In this paper, we revisit the classical perspective-n-point(PnP) problem, and propose the first non-iterative O(n) solution that is fast, generally applicable and globally optimal. Our basic idea is to formulate the PnP problem into a functional minimization problem and retrieve all its stationary points by using the Gr"obner basis technique. The novelty lies in a non-unit quaternion representation to parameterize the rotation and a simple but elegant formulation of the PnP problem into an unconstrained optimization problem. Interestingly, the polynomial system arising from its first-order optimality condition assumes two-fold symmetry, a nice property that can be utilized to improve speed and numerical stability of a Grobner basis solver. Experiment results have demonstrated that, in terms of accuracy, our proposed solution is definitely better than the state-of-the-art O(n) methods, and even comparable with the reprojection error minimization method.
Reference
Zheng, Yinqiang, et al."Revisiting the pnp problem: A fast, general and optimal solution." 2013 IEEE International Conference on Computer Vision(ICCV).
Department of Mechanical and Control Engineering, Tokyo Institute of Technology, JAPAN
2015-02-24