A method for the evaluation of projective geometric consistency in weakly calibrated stereo with application to point matching

• We propose a method for the indexing of point matches based on cross ratios.
• Matches are characterised by the distribution of a scalar measure derived from multiple point relations.
• Our consistency measure is processed statistically using random sampling.
• We propose applications both in weekly calibrated and uncalibrated scenarios.
• Our method exhibits low false positive rates without the use of thresholds.

We present a novel method that evaluates the geometric consistency of putative point matches in weakly calibrated settings, i.e. when the epipolar geometry but not the camera calibration is known, using only the point coordinates as information. The main idea behind our approach is the fact that each point correspondence in our data belongs to one of two classes (inliers/outlier). The classification of each point match relies on the histogram of a quantity representing the difference between cross ratios derived from a construction involving 6-tuples of point matches. Neither constraints nor scenario dependent parameters/thresholds are needed. Even for few candidate point matches the ensemble of 6-tuples containing each of them turns to provide statistically reliable histograms that prove to discriminate between inliers and outliers. In fact, in most cases a random sampling among this population is sufficient. Nevertheless, the accuracy of the method is positively correlated to its sampling density leading to an accuracy versus resulting computational complexity trade-off. Theoretical analysis and experiments are given that show the consistent performance of the proposed classification method when applied in inlier/outlier discrimination. The achieved accuracy is favourably evaluated against established methods that employ geometric only information, i.e. those relying on the Sampson, the algebraic and the symmetric epipolar distances. Finally, we also present an application of our scheme in uncalibrated stereo inside a RANSAC framework and compare it to the same as above methods.