This paper proposes a new approach to estimate the camera displacement of stereo vision systems via minimization of the algebraic error over the essential matrices manifold. The proposed approach is based on the use of homogeneous forms and linear matrix inequality (LMI) optimizations, and has the advantages of not presenting local minima and not introducing approximations of nonlinear terms. Numerical investigations carried out with both synthetic and real data show that the proposed approach provides significantly better results than SVD methods as well as minimizations of the algebraic error over the essential matrices manifold via both gradient descent and simplex search algorithms.