A simple model

In the simplest case where the projection center is placed at the origin of the world frame and the image plane is the plane $Z=1$, the projection process can be modeled as follows:

$$\begin{array}{cc} x= \frac{X}{Z} & y= \frac{Y}{Z} \end{array}$$ (C1)

For a world point $(X,Y,Z)$ and the corresponding image point $(x,y)$. Using the homogeneous representation of the points a linear projection equation is obtained:

$$\left[\begin{array}{c} x \\ y\\ 1 \end{array} \right] \sim \... ...t] \left[\begin{array}{c} X \\ Y \\ Z \\ 1 \end{array} \right]$$ (C2)

This projection is illustrated in Figure 3.2. The optical axis passes through the center of projection ${\tt C}$ and is orthogonal to the retinal plane ${\cal R}$. It's intersection with the retinal plane is defined as the principal point ${\tt c}$.

Figure 3.2: Perspective projection