  This study introduces a novel framework, G3Reg, for fast and robust global
registration of LiDAR point clouds. In contrast to conventional complex
keypoints and descriptors, we extract fundamental geometric primitives,
including planes, clusters, and lines (PCL) from the raw point cloud to obtain
low-level semantic segments. Each segment is represented as a unified Gaussian
Ellipsoid Model (GEM), using a probability ellipsoid to ensure the ground truth
centers are encompassed with a certain degree of probability. Utilizing these
GEMs, we present a distrust-and-verify scheme based on a Pyramid Compatibility
Graph for Global Registration (PAGOR). Specifically, we establish an upper
bound, which can be traversed based on the confidence level for compatibility
testing to construct the pyramid graph. Then, we solve multiple maximum cliques
(MAC) for each level of the pyramid graph, thus generating the corresponding
transformation candidates. In the verification phase, we adopt a precise and
efficient metric for point cloud alignment quality, founded on geometric
primitives, to identify the optimal candidate. The algorithm's performance is
validated on three publicly available datasets and a self-collected
multi-session dataset. Parameter settings remained unchanged during the
experiment evaluations. The results exhibit superior robustness and real-time
performance of the G3Reg framework compared to state-of-the-art methods.
Furthermore, we demonstrate the potential for integrating individual GEM and
PAGOR components into other registration frameworks to enhance their efficacy.
Code: https://github.com/HKUST-Aerial-Robotics/G3Reg
