Global multiview registration using non-convex ADMM

We consider the problem of aligning multiview scans obtained using a range scanner. The computational pipeline for this problem can be divided into two phases: (i) finding point-to-point correspondences between overlapping scans, and (ii) registration of the scans based on the correspondences. The focus of this work is on global registration in which the scans (modeled as point clouds) are required to be jointly registered in a common reference frame. We consider an optimization framework for global registration that is based on rank-constrained semidefinite programming. We propose to solve this semidefinite program using a non-convex variant of the ADMM (Alternating Direction Method of Multipliers) algorithm. This results in an efficient and scalable iterative method that requires just one eigendecompostion per iteration. We present simulations results on synthetic 3D models, using both clean and noisy correspondences. An interesting finding is that the algorithm is robust to wrong correspondences - it yields high-quality reconstructions even when a significant fraction of the correspondences are corrupted. Finally, by using ICP to infer the correspondences, we present some promising preliminary results for multiview reconstruction.