On focal length calibration from two views

We consider the problem of self-calibration of a camera whose intrinsic parameters are known, besides the focal length. In the past, algorithms were mainly proposed for estimating two values of the focal length, for two images taken with different zoom. While there exist closed form solutions based on the fundamental matrix, their applicability is limited due to a generic singularity that occurs whenever the optical axes intersect, leading to numerical instabilities in most practical situations. Here, we consider the case of two views with identical focal length. We derive closed form solutions (one quadratic and two linear equations). Their respective singularity conditions are studied analytically and experimental results on their stability are given.