Global point cloud registration is essential in many robotics tasks like loop closing and relocalization. Unfortunately, the registration often suffers from the low overlap between point clouds, a frequent occurrence in practical applications due to occlusion and viewpoint change. In this paper, we propose a graph-theoretic framework to address the problem of global point cloud registration with low overlap. To this end, we construct a consistency graph to facilitate robust data association and employ graduated non-convexity (GNC) for reliable pose estimation, following the state-of-the-art (SoTA) methods. Unlike previous approaches, we use semantic cues to scale down the dense point clouds, thus reducing the problem size. Moreover, we address the ambiguity arising from the consistency threshold by constructing a pyramid graph with multi-level consistency thresholds. Then we propose a cascaded gradient ascend method to solve the resulting densest clique problem and obtain multiple pose candidates for every consistency threshold. Finally, fast geometric verification is employed to select the optimal estimation from multiple pose candidates. Our experiments, conducted on a self-collected indoor dataset and the public KITTI dataset, demonstrate that our method achieves the highest success rate despite the low overlap of point clouds and low semantic quality. We have open-sourced our code https://github.com/HKUST-Aerial-Robotics/Pagor for this project.

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