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A technique for efficient and accurate camera registration based on stereo image analysis is presented. Initially, few correspondences are estimated with high accuracy using a probabilistic relaxation technique. Accuracy is achieved by considering the continuous approximations of selected image areas using second order polynomials and a relaxation rule defined according to the likelihood that estimates obey stereoscopic constraints. The extrinsic camera parameters are then obtained using a novel efficient and robust approach derived from the classic eight point algorithm. Efficiency is achieved by solving a parametric linear optimization problem rather than a nonlinear one as more conventional methods attempt to do. Robustness is obtained by applying two novel strategies: normalization of the initial data via a simple but efficient diagonal scaling approach, and regularization of the underlying linear parametric optimization problem using meaningful constraints. The performance of the presented methods is assessed in several computer experiments using natural video data.