noRANSAC for fundamental matrix estimation

The estimation of the fundamental matrix from a set of corresponding points is a relevant topic in epipolar stereo geometry [2]. Due to the high amount of outliers between the matches, RANSAC-based approaches [1] have been used to obtain the fundamental matrix. We introduce a new normalized epipolar error measure which takes into account the shape of the features used as matches [3] and does not introduce any relevant computational cost. Moreover, a new evaluation strategy is described as a valid tool to compare the estimated fundamental matrices. 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. Let R1, R2 be two elliptical feature patches belonging respectively to the images I1, I2, centred in x1, x2 as commonly extracted by feature detectors [3], with minor and major axes respectively αmini , αmaxi , i ∈ {1,2}. The error measure κi in the image Ii, for the feature pair (R1,R2) is defined as κi = min ( d(xi, li) αmini ,1 ) (1)