Approximating the Polynomial System for Effective Relative Pose Estimation

Abstract

Finding relative pose for cameras is of vital importance in computer vision and robotics. We investigate the problem of relative motion estimation between successive frames from a minimal number of correspondences. Existing approximated methods use a first-order approximation to relative pose in order to simplify the problem and produce an estimate quickly. Our solution uses Cayley parameterization to represent rotation and simplifies the high-degree polynomials only at the very end of the formulation, resulting in more accurate models. Furthermore, our method can be more effective if the camera rotates mainly around one coordinate axis. By treating the main rotation component as the hidden variable in the solution, we can retain more high-degree terms for the main rotation part, considerably widening the effective approximation range. Our experiments show that our method is more accurate than existing approximated solver, and that it is still effective for relatively large motions. Besides, our method produces far fewer solutions than essential matrix parameterized solvers.