The 3D-3D registration problem revisited

Abstract

We describe a new framework for globally solving the 3D-3D registration problem with unknown point correspondences. This problem is significant as it is frequently encountered in many applications. Existing methods are not fully satisfactory, mainly due to the risk of local minima. Our framework is grounded on the Lipschitz global optimization theory. It achieves a guaranteed global optimality without any initialization. By exploiting the special structure of the problem itself and of the 3D rotation space SO(3), we propose a Box-and-Ball algorithm, which solves the problem efficiently. The main idea of the work can be applied to many other problems as well.