Abstract

In this paper, we revisit the pose determination problem of a partially calibrated camera with unknown focal length, hereafter referred to as the PnPf problem, by using n v> n (n ≥ 4) 3D-to-2D point correspondences. Our core contribution is to introduce the angle constraint and derive a compact bivariate polynomial equation for each point triplet. Based on this polynomial equation, we propose a truly general method for the PnPf problem, which is suited both to the minimal 4-point based RANSAC application, and also to large scale scenarios with thousands of points, irrespective of the 3D point configuration. In addition, by solving bivariate polynomial systems via the Sylvester resultant, our method is very simple and easy to implement. Its simplicity is especially obvious when one needs to develop a fast solver for the 4-point case on the basis of the characteristic polynomial technique. Experiment results have also demonstrated its superiority in accuracy and e?ciency when compared with the existing state-of-the-art solutions.