A Generalized Ordering Constraint for Stereo Correspondence

Abstract

The ordering constraint along epipolar lines is a powerful constraint that has been exploited by some recent stereomatching algorithms. We formulate a generalized ordering constraint, not restricted to epipolar lines. We prove several properties of the generalized ordering constraint and of the "forbidden zone", the set of matches that would violate the constraint. We consider both the orthographic and the perspective projection case, the latter for a simplified but standard stereo geometry. The disparity gradient limit found in the human stereo system may be related to a form of the ordering constraint. To illustrate our analysis we outline a simple algorithm that exploits the generalized ordering constraint for matching contours of wireframe objects. We also show that the use of the generalized ordering constraint implies several other stereo matching constraints: a0 the ordering constraint along epipolar lines, b) figural continuity, c) Binford's cross-product constraint, d) Mayhew and Frisby's figural continuity constraint. We finally discuss ways of extending the algorithm to arbitrary 3-D objects.