  This paper proposes the geometric relationship of epipolar geometry and
orientation- and scale-covariant, e.g., SIFT, features. We derive a new linear
constraint relating the unknown elements of the fundamental matrix and the
orientation and scale. This equation can be used together with the well-known
epipolar constraint to, e.g., estimate the fundamental matrix from four SIFT
correspondences, essential matrix from three, and to solve the semi-calibrated
case from three correspondences. Requiring fewer correspondences than the
well-known point-based approaches (e.g., 5PT, 6PT and 7PT solvers) for epipolar
geometry estimation makes RANSAC-like randomized robust estimation
significantly faster. The proposed constraint is tested on a number of problems
in a synthetic environment and on publicly available real-world datasets on
more than 80000 image pairs. It is superior to the state-of-the-art in terms of
processing time while often leading to more accurate results.
