Least-squares Optimal Relative Planar Motion for Vehicle-mounted Cameras

A new closed-form solver is proposed minimizing the algebraic error optimally, in the least-squares sense, to estimate the relative planar motion of two calibrated cameras. The main objective is to solve the over-determined case, i.e., when a larger-than-minimal sample of point correspondences is given - thus, estimating the motion from at least three correspondences. The algorithm requires the camera movement to be constrained to a plane, e.g. mounted to a vehicle, and the image plane to be orthogonal to the ground. The solver obtains the motion parameters as the roots of a 6-th degree polynomial. It is validated both in synthetic experiments and on publicly available real-world datasets that using the proposed solver leads to results superior to the state-of-the-art in terms of geometric accuracy with no noticeable deterioration in the processing time.