Gaussian mixture alignment is a family of approaches that are frequently used
for robustly solving the point-set registration problem. However, since they
use local optimisation, they are susceptible to local minima and can only
guarantee local optimality. Consequently, their accuracy is strongly dependent
on the quality of the initialisation. This paper presents the first
globally-optimal solution to the 3D rigid Gaussian mixture alignment problem
under the L2 distance between mixtures. The algorithm, named GOGMA, employs a
branch-and-bound approach to search the space of 3D rigid motions SE(3),
guaranteeing global optimality regardless of the initialisation. The geometry
of SE(3) was used to find novel upper and lower bounds for the objective
function and local optimisation was integrated into the scheme to accelerate
convergence without voiding the optimality guarantee. The evaluation
empirically supported the optimality proof and showed that the method performed
much more robustly on two challenging datasets than an existing
globally-optimal registration solution.

该论文提出了解决点集配准问题的一种新方法，名为 GOGMA，它利用 SE（3）空间的几何特征，采用分支限界的方法来搜索 3D 刚性运动的空间，从而保证全局最优解，同时还能加速收敛，而且经过实验证明该方法比现有的全局最优解方法具有更强的鲁棒性。