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The Projective Camera

The most general mapping from ${\cal P}^{3}$ to ${\cal P}^{2}$ is

\begin{displaymath}
\left[\begin{array}{c}
x_{1} \\ x_{2} \\ x_{3}
\end{arra...
...ay}{c}
X_{1} \\ X_{2} \\ X_{3} \\ X_{4}
\end{array} \right]
\end{displaymath}

where $(x_{1},x_{2},x_{3})^{T}$ and $(X_{1},X_{2},X_{3},X_{4})^{T}$ are homogeneous coordinates related to ${\bf x}$ and ${\bf X}$ by

\begin{displaymath}
\begin{array}{ccc}
(x,y) & = & (x_{1}/x_{3},x_{1}/x_{3}) ...
...,Y,Z) & = & (X_{1}/X_{4},X_{2}/X_{4},X_{3}/X_{4})
\end{array} \end{displaymath}

The transformation matrix ${\bf T} = [T_{ij}]$ has 11 degrees of freedom since only the ratios of elements $T_{ij}$ are important.

(see Zisserman and Mundy).



Subhashis Banerjee 2002-02-18