The Iterative Closest Point (ICP) algorithm is one of the most widely used
methods for point-set registration. However, being based on local iterative
optimization, ICP is known to be susceptible to local minima. Its performance
critically relies on the quality of the initialization and only local
optimality is guaranteed. This paper presents the first globally optimal
algorithm, named Go-ICP, for Euclidean (rigid) registration of two 3D
point-sets under the L2 error metric defined in ICP. The Go-ICP method is based
on a branch-and-bound (BnB) scheme that searches the entire 3D motion space
SE(3). By exploiting the special structure of SE(3) geometry, we derive novel
upper and lower bounds for the registration error function. Local ICP is
integrated into the BnB scheme, which speeds up the new method while
guaranteeing global optimality. We also discuss extensions, addressing the
issue of outlier robustness. The evaluation demonstrates that the proposed
method is able to produce reliable registration results regardless of the
initialization. Go-ICP can be applied in scenarios where an optimal solution is
desirable or where a good initialization is not always available.

本文提出了一种被称为 Go-ICP 的全局最优算法，它基于分支定界结构搜索整个 3D 运动空间 SE (3)，并且集成了局部 ICP 以提高速度，保证全局最优性，可以用于解决初始位置不佳及需要最优解决的场景。