  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%.
