Camera Pose and Focal Length Estimation Using Regularized Distance Constraints

Abstract

We propose a new method for camera pose estimation with unknown focal length (PnPf problem). We combine projection equations and distance constraints in a single statistically significant cost function in the form of least squares. We fix the space of the search as a linear combination of several right singular vectors of the least squares system matrix. We use linear programming techniques to find feasible solutions faster. Then we do nonlinear refinement with Levenberg-Marquardt. Numerical experiments demonstrated that the method is faster than the state-of-the-art methods for point numbers up to several hundreds, and real-life structure-from-motion demonstrates its applicability for models having $10^3$-$10^5$ points. It has the same accuracy of estimates as the the state-of-the-art methods. We show that the method offers a tradeoff between speed and accuracy, allowing the estimation to run several times faster while slightly increasing the mean reprojection error.