  The problem of self-calibration of two cameras from a given fundamental
matrix is one of the basic problems in geometric computer vision. Under the
assumption of known principal points and square pixels, the well-known Bougnoux
formula offers a means to compute the two unknown focal lengths. However, in
many practical situations, the formula yields inaccurate results due to
commonly occurring singularities. Moreover, the estimates are sensitive to
noise in the computed fundamental matrix and to the assumed positions of the
principal points. In this paper, we therefore propose an efficient and robust
iterative method to estimate the focal lengths along with the principal points
of the cameras given a fundamental matrix and priors for the estimated camera
parameters. In addition, we study a computationally efficient check of models
generated within RANSAC that improves the accuracy of the estimated models
while reducing the total computational time. Extensive experiments on real and
synthetic data show that our iterative method brings significant improvements
in terms of the accuracy of the estimated focal lengths over the Bougnoux
formula and other state-of-the-art methods, even when relying on inaccurate
priors.
