Quasi-Euclidean Epipolar Rectification

The binocular stereo pipeline performs the following task: from a pair of images of a scene captured by two cameras (or the same one) at different positions, compute the distance map to one camera. Under particular conditions (called the rectified case) corresponding points are at same ordinate in both images and the distance is the inverse of an affine transform (whose coefficients depend on camera parameters) of the abscissa difference, called the disparity. In general, the output is simply the disparity map. If the cameras satisfy the pinhole model assumption, an adequately chosen combination of rotations and adjustment of cameras' internal parameters yield the rectified case. This amounts to applying homographies to the images. Finding and applying these homographies is called epipolar rectification. The input is a discrete set of corresponding points in images. Since there are more degrees of freedom than constraints, several methods exist, each trying to minimize the change applied to images according to its own measure. One method to achieve this and more discussion can be found in this book. The method of reference 2, expanded in reference 3, assumes both cameras are the same (thus they must have the same size) but only partial knowledge of camera's internal parameters (uncalibrated case): square pixels, unknown focal length and principal point at image center. It then simulates appropriate pure rotations of each view, which can be done when the correct focal length is estimated.