Epipolar geometry

The epipolar geometry describes the relations that exist between two images. The epipolar geometry is described by the following equation:

$${\tt m'}^\top{\bf F}{\tt m}=0$$ (G1)

where ${\tt m}$ and ${\tt m'}$ are homogeneous representations of corresponding image points and ${\bf F}$ is the fundamental matrix. This matrix has rank two, the right and left null-space correspond to the epipoles ${\tt e}$ and ${\tt e'}$ which are common to all epipolar lines. The epipolar line corresponding to a point ${\tt m}$ is given by ${\tt l}' \sim {\bf F}{\tt m}$ with $\sim$ meaning equality up to a non-zero scale factor (a strictly positive scale factor when oriented geometry is used, see further).