Camera motion

Motion of scene points can be modeled as follows

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

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

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