Determining the pose of a moving camera is an important task in computer vision. In this paper, we derive a projective Newton algorithm on the manifold to refine the pose estimate of a camera. The main idea is to benefit from the fact that the 3D rigid motion is described by the Special Euclidean group which is a Riemannian manifold. The latter is equipped with a tangent space defined by the corresponding Lie algebra. This enables us to compute the optimization direction, i.e. gradient and

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... an, at each iteration of the projective Newton scheme on the tangent space of the manifold. Then, the motion is updated by projecting back the variables on the manifold itself. We also derive another version of the algorithm that employs a homeomorphic parameterization to the Special Euclidean group. We test the algorithm on several simulated and real image data sets. Compared to the standard Newton minimization scheme, we are now able to obtain the full numerical formula of the Hessian with 60% decrease in the computational complexity. Compared to Levenberg-Marquardt, the results obtained are more accurate while having a rather similar complexity.