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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:

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

which gives the familiar equations

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

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



Subhashis Banerjee 2002-02-18