Following [4],
we consider a stereo pair composed of two pinhole cameras,
each modelled by its optical center
and its retinal plane (or image plane) 
.
In each camera, a
point 
in 3-D space is projected into an
image point 
, which is the intersection of the line 
with .
The transformation from to
is modelled by the linear transformation 
in
projective (or homogeneous) coordinate:
where
The points for which S=0 define the focal plane and are
projected to infinity.
The projection matrix can be decomposed into the product
.
maps from world to
camera coordinates and depends on the extrinsic parameters of the stereo
rig only; 
, which maps from camera to pixel coordinates and
depends on
the intrinsic parameters only, has the following form:
where f is the focal length in millimeters,
are the scale factors along the u and v axes
respectively (the number of pixels per millimiter), and
, and 
are the focal lengths in
horizontal and vertical pixels, respectively.
If we write the projection matrix as
we see that the plane 
(S=0) is the focal
plane, and the two planes 
and 
intersect the retinal
plane in the vertical (U=0) and horizontal (V=0) axis of the
retinal coordinates, respectively.
The optical center, , is the intersection of the three planes
introduced in the previous paragraph;
therefore
,
and 
.
The optical ray associated to an image point is the line
, i.e. the set of points 
. The equation of this ray can
be written in parametric form as
.
