Estimating the rigid transformation between two LiDAR scans through putative 3D correspondences is a typical point cloud registration paradigm. Current 3D feature matching approaches commonly lead to numerous outlier correspondences, making outlier-robust registration techniques indispensable. Many recent studies have adopted the branch and bound (BnB) optimization framework to solve the correspondence-based point cloud registration problem globally and deterministically. Nonetheless, BnB-based methods are time-consuming to search the entire 6-dimensional parameter space, since their computational complexity is exponential to the dimension of the solution domain. In order to enhance algorithm efficiency, existing works attempt to decouple the 6 degrees of freedom (DOF) original problem into two 3-DOF sub-problems, thereby reducing the dimension of the parameter space. In contrast, our proposed approach introduces a novel pose decoupling strategy based on residual projections, effectively decomposing the raw problem into three 2-DOF rotation search sub-problems. Subsequently, we employ a novel BnB-based search method to solve these sub-problems, achieving efficient and deterministic registration. Furthermore, our method can be adapted to address the challenging problem of simultaneous pose and correspondence registration (SPCR). Through extensive experiments conducted on synthetic and real-world datasets, we demonstrate that our proposed method outperforms state-of-the-art methods in terms of efficiency, while simultaneously ensuring robustness.

翻译：通过假设的三维对应关系估计两帧激光雷达扫描之间的刚体变换是点云配准的典型范式。当前三维特征匹配方法通常导致大量离群对应点，因此鲁棒性配准技术不可或缺。许多近期研究采用分支定界（BnB）优化框架来全局且确定性地解决基于对应点的点云配准问题。然而，基于BnB的方法在搜索整个六维参数空间时耗时较长，因其计算复杂度与解空间维度呈指数关系。为提升算法效率，现有研究尝试将六自由度（DOF）原始问题解耦为两个三自由度子问题，从而降低参数空间维度。相比之下，本文提出的方法引入了一种新颖的基于残差投影的位姿解耦策略，有效将原始问题分解为三个二自由度旋转搜索子问题。随后，我们采用新型的基于BnB的搜索方法求解这些子问题，实现了高效且确定性的配准。此外，本方法可扩展应用于同时位姿与对应点配准（SPCR）这一挑战性问题。通过在合成数据集和真实数据集上的大量实验证明，本文方法在保证鲁棒性的同时，其效率超越了当前最先进的方法。