The registration problem revisited: Optimal solutions from points, lines and planes

In this paper we propose a practical and efficient method for finding the globally optimal solution to the problem of pose estimation of a known object. We present a framework that allows us to use both point-to-point, point-to-line and point-to-plane correspondences in the optimization algorithm. Traditional methods such as the iterative closest point algorithm may get trapped in local minima due to the non-convexity of the problem, however, our approach guarantees global optimality. The approach is based on ideas from global optimization theory, in particular, convex under-estimators in combination with branch and bound. We provide a provably optimal algorithm and demonstrate good performance on both synthetic and real data.