ed 
- 
Finally we need a transformation TRANS 3 (X, OR) with the dimension X (3) and OR (2). 
Reading the picture coordinates xÜ ; Y ; € into X and the coordinates of the principal-point 
xd 3 Yo into OR the transformation performs a plane displacement 
x’ = x! x 
modu Oo 
N 
¥ =v v5 
= C 
Calling TRANS 3 with the principal-point-located picture coordinates and the coordinates 
of the principal-point as input, the transformation gives as output the picture coordinates in a 
system located by the fiducial marks. 
Calling the 3 transformation routines immediately after each other the computation of 
the fundamental equations is performed. 
Example 2 : Establishing the fundamental equations for a camera with a radial-symmetric 
distortion around the optical axis. 
This is now quite simple. First we must introduce some more parametres : 
c, is the distance between the perspective center and a plane perpendicular to the optical 
axis. The distortion correction is done in this plane, 
ag, ag, ap are usual parametres for describing distortion, 
X 4 3; yt ; end are uncorrected picture coordinates in a non-physical plane perpendicular 
to the optical axis, 
picture plane 
   
  
perspective center 
  
  
Fig. 4. Distortion correction in a plane perpendicular to the optical axis. 
—1i7 ne