# Surfel-based 3D Registration with Equivariant SE(3) Features

arXiv: https://arxiv.org/abs/2508.20789 · HTML: https://mlsanity.com/paper/2508.20789/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 32 references that are in the map.
- First posted on arXiv 28 Aug 2025.

## Builds on (most cited first, 16 of 16)

- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [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)
- [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)
- [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)
- [LoopReg: Self-supervised Learning of Implicit Surface Correspondences, Pose and Shape for 3D Human Mesh Registration](https://mlsanity.com/paper/2010.12447/) (2020)
- [3D Registration with Maximal Cliques](https://mlsanity.com/paper/2305.10854/) (2023)
- [GeoTransformer: Fast and Robust Point Cloud Registration with Geometric Transformer](https://mlsanity.com/paper/2308.03768/) (2023)
- [Equivariant Point Network for 3D Point Cloud Analysis](https://mlsanity.com/paper/2103.14147/) (2021)
- [SurfelMeshing: Online Surfel-Based Mesh Reconstruction](https://mlsanity.com/paper/1810.00729/) (2018)
- [Efficient and Probabilistic Adaptive Voxel Mapping for Accurate Online LiDAR Odometry](https://mlsanity.com/paper/2109.07082/) (2021)
- [3D Reconstruction & Assessment Framework based on affordable 2D Lidar](https://mlsanity.com/paper/1803.09167/) (2018)
- [Equi-GSPR: Equivariant SE(3) Graph Network Model for Sparse Point Cloud Registration](https://mlsanity.com/paper/2410.05729/) (2024)

## Abstract (arXiv)

Point cloud registration is crucial for ensuring 3D alignment consistency of multiple local point clouds in 3D reconstruction for remote sensing or digital heritage. While various point cloud-based registration methods exist, both non-learning and learning-based, they ignore point orientations and point uncertainties, making the model susceptible to noisy input and aggressive rotations of the input point cloud like orthogonal transformation; thus, it necessitates extensive training point clouds with transformation augmentations. To address these issues, we propose a novel surfel-based pose learning regression approach. Our method can initialize surfels from Lidar point cloud using virtual perspective camera parameters, and learns explicit SE(3) equivariant features, including both position and rotation through SE(3) equivariant convolutional kernels to predict relative transformation between source and target scans. The model comprises an equivariant convolutional encoder, a cross-attention mechanism for similarity computation, a fully-connected decoder, and a non-linear Huber loss. Experimental results on indoor and outdoor datasets demonstrate our model superiority and robust performance on real point-cloud scans compared to state-of-the-art methods.