Pinhole Camera Model

The basic pinhole model

We consider the central projection of points in space onto a plane. Let the centre of projection be the origin of a Euclidean coordinate system, and consider the plane $Z=f$, which is called the image plane or focal plane. Under the pinhole camera model, a point in space with coordinates $X=(X,Y,Z{)}^T$ is mapped to the point on the image plane where a line joining the point X to the centre of projection meets the image plane.

By similar triangles, one quickly computes that the point $(X,Y,Z{)}^T$ is mapped to the point $(fX/Z,fY/Z,f{)}^T$ on the image plane. Ignoring the final image coordinate, we see that

$$(X,Y,Z{)}^T\mapsto (fX/Z,fY/Z)$$

describes the central projection mapping from world to image coordinates. This is a mapping from Euclidean 3-space $R^3$ to Euclidean 2-space $R^2$.