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The Affine Camera

The affine camera is a special case of the projective camera and is obtained by constraining the matrix ${\bf T}$ such that $T_{31} = T_{32} = T_{33} = 0$, thereby reducing the degrees of freedom from 11 to 8:

\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}

In terms of image and scene coordinates, the mapping takes the form

\begin{displaymath}
{\bf x} = {\bf M}{\bf X} + {\bf t}
\end{displaymath}

where ${\bf M}$ is a general $2 \times 3$ matrix with elements $M_{ij} = T_{ij}/T_{34}$ while ${\bf t}$ is a general 2-vector representing the image center.

The affine camera preserves parallelism.



Subhashis Banerjee 2002-02-18