Given a pair of stereo images, epipolar rectification (or simply rectification) determines a transformation of each image plane such that pairs of conjugate epipolar lines become collinear and parallel to one of the image axes (usually the horizontal one). The rectified images can be thought of as acquired by a new stereo rig, obtained by rotating the original cameras. The important advantage of rectification is that computing stereo correspondences [3] is made simpler, because search is done along the horizontal lines of the rectified images.
We assume that the stereo rig is calibrated, i.e., the cameras' internal parameters, mutual position and orientation are known. This assumption is not strictly necessary, but leads to a simpler technique. On the other hand, when reconstructing 3-D shape of objects from stereo, calibration is mandatory in practice, and can be easily achieved [2,13].
Rectification is a classical problem of stereo vision. Ayache [1] introduced a rectification algorithm, in which a matrix satisfying a number of constraints is hand-crafted. The distinction between necessary and arbitrary constraints is unclear. Some authors report rectification under restrictive assumptions; for instance, [11] assumes a very restrictive geometry (parallel vertical axes of the camera reference frames). Recently, [6,14,8] have introduced algorithms which perform rectification given a weakly calibrated stereo rig, i.e., a rig for which only points correspondences between images are given (or, equivalently, for which the fundamental matrix could be computed).
Latest works includes [10,9,12]. Some of them concentrates on the issue of minimizing the rectified image distortion. We will not address this problem, also because distortion is less severe than in the weakly calibrated case.
This document have been adapted from [5].