Data to 7 Oct 2026

Topology-Preserving Deep Image Segmentation

arXiv 1906.05404 ↗First posted 12 Jun 2019cs.CV cs.CGcited by 198

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Abstract (arXiv)

Segmentation algorithms are prone to make topological errors on fine-scale structures, e.g., broken connections. We propose a novel method that learns to segment with correct topology. In particular, we design a continuous-valued loss function that enforces a segmentation to have the same topology as the ground truth, i.e., having the same Betti number. The proposed topology-preserving loss function is differentiable and we incorporate it into end-to-end training of a deep neural network. Our method achieves much better performance on the Betti number error, which directly accounts for the topological correctness. It also performs superiorly on other topology-relevant metrics, e.g., the Adjusted Rand Index and the Variation of Information. We illustrate the effectiveness of the proposed method on a broad spectrum of natural and biomedical datasets.

Key facts. Cited by 198 papers in the map (data through 7 Oct 2026). First posted on arXiv 12 Jun 2019.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 28; 2022: 27; 2023: 28; 2024: 38; 2025: 37; 2026: 40.

198 papers.

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2023Dynamic Snake Convolution based on Topological Geometric Constraints for Tubular Structure Segmentationcited by 83
2021Topology-Aware Segmentation Using Discrete Morse Theorycited by 75
2024Position: Topological Deep Learning is the New Frontier for Relational Learningcited by 65
2022ImageCAS: A Large-Scale Dataset and Benchmark for Coronary Artery Segmentation based on Computed Tomography Angiography Imagescited by 54
2022Topologically faithful image segmentation via induced matching of persistence barcodescited by 48
2023The TopCoW Challenge -- Topology-Aware Circle of Willis Segmentation for CT and MR Angiographycited by 48
2024Skeleton Recall Loss for Connectivity Conserving and Resource Efficient Segmentation of Thin Tubular Structurescited by 43
2021Trigger Hunting with a Topological Prior for Trojan Detectioncited by 39
2021Link Prediction with Persistent Homology: An Interactive Viewcited by 37
2021Topological Detection of Trojaned Neural Networkscited by 34
2023Topological Deep Learning: A Review of an Emerging Paradigmcited by 34
2023Topology-Aware Uncertainty for Image Segmentationcited by 32

38 more

2023Directional Connectivity-based Segmentation of Medical Imagescited by 30
2022Learning Topological Interactions for Multi-Class Medical Image Segmentationcited by 28
2024Centerline Boundary Dice Loss for Vascular Segmentationcited by 27
2021Structure-Aware Image Segmentation with Homotopy Warpingcited by 24
2021Cycle Representation Learning for Inductive Relation Predictioncited by 23
2021A persistent homology-based topological loss for CNN-based multi-class segmentation of CMRcited by 21
2023Going beyond persistent homology using persistent homologycited by 21
2022Learning Probabilistic Topological Representations Using Discrete Morse Theorycited by 20
2022On the effectiveness of persistent homologycited by 20
2024Beyond Euclid: An Illustrated Guide to Modern Machine Learning with Geometric, Topological, and Algebraic Structurescited by 20
2021TA-Net: Topology-Aware Network for Gland Segmentationcited by 17
2024Topograph: An efficient Graph-Based Framework for Strictly Topology Preserving Image Segmentationcited by 17
2022Neural Approximation of Graph Topological Featurescited by 16
2024TopoCellGen: Generating Histopathology Cell Topology with a Diffusion Modelcited by 16
2021A survey on shape-constraint deep learning for medical image segmentationcited by 15
2022Capturing Shape Information with Multi-Scale Topological Loss Terms for 3D Reconstructioncited by 14
2023Enhancing Modality-Agnostic Representations via Meta-Learning for Brain Tumor Segmentationcited by 14
2021TopoTxR: A Topological Biomarker for Predicting Treatment Response in Breast Cancercited by 13
2024Representing Topological Self-Similarity Using Fractal Feature Maps for Accurate Segmentation of Tubular Structurescited by 13
2022Local Intensity Order Transformation for Robust Curvilinear Object Segmentationcited by 12
2022DTU-Net: Learning Topological Similarity for Curvilinear Structure Segmentationcited by 12
2023Topology-Aware Focal Loss for 3D Image Segmentationcited by 12
2024Geometry-Informed Neural Networkscited by 12
2024Topologically Faithful Multi-class Segmentation in Medical Imagescited by 12
2023Semi-supervised Segmentation of Histopathology Images with Noise-Aware Topological Consistencycited by 11
2024Enabling Uncertainty Estimation in Iterative Neural Networkscited by 11
2021Persistent Homology with Improved Locality Information for more Effective Delineationcited by 10
2022A Learning-based Framework for Topology-Preserving Segmentation using Quasiconformal Mappingscited by 10
2024TopoDiffusionNet: A Topology-aware Diffusion Modelcited by 10
2021CP-loss: Connectivity-preserving Loss for Road Curb Detection in Autonomous Driving with Aerial Imagescited by 9
2023Multi-site, Multi-domain Airway Tree Modeling (ATM'22): A Public Benchmark for Pulmonary Airway Segmentationcited by 9
2025GLCP: Global-to-Local Connectivity Preservation for Tubular Structure Segmentationcited by 9
2021Cycle Registration in Persistent Homology with Applications in Topological Bootstrapcited by 8
2022PointScatter: Point Set Representation for Tubular Structure Extractioncited by 8
2023Cycle Invariant Positional Encoding for Graph Representation Learningcited by 8
2023VSR-Net: Vessel-like Structure Rehabilitation Network with Graph Clusteringcited by 8
2024Enhancing Boundary Segmentation for Topological Accuracy with Skeleton-based Methodscited by 8
2024Topology-Preserving Image Segmentation with Spatial-Aware Persistent Feature Matchingcited by 8

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