mlsanityData to 7 Oct 2026

Topology-Aware Segmentation Using Discrete Morse Theory

arXiv 2103.09992 ↗First posted 18 Mar 2021cs.CV cs.CGcited by 75

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Abstract (arXiv)

In the segmentation of fine-scale structures from natural and biomedical images, per-pixel accuracy is not the only metric of concern. Topological correctness, such as vessel connectivity and membrane closure, is crucial for downstream analysis tasks. In this paper, we propose a new approach to train deep image segmentation networks for better topological accuracy. In particular, leveraging the power of discrete Morse theory (DMT), we identify global structures, including 1D skeletons and 2D patches, which are important for topological accuracy. Trained with a novel loss based on these global structures, the network performance is significantly improved especially near topologically challenging locations (such as weak spots of connections and membranes). On diverse datasets, our method achieves superior performance on both the DICE score and topological metrics.

Key facts. Cited by 75 papers in the map (data through 7 Oct 2026). Builds on 24 of its 68 references that are in the map. First posted on arXiv 18 Mar 2021.

Builds on

24 of 68 references.

References · 24

  1. 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,604
  2. 2017Mask R-CNNcited by 7,259
  3. 2014Fully Convolutional Networks for Semantic Segmentationcited by 4,845
  4. 2016DeepLab: Semantic Image Segmentation with Deep Convolutional Nets, Atrous Convolution, and Fully Connected CRFscited by 3,239
  5. 2017Rethinking Atrous Convolution for Semantic Image Segmentationcited by 2,154
  6. 2015SegNet: A Deep Convolutional Encoder-Decoder Architecture for Image Segmentationcited by 1,483
  7. 20163D U-Net: Learning Dense Volumetric Segmentation from Sparse Annotationcited by 1,471
  8. 2014Semantic Image Segmentation with Deep Convolutional Nets and Fully Connected CRFscited by 552
  9. 2015Train faster, generalize better: Stability of stochastic gradient descentcited by 547
  10. 2015Persistence Images: A Stable Vector Representation of Persistent Homologycited by 235
  11. 2019Topology-Preserving Deep Image Segmentationcited by 198
  12. 2018Boundary loss for highly unbalanced segmentationcited by 187
12 more
  1. 2019A Topological Loss Function for Deep-Learning based Image Segmentation using Persistent Homologycited by 134
  2. 2019Reducing the Hausdorff Distance in Medical Image Segmentation with Convolutional Neural Networkscited by 116
  3. 2017Deep Learning with Topological Signaturescited by 113
  4. 2019Boundary-Aware Feature Propagation for Scene Segmentationcited by 107
  5. 2017Beyond the Pixel-Wise Loss for Topology-Aware Delineationcited by 82
  6. 2017Sliced Wasserstein Kernel for Persistence Diagramscited by 77
  7. 2014A Stable Multi-Scale Kernel for Topological Machine Learningcited by 74
  8. 2018A Topological Regularizer for Classifiers via Persistent Homologycited by 62
  9. 2019Connectivity-Optimized Representation Learning via Persistent Homologycited by 43
  10. 2019Road Network Reconstruction from Satellite Images with Machine Learning Supported by Topological Methodscited by 10
  11. 2017Large Scale Image Segmentation with Structured Loss based Deep Learning for Connectome Reconstructioncited by 5
  12. 2018Graph Reconstruction by Discrete Morse Theorycited by 5

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 7; 2022: 12; 2023: 9; 2024: 23; 2025: 14; 2026: 10.

75 papers.

