Determining the common region

Before determining the common epipolar lines the extremal epipolar lines for a single image should be determined. These are the epipolar lines that touch the outer image corners. The different regions for the position of the epipole are given in Figure 7.7. The extremal epipolar lines always pass through corners of the image (e.g. if the epipole ${\tt e}$ is in region 1 the area between ${\tt eb}$ and ${\tt ed}$).

Figure 7.7: the extreme epipolar lines can easily be determined depending on the location of the epipole in one of the 9 regions. The image corners are given by ${\tt a, b, c, d}$.

The extreme epipolar lines from the second image can be obtained through the same procedure. They should then be transfered to the first image. The common region is then easily determined as in Figure 7.8

Figure 7.8: Determination of the common region. The extreme epipolar lines are used to determine the maximum angle.