Efficient and Deterministic Search Strategy Based on Residual Projections for Point Cloud Registration

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.