A SVD decomposition of essential matrix with eight solutions for the relative positions of two perspective cameras

We improve the robustness of a singular value decomposition method to compute the relative positions between two calibrated perspective cameras. The first one is an optimal step to constrain the essential matrix E to have two equal non-zero and one zero singular values in the presence of noise, which is the sufficient condition for E to be factored as a rotation matrix R and translation vector t. The other contribution is that we have found 4 new possible solutions of R and t to the relative positions of two cameras, which have not been reported in any other SVD methods. Furthermore, these 8 possible solutions are derived directly from the 8 feasible SVD decompositions. Based on the experiments on both simulation data and real images, this method performs very well and the estimation error of R and t are almost at the same level as the noise.