  Determining the position and orientation of a calibrated camera from a single
image with respect to a 3D model is an essential task for many applications.
When 2D-3D correspondences can be obtained reliably, perspective-n-point
solvers can be used to recover the camera pose. However, without the pose it is
non-trivial to find cross-modality correspondences between 2D images and 3D
models, particularly when the latter only contains geometric information.
Consequently, the problem becomes one of estimating pose and correspondences
jointly. Since outliers and local optima are so prevalent, robust objective
functions and global search strategies are desirable. Hence, we cast the
problem as a 2D-3D mixture model alignment task and propose the first
globally-optimal solution to this formulation under the robust $L_2$ distance
between mixture distributions. We search the 6D camera pose space using
branch-and-bound, which requires novel bounds, to obviate the need for a pose
estimate and guarantee global optimality. To accelerate convergence, we
integrate local optimization, implement GPU bound computations, and provide an
intuitive way to incorporate side information such as semantic labels. The
algorithm is evaluated on challenging synthetic and real datasets,
outperforming existing approaches and reliably converging to the global
optimum.
