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Estimating the 6-DoF pose of a camera from a single image relative to apre-computed 3D point-set is an important task for many computer visionapplications. Perspective-n-Point (PnP) solvers are routinely used for camerapose estimation, provided that a good quality set of 2D-3D featurecorrespondences are known beforehand. However, finding optimal correspondencesbetween 2D key-points and a 3D point-set is non-trivial, especially when onlygeometric (position) information is known. Existing approaches to thesimultaneous pose and correspondence problem use local optimisation, and aretherefore unlikely to find the optimal solution without a good poseinitialisation, or introduce restrictive assumptions. Since a large proportionof outliers are common for this problem, we instead propose a globally-optimalinlier set cardinality maximisation approach which jointly estimates optimalcamera pose and optimal correspondences. Our approach employs branch-and-boundto search the 6D space of camera poses, guaranteeing global optimality withoutrequiring a pose prior. The geometry of SE(3) is used to find novel upper andlower bounds for the number of inliers and local optimisation is integrated toaccelerate convergence. The evaluation empirically supports the optimalityproof and shows that the method performs much more robustly than existingapproaches, including on a large-scale outdoor data-set.

Globally-Optimal Inlier Set Maximisation for Simultaneous Camera Pose and Feature Correspondence