11. A New Evaluation Criterion for Point Correspondences in Stereo Images

In this chapter, we present a new criterion to evaluate point correspondences within a stereo setup. Many applications such as stereo matching, triangulation, lens distortion correction, and camera calibration require an evaluation criterion for point correspondences. The common criterion here is the epipolar distance. The uncertainty of the epipolar geometry provides additional information, and our method uses this information for a new distance measure. The basic idea behind our criterion is to determine the most probable epipolar geometry that explains the point correspondence in the two views. This criterion considers the fact that the uncertainty increases for point correspondences induced by world points that are located at a different depth-level compared to those that were used for the fundamental matrix computation. Furthermore, we show that by using Lagrange multipliers, this constrained minimization problem can be reduced to solving a set of three linear equations with a computational complexity practically equal to the complexity of the epipolar distance.