Computing matched-epipolar projections

Abstract

This paper gives a new method for image rectifi- cation, the process of resampling pairs of stereo im- ages 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 consequently, disparities between the images are in the x-direction only. The method is based on an examination of the essential matrix of Longuet-Higgins which describes the epipo- lar geometry of the image pair. The approach taken is consistent with that recently advocated strongly by Faugeras ((1)) of avoiding camera calibration. The paper uses methods of projective geometry to define a matrix called the "epipolar transformation matrix" used to determine a pair of 2D projective transforms to be applied to the two images in order to match the epipolar lines. The advantages include the simplicity of the 2D projective transformation which allows very fast resampling as well as subsequent simplification in the identification of matched points and scene recon- struction.