# Equi-GSPR: Equivariant SE(3) Graph Network Model for Sparse Point Cloud Registration

arXiv: https://arxiv.org/abs/2410.05729 · HTML: https://mlsanity.com/paper/2410.05729/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 41 of its 57 references that are in the map.
- First posted on arXiv 8 Oct 2024.

## Builds on (most cited first, 30 of 41)

- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks](https://mlsanity.com/paper/2006.10503/) (2020)
- [Spherical CNNs](https://mlsanity.com/paper/1801.10130/) (2018)
- [General E(2)-Equivariant Steerable CNNs](https://mlsanity.com/paper/1911.08251/) (2019)
- [3D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Data](https://mlsanity.com/paper/1807.02547/) (2018)
- [3DMatch: Learning Local Geometric Descriptors from RGB-D Reconstructions](https://mlsanity.com/paper/1603.08182/) (2016)
- [Point-GNN: Graph Neural Network for 3D Object Detection in a Point Cloud](https://mlsanity.com/paper/2003.01251/) (2020)
- [Deep Closest Point: Learning Representations for Point Cloud Registration](https://mlsanity.com/paper/1905.03304/) (2019)
- [Vector Neurons: A General Framework for SO(3)-Equivariant Networks](https://mlsanity.com/paper/2104.12229/) (2021)
- [PREDATOR: Registration of 3D Point Clouds with Low Overlap](https://mlsanity.com/paper/2011.13005/) (2020)
- [Equivariant Flows: Exact Likelihood Generative Learning for Symmetric Densities](https://mlsanity.com/paper/2006.02425/) (2020)
- [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)
- [Geometric and Physical Quantities Improve E(3) Equivariant Message Passing](https://mlsanity.com/paper/2110.02905/) (2021)
- [Geometric Transformer for Fast and Robust Point Cloud Registration](https://mlsanity.com/paper/2202.06688/) (2022)
- [Learning Steerable Filters for Rotation Equivariant CNNs](https://mlsanity.com/paper/1711.07289/) (2017)
- [Universal Invariant and Equivariant Graph Neural Networks](https://mlsanity.com/paper/1905.04943/) (2019)
- [D3Feat: Joint Learning of Dense Detection and Description of 3D Local Features](https://mlsanity.com/paper/2003.03164/) (2020)
- [Go-ICP: A Globally Optimal Solution to 3D ICP Point-Set Registration](https://mlsanity.com/paper/1605.03344/) (2016)
- [SpinNet: Learning a General Surface Descriptor for 3D Point Cloud Registration](https://mlsanity.com/paper/2011.12149/) (2020)
- [PointDSC: Robust Point Cloud Registration using Deep Spatial Consistency](https://mlsanity.com/paper/2103.05465/) (2021)
- [Lorentz Group Equivariant Neural Network for Particle Physics](https://mlsanity.com/paper/2006.04780/) (2020)
- [LieTransformer: Equivariant self-attention for Lie Groups](https://mlsanity.com/paper/2012.10885/) (2020)
- [3DRegNet: A Deep Neural Network for 3D Point Registration](https://mlsanity.com/paper/1904.01701/) (2019)
- [Equivariant Point Network for 3D Point Cloud Analysis](https://mlsanity.com/paper/2103.14147/) (2021)

## Built on by (most cited first, 2 of 2)

- [Surfel-based 3D Registration with Equivariant SE(3) Features](https://mlsanity.com/paper/2508.20789/) (2025)
- [Skeleton-based Robust Registration Framework for Corrupted 3D Point Clouds](https://mlsanity.com/paper/2509.24273/) (2025)

## Abstract (arXiv)

Point cloud registration is a foundational task for 3D alignment and reconstruction applications. While both traditional and learning-based registration approaches have succeeded, leveraging the intrinsic symmetry of point cloud data, including rotation equivariance, has received insufficient attention. This prohibits the model from learning effectively, resulting in a requirement for more training data and increased model complexity. To address these challenges, we propose a graph neural network model embedded with a local Spherical Euclidean 3D equivariance property through SE(3) message passing based propagation. Our model is composed mainly of a descriptor module, equivariant graph layers, match similarity, and the final regression layers. Such modular design enables us to utilize sparsely sampled input points and initialize the descriptor by self-trained or pre-trained geometric feature descriptors easily. Experiments conducted on the 3DMatch and KITTI datasets exhibit the compelling and robust performance of our model compared to state-of-the-art approaches, while the model complexity remains relatively low at the same time.