A Direct Least-Squares Solution to the PnP Problem with Unknown Focal Length

In this work, we propose a direct least-squares solution to the perspective-n-point (PnP) pose estimation problem of a partially uncalibrated camera, whose intrinsic parameters except the focal length are known. The basic idea is to construct a proper objective function with respect to the target variables and extract all its stationary points so as to find the global minimum. The advantages of our proposed solution over existing ones are that (i) the objective function is directly built upon the imaging equation, such that all the 3D-to-2D correspondences contribute equally to the minimized error, and that (ii) the proposed solution is noniterative, in the sense that the stationary points are retrieved by means of eigenvalue factorization and the common iterative refinement step is not needed. In addition, the proposed solution has O(n) complexity, and can be used to handle both planar and nonplanar 3D points. Experimental results show that the proposed solution is much more accurate than the existing state-of-the-art solutions, and is even comparable to the maximum likelihood estimation by minimizing the reprojection error.