Automatic focal length estimation as an eigenvalue problem

•A novel multi-view camera focal length estimation method is presented in the study.•The method works on semi-calibrated cameras with fixed/variable focal length.•The proposed method is fast, precise and deals with missing data.•Solution is based on the generalized rectangular eigenvalue problem.•Efficient iterative refinement is required to obtain an accurate solution.

This paper focuses on automatic focal length estimation. In several vision applications one can assume that the utilized cameras are semi-calibrated, which means that all the intrinsic camera parameters but the focal length (aspect ratio, principal point, and skew) are known. In this case the camera calibration procedure reduces to the computation of the focal length(s). The main contribution of the study is a novel automatic focal length estimator algorithm for semi-calibrated cameras which handles both the fixed and the variable focal length cases. The method transforms the focal length estimation problem into the generalized eigenvalue problem class. The input of the algorithm is a set of fundamental matrices. The proposed method is validated on both synthetic and real data. For real sequences, the 3D structure is also reconstructed based on the cameras constructed from the output of the algorithm.