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:

$$\left[\begin{array}{c} x_{1} \\ x_{2} \\ x_{3} \end{array} \rig... ...t] \left[ \begin{array}{c} X_{1} \\ X_{2} \\ X_{3} \\ X_{4} \end{array}\right]$$

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

$${\bf x} = {\bf M}{\bf X} + {\bf t}$$

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.