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Estimation of the camera pose from image point correspondences through the essential matrix and convex optimization

Estimating the camera pose in stereo vision systems is an important issue in computer vision and robotics. One popular way to handle this problem consists of determining the essential matrix which minimizes the algebraic error obtained from image point correspondences. Unfortunately, this search amounts to solving a nonconvex optimization, and the existing methods either rely on some approximations in order to get rid of the non-convexity or provide a solution that may be affected by the presence of local minima. This paper proposes a new approach to address this search without presenting such problems. In particular, we show that the sought essential matrix can be obtained by solving a convex optimization built through a suitable reformulation of the considered minimization via appropriate techniques for representing polynomials. Numerical results show the proposed approach compares favorably with some standard methods in both cases of synthetic data and real data.