Camera self-calibration from bivariate polynomials derived from Kruppa's equations

This paper presents a new set of equations for the self-calibration of a moving camera with constant intrinsic parameters. Unlike most existing methods that require solving equations in three or more unknowns, the proposed equations are only bivariate. In particular, we show that the three scale factors appearing in the Kruppa's equations, that are due to a triplet of images, are not independent but rather closely related. This relationship is used to derive sextic bivariate polynomial equations and allow the recovery of the unknown scale factors using a homotopy continuation method. Once the scale factors are calculated, an estimate of Kruppa's coefficients can be linearly retrieved and then refined through a nonlinear least-squares optimization procedure. The results of our experiments conducted on simulated data as well as the three-dimensional structure reconstruction using real images are also presented in the paper.