From Correspondences to Pose: Non-minimal Certifiably Optimal Relative Pose without Disambiguation

Estimating the relative camera pose from n \geq 5 correspondences between two calibrated views is a fundamental task in computer vision. This process typically involves two stages: 1) estimating the essential matrix between the views and 2) disambiguating among the four candidate relative poses that satisfy the epipolar geometry. In this paper we demonstrate a novel approach that for the first time bypasses the second stage. Specifically we show that it is possible to directly estimate the correct relative camera pose from correspondences without needing a post-processing step to enforce the cheirality constraint on the correspondences. Building on recent advances in certifiable non-minimal optimization we frame the relative pose estimation as a Quadratically Constrained Quadratic Program (QCQP). By applying the appropriate constraints we ensure the estimation of a camera pose that corresponds to a valid 3D geometry and that is globally optimal when certified. We validate our method through exhaustive synthetic and real-world experiments confirming the efficacy efficiency and accuracy of the proposed approach. Code is available at https://github.com/javrtg/C2P.