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intersections while the van is moving along a straight line. 
The motion vector of the antenna equals the vehicle axis 
(Yy). The origin of the vehicle coordinate system is 
located at the GPS antenna. 
When we transform from camera coordinates (X¢, Yo, 
Z.) to vehicle coordinates (Xv, Yv, Zy), the origin is shifted 
from the left perspective center to the GPS antenna (figure 
5). This offset is known from the theodolite measurements. 
There is a rotation involved, too, which is defined by the 
downward tilt (t) of the two cameras. They are dipped by 
about 8° on the van in order to provide for better coverage 
of the road. The mathematical transformation from the 
camera to the vehicle system is given by (10). 
Xv AX 1 0 0 Xe 
Yv |"| AY |* 0 cost' -sint ||Yc| (10) 
Zv AZ 0 sint . cosa Ji. 
offset between 
O1 and GPS 7 2900-14 
   
  
  
  
stereo - images 
GPS antenna 
X, MX. 
Xc 
Figure 5: Transformation from the stereo-vision system 
(Xe, Yc, Zc) to a vehicle coordinate system (Xy, Yy, Zy). 
  
  
  
  
rear 
axle ix 
directional gyro 
A» 
  
  
4.2 Transformation to a Topo-centric Coordinate 
System 
This transformation rotates the local vehicle coordinates 
(Xv, Yv, Zy) into a topo-centric system (XT, YT, ZT) With 
the origin at the GPS antenna. The topo-centric system is 
defined by a tangential plane through the GPS antenna. 
Therefore, the vehicle system needs to be rotated according 
to the angles specified by the three gyros (direction [a], 
pitch [5], and roll [x]): the direction is the primary rotation, 
pitch is secondary, and roll tertiary. The transformation is 
given by (11). 
  
  
  
  
XT Xy 
Yr |= RoReRk Yv (11) 
Zr Zv 
The local topo-centric coordinates can be easily 
transformed into geo-centric coordinates by shifting the 
origin from the GPS antenna to the center of the earth (this 
vector corresponds to the geo-centric coordinates of the 
antenna), and by applying the appropriate rotations defined 
by longitude and latitude (geographic coordinates). Geo- 
centric as well as geographic coordinates can be used for 
comparing different positions in a unique worldwide 
system. 
5. NUMERICAL RESULTS OF THE CALIBRATION 
The algorithms described above were implemented on 
our post-processing workstation (Data General Aviion 400 
Series). The results of the calibration prove that the 
accuracies that can be obtained by stereo-positioning from 
a mobile platform are sufficient for many road mapping 
applications. The results relate to the two Cohu 4110, 
digital CCD cameras, which were part of the GPS-Van. 
They have a resolution of 732 (H) x 484 (V) pixels and use 
C-mount lenses. 
  
Figure 6: Transformation of vehicle coordinates (Xy, Yy, Zy) into a topo-centric system 
(East, North, Up).