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

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}.