Projective rectification based on relative modification and size extension for stereo image pairs

For stereo vision applications, projective geometry has proved to be a useful tool for solving the rectification problem without camera calibration. However, the criterion of minimisation for projective rectification must be chosen properly in order to avoid unduly geometric distortion. In this paper, an improved algorithm to minimise the distortion by combining a newly developed projective transform with a properly chosen shearing transform is proposed. The emphasis on low geometric distortion makes this method not only appropriate for 3D reconstruction but also for stereoscopic viewing applications. On the basis of relative modification, this new method contains fewer parameters (6 degrees of freedom) for minimisation, which reduces the processing time, and improves the rectification result. Several different types of image pairs were tested to demonstrate the applicability and reliability of the proposed algorithm visually and quantitatively. Comparisons with other methods are also provided to verify the improvement of this new scheme.