st satisfy 
(5) 
se vector 
tem: 
(6) 
1age 
for every 
(7) 
| (7) are 
tment to 
irameters 
the two 
rspective 
(8) 
e three- 
left and 
ector (1, 
, AK) of 
ordinate 
ameters. 
( relative 
9 control 
ion. For 
the GPSVan, this method is used to check or 
update the relative orientation parameter when 
the stereo vision system is reinstalled. 
2.3. Rotation Offset Determination 
The rotation offset angles are defined as the 
rotation difference between the stereo vision 
system and the positioning system. In the 
GPSVan, they are small angles ( « 5 degrees for 
most cases). The only way to determine them is 
by an analytical method. The following 
constraints are used to compute rotation offsets: 
* Same points measured in different image 
pairs have the same X, Y, Z coordinates 
Points with the same elevation measured 
from a single image pair have the same Z 
coordinate. 
* 
Our method is based on the following coordinate 
transformation equation of the GPSVan: 
X X X X 
y zy ¥ t Y ={"Y + 
Z global Z), Zi. ps 
X 
R nori] BR Lien sysrot y +| AY 
Z 
vision 
(9) 
This equation defines how a point can be 
transferred from the stereo vision system into 
the global coordinate system. We want to 
determine the rotation offset between the stereo 
vision system and the positioning system. These 
offsets are small angles and can be expressed 
by (da, d$, dK). The first derivative of rotation 
angles is used in the rotation matrix: 
1 —d& -dKk 
R fier =| da 1 T (10) 
-dk dé 1 
Let : 
X X X AX 
Y, mE] SER nori] R sysrot y [AY 
Zo Z gps zZ vision AZ 
(11) 
483 
Xo X 
Ya | Ro Y (12) 
20 vision 
then 
X Xo X9 Xo 
Y m|iYo [5 RoeiRonel Yor | = | Xp | 
sort (20 20 Zo 
—320 0 dé 
0" °y, Vey Ride 
| Canari 
(13) 
This is a linear equation with three unknowns and 
it is used to form the constraints to derive the 
rotation offsets. 
A point measured from image pair i and j forms 
three constraints: 
x 
Y = (14) 
N ^X X 
global global 
Constraints (14) determine parameter da, dé. 
For the same elevation points m and n, their Z 
coordinates are equaled by : 
global 7 Zzlobai (15) 
Constraint (14) determines dó,dx. 
Collecting all the equations in (14) and (15), the 
rotation offsets are computed by a least squares 
solution. 
3. Accuracy Evaluation 
3.1 Positioning Accuracy of the 
Stereo Vision System 
The algorithms described above were 
implemented on our post-processing workstation. 
To evaluate the positioning accuracy, 
calibrations with different camera parameters 
and constraints were conducted. All tests were 
based on two Kodak DCS digital CCD cameras, 
which were part of the vision System on the 
GPSVan. They have a resolution of 1280(H) X