Camera motion estimation via optimization-on-a-manifold

In this paper, we study the problem of recovering the camera motion in a multiview setting given observation of tracked features in a three-dimensional environment. We propose a novel algorithm to simultaneously recover the pose (orientation and translation to within a scale) of every camera directly using a manifold optimization approach. Our contributions are four-fold. We present a new analytic method based on singular value decomposition that yields a closed-form solution for the multiview motion estimation problem in the noise-free case. Secondly, we use this method to derive a good initial estimate of a solution in the noisy case. This initialization step may, independently, be of use in any general iterative scheme. Thirdly, we present an iterative scheme based on Gauss-Newton´s method on a product manifold that exhibits local quadratic convergence. Finally, we also present a simple linear least squares approach to recover the individual camera centers from relative translations obtained after the iteration process. Our algorithm has been implemented, and we demonstrate the efficacy of our scheme on both synthetic data and real data.