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Planar rectification

The standard rectification approach is relatively simple. It consists of selecting a plane parallel with the baseline. The two image are then reprojected into this plane. This is illustrated in Figure 7.1. These new images satisfy the standard stereo setup.

Figure 7.1: Planar rectification: $({\bf I}_k^l,{\bf I}_l^k)$ are the rectified images for the pair $({\bf I}_k,{\bf I}_l)$ (the plane $\Pi _R$ should be parallel to the baseline $({\bf P}_k,{\bf P}_l)$).
The different methods for rectification mainly differ in how the remaining degrees of freedom are chosen. In the calibrated case one can choose the distance from the plane to the baseline so that no pixels are compressed during the warping from the images to the rectified images and the normal on the plane can be chosen in the middle of the two epipolar planes containing the optical axes. In the uncalibrated case the choice is less obvious. Several approaches were proposed (e.g. [29,179]).

Marc Pollefeys 2002-11-22