Binocular Grouping.

In this chapter, we present an application of meaningful events to binocular vision. Binocular vision, also called Stereovision, is a major part of Computer Vision, as it theoretically allows us to reconstruct a 3-D representation of the world from two images taken from slightly different points of view. We focus here on the following problem: Given a set of n point matches between two images (i.e., a set of n points for each image with a one-to-one correspondence), can we decide when these points are the perspective projections on the two images of n physical points? Can we find the maximal group that satisfies this property? As we will see, the position of the point matches are constrained by the perspective projection as soon as n ≥ 8 (for uncalibrated cameras). However, to prove in practice the existence of a rigid motion between two images, more than 8 point matches are desirable to compensate for the limited accuracy of the matches. In this chapter we describe a computational definition of rigidity and show how the Heimholte principle can be applied to define a probabilistic criterion that rates 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 many points. It also yields absolute accuracy requirements for rigidity detection in the case of nonmatched points (i.e., when no one-to-one correspondence is available) and optimal values of n, depending on the expected accuracy of the matches and on the proportion of outliers. It can be used 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. [ABSTRACT FROM AUTHOR]