Two-View Focal Length Estimation for All Camera Motions Using Priors

Direct solutions to systems of polynomial equalities have been established in literature pertaining to two-view geometry to extract the focal lengths of a camera pair from the fundamental matrix, when other intrinsic calibration parameters are known. But these formulae break down near degeneracies characterized as critical motions, which occur quite commonly in practical scenarios. The contribution of this report is twofold. First, a novel method of imposing priors on the calibration matrix is presented that allows us to formulate the problem of evaluating the focal length as a constrained minimization and arrive at a correct estimate even for degenerate configurations. Second, we explore solution techniques that achieve a global minimum for polynomial objective functions with feasible region constrained to be a semialgebraic set defined by polynomial equalities. Preliminary experimental results are presented on simulated noiseless data to demonstrate the validity of our theory, both in achieving a global minimum and doing so even for critical motions.