# Coarse-to-Fine Point Cloud Registration with SE(3)-Equivariant Representations

arXiv: https://arxiv.org/abs/2210.02045 · HTML: https://mlsanity.com/paper/2210.02045/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 48 references that are in the map.
- First posted on arXiv 5 Oct 2022.

## Builds on (most cited first, 30 of 33)

- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks](https://mlsanity.com/paper/2006.10503/) (2020)
- [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)
- [Deep Global Registration](https://mlsanity.com/paper/2004.11540/) (2020)
- [Neural Descriptor Fields: SE(3)-Equivariant Object Representations for Manipulation](https://mlsanity.com/paper/2112.05124/) (2021)
- [Geometric Transformer for Fast and Robust Point Cloud Registration](https://mlsanity.com/paper/2202.06688/) (2022)
- [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)
- [Go-ICP: A Globally Optimal Solution to 3D ICP Point-Set Registration](https://mlsanity.com/paper/1605.03344/) (2016)
- [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)
- [REGTR: End-to-end Point Cloud Correspondences with Transformers](https://mlsanity.com/paper/2203.14517/) (2022)
- [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)
- [LCDNet: Deep Loop Closure Detection and Point Cloud Registration for LiDAR SLAM](https://mlsanity.com/paper/2103.05056/) (2021)
- [Learning 3D Shape Completion under Weak Supervision](https://mlsanity.com/paper/1805.07290/) (2018)
- [Correspondence-Free Point Cloud Registration with SO(3)-Equivariant Implicit Shape Representations](https://mlsanity.com/paper/2107.10296/) (2021)
- [ReAgent: Point Cloud Registration using Imitation and Reinforcement Learning](https://mlsanity.com/paper/2103.15231/) (2021)
- [GOGMA: Globally-Optimal Gaussian Mixture Alignment](https://mlsanity.com/paper/1603.00150/) (2016)
- [The Alignment of the Spheres: Globally-Optimal Spherical Mixture Alignment for Camera Pose Estimation](https://mlsanity.com/paper/1812.01232/) (2018)
- [ImLoveNet: Misaligned Image-supported Registration Network for Low-overlap Point Cloud Pairs](https://mlsanity.com/paper/2207.00826/) (2022)

## Built on by (most cited first, 9 of 9)

- [Leveraging SE(3) Equivariance for Learning 3D Geometric Shape Assembly](https://mlsanity.com/paper/2309.06810/) (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)
- [NeuSE: Neural SE(3)-Equivariant Embedding for Long-Term Object-Based Simultaneous Localization and Mapping](https://mlsanity.com/paper/2303.07308/) (2023)
- [Approximately Piecewise E(3) Equivariant Point Networks](https://mlsanity.com/paper/2402.08529/) (2024)
- [SE(3)-bi-equivariant Transformers for Point Cloud Assembly](https://mlsanity.com/paper/2407.09167/) (2024)
- [Rigid Single-Slice-in-Volume registration via rotation-equivariant 2D/3D feature matching](https://mlsanity.com/paper/2410.18683/) (2024)
- [BYE: Build Your Encoder with One Sequence of Exploration Data for Long-Term Dynamic Scene Understanding](https://mlsanity.com/paper/2412.02449/) (2024)
- [Learning Generalizable Shape Completion with SIM(3) Equivariance](https://mlsanity.com/paper/2509.26631/) (2025)

## Abstract (arXiv)

Point cloud registration is a crucial problem in computer vision and robotics. Existing methods either rely on matching local geometric features, which are sensitive to the pose differences, or leverage global shapes, which leads to inconsistency when facing distribution variances such as partial overlapping. Combining the advantages of both types of methods, we adopt a coarse-to-fine pipeline that concurrently handles both issues. We first reduce the pose differences between input point clouds by aligning global features; then we match the local features to further refine the inaccurate alignments resulting from distribution variances. As global feature alignment requires the features to preserve the poses of input point clouds and local feature matching expects the features to be invariant to these poses, we propose an SE(3)-equivariant feature extractor to simultaneously generate two types of features. In this feature extractor, representations that preserve the poses are first encoded by our novel SE(3)-equivariant network and then converted into pose-invariant ones by a pose-detaching module. Experiments demonstrate that our proposed method increases the recall rate by 20% compared to state-of-the-art methods when facing both pose differences and distribution variances.