Computing matched-epipolar projections

Richard I. Hartley, Rajiv Gupta

Abstract: A new method is given for image rectification, the process of resampling pairs of stereo images taken from widely differing viewpoints in order to produce a pair of matched epipolar projections. These are projections in which the epipolar lines run parallel with the x-axis and disparities between the images are in the x-direction only. The method is based on an examination of the essential matrix of Longuet-Higgins (1981), which describes the epipolar geometry of the image pair. The approach taken is consistent with that advocated by O. Faugeras (1992) of avoiding camera calibration. A matrix called the epipolar transformation matrix is defined. It is used to determine a pair of 2-D projective transforms to be applied to the two images in order to match the epipolar lines. The advantages include the simplicity of the 2-D projective transformation, which allows very fast resampling, as well as subsequent simplification in identifying matched points and in scene reconstruction.<