Camera Motion Estimation by Convex Programming

3D structure recovery from a collection of 2D images requires the estimation of the camera locations and orientations, i.e. the camera motion. Estimating camera motion for a large, irregular collection of images, and particularly estimating camera positions, turns out to be an ill-conditioned problem. This is mainly due to the unknown scale involved in the pairwise location information that may lead to spurious solutions that are clustered around a few locations. In this paper we introduce an efficient semidefinite programming (SDP) formulation to overcome the clustering phenomenon. We further identify the implications of parallel rigidity theory for the uniqueness of location estimation, and prove exact (in the noiseless case) and stable location recovery results. We also introduce a distributed version of our formulation for large collections of images. Lastly, we demonstrate the utility of our approach through experiments on real images.