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Epipolar line transfer

The transfer of corresponding epipolar lines is described by the following equations:
\begin{displaymath}
{\tt l}' \sim {\bf H}^{-\top} {\tt l} \mbox{ or } {\tt l} \sim {\bf H}^{\top} {\tt l}'
\end{displaymath} (G2)

with ${\bf H}$ a homography for an arbitrary plane. As seen in [83] a valid homography can be obtained immediately from the fundamental matrix:
\begin{displaymath}
{\bf H} = [{\tt e'}]_\times {\bf F} + {\tt e}'{\tt a}^\top
\end{displaymath} (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:
\begin{displaymath}
{\bf H}^{-\top} = \left({\bf P'}^\top \right)^\dagger {\bf P}^\top
\end{displaymath} (G4)

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



Marc Pollefeys 2002-11-22