A Versatile Approach for Solving PnP, PnPf, and PnPfr Problems

Abstract

This paper proposes a versatile approach for solving three kinds of absolute camera pose estimation problem: PnP problem for calibrated cameras, PnPf problem for cameras with unknown focal length, and PnPfr problem for cameras with unknown focal length and unknown radial distortion. This is not only the first least squares solution to PnPfr problem, but also the first approach formulating three problems in the same theoretical manner. We show that all problems have a common subproblem represented as multivariate polynomial equations. Solving these equations by Gröbner basis method, we derive a linear form for the remaining parameters of each problem. Finally, we apply root polishing to strictly satisfy the original KKT condition. The proposed PnP and PnPf solvers have comparable performance to the state-of-the-art methods on synthetic distortion-free data. Moreover, the novel PnPfr solver gives the best result on distorted point data and demonstrates real image rectification against significant distortion.