Accurate Closed-form Estimation of Local Affine Transformations Consistent with the Epipolar Geometry

For a pair of images satisfying the epipolar constraint, a method for accurate estimation of local affine transformations is proposed. The method returns the local affine transformation consistent with the epipolar geometry that is closest in the least squares sense to the initial estimate provided by an affine-covariant detector. The minimized L2 norm of the affine matrix elements is found in closed-form. We show that the used norm has an intuitive geometric interpretation. The method, with negligible computational requirements, is validated on publicly available benchmarking datasets and on synthetic data. The accuracy of the local affine transformations is improved for all detectors and all image pairs. Implicitly, precision of the tested feature detectors was compared. The Hessian-Affine detector combined with ASIFT view synthesis was the most accurate.