mlsanityData to 7 Oct 2026

Learning Probabilistic Topological Representations Using Discrete Morse Theory

arXiv 2206.01742 ↗First posted 3 Jun 2022eess.IV cs.CVcited by 20

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Abstract (arXiv)

Accurate delineation of fine-scale structures is a very important yet challenging problem. Existing methods use topological information as an additional training loss, but are ultimately making pixel-wise predictions. In this paper, we propose the first deep learning based method to learn topological/structural representations. We use discrete Morse theory and persistent homology to construct an one-parameter family of structures as the topological/structural representation space. Furthermore, we learn a probabilistic model that can perform inference tasks in such a topological/structural representation space. Our method generates true structures rather than pixel-maps, leading to better topological integrity in automatic segmentation tasks. It also facilitates semi-automatic interactive annotation/proofreading via the sampling of structures and structure-aware uncertainty.

Key facts. Cited by 20 papers in the map (data through 7 Oct 2026). Builds on 19 of its 68 references that are in the map. First posted on arXiv 3 Jun 2022.

Builds on

19 of 68 references.

References · 19

  1. 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,604
  2. 2015Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learningcited by 4,416
  3. 2016Simple and Scalable Predictive Uncertainty Estimation using Deep Ensemblescited by 3,888
  4. 2017What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?cited by 2,335
  5. 2020clDice -- A Novel Topology-Preserving Loss Function for Tubular Structure Segmentationcited by 286
  6. 2018A Probabilistic U-Net for Segmentation of Ambiguous Imagescited by 281
  7. 2015Bayesian SegNet: Model Uncertainty in Deep Convolutional Encoder-Decoder Architectures for Scene Understandingcited by 218
  8. 2019Topology-Preserving Deep Image Segmentationcited by 198
  9. 2018Uncertainty Estimates and Multi-Hypotheses Networks for Optical Flowcited by 135
  10. 2019A Topological Loss Function for Deep-Learning based Image Segmentation using Persistent Homologycited by 134
  11. 2020Confidence-Aware Learning for Deep Neural Networkscited by 113
  12. 2016Learning in an Uncertain World: Representing Ambiguity Through Multiple Hypothesescited by 96
7 more
  1. 2017Beyond the Pixel-Wise Loss for Topology-Aware Delineationcited by 82
  2. 2021Topology-Aware Segmentation Using Discrete Morse Theorycited by 75
  3. 2021Trigger Hunting with a Topological Prior for Trojan Detectioncited by 39
  4. 2021Structure-Aware Image Segmentation with Homotopy Warpingcited by 24
  5. 2019Road Network Reconstruction from Satellite Images with Machine Learning Supported by Topological Methodscited by 10
  6. 2018Graph Reconstruction by Discrete Morse Theorycited by 5
  7. 2022A Manifold View of Adversarial Riskcited by 4

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 1; 2023: 4; 2024: 8; 2025: 6; 2026: 1.

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  1. 2023Topology-Aware Uncertainty for Image Segmentationcited by 32
  2. 2022Learning Topological Interactions for Multi-Class Medical Image Segmentationcited by 28
  3. 2023Calibrating Uncertainty for Semi-Supervised Crowd Countingcited by 22
  4. 2024TopoCellGen: Generating Histopathology Cell Topology with a Diffusion Modelcited by 16
  5. 2023Enhancing Modality-Agnostic Representations via Meta-Learning for Brain Tumor Segmentationcited by 14
  6. 2023Semi-supervised Segmentation of Histopathology Images with Noise-Aware Topological Consistencycited by 11
  7. 2024TopoDiffusionNet: A Topology-aware Diffusion Modelcited by 10
  8. 2024Spatial Diffusion for Cell Layout Generationcited by 5
  9. 2024Neurovascular Segmentation in sOCT with Deep Learning and Synthetic Training Datacited by 4
  10. 2024Universal Topology Refinement for Medical Image Segmentation with Polynomial Feature Synthesiscited by 3
  11. 2025Efficient Connectivity-Preserving Instance Segmentation with Supervoxel-Based Loss Functioncited by 3
  12. 2025MATCH: Multi-faceted Adaptive Topo-Consistency for Semi-Supervised Histopathology Segmentationcited by 3
8 more
  1. 2024Scale-Free Image Keypoints Using Differentiable Persistent Homologycited by 2
  2. 2024Probabilistic U-Net with Kendall Shape Spaces for Geometry-Aware Segmentations of Imagescited by 1
  3. 2025TopoMortar: A dataset to evaluate image segmentation methods focused on topology accuracycited by 1
  4. 2025Disconnect to Connect: A Data Augmentation Method for Improving Topology Accuracy in Image Segmentationcited by 1
  5. 2025Topology-Aware CLIP Few-Shot Learningcited by 1
  6. 2025TopoSculpt: Betti-Steered Topological Sculpting of 3D Fine-grained Tubular Shapescited by 1
  7. 2024Learning Topological Representations for Deep Image Understandingcited by 0
  8. 2026Graph Representation via Elements of Discrete Morse and Cobordism Theoriescited by 0