Globally Optimal Pose from Orthographic Silhouettes

We solve the problem of determining the pose of known shapes in $\mathbb{R}^3$ from their unoccluded silhouettes. The pose is determined up to global optimality using a simple yet under-explored property of the area-of-silhouette: its continuity w.r.t trajectories in the rotation space. The proposed method utilises pre-computed silhouette-signatures, modelled as a response surface of the area-of-silhouettes. Querying this silhouette-signature response surface for pose estimation leads to a strong branching of the rotation search space, making resolution-guided candidate search feasible. Additionally, we utilise the aspect ratio of 2D ellipses fitted to projected silhouettes as an auxiliary global shape signature to accelerate the pose search. This combined strategy forms the first method to efficiently estimate globally optimal pose from just the silhouettes, without being guided by correspondences, for any shape, irrespective of its convexity and genus. We validate our method on synthetic and real examples, demonstrating significantly improved accuracy against comparable approaches.