A Minimal Solution for Two-View Focal-Length Estimation Using Two Affine Correspondences

Abstract

A minimal solution using two affine correspondences is presented to estimate the common focal length and the fundamental matrix between two semi-calibrated cameras - known intrinsic parameters except a common focal length. To the best of our knowledge, this problem is unsolved. The proposed approach extends point correspondence-based techniques with linear constraints derived from local affine transformations. The obtained multivariate polynomial system is efficiently solved by the hidden-variable technique. Observing the geometry of local affinities, we introduce novel conditions eliminating invalid roots. To select the best one out of the remaining candidates, a root selection technique is proposed outperforming the recent ones especially in case of high-level noise. The proposed 2-point algorithm is validated on both synthetic data and 104 publicly available real image pairs. A Matlab implementation of the proposed solution is included in the paper.