The key idea of our new rectification method consists of reparameterizing the image with polar coordinates (around the epipoles). Since the ambiguity can be reduced to half epipolar lines only positive longitudinal coordinates have to be taken into account. The corresponding half epipolar lines are determined through equation (7.2) taking orientation into account.
The first step consists of determining the common region for both images. Then, starting from one of the extreme epipolar lines, the rectified image is built up line by line. If the epipole is in the image an arbitrary epipolar line can be chosen as starting point. In this case boundary effects can be avoided by adding an overlap of the size of the matching window of the stereo algorithm (i.e. use more than 360 degrees). The distance between consecutive epipolar lines is determined independently for every half epipolar line so that no pixel compression occurs. This non-linear warping allows to obtain the minimal achievable image size without losing image information.
The different steps of this methods are described more in detail in the following paragraphs.