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Camera motion

Motion of scene points can be modeled as follows

{\tt M}' = \left[ \begin{array}{cc} {\bf R} & {\tt t} \\
0_3^\top & 1 \end{array} \right] {\tt M}
\end{displaymath} (C5)

with $ {\bf R} $ a rotation matrix and ${\tt t}=[t_x t_y t_z]^\top$ a translation vector.

The motion of the camera is equivalent to an inverse motion of the scene and can therefore be modeled as

{\tt M}' = \left[ \begin{array}{cc} {\bf R}^\top & -{\bf R}^\top {\tt t} \\
0_3^\top & 1 \end{array} \right] {\tt M} \, ,
\end{displaymath} (C6)

with $ {\bf R} $ and ${\tt t}$ indicating the motion of the camera.

Marc Pollefeys 2002-11-22