Fast and Robust Certifiable Estimation of the Relative Pose Between Two Calibrated Cameras

Abstract: This work contributes an efficient algorithm to compute the Relative Pose problem (RPp) between calibrated cameras and certify the optimality of the solution, given a set of pair-wise feature correspondences affected by noise and probably corrupted by wrong matches. We propose a family of certifiers that is shown to increase the ratio of detected optimal solutions. This set of certifiers is incorporated into a fast essential matrix estimation pipeline that, given any initial guess for the RPp, refines it iteratively on the product space of 3D rotations and 2-sphere. In addition, this fast certifiable pipeline is integrated into a robust framework that combines Graduated Non-convexity and the Black-Rangarajan duality between robust functions and line processes. We proved through extensive experiments on synthetic and real data that the proposed framework provides a fast and robust relative pose estimation. We make the code publicly available \url{https://github.com/mergarsal/FastCertRelPose.git}.