Geometric Constraints for Establishing Point Correspondence Between Stereo Images

Finding point correspondence between stereo images of a 3D point set is a basic open problem in computer vision. It is usually the prerequisite for 3D reconstruction and object recognition. However, since geometric depth information is lost in 3D to 2D projection, there is no scalar geometric invariant among multiple images. So, there is no method based on pure geometric information to establish point correspondence among multiple images previously. In the literature, the epipolar constraint is widely applied to restrict the correspondence search space. In this paper we derive novel geometric constraints for nine corresponding points between stereo images. Using these constraints, we can design purely geometric method for establishing point correspondence. These constraints can also be used in conjunction with other methods to optimize the correspondence search algorithm.