  The Relative Pose problem (RPp) for cameras aims to estimate the relative
orientation and translation (pose) given a set of pair-wise feature
correspondences between two central and calibrated cameras. The RPp is stated
as an optimization problem where the squared, normalized epipolar error is
minimized over the set of normalized essential matrices. In this work, we
contribute an efficient and complete algorithm based on results from duality
theory that is able to certify whether the solution to a RPp instance is the
global optimum. Specifically, we present a family of certifiers that is shown
to increase the ratio of detected optimal solutions. This set of certifiers is
incorporated into an efficient 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 and thereupon, certifies the optimality of the
solution.
  We integrate our fast certifiable pipeline into a robust framework that
combines Graduated Non-convexity and the Black-Rangarajan duality between
robust functions and line processes. This combination has been shown in the
literature to outperform the robustness to outliers provided by approaches
based on RANSAC.
  We proved through extensive experiments on synthetic and real data that the
proposed framework provides a fast and robust relative pose estimation. We
compare our proposal against the state-of-the-art methods on both accuracy and
computational cost, and show that our estimations improve the output of the
gold-standard approach for the RPp, the 2-view Bundle-Adjustment.
  We make the code publicly available
\url{https://github.com/mergarsal/FastCertRelPose.git}.
