In this paper, we present a second order spatial compatibility (SC^2) measure
based method for efficient and robust point cloud registration (PCR), called
SC^2-PCR. Firstly, we propose a second order spatial compatibility (SC^2)
measure to compute the similarity between correspondences. It considers the
global compatibility instead of local consistency, allowing for more
distinctive clustering between inliers and outliers at early stage. Based on
this measure, our registration pipeline employs a global spectral technique to
find some reliable seeds from the initial correspondences. Then we design a
two-stage strategy to expand each seed to a consensus set based on the SC^2
measure matrix. Finally, we feed each consensus set to a weighted SVD algorithm
to generate a candidate rigid transformation and select the best model as the
final result. Our method can guarantee to find a certain number of outlier-free
consensus sets using fewer samplings, making the model estimation more
efficient and robust. In addition, the proposed SC^2 measure is general and can
be easily plugged into deep learning based frameworks. Extensive experiments
are carried out to investigate the performance of our method. Code will be
available at https://github.com/ZhiChen902/SC2-PCR.

本文提出了一种基于空间兼容性 (SC2) 的点云配准方法 (SC2-PCR)，使用二阶空间兼容性 (SC2) 度量来计算对应关系的相似度，运用全局光谱技术找到可靠种子点并使用二阶空间兼容性 (SC2) 矩阵来设计一个两阶段的策略扩展每个种子点的一致性集，然后使用加权奇异值分解算法将每个一致性集提供给生成候选刚性变换，并选择最佳模型作为最终结果，能够保证使用更少的采样找到一定数量的无离群值的一致性集，使模型估计更有效和健壮。

SC^2-PCR: 二阶空间兼容性方法用于高效、鲁棒的点云配准

SC^2-PCR: A Second Order Spatial Compatibility for Efficient and Robust  Point Cloud Registration

Unsupervised point cloud registration algorithm usually suffers from the
unsatisfied registration precision in the partially overlapping problem due to
the lack of effective inlier evaluation. In this paper, we propose a
neighborhood consensus based reliable inlier evaluation method for robust
unsupervised point cloud registration. It is expected to capture the
discriminative geometric difference between the source neighborhood and the
corresponding pseudo target neighborhood for effective inlier distinction.
Specifically, our model consists of a matching map refinement module and an
inlier evaluation module. In our matching map refinement module, we improve the
point-wise matching map estimation by integrating the matching scores of
neighbors into it. The aggregated neighborhood information potentially
facilitates the discriminative map construction so that high-quality
correspondences can be provided for generating the pseudo target point cloud.
Based on the observation that the outlier has the significant structure-wise
difference between its source neighborhood and corresponding pseudo target
neighborhood while this difference for inlier is small, the inlier evaluation
module exploits this difference to score the inlier confidence for each
estimated correspondence. In particular, we construct an effective graph
representation for capturing this geometric difference between the
neighborhoods. Finally, with the learned correspondences and the corresponding
inlier confidence, we use the weighted SVD algorithm for transformation
estimation. Under the unsupervised setting, we exploit the Huber function based
global alignment loss, the local neighborhood consensus loss, and spatial
consistency loss for model optimization. The experimental results on extensive
datasets demonstrate that our unsupervised point cloud registration method can
yield comparable performance.

该论文提出了一种基于邻域一致性的可靠内点评估方法，以提高无监督点云配准的精度，并利用匹配映射细化模块和内点评估模块配合实现精确配准，最终使用加权 SVD 算法进行转换估计。