Pose Estimation via Gauss-Newton-on-manifold

We present a Gauss-Newton-on-manifold approach for estimating the relative pose (position and orientation) between a 3D object and its projection on a 2D image plane from a set of point correspondences. The pose estimation problem is formulated as an optimization over three rotation parameters on the intersection of the manifold of the rotation matrices and a cone constraint on these matrices to ensure positive depth parameters. The optimization is based on Newton-type iterations and is locally quadratically convergent. A key feature of the proposed approach, not used in earlier studies, is an analytic geodesic search, alternating between gradient, Gauss-Newton and a random direction, which ensures the escape from local minima and convergence to a global minimum without the need to reinitialize the algorithm. Indeed, for a prescribed number of iterations, the proposed algorithm achieves significantly lower pose estimation errors than earlier methods and it converges to a global minimum in typically 5–10 iterations.