The stereo matching problem can be solved much more efficiently if images are rectified. This step consists of transforming the images so that the epipolar lines are aligned horizontally. In this case stereo matching algorithms can easily take advantage of the epipolar constraint and reduce the search space to one dimension (i.e. corresponding rows of the rectified images).
The traditional rectification scheme consists of transforming the image planes so that the corresponding space planes are coinciding [5]. There exist many variants of this traditional approach (e.g. [5,42,128,227]), it was even implemented in hardware [25]. This approach fails when the epipoles are located in the images since this would have to results in infinitely large images. Even when this is not the case the image can still become very large (i.e. if the epipole is close to the image).
Roy et al. [163] proposed a method to avoid this problem, but their approach is relatively complex and shows some problems. Recently Pollefeys et al. [136] proposed a simple method which guarantees minimal image size and works for all possible configuration. This method will be presented in detail further on, but first the standard planar rectification is briefly discussed.