Eight Points Geometric Constraint for Stereo Matching

Stereo point matching is a critical and fundamental problem in 3D vision. Numerous algorithms have been proposed to solve this problem. Since images obtained from 3D to 2D projection of a 3D scene lose depth information of the 3D scene, there is no numerical geometric invariant between stereo images. So, we do not have similar algorithms that use geometric invariants for point matching as in the case of 2D to 2D projective transformations. However, it is discovered that geometric constraints can be used to restrict the search space and eliminate faulty correspondences. In this paper we derive a new mathematical constraint relating eight corresponding points in stereo images. It is a simple formula consisting of coordinates of the eight points that compute to zero for the eight points to be in correspondence. This constraint can be used as a preliminary necessity testing step before other time-consuming methods to speed up the matching procedure.