Image rectification

  Since parallel stereo configurations greatly simplify the matching process of two images, if a pair of images is taken with a general stereo configuration, an operation known as rectification can be applied to bring the two retinal planes to be coplanar to a common plane ${\cal R}$ in space. This plane ${\cal R}$ can be chosen as follows (Fig. 11):

  

Figure 11: Image rectification (after Faugeras).

• compute $\overline{PQ}$, the line of intersection between the original retinal planes $\Pi$ and $\Pi'$.
• compute the baseline vector CC'.
• compute the equation of the plane that contains $\overline{PQ}$ and parallel to CC'.
• assign this computed plane to ${\cal R}$.

An alternative way of choosing ${\cal R}$ is: instead of step 3 above, look for a plane that contains CC' and that minimizes the projective distortion.

Fig. 12 shows an image triplet before and after applying image rectification. After rectification, the epipolar lines between images 1 and 2 coincide with the horizontal scanlines, the epipolar lines between images 1 and 3 coincide with the vertical scanlines.

  

Figure 12: Image triplets of a room scene before and after rectification (after Ayache and Hansen)