mlsanityData to 7 Oct 2026

Point-set Distances for Learning Representations of 3D Point Clouds

arXiv 2102.04014 ↗First posted 8 Feb 2021cs.CVcited by 48

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Abstract (arXiv)

Learning an effective representation of 3D point clouds requires a good metric to measure the discrepancy between two 3D point sets, which is non-trivial due to their irregularity. Most of the previous works resort to using the Chamfer discrepancy or Earth Mover's distance, but those metrics are either ineffective in measuring the differences between point clouds or computationally expensive. In this paper, we conduct a systematic study with extensive experiments on distance metrics for 3D point clouds. From this study, we propose to use sliced Wasserstein distance and its variants for learning representations of 3D point clouds. In addition, we introduce a new algorithm to estimate sliced Wasserstein distance that guarantees that the estimated value is close enough to the true one. Experiments show that the sliced Wasserstein distance and its variants allow the neural network to learn a more efficient representation compared to the Chamfer discrepancy. We demonstrate the efficiency of the sliced Wasserstein metric and its variants on several tasks in 3D computer vision including training a point cloud autoencoder, generative modeling, transfer learning, and point cloud registration.

Key facts. Cited by 48 papers in the map (data through 7 Oct 2026). Builds on 42 of its 57 references that are in the map. First posted on arXiv 8 Feb 2021.

Builds on

42 of 57 references.

References · 42

  1. 2016PointNet: Deep Learning on Point Sets for 3D Classification and Segmentationcited by 5,223
  2. 2015ShapeNet: An Information-Rich 3D Model Repositorycited by 2,880
  3. 2013Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distancescited by 2,277
  4. 2016A Point Set Generation Network for 3D Object Reconstruction from a Single Imagecited by 972
  5. 2018Computational Optimal Transportcited by 765
  6. 2019Deep Hough Voting for 3D Object Detection in Point Cloudscited by 648
  7. 2018AtlasNet: A Papier-Mach'e Approach to Learning 3D Surface Generationcited by 539
  8. 2019PointFlow: 3D Point Cloud Generation with Continuous Normalizing Flowscited by 487
  9. 2017Wasserstein Auto-Encoderscited by 371
  10. 20163DMatch: Learning Local Geometric Descriptors from RGB-D Reconstructionscited by 333
  11. 2019Sliced Wasserstein Discrepancy for Unsupervised Domain Adaptationcited by 235
  12. 2018PU-Net: Point Cloud Upsampling Networkcited by 208
30 more
  1. 2019Generalized Sliced Wasserstein Distancescited by 205
  2. 2018PPFNet: Global Context Aware Local Features for Robust 3D Point Matchingcited by 180
  3. 20193D Point Cloud Generative Adversarial Network Based on Tree Structured Graph Convolutionscited by 173
  4. 2018The Perfect Match: 3D Point Cloud Matching with Smoothed Densitiescited by 169
  5. 2018PPF-FoldNet: Unsupervised Learning of Rotation Invariant 3D Local Descriptorscited by 140
  6. 2017Learning Efficient Point Cloud Generation for Dense 3D Object Reconstructioncited by 133
  7. 2017Pointwise Convolutional Neural Networkscited by 126
  8. 2019Max-Sliced Wasserstein Distance and its use for GANscited by 118
  9. 2018Generative Modeling using the Sliced Wasserstein Distancecited by 108
  10. 20183D Point Capsule Networkscited by 106
  11. 2018PointGrow: Autoregressively Learned Point Cloud Generation with Self-Attentioncited by 105
  12. 2018Point Cloud GANcited by 79
  13. 2020Distributional Sliced-Wasserstein and Applications to Generative Modelingcited by 69
  14. 2015Sliced Wasserstein Kernels for Probability Distributionscited by 64
  15. 2019JSIS3D: Joint Semantic-Instance Segmentation of 3D Point Clouds with Multi-Task Pointwise Networks and Multi-Value Conditional Random Fieldscited by 62
  16. 2019Sliced Wasserstein Generative Modelscited by 61
  17. 2019On Efficient Optimal Transport: An Analysis of Greedy and Accelerated Mirror Descent Algorithmscited by 60
  18. 2017Sliced Wasserstein Distance for Learning Gaussian Mixture Modelscited by 59
  19. 2019Total Denoising: Unsupervised Learning of 3D Point Cloud Cleaningcited by 58
  20. 2017Multilevel Clustering via Wasserstein Meanscited by 48
  21. 2020Progressive Point Cloud Deconvolution Generation Networkcited by 46
  22. 2019Asymptotic Guarantees for Learning Generative Models with the Sliced-Wasserstein Distancecited by 43
  23. 2019Orthogonal Estimation of Wasserstein Distancescited by 32
  24. 2019Geometric Disentanglement for Generative Latent Shape Modelscited by 30
  25. 2019LCD: Learned Cross-Domain Descriptors for 2D-3D Matchingcited by 29
  26. 20193D Local Features for Direct Pairwise Registrationcited by 26
  27. 20193D Point Cloud Denoising via Deep Neural Network based Local Surface Estimationcited by 20
  28. 2019LBS Autoencoder: Self-supervised Fitting of Articulated Meshes to Point Cloudscited by 14
  29. 2020Improving Relational Regularized Autoencoders with Spherical Sliced Fused Gromov Wassersteincited by 13
  30. 2019On Efficient Multilevel Clustering via Wasserstein Distancescited by 5

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 5; 2022: 6; 2023: 11; 2024: 13; 2025: 9; 2026: 4.

