Point cloud registration is challenging in the presence of heavy outlier correspondences. This paper focuses on addressing the robust correspondence-based registration problem with gravity prior that often arises in practice. The gravity directions are typically obtained by inertial measurement units (IMUs) and can reduce the degree of freedom (DOF) of rotation from 3 to 1. We propose a novel transformation decoupling strategy by leveraging screw theory. This strategy decomposes the original 4-DOF problem into three sub-problems with 1-DOF, 2-DOF, and 1-DOF, respectively, thereby enhancing the computation efficiency. Specifically, the first 1-DOF represents the translation along the rotation axis and we propose an interval stabbing-based method to solve it. The second 2-DOF represents the pole which is an auxiliary variable in screw theory and we utilize a branch-and-bound method to solve it. The last 1-DOF represents the rotation angle and we propose a global voting method for its estimation. The proposed method sequentially solves three consensus maximization sub-problems, leading to efficient and deterministic registration. In particular, it can even handle the correspondence-free registration problem due to its significant robustness. Extensive experiments on both synthetic and real-world datasets demonstrate that our method is more efficient and robust than state-of-the-art methods, even when dealing with outlier rates exceeding 99%.

翻译：点云配准在存在大量异常对应点时极具挑战性。本文专注于解决实际应用中常出现的带有重力先验的鲁棒对应点配准问题。重力方向通常由惯性测量单元（IMU）获取，可将旋转自由度（DOF）从3降至1。我们提出了一种基于螺旋理论的新型变换解耦策略。该策略将原始的4自由度问题分解为三个子问题，分别具有1自由度、2自由度和1自由度，从而提升了计算效率。具体而言，第一个1自由度代表沿旋转轴的平移，我们提出了一种基于区间穿刺的方法求解；第二个2自由度代表极点（螺旋理论中的辅助变量），我们采用分支定界法求解；最后一个1自由度代表旋转角，我们提出了一种全局投票法进行估计。所提方法依次求解三个一致性最大化子问题，实现了高效且确定性的配准。尤其值得注意的是，由于具备显著鲁棒性，该方法甚至可处理无对应点的配准问题。在合成数据集与真实数据集上的大量实验表明，即使面对超过99%的异常点比例，我们的方法在效率和鲁棒性方面均优于当前最优方法。