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

Estimating the relative camera pose from n ≥ 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 postprocessing 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.