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

arXiv: https://arxiv.org/abs/2107.10296 · HTML: https://mlsanity.com/paper/2107.10296/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 56 references that are in the map.
- First posted on arXiv 21 Jul 2021.

## Builds on (most cited first, 30 of 35)

- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks](https://mlsanity.com/paper/2006.10503/) (2020)
- [INeRF: Inverting Neural Radiance Fields for Pose Estimation](https://mlsanity.com/paper/2012.05877/) (2020)
- [3DMatch: Learning Local Geometric Descriptors from RGB-D Reconstructions](https://mlsanity.com/paper/1603.08182/) (2016)
- [Deep Closest Point: Learning Representations for Point Cloud Registration](https://mlsanity.com/paper/1905.03304/) (2019)
- [Steerable CNNs](https://mlsanity.com/paper/1612.08498/) (2016)
- [Vector Neurons: A General Framework for SO(3)-Equivariant Networks](https://mlsanity.com/paper/2104.12229/) (2021)
- [On the Generalization of Equivariance and Convolution in Neural Networks to the Action of Compact Groups](https://mlsanity.com/paper/1802.03690/) (2018)
- [PREDATOR: Registration of 3D Point Clouds with Low Overlap](https://mlsanity.com/paper/2011.13005/) (2020)
- [Learning SO(3) Equivariant Representations with Spherical CNNs](https://mlsanity.com/paper/1711.06721/) (2017)
- [Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Data](https://mlsanity.com/paper/2002.12880/) (2020)
- [PointNetLK: Robust & Efficient Point Cloud Registration using PointNet](https://mlsanity.com/paper/1903.05711/) (2019)
- [Deep Global Registration](https://mlsanity.com/paper/2004.11540/) (2020)
- [RPM-Net: Robust Point Matching using Learned Features](https://mlsanity.com/paper/2003.13479/) (2020)
- [PPFNet: Global Context Aware Local Features for Robust 3D Point Matching](https://mlsanity.com/paper/1802.02669/) (2018)
- [D3Feat: Joint Learning of Dense Detection and Description of 3D Local Features](https://mlsanity.com/paper/2003.03164/) (2020)
- [The Perfect Match: 3D Point Cloud Matching with Smoothed Densities](https://mlsanity.com/paper/1811.06879/) (2018)
- [PRNet: Self-Supervised Learning for Partial-to-Partial Registration](https://mlsanity.com/paper/1910.12240/) (2019)
- [SpinNet: Learning a General Surface Descriptor for 3D Point Cloud Registration](https://mlsanity.com/paper/2011.12149/) (2020)
- [Feature-metric Registration: A Fast Semi-supervised Approach for Robust Point Cloud Registration without Correspondences](https://mlsanity.com/paper/2005.01014/) (2020)
- [3DFeat-Net: Weakly Supervised Local 3D Features for Point Cloud Registration](https://mlsanity.com/paper/1807.09413/) (2018)
- [3DRegNet: A Deep Neural Network for 3D Point Registration](https://mlsanity.com/paper/1904.01701/) (2019)
- [DeepGMR: Learning Latent Gaussian Mixture Models for Registration](https://mlsanity.com/paper/2008.09088/) (2020)
- [DeepICP: An End-to-End Deep Neural Network for 3D Point Cloud Registration](https://mlsanity.com/paper/1905.04153/) (2019)
- [SampleNet: Differentiable Point Cloud Sampling](https://mlsanity.com/paper/1912.03663/) (2019)
- [USIP: Unsupervised Stable Interest Point Detection from 3D Point Clouds](https://mlsanity.com/paper/1904.00229/) (2019)
- [DI-Fusion: Online Implicit 3D Reconstruction with Deep Priors](https://mlsanity.com/paper/2012.05551/) (2020)

## Built on by (most cited first, 24 of 24)

- [Neural Descriptor Fields: SE(3)-Equivariant Object Representations for Manipulation](https://mlsanity.com/paper/2112.05124/) (2021)
- [You Only Hypothesize Once: Point Cloud Registration with Rotation-equivariant Descriptors](https://mlsanity.com/paper/2109.00182/) (2021)
- [Neural Shape Mating: Self-Supervised Object Assembly with Adversarial Shape Priors](https://mlsanity.com/paper/2205.14886/) (2022)
- [SE(3)-Equivariant Attention Networks for Shape Reconstruction in Function Space](https://mlsanity.com/paper/2204.02394/) (2022)
- [4D Panoptic Segmentation as Invariant and Equivariant Field Prediction](https://mlsanity.com/paper/2303.15651/) (2023)
- [Banana: Banach Fixed-Point Network for Pointcloud Segmentation with Inter-Part Equivariance](https://mlsanity.com/paper/2305.16314/) (2023)
- [EFEM: Equivariant Neural Field Expectation Maximization for 3D Object Segmentation Without Scene Supervision](https://mlsanity.com/paper/2303.15440/) (2023)
- [E2PN: Efficient SE(3)-Equivariant Point Network](https://mlsanity.com/paper/2206.05398/) (2022)
- [Living Scenes: Multi-object Relocalization and Reconstruction in Changing 3D Environments](https://mlsanity.com/paper/2312.09138/) (2023)
- [Generalizing Neural Human Fitting to Unseen Poses With Articulated SE(3) Equivariance](https://mlsanity.com/paper/2304.10528/) (2023)
- [Certifiable 3D Object Pose Estimation: Foundations, Learning Models, and Self-Training](https://mlsanity.com/paper/2206.11215/) (2022)
- [NeuSE: Neural SE(3)-Equivariant Embedding for Long-Term Object-Based Simultaneous Localization and Mapping](https://mlsanity.com/paper/2303.07308/) (2023)
- [Coarse-to-Fine Point Cloud Registration with SE(3)-Equivariant Representations](https://mlsanity.com/paper/2210.02045/) (2022)
- [Pyramid Semantic Graph-based Global Point Cloud Registration with Low Overlap](https://mlsanity.com/paper/2307.12116/) (2023)
- [Lie Neurons: Adjoint-Equivariant Neural Networks for Semisimple Lie Algebras](https://mlsanity.com/paper/2310.04521/) (2023)
- [An intuitive multi-frequency feature representation for SO(3)-equivariant networks](https://mlsanity.com/paper/2405.04537/) (2024)
- [Approximately Piecewise E(3) Equivariant Point Networks](https://mlsanity.com/paper/2402.08529/) (2024)
- [Correspondence-Free SE(3) Point Cloud Registration in RKHS via Unsupervised Equivariant Learning](https://mlsanity.com/paper/2407.20223/) (2024)
- [Equi-GSPR: Equivariant SE(3) Graph Network Model for Sparse Point Cloud Registration](https://mlsanity.com/paper/2410.05729/) (2024)
- [Point-PNG: Conditional Pseudo-Negatives Generation for Point Cloud Pre-Training](https://mlsanity.com/paper/2409.15832/) (2024)
- [Multiview Point Cloud Registration via Optimization in an Autoencoder Latent Space](https://mlsanity.com/paper/2504.21467/) (2025)
- [Generalized-CVO: Fast and Correspondence-Free Local Point Cloud Registration with Second Order Riemannian Optimization](https://mlsanity.com/paper/2606.10019/) (2026)
- [DPCN++: Differentiable Phase Correlation Network for Versatile Pose Registration](https://mlsanity.com/paper/2206.05707/) (2022)
- [Correspondence-Free Pose Estimation with Patterns: A Unified Approach for Multi-Dimensional Vision](https://mlsanity.com/paper/2503.00051/) (2025)

## 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.