Epipolar Geometry from Three Correspondences

In this paper, LO-RANSAC 3-LAF – a new algorithm for the correspondence problem – is described. Exploiting processes proposed for computation of affineinvariant local frames, three point-to-point correspondences are found for each region-to-region correspondence. Consequently, it is sufficient to select only triplets of region correspondences in the hypothesis stage of epipolar geometry estimation by RANSAC. We experimentally show that: 1. LO-RANSAC 3-LAF estimates epipolar geometry in time that is orders of magnitude faster than the standard method, 2. that the precision of the LO-RANSAC 3-LAF and the standard method are comparable, and 3. that RANSAC without local optimisation applied to triplets of points from a single region is significantly less precise than the new LO-RANSAC 3-LAF algorithm. In the experiments, a speed-up factor in orders of thousands is achieved on the problem of epipolar geometry estimation. The proposed method is pushing the limit of solvable problems, allowing EG estimation in correspondence problems with the number of inliers below 10%.