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  1. 2024Position: Topological Deep Learning is the New Frontier for Relational Learningcited by 65
  2. 2022ImageCAS: A Large-Scale Dataset and Benchmark for Coronary Artery Segmentation based on Computed Tomography Angiography Imagescited by 54
  3. 2022Topologically faithful image segmentation via induced matching of persistence barcodescited by 48
  4. 2021Trigger Hunting with a Topological Prior for Trojan Detectioncited by 39
  5. 2021Topological Detection of Trojaned Neural Networkscited by 34
  6. 2022Learning Topological Interactions for Multi-Class Medical Image Segmentationcited by 28
  7. 2021Structure-Aware Image Segmentation with Homotopy Warpingcited by 24
  8. 2021Cycle Representation Learning for Inductive Relation Predictioncited by 23
  9. 2022Learning Probabilistic Topological Representations Using Discrete Morse Theorycited by 20
  10. 2024Beyond Euclid: An Illustrated Guide to Modern Machine Learning with Geometric, Topological, and Algebraic Structurescited by 20
  11. 2024Topograph: An efficient Graph-Based Framework for Strictly Topology Preserving Image Segmentationcited by 17
  12. 2024TopoCellGen: Generating Histopathology Cell Topology with a Diffusion Modelcited by 16
38 more
  1. 2022Capturing Shape Information with Multi-Scale Topological Loss Terms for 3D Reconstructioncited by 14
  2. 2023Enhancing Modality-Agnostic Representations via Meta-Learning for Brain Tumor Segmentationcited by 14
  3. 2021TopoTxR: A Topological Biomarker for Predicting Treatment Response in Breast Cancercited by 13
  4. 2024Representing Topological Self-Similarity Using Fractal Feature Maps for Accurate Segmentation of Tubular Structurescited by 13
  5. 2022Local Intensity Order Transformation for Robust Curvilinear Object Segmentationcited by 12
  6. 2022DTU-Net: Learning Topological Similarity for Curvilinear Structure Segmentationcited by 12
  7. 2024Topologically Faithful Multi-class Segmentation in Medical Imagescited by 12
  8. 2023Semi-supervised Segmentation of Histopathology Images with Noise-Aware Topological Consistencycited by 11
  9. 2021Persistent Homology with Improved Locality Information for more Effective Delineationcited by 10
  10. 2024TopoDiffusionNet: A Topology-aware Diffusion Modelcited by 10
  11. 2023Multi-site, Multi-domain Airway Tree Modeling (ATM'22): A Public Benchmark for Pulmonary Airway Segmentationcited by 9
  12. 2024Enhancing Boundary Segmentation for Topological Accuracy with Skeleton-based Methodscited by 8
  13. 2024Topology-Preserving Image Segmentation with Spatial-Aware Persistent Feature Matchingcited by 8
  14. 2023Euler Characteristic Transform Based Topological Loss for Reconstructing 3D Images from Single 2D Slicescited by 6
  15. 2024Self Pre-training with Topology- and Spatiality-aware Masked Autoencoders for 3D Medical Image Segmentationcited by 6
  16. 2024Spatial Diffusion for Cell Layout Generationcited by 5
  17. 2024Beyond Accuracy Optimization: Computer Vision Losses for Large Language Model Fine-Tuningcited by 5
  18. 2025Topology Optimization in Medical Image Segmentation with Fast Euler Characteristiccited by 5
  19. 2025BrainMRDiff: A Diffusion Model for Anatomically Consistent Brain MRI Synthesiscited by 4
  20. 2022Enforcing connectivity of 3D linear structures using their 2D projectionscited by 3
  21. 2022Affinity Feature Strengthening for Accurate, Complete and Robust Vessel Segmentationcited by 3
  22. 2023Wasserstein Auto-Encoders of Merge Trees (and Persistence Diagrams)cited by 3
  23. 2024Universal Topology Refinement for Medical Image Segmentation with Polynomial Feature Synthesiscited by 3
  24. 2025Efficient Connectivity-Preserving Instance Segmentation with Supervoxel-Based Loss Functioncited by 3
  25. 2025Encoder-Only Image Registrationcited by 3
  26. 2025MATCH: Multi-faceted Adaptive Topo-Consistency for Semi-Supervised Histopathology Segmentationcited by 3
  27. 2022A Topology-Attention ConvLSTM Network and Its Application to EM Imagescited by 2
  28. 2022On the Convergence of Optimizing Persistent-Homology-Based Lossescited by 2
  29. 2023Not All Pixels Are Equal: Learning Pixel Hardness for Semantic Segmentationcited by 2
  30. 2023Pairwise-Constrained Implicit Functions for 3D Human Heart Modellingcited by 2
  31. 2024Scale-Free Image Keypoints Using Differentiable Persistent Homologycited by 2
  32. 2025TopoImages: Incorporating Local Topology Encoding into Deep Learning Models for Medical Image Classificationcited by 2
  33. 2026Topology-Guaranteed Image Segmentation: Enforcing Connectivity, Genus, and Width Constraintscited by 2
  34. 2024P-Count: Persistence-based Counting of White Matter Hyperintensities in Brain MRIcited by 1
  35. 2025TopoMortar: A dataset to evaluate image segmentation methods focused on topology accuracycited by 1
  36. 2025Topology-Aware CLIP Few-Shot Learningcited by 1
  37. 2025TopoSculpt: Betti-Steered Topological Sculpting of 3D Fine-grained Tubular Shapescited by 1
  38. 2021Quantifying Topology In Pancreatic Tubular Networks From Live Imaging 3D Microscopycited by 0

50 most cited of 75 All 75 (JSON)