mlsanityData to 7 Oct 2026

Correspondence-Free Point Cloud Registration with SO(3)-Equivariant Implicit Shape Representations

arXiv 2107.10296 ↗First posted 21 Jul 2021cs.CV cs.LGcited by 24

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Abstract (arXiv)

This paper proposes a correspondence-free method for point cloud rotational registration. We learn an embedding for each point cloud in a feature space that preserves the SO(3)-equivariance property, enabled by recent developments in equivariant neural networks. The proposed shape registration method achieves three major advantages through combining equivariant feature learning with implicit shape models. First, the necessity of data association is removed because of the permutation-invariant property in network architectures similar to PointNet. Second, the registration in feature space can be solved in closed-form using Horn's method due to the SO(3)-equivariance property. Third, the registration is robust to noise in the point cloud because of the joint training of registration and implicit shape reconstruction. The experimental results show superior performance compared with existing correspondence-free deep registration methods.

Key facts. Cited by 24 papers in the map (data through 7 Oct 2026). Builds on 35 of its 56 references that are in the map. First posted on arXiv 21 Jul 2021.

Builds on

35 of 56 references.

References · 35

  1. 2016PointNet: Deep Learning on Point Sets for 3D Classification and Segmentationcited by 5,223
  2. 2019DeepSDF: Learning Continuous Signed Distance Functions for Shape Representationcited by 2,682
  3. 2018Dynamic Graph CNN for Learning on Point Cloudscited by 2,220
  4. 2018Occupancy Networks: Learning 3D Reconstruction in Function Spacecited by 2,037
  5. 2020SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networkscited by 602
  6. 2020INeRF: Inverting Neural Radiance Fields for Pose Estimationcited by 381
  7. 20163DMatch: Learning Local Geometric Descriptors from RGB-D Reconstructionscited by 333
  8. 2019Deep Closest Point: Learning Representations for Point Cloud Registrationcited by 318
  9. 2021Vector Neurons: A General Framework for SO(3)-Equivariant Networkscited by 304
  10. 2016Steerable CNNscited by 298
  11. 2018On the Generalization of Equivariance and Convolution in Neural Networks to the Action of Compact Groupscited by 296
  12. 2020PREDATOR: Registration of 3D Point Clouds with Low Overlapcited by 287
23 more
  1. 2020Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Datacited by 248
  2. 2017Learning SO(3) Equivariant Representations with Spherical CNNscited by 244
  3. 2019PointNetLK: Robust & Efficient Point Cloud Registration using PointNetcited by 231
  4. 2020Deep Global Registrationcited by 228
  5. 2020RPM-Net: Robust Point Matching using Learned Featurescited by 181
  6. 2018PPFNet: Global Context Aware Local Features for Robust 3D Point Matchingcited by 180
  7. 2020D3Feat: Joint Learning of Dense Detection and Description of 3D Local Featurescited by 175
  8. 2018The Perfect Match: 3D Point Cloud Matching with Smoothed Densitiescited by 169
  9. 2019PRNet: Self-Supervised Learning for Partial-to-Partial Registrationcited by 146
  10. 2020SpinNet: Learning a General Surface Descriptor for 3D Point Cloud Registrationcited by 141
  11. 2020Feature-metric Registration: A Fast Semi-supervised Approach for Robust Point Cloud Registration without Correspondencescited by 108
  12. 20183DFeat-Net: Weakly Supervised Local 3D Features for Point Cloud Registrationcited by 100
  13. 20193DRegNet: A Deep Neural Network for 3D Point Registrationcited by 96
  14. 2020DeepGMR: Learning Latent Gaussian Mixture Models for Registrationcited by 91
  15. 2019DeepICP: An End-to-End Deep Neural Network for 3D Point Cloud Registrationcited by 77
  16. 2019SampleNet: Differentiable Point Cloud Samplingcited by 74
  17. 2019USIP: Unsupervised Stable Interest Point Detection from 3D Point Cloudscited by 70
  18. 2020DI-Fusion: Online Implicit 3D Reconstruction with Deep Priorscited by 70
  19. 2019PCRNet: Point Cloud Registration Network using PointNet Encodingcited by 63
  20. 2014Learning the Irreducible Representations of Commutative Lie Groupscited by 41
  21. 2018Learning 3D Shape Completion under Weak Supervisioncited by 40
  22. 2019Continuous Direct Sparse Visual Odometry from RGB-D Imagescited by 7
  23. 2020A New Framework for Registration of Semantic Point Clouds from Stereo and RGB-D Camerascited by 6

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 2; 2022: 6; 2023: 8; 2024: 5; 2025: 2; 2026: 1.

24 papers.

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  1. 2021Neural Descriptor Fields: SE(3)-Equivariant Object Representations for Manipulationcited by 204
  2. 2021You Only Hypothesize Once: Point Cloud Registration with Rotation-equivariant Descriptorscited by 68
  3. 2022Neural Shape Mating: Self-Supervised Object Assembly with Adversarial Shape Priorscited by 42
  4. 2022SE(3)-Equivariant Attention Networks for Shape Reconstruction in Function Spacecited by 26
  5. 20234D Panoptic Segmentation as Invariant and Equivariant Field Predictioncited by 19
  6. 2023Banana: Banach Fixed-Point Network for Pointcloud Segmentation with Inter-Part Equivariancecited by 19
  7. 2023EFEM: Equivariant Neural Field Expectation Maximization for 3D Object Segmentation Without Scene Supervisioncited by 18
  8. 2022E2PN: Efficient SE(3)-Equivariant Point Networkcited by 17
  9. 2023Living Scenes: Multi-object Relocalization and Reconstruction in Changing 3D Environmentscited by 15
  10. 2023Generalizing Neural Human Fitting to Unseen Poses With Articulated SE(3) Equivariancecited by 14
  11. 2022Certifiable 3D Object Pose Estimation: Foundations, Learning Models, and Self-Trainingcited by 12
  12. 2023NeuSE: Neural SE(3)-Equivariant Embedding for Consistent Spatial Understanding with Objectscited by 10
12 more
  1. 2022Coarse-to-Fine Point Cloud Registration with SE(3)-Equivariant Representationscited by 9
  2. 2023Pyramid Semantic Graph-based Global Point Cloud Registration with Low Overlapcited by 6
  3. 2023Lie Neurons: Adjoint-Equivariant Neural Networks for Semisimple Lie Algebrascited by 6
  4. 2024An intuitive multi-frequency feature representation for SO(3)-equivariant networkscited by 5
  5. 2024Approximately Piecewise E(3) Equivariant Point Networkscited by 4
  6. 2024Correspondence-Free SE(3) Point Cloud Registration in RKHS via Unsupervised Equivariant Learningcited by 3
  7. 2024Equi-GSPR: Equivariant SE(3) Graph Network Model for Sparse Point Cloud Registrationcited by 2
  8. 2024Point-PNG: Conditional Pseudo-Negatives Generation for Point Cloud Pre-Trainingcited by 1
  9. 2025Multiview Point Cloud Registration via Optimization in an Autoencoder Latent Spacecited by 1
  10. 2026Generalized-CVO: Fast and Correspondence-Free Local Point Cloud Registration with Second Order Riemannian Optimizationcited by 1
  11. 2022DPCN++: Differentiable Phase Correlation Network for Versatile Pose Registrationcited by 0
  12. 2025Correspondence-Free Pose Estimation with Patterns: A Unified Approach for Multi-Dimensional Visioncited by 0