Ondrej Chum, Tomáš Werner, and Jirí Matas. Two-view geometry estimation unaffected by a dominant plane. In Cordelia Schmid, Stefano Soatto, and Carlo Tomasi, editors, Proc. of Conference on Computer Vision and Pattern Recognition (CVPR), volume 1, pages 772-780, Los Alamitos, California, USA, June 2005. IEEE Computer Society.
A RANSAC-based algorithm for robust estimation of epipolar geometry from point correspondences in the possible presence of a dominant scene plane is presented. The algorithm handles scenes with (i) all points in a single plane, (ii) majority of points in a single plane and the rest off the plane, (iii) no dominant plane. It is not required to know a priori which of the cases (i)-(iii) occurs. The algorithm exploits a theorem we proved, that if five or more of seven correspondences are related by a homography then there is an epipolar geometry consistent with the seven-tuple as well as with all correspondences related by the homography. This means that a seven point sample consisting of two outliers and five inliers lying in a dominant plane produces an epipolar geometry which is wrong and yet consistent with a high number of correspondences. The theorem explains why RANSAC often fails to estimate epipolar geometry in the presence of a dominant plane. Rather surprisingly, the theorem also implies that RANSAC-based homography estimation is faster when drawing nonminimal samples of seven correspondences than minimal samples of four correspondences.
