Automatic detection of rigid point matches

The perspective projections of n physical points on two views (stereovision) are constrained as soon as n ≥ 8. However, to prove, in practice, the existence of a rigid motion between two images, more than 8 point matches are desirable in order to compensate for the limited accuracy of the matches. We propose a computational definition of rigidity and a probabilistic criterion to rate the meaningfulness of a rigid set as a function of both the number of pairs of points (n) and the accuracy of the matches.. This criterion yields an objective way to compare, say, precise matches of a few points and approximate matches of a lot of points. It gives a yes/no answer to the question: "Could this rigid point correspondence have occurred by chance?", since it guarantees that the expected number of rigid sets found by chance in a random distribution of points is as small as desired. We use it to build an optimized random sampling algorithm that is able to detect a rigid motion and estimate the fundamental matrix when the set of point matches contains up to 90% of outliers, which outperforms classical methods like M-estimators, LMedS and RANSAC, known to break down around or before 50% of outliers.