The calibration was done with three digital stereo-pairs
of our test-field. They were taken at different distances in
front of the wall, ranging from 19 meters to 9 meters, and at
different viewing angles relative to the test-field. This
variety of angles and distances is important for the reliable