Optimisation-on-a-manifold for global registration of multiple 3D point sets

We propose a novel algorithm to register multiple 3D point sets within a common reference frame simultaneously. Our approach performs an explicit optimisation on the manifold of rotations. Firstly, we present a new closed-form solution for simultaneous multiview registration in the noise-free case. Secondly, we use this as a first step to derive a good initial estimate of a solution in the case of noisy data. This initialisation step may be of use in any general iterative scheme. Finally, we present an iterative scheme based on Gauss-Newton method evolving on rotations manifold that has locally quadratic convergence. We demonstrate the efficacy of our scheme on scan data taken both from the Digital Michelangelo Project and from scans extracted from models. In all cases under study, our algorithm converges much faster than the other well-known approaches (in some cases orders of magnitude faster) and generates consistently higher quality registrations.