  Estimating the 6-DoF pose of a camera from a single image relative to a
pre-computed 3D point-set is an important task for many computer vision
applications. Perspective-n-Point (PnP) solvers are routinely used for camera
pose estimation, provided that a good quality set of 2D-3D feature
correspondences are known beforehand. However, finding optimal correspondences
between 2D key-points and a 3D point-set is non-trivial, especially when only
geometric (position) information is known. Existing approaches to the
simultaneous pose and correspondence problem use local optimisation, and are
therefore unlikely to find the optimal solution without a good pose
initialisation, or introduce restrictive assumptions. Since a large proportion
of outliers are common for this problem, we instead propose a globally-optimal
inlier set cardinality maximisation approach which jointly estimates optimal
camera pose and optimal correspondences. Our approach employs branch-and-bound
to search the 6D space of camera poses, guaranteeing global optimality without
requiring a pose prior. The geometry of SE(3) is used to find novel upper and
lower bounds for the number of inliers and local optimisation is integrated to
accelerate convergence. The evaluation empirically supports the optimality
proof and shows that the method performs much more robustly than existing
approaches, including on a large-scale outdoor data-set.
