  An approach is proposed for recovering affine correspondences (ACs) from
orientation- and scale-invariant, e.g. SIFT, features. The method calculates
the affine parameters consistent with a pre-estimated epipolar geometry from
the point coordinates and the scales and rotations which the feature detector
obtains. The closed-form solution is given as the roots of a quadratic
polynomial equation, thus having two possible real candidates and fast
procedure, i.e. <1 millisecond. It is shown, as a possible application, that
using the proposed algorithm allows us to estimate a homography for every
single correspondence independently. It is validated both in our synthetic
environment and on publicly available real world datasets, that the proposed
technique leads to accurate ACs. Also, the estimated homographies have similar
accuracy to what the state-of-the-art methods obtain, but due to requiring only
a single correspondence, the robust estimation, e.g. by locally optimized
RANSAC, is an order of magnitude faster.
