In the realm of large-scale point cloud registration, designing a compact symbolic representation is crucial for efficiently processing vast amounts of data, ensuring registration robustness against significant viewpoint variations and occlusions. This paper introduces a novel point cloud registration method, i.e., QuadricsReg, which leverages concise quadrics primitives to represent scenes and utilizes their geometric characteristics to establish correspondences for 6-DoF transformation estimation. As a symbolic feature, the quadric representation fully captures the primary geometric characteristics of scenes, which can efficiently handle the complexity of large-scale point clouds. The intrinsic characteristics of quadrics, such as types and scales, are employed to initialize correspondences. Then we build a multi-level compatibility graph set to find the correspondences using the maximum clique on the geometric consistency between quadrics. Finally, we estimate the 6-DoF transformation using the quadric correspondences, which is further optimized based on the quadric degeneracy-aware distance in a factor graph, ensuring high registration accuracy and robustness against degenerate structures. We test on 5 public datasets and the self-collected heterogeneous dataset across different LiDAR sensors and robot platforms. The exceptional registration success rates and minimal registration errors demonstrate the effectiveness of QuadricsReg in large-scale point cloud registration scenarios. Furthermore, the real-world registration testing on our self-collected heterogeneous dataset shows the robustness and generalization ability of QuadricsReg on different LiDAR sensors and robot platforms. The codes and demos will be released at \url{https://levenberg.github.io/QuadricsReg}.

翻译：在大规模点云配准领域，设计紧凑的符号化表示对于高效处理海量数据、确保配准在显著视角变化与遮挡下的鲁棒性至关重要。本文提出一种新颖的点云配准方法——QuadricsReg，该方法利用简洁的二次曲面基元表示场景，并利用其几何特性建立对应关系以进行六自由度变换估计。作为一种符号化特征，二次曲面表示充分捕捉了场景的主要几何特性，能够高效处理大规模点云的复杂性。我们利用二次曲面的内在特性（如类型与尺度）来初始化对应关系。随后构建多级兼容图集，基于二次曲面间的几何一致性，通过最大团搜索来确立对应关系。最后，我们利用二次曲面对应关系估计六自由度变换，并进一步在因子图中基于二次曲面退化感知距离进行优化，从而确保高配准精度以及对退化结构的鲁棒性。我们在5个公开数据集及自采集的跨不同激光雷达传感器与机器人平台的异构数据集上进行了测试。优异的配准成功率和极低的配准误差证明了QuadricsReg在大规模点云配准场景中的有效性。此外，在自采集异构数据集上的真实世界配准测试表明，QuadricsReg在不同激光雷达传感器与机器人平台上均具备鲁棒性与泛化能力。代码与演示将发布于 \url{https://levenberg.github.io/QuadricsReg}。