The Perspective Camera

A special case of the projective camera is the perspective (or central) projection, reducing to the familiar pin-hole camera when the leftmost $ 3 \times 3$ sub-matrix of $ {\bf T}$ is a rotation matrix with its third row scaled by the inverse focal length $ 1/f$ . The simplest form is:

$\displaystyle {\bf T}_{p} =
\left[ \begin{array}{cccc}
1 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 \\
0 & 0 & 1/f & 0 \\
\end{array}
\right]
$

which gives the familiar equations

$\displaystyle \left[ \begin{array}{c}
x \\ y
\end{array}\right]
= \frac{f}{Z}
\left[ \begin{array}{c}
X \\ Y
\end{array}\right]
$

Each point is scaled by its individual depth, and all projection rays converge to the optic center.



Subhashis Banerjee 2008-01-20