Efficient and Deterministic Search Strategy Based on Residual
  Projections for Point Cloud Registration
Xinyi Li Yinlong Liu Hu Cao Xueli Liu Feihu Zhang Alois Knoll
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.