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A Globally Optimal Method for the PnP Problem with MRP Rotation Parameterization

The perspective-n-point (PnP) problem is of fundamental importance in computer vision. A global optimality condition for PnP that is independent of a particular rotation parameterization was recently developed by Nakano. This paper puts forward a direct least squares, algebraic PnP solution that extends Nakano's work by combining his optimality condition with the modified Rodrigues parameters (MRPs) for parameterizing rotation. The result is a system of polynomials that is solved using the Gröbner basis approach. An MRP vector has twice the rotational range of the classical Rodrigues (i.e., Cayley) vector used by Nakano to represent rotation. The proposed solution provides strong guarantees that the full rotation singularity associated with MRPs is avoided. Furthermore, detailed experiments provide evidence that our solution attains accuracy that is indistinguishable from Nakano's Cayley-based method with a moderate increase in computational cost.