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%.

通过利用螺旋理论，将原始的四个自由度点云配准问题分解为三个子问题，并提出了一种新的转换解耦策略，以提高计算效率和准确性。这种方法可以有效处理重度异常值对应的点云配准问题。

基于螺旋理论的确定性点云配准中的转换解耦策略与重力先验

Transformation Decoupling Strategy based on Screw Theory for  Deterministic Point Cloud Registration with Gravity Prior

Removing outlier correspondences is one of the critical steps for successful
feature-based point cloud registration. Despite the increasing popularity of
introducing deep learning methods in this field, spatial consistency, which is
essentially established by a Euclidean transformation between point clouds, has
received almost no individual attention in existing learning frameworks. In
this paper, we present PointDSC, a novel deep neural network that explicitly
incorporates spatial consistency for pruning outlier correspondences. First, we
propose a nonlocal feature aggregation module, weighted by both feature and
spatial coherence, for feature embedding of the input correspondences. Second,
we formulate a differentiable spectral matching module, supervised by pairwise
spatial compatibility, to estimate the inlier confidence of each correspondence
from the embedded features. With modest computation cost, our method
outperforms the state-of-the-art hand-crafted and learning-based outlier
rejection approaches on several real-world datasets by a significant margin. We
also show its wide applicability by combining PointDSC with different 3D local
descriptors.

本研究提出 PointDSC，一个基于深度学习的神经网络，在点云配准中明确地引入空间一致性，通过非局部特征聚合模块和可微分谱匹配模块进行同型剪枝，实现对离群点对应关系的修剪，结果表明 PointDSC 在多个实际数据集上比基于手工和基于深度学习的离群点拒绝方法都有更好的表现，并通过与不同的 3D 局部描述符进行组合来展示其广泛的适用性。