noRANSAC for fundamental matrix estimation

Abstract

The estimation of the fundamental matrix from a set of corresponding points is a relevant topic in epipolar stereo geometry [10]. Due to the high amount of outliers between the matches, RANSAC-based approaches [7,13,29] have been used to obtain the fundamental matrix. In this paper two new contributes are presented: a new normalized epipolar error measure which takes into account the shape of the features used as matches [17] and a new strategy to compare fundamental matrices. The proposed error measure gives good results and it does not depend on the image scale. Moreover, the new evaluation strategy describes a valid tool to compare different RANSAC-based methods because it does not rely on the inlier ratio, which could not correspond to the best allowable fundamental matrix estimated model, but it makes use of a reference ground truth fundamental matrix obtained by a set of corresponding points given by the user.

Keypoint descriptor matching with context-based orientation estimation

“…In case the evaluation is more stressed towards the matching coverage, combining epipolar geometry with local information collected by sparse hand-taken correspondences to define the GT can be a plausible approach [7]. An alternative metric in case the evaluation is more focused on the precision of the matches can be to use as a proxy to the effective matching error the error on the camera poses [8], also in the case of planar scenes [48], or the error on the fundamental matrix relating two images [9], [49].…”

“…In the case of non-planar scenes, E η 12 compares the pointwise error of the fundamental matrix F computed from the matches against the GT fundamental matrix F GT , and likewise E η 21 . Specifically, the average is computed defining the error on a valid point x ∈ I 1 as the minimum area given by intersecting the two semi-planes on I 2 defined by the epipolar lines F x and F GT x, as done in [9] but normalizing the area by the image diagonal to get a linear measure. The final accuracy over all the image pairs is aggregated as for Eq.…”

“…Another aspect in which the proposed evaluation differs from the others is for the metrics employed. In particular, the recall is replaced by a coverage measure to take into account semi-dense deep image matching networks, such as LoFTR, which can distort the recall measurement, and in the case of non-planar scenes the error on the camera pose is replaced by a error on the fundamental matrix [9] more directly related to the images and closer to the homography reprojection error used in planar scenes, so as to unify the two cases.…”