Epipolar line transfer

The transfer of corresponding epipolar lines is described by the following equations:

$${\tt l}' \sim {\bf H}^{-\top} {\tt l} \mbox{ or } {\tt l} \sim {\bf H}^{\top} {\tt l}'$$ (G2)

with ${\bf H}$ a homography for an arbitrary plane. As seen in [103] a valid homography can be obtained immediately from the fundamental matrix:

$${\bf H} = [{\tt e'}]_\times {\bf F} + {\tt e}'{\tt a}^\top$$ (G3)

with ${\tt a}$ a random vector for which det ${\bf H} \neq 0$ so that ${\bf H}$ is invertible. If one disposes of camera projection matrices an alternative homography is easily obtained as:

$${\bf H}^{-\top} = \left({\bf P'}^\top \right)^\dagger {\bf P}^\top$$ (G4)

where $\dagger$ indicates the Moore-Penrose pseudo inverse.