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

## TL;DR

This paper introduces a surfel-based 3D registration method that learns explicit SE(3) equivariant features, improving robustness to noise and rotations in point cloud alignment tasks.

## Contribution

It proposes a novel surfel-based pose regression approach that incorporates SE(3) equivariant convolutional features for more accurate and robust point cloud registration.

## Key findings

- Outperforms state-of-the-art methods on indoor datasets
- Demonstrates robustness to noisy and rotated point clouds
- Effective in both indoor and outdoor 3D reconstruction scenarios

## Abstract

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 $\mathbf{SE(3)}$ equivariant features, including both position and rotation through $\mathbf{SE(3)}$ 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.