48 papers.

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  1. 2021Density-aware Chamfer Distance as a Comprehensive Metric for Point Cloud Completioncited by 111
  2. 2021Improving Mini-batch Optimal Transport via Partial Transportationcited by 40
  3. 2023Energy-Based Sliced Wasserstein Distancecited by 39
  4. 2022Topologically-Aware Deformation Fields for Single-View 3D Reconstructioncited by 29
  5. 2023Scalable Optimal Transport Methods in Machine Learning: A Contemporary Surveycited by 27
  6. 2022Hierarchical Sliced Wasserstein Distancecited by 23
  7. 2023Beyond Statistical Similarity: Rethinking Metrics for Deep Generative Models in Engineering Designcited by 22
  8. 2022Sobolev Transport: A Scalable Metric for Probability Measures with Graph Metricscited by 18
  9. 2021Entropic Gromov-Wasserstein between Gaussian Distributionscited by 12
  10. 2024Geometry-Informed Neural Networkscited by 12
  11. 2024Integrating Efficient Optimal Transport and Functional Maps For Unsupervised Shape Correspondence Learningcited by 12
  12. 2023Scalable Unbalanced Sobolev Transport for Measures on a Graphcited by 10
36 more
  1. 2021On Multimarginal Partial Optimal Transport: Equivalent Forms and Computational Complexitycited by 8
  2. 2023Lidar Upsampling with Sliced Wasserstein Distancecited by 8
  3. 20243DMambaComplete: Exploring Structured State Space Model for Point Cloud Completioncited by 8
  4. 2023Self-Attention Amortized Distributional Projection Optimization for Sliced Wasserstein Point-Cloud Reconstructioncited by 7
  5. 2023Diffeomorphic Mesh Deformation via Efficient Optimal Transport for Cortical Surface Reconstructioncited by 7
  6. 2023Optimal Transport for Measures with Noisy Tree Metriccited by 7
  7. 2024Dynamic 3D Point Cloud Sequences as 2D Videoscited by 7
  8. 2024Tree-Sliced Wasserstein Distance: A Geometric Perspectivecited by 7
  9. 2023Scalable Counterfactual Distribution Estimation in Multivariate Causal Modelscited by 6
  10. 2022Adversarial Support Alignmentcited by 5
  11. 2024DDM: A Metric for Comparing 3D Shapes Using Directional Distance Fieldscited by 5
  12. 2024Point2SSM++: Self-Supervised Learning of Anatomical Shape Models from Point Cloudscited by 5
  13. 2025Slicing Wasserstein Over Wasserstein Via Functional Optimal Transportcited by 5
  14. 2024iBA: Backdoor Attack on 3D Point Cloud via Reconstructing Itselfcited by 4
  15. 2025Distance-Based Tree-Sliced Wasserstein Distancecited by 4
  16. 2022Improving Generative Flow Networks with Path Regularizationcited by 3
  17. 2023Hybrid-CSR: Coupling Explicit and Implicit Shape Representation for Cortical Surface Reconstructioncited by 3
  18. 2024Efficient approximation of Earth Mover's Distance Based on Nearest Neighbor Searchcited by 3
  19. 2025Tree-Sliced Wasserstein Distance with Nonlinear Projectioncited by 3
  20. 2025APML: Adaptive Probabilistic Matching Loss for Robust 3D Point Cloud Reconstructioncited by 3
  21. 2021OMASGAN: Out-of-Distribution Minimum Anomaly Score GAN for Sample Generation on the Boundarycited by 2
  22. 2023Unleash the Potential of 3D Point Cloud Modeling with A Calibrated Local Geometry-driven Distance Metriccited by 2
  23. 2024GERA: Geometric Embedding for Efficient Point Registration Analysiscited by 2
  24. 2025Rethinking Metrics and Diffusion Architecture for 3D Point Cloud Generationcited by 2
  25. 2024Collision Avoidance Metric for 3D Camera Evaluationcited by 1
  26. 2024Neural varifolds: an aggregate representation for quantifying the geometry of point cloudscited by 1
  27. 2025Scalable Sobolev IPM for Probability Measures on a Graphcited by 1
  28. 2025Generating Adversarial Point Clouds Using Diffusion Modelcited by 1
  29. 2026Learning Permutation-invariant Macroscopic Dynamicscited by 1
  30. 2022An Interpretable Joint Nonnegative Matrix Factorization-Based Point Cloud Distance Measurecited by 0
  31. 2024Stealthy and Robust Backdoor Attack against 3D Point Clouds through Additional Point Featurescited by 0
  32. 2025Wasserstein Hypergraph Neural Networkcited by 0
  33. 2025Denoising-While-Completing Network (DWCNet): Robust Point Cloud Completion Under Corruptioncited by 0
  34. 2026AdamFlow: Adam-based Wasserstein Gradient Flows for Surface Registration in Medical Imagingcited by 0
  35. 2026The Observable Wasserstein Distancecited by 0
  36. 2026Autoregressive Frontier Expansion: Growing Trees with Graph Machine Learningcited by 0