@InProceedings{chum-degen-cvpr05, IS = { zkontrolovano 30 Nov 2005 }, UPDATE = { 2005-07-18 }, author = {Chum, Ond{\v r}ej and Werner, Tom{\' a}{\v s} and Matas, Ji{\v r}{\' \i}}, title = {Two-view Geometry Estimation Unaffected by a Dominant Plane}, booktitle = {Proc. of Conference on Computer Vision and Pattern Recognition (CVPR)}, address = {Los Alamitos, USA} , year = {2005}, month = {June}, day = {20--25}, isbn = {0-7695-2372-2}, publisher = {IEEE Computer Society}, book_pages = {1219}, pages = {772--780}, authorship = {34-33-33}, psurl = {[pdf]}, project = {IST-004176, 1ET101210406}, annote = { 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 completely 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 non-minimal samples of seven correspondences than minimal samples of four correspondences. }, keywords = {RANSAC, wide-baseline stereo, dominant plane}, editor = {Schmid, Cordelia and Soatto, Stefano and Tomasi, Carlo}, venue = {San Diego, California, USA }, volume = { 1 }, }