Two Points Fundamental Matrix.
Gil Ben-Artzi, Tavi Halperin, Michael Werman, Bezalel Peleg · arXiv (Cornell University) · 2016
It is well known that computing the fundamental matrix of two uncalibrated cameras requires at least seven corresponding points. We present a method to compute the fundamental matrix between two cameras with only two pairs of corresponding points. Given these two points, we show how to find three pairs of corresponding epipolar lines, from which the fundamental matrix can be computed. Two pairs of epipolar lines, incident to the two pairs of corresponding points, are found by maximizing stereo consistency between lines; corresponding epipolar lines yield a good stereo correspondence. These two epipolar lines intersect at the epipoles, giving a third pair of corresponding points. A third pair of matching epipolar lines, needed to compute the fundamental matrix, is found from lines incident to the epipoles. We validate our method using real-world images and compare it to state-of-the-art methods. Our approach is more accurate by a factor of five compared to the standard method using seven corresponding points, and its accuracy is comparable to the 8-points algorithm.