Point cloud alignment is a common problem in computer vision and robotics,
with applications ranging from 3D object recognition to reconstruction. We
propose a novel approach to the alignment problem that utilizes Bayesian
nonparametrics to describe the point cloud and surface normal densities, and
branch and bound (BB) optimization to recover the relative transformation. BB
uses a novel, refinable, near-uniform tessellation of rotation space using 4D
tetrahedra, leading to more efficient optimization compared to the common
axis-angle tessellation. We provide objective function bounds for pruning given
the proposed tessellation, and prove that BB converges to the optimum of the
cost function along with providing its computational complexity. Finally, we
empirically demonstrate the efficiency of the proposed approach as well as its
robustness to real-world conditions such as missing data and partial overlap.

本文提出了一种利用贝叶斯非参数方法描述点云和表面法线密度，利用分支定界优化恢复相对变换的点云对准的全新方法，采用 4D 四面体的旋转空间细分来提高优化效率，并在最后的实验中展示了该方法的高效性和对真实世界的鲁棒性。