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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
\end{displaymath} (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).


Marc Pollefeys 2002-11-22