multi-class segmentation of CMR](https://mlsanity.com/paper/2107.12689/) (2021)
- [TA-Net: Topology-Aware Network for Gland Segmentation](https://mlsanity.com/paper/2110.14593/) (2021)
- [Topograph: An efficient Graph-Based Framework for Strictly Topology Preserving Image Segmentation](https://mlsanity.com/paper/2411.03228/) (2024)
- [Fully Automated Artery-Vein ratio and vascular tortuosity measurement in retinal fundus images](https://mlsanity.com/paper/2301.01791/) (2023)

## Built on by (most cited first, 8 of 8)

- [Universal Vessel Segmentation for Multi-Modality Retinal Images](https://mlsanity.com/paper/2502.06987/) (2025)
- [MATCH: Multi-faceted Adaptive Topo-Consistency for Semi-Supervised Histopathology Segmentation](https://mlsanity.com/paper/2510.01532/) (2025)
- [High-Resolution Underwater Camouflaged Object Detection: GBU-UCOD Dataset and Topology-Aware and Frequency-Decoupled Networks](https://mlsanity.com/paper/2602.03591/) (2026)
- [SAMSEM -- A Generic and Scalable Approach for IC Metal Line Segmentation](https://mlsanity.com/paper/2603.16548/) (2026)
- [Topology-Guided Biomechanical Profiling: A White-Box Framework for Opportunistic Screening of Spinal Instability on Routine CT](https://mlsanity.com/paper/2603.16963/) (2026)
- [Beyond Instance-Level Self-Supervision in 3D Multi-Modal Medical Imaging](https://mlsanity.com/paper/2605.14654/) (2026)
- [Widest-Path Reachability Fields for Connectivity-Preserving Slender Structure Segmentation](https://mlsanity.com/paper/2607.07123/) (2026)
- [Sparse cubical complexes for efficient topology-preservation in image data](https://mlsanity.com/paper/2609.37177/) (2026)

## Abstract (arXiv)

Topological correctness is critical for segmentation of tubular structures, which pervade in biomedical images. Existing topological segmentation loss functions are primarily based on the persistent homology of the image. They match the persistent features from the segmentation with the persistent features from the ground truth and minimize the difference between them. However, these methods suffer from an ambiguous matching problem since the matching only relies on the information in the topological space. In this work, we propose an effective and efficient Spatial-Aware Topological Loss Function that further leverages the information in the original spatial domain of the image to assist the matching of persistent features. Extensive experiments on images of various types of tubular structures show that the proposed method has superior performance in improving the topological accuracy of the segmentation compared with state-of-the-art methods. Code is available at https://github.com/JRC-VPLab/SATLoss.