Two-View Geometry Estimation Unaffected by a Dominant Plane

Abstract

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 non-minimal samples of seven correspondences than minimal samples of four correspondences.

Robust Focal Length Estimation by Voting in Multi-view Scene Reconstruction

“…This can be seen in Figure 2 (a) and (b) which shows boxplots of focal lengths obtained by 1000 runs of the DEGENSAC [10], where we extracted focal lengths using the Bougnoux equations [2] inside the DEGENSAC loop. In each run of the DEGENSAC the real focal length with the highest support was returned.…”

“…It is important to use DEGENSAC [10] or a similar algorithm which is capable of detecting panoramas and pure planar scene configurations and obtaining inliers which are not affected by presence of dominant planes. Panoramas and planar scenes are rejected.…”

“…(0, 0, 1)F(0, 0, 1) T = 0, are rejected. For the plane degeneracy test we are using test developed in DEGENSAC [10].…”

“…We run DEGENSAC [10] which returns a set of matches in which the proportion of mismatches is greatly reduced and most of correct matches are preserved. In other words the decision process of the first phase generates a negligible number of falsely rejected good matches (false negatives) but a non-negligible number of correctly rejected false matches (true negatives).…”

“…Here we use a more complex, hybrid, sampling strategy, which turns out to be more efficient than the approach of [28,29]. In our method, statistics are collected either directly inside a RANSAC loop or in separate sampling process executed on an inliers set returned by a robust RANSAC estimator like DEGENSAC [10]. This is followed by the kernel voting weighted using weights derived from the number of inliers of each particular vote.…”