Two-view geometry estimation unaffected by a dominant plane

• Published in: 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) Vol. 1; pp. 772 - 779 vol. 1
• Main Authors: Chum, O., Werner, T., Matas, J.
• Format: Conference Proceeding
• Language: English
• Published: IEEE 2005
• Subjects: Computational complexity; Computer Society; Computer vision; Cybernetics; Geometry; Lamps; Layout; Measurement standards; Pattern recognition; Robustness
• ISBN: 0769523722; 9780769523729
• ISSN: 1063-6919; 1063-6919
• DOI: 10.1109/CVPR.2005.354

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.