  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}.
