mlsanityData to 7 Oct 2026

Quaternion Equivariant Capsule Networks for 3D Point Clouds

arXiv 1912.12098 ↗First posted 27 Dec 2019cs.LG cs.CV cs.GRcited by 41

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Abstract (arXiv)

We present a 3D capsule module for processing point clouds that is equivariant to 3D rotations and translations, as well as invariant to permutations of the input points. The operator receives a sparse set of local reference frames, computed from an input point cloud and establishes end-to-end transformation equivariance through a novel dynamic routing procedure on quaternions. Further, we theoretically connect dynamic routing between capsules to the well-known Weiszfeld algorithm, a scheme for solving iterative re-weighted least squares (IRLS) problems with provable convergence properties. It is shown that such group dynamic routing can be interpreted as robust IRLS rotation averaging on capsule votes, where information is routed based on the final inlier scores. Based on our operator, we build a capsule network that disentangles geometry from pose, paving the way for more informative descriptors and a structured latent space. Our architecture allows joint object classification and orientation estimation without explicit supervision of rotations. We validate our algorithm empirically on common benchmark datasets.

Key facts. Cited by 41 papers in the map (data through 7 Oct 2026). First posted on arXiv 27 Dec 2019.

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Citing papers per year: 2021: 17; 2022: 9; 2023: 7; 2024: 5; 2025: 2; 2026: 1.

41 papers.

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  1. 2021Scalars are universal: Equivariant machine learning, structured like classical physicscited by 127
  2. 2021Equivariant Point Network for 3D Point Cloud Analysiscited by 81
  3. 2021Intrinsic Dimension, Persistent Homology and Generalization in Neural Networkscited by 70
  4. 2021You Only Hypothesize Once: Point Cloud Registration with Rotation-equivariant Descriptorscited by 68
  5. 2021Leveraging SE(3) Equivariance for Self-Supervised Category-Level Object Pose Estimationcited by 45
  6. 2022Equivariant Point Cloud Analysis via Learning Orientations for Message Passingcited by 32
  7. 2021Projective Manifold Gradient Layer for Deep Rotation Regressioncited by 31
  8. 2021Multiway Non-rigid Point Cloud Registration via Learned Functional Map Synchronizationcited by 30
  9. 2022RIConv++: Effective Rotation Invariant Convolutions for 3D Point Clouds Deep Learningcited by 29
  10. 2023Leveraging SE(3) Equivariance for Learning 3D Geometric Shape Assemblycited by 27
  11. 2023Self-Supervised Category-Level Articulated Object Pose Estimation with Part-Level SE(3) Equivariancecited by 26
  12. 2021Towards Efficient Graph Convolutional Networks for Point Cloud Handlingcited by 18
29 more
  1. 2022E2PN: Efficient SE(3)-Equivariant Point Networkcited by 17
  2. 2021Unsupervised Motion Representation Learning with Capsule Autoencoderscited by 16
  3. 2021PRIN/SPRIN: On Extracting Point-wise Rotation Invariant Featurescited by 15
  4. 2021Field Convolutions for Surface CNNscited by 14
  5. 2024Beyond Canonicalization: How Tensorial Messages Improve Equivariant Message Passingcited by 13
  6. 2022ART-Point: Improving Rotation Robustness of Point Cloud Classifiers via Adversarial Rotationcited by 12
  7. 2025Lorentz Local Canonicalization: How to Make Any Network Lorentz-Equivariantcited by 12
  8. 2022Learning with Capsules: A Surveycited by 10
  9. 2025ReQFlow: Rectified Quaternion Flow for Efficient and High-Quality Protein Backbone Generationcited by 10
  10. 2023Chordal Averaging on Flag Manifolds and Its Applicationscited by 9
  11. 2021Deformation Robust Roto-Scale-Translation Equivariant CNNscited by 7
  12. 2023PaRot: Patch-Wise Rotation-Invariant Network via Feature Disentanglement and Pose Restorationcited by 7
  13. 2021End-to-end Learning the Partial Permutation Matrix for Robust 3D Point Cloud Registrationcited by 5
  14. 2024A Clifford Algebraic Approach to E(n)-Equivariant High-order Graph Neural Networkscited by 5
  15. 20243D Equivariant Pose Regression via Direct Wigner-D Harmonics Predictioncited by 4
  16. 2021Steerable 3D Spherical Neuronscited by 3
  17. 2022Learning a Task-specific Descriptor for Robust Matching of 3D Point Cloudscited by 3
  18. 2023Stable and Consistent Prediction of 3D Characteristic Orientation via Invariant Residual Learningcited by 3
  19. 2021Disentangling Geometric Deformation Spaces in Generative Latent Shape Modelscited by 2
  20. 2022TetraSphere: A Neural Descriptor for O(3)-Invariant Point Cloud Analysiscited by 2
  21. 2023General Rotation Invariance Learning for Point Clouds via Weight-Feature Alignmentcited by 2
  22. 2024DifAttack++: Query-Efficient Black-Box Adversarial Attack via Hierarchical Disentangled Feature Space in Cross-Domaincited by 2
  23. 2024Current Symmetry Group Equivariant Convolution Frameworks for Representation Learningcited by 2
  24. 2021Augmenting Imitation Experience via Equivariant Representationscited by 1
  25. 2021PointCaps: Raw Point Cloud Processing using Capsule Networks with Euclidean Distance Routingcited by 1
  26. 2022Design equivariant neural networks for 3D point cloudcited by 0
  27. 2022Affordance detection with Dynamic-Tree Capsule Networkscited by 0
  28. 2023Evaluating 3D Shape Analysis Methods for Robustness to Rotation Invariancecited by 0
  29. 2026Rotational Equivariance in Machine Learning: A Comprehensive Tutorialcited by 0