Projective Rectification Without Epipolar Geometry

We present a novel algorithm performing projective rectification which does not require explicit computation of the epipolar geometry, and specifically of the fundamental matrix. Instead of finding the epipoles and computing two homographies mapping the epipoles to infinity, as done in recent work on projective rectification, we exploit the fact that the fundamental matrix of a pair of rectified images has a particular, known form. This allows us to set up a minimization that yields the rectifying homographies directly from image correspondences. Experimental results show that our method works quite robustly even in the presence of noise, and with inaccurate point correspondences. The code of our implementation will be made available at the author’s web site.