  This study presents a high-accuracy, efficient, and physically induced method
for 3D point cloud registration, which is the core of many important 3D vision
problems. In contrast to existing physics-based methods that merely consider
spatial point information and ignore surface geometry, we explore geometry
aware rigid-body dynamics to regulate the particle (point) motion, which
results in more precise and robust registration. Our proposed method consists
of four major modules. First, we leverage the graph signal processing (GSP)
framework to define a new signature, (i.e., point response intensity for each
point), by which we succeed in describing the local surface variation,
resampling keypoints, and distinguishing different particles. Then, to address
the shortcomings of current physics-based approaches that are sensitive to
outliers, we accommodate the defined point response intensity to median
absolute deviation (MAD) in robust statistics and adopt the X84 principle for
adaptive outlier depression, ensuring a robust and stable registration.
Subsequently, we propose a novel geometric invariant under rigid
transformations to incorporate higher-order features of point clouds, which is
further embedded for force modeling to guide the correspondence between
pairwise scans credibly. Finally, we introduce an adaptive simulated annealing
(ASA) method to search for the global optimum and substantially accelerate the
registration process. We perform comprehensive experiments to evaluate the
proposed method on various datasets captured from range scanners to LiDAR.
Results demonstrate that our proposed method outperforms representative
state-of-the-art approaches in terms of accuracy and is more suitable for
registering large-scale point clouds. Furthermore, it is considerably faster
and more robust than most competitors.
