A Scalable ADMM Algorithm for Rigid Registration

A fundamental problem that comes up in computer vision, image processing, manifold learning, and sensor networks is that of registering multiple point sets using rigid transforms. A standard result in this regard is that the least-square formulation of the registration problem admits a closed-form solution for two point sets. However, since the group of rigid transforms is not convex, solving the least-square optimization for multiple point sets is computationally challenging. It was recently demonstrated that the least-square formulation can be relaxed into a tractable semidefinite program, and that the relaxation is provably tight under certain assumptions. The difficulty is that standard solvers for semidefinite programming (e.g., interior-point solvers) cannot be scaled to handle large-sized problems. In this letter, we propose an iterative solver based on variable splitting and the alternating direction method of multipliers. Since each iteration essentially involves an eigendecomposition, the proposed solver can be scaled to problems that are beyond the reach of interior-point solvers. We present results on simulated and real data to demonstrate the potential of the solver.