Focal length calibration from two views: method and analysis of singular cases

We consider the problem of estimating the focal length of a camera from two views while the focal length is not varied during the motion of the camera. An approach based on Kruppa's equations is proposed. Specifically, we derive two linear and one quadratic equations to solve the problem. Although the three equations are interdependent in general, each one may be singular for different configurations. We study in detail the generic singularities of the problem and the actual singularities of the individual calibration equations. Results of our experiments using synthetic and real data underline the effect that singular configurations may have on self-calibration. However, these results are stable once the singularities are avoided.