where . This can be written as
where the unit of 's are pixel/length. This can be expressed as
is called the camera calibration matrix and it provides the transformation between an image point and a ray in Euclidean 3-space.
The Euclidean transformation between the camera and world coordinates is:
and is expressed projectively as:
Finally, concatenating the three matrices, we have
which defines the projection from Euclidean 3-space to an image: