Abstract. Three-dimensional rigid point cloud registration has many applications in computer vision and robotics. Local methods tend to fail, causing global methods to be needed, when the relative transformation is large or the overlap ratio is small. Most existing global methods utilize BnB optimization over the 6D parameter space of SE(3). Such methods are usually very slow because the time complexity of BnB optimization is exponential in the dimensionality of the parameter space. In this paper, we decouple the optimization of translation and rotation, and we propose a fast BnB algorithm to globally optimize the 3D translation parameter first. The optimal rotation is then calculated by utilizing the global optimal translation found by the BnB algorithm. The separate optimization of translation and rotation is realized by using a newly proposed rotation invariant feature. Experiments on challenging data sets demonstrate that the proposed method outperforms state-of-the-art global methods in terms of both speed and accuracy