Determining the distance between epipolar lines

To avoid losing pixel information the area of every pixel should be at least preserved when transformed to the rectified image. The worst case pixel is always located on the image border opposite to the epipole. A simple procedure to compute this step is depicted in Figure 7.9.

Figure 7.9: Determining the minimum distance between two consecutive epipolar lines. On the left a whole image is shown, on the right a magnification of the area around point ${\tt b}_i$ is given. To avoid pixel loss the distance $\vert{\tt a}'{\tt c}'\vert$ should be at least one pixel. This minimal distance is easily obtained by using the congruence of the triangles ${\tt abc}$ and ${\tt a'b'c'}$. The new point ${\tt b}$ is easily obtained from the previous by moving $\frac{\vert{\tt bc}\vert}{\vert{\tt ac}\vert}$ pixels (down in this case).

The same procedure can be carried out in the other image. In this case the obtained epipolar line should be transferred back to the first image. The minimum of both displacements is carried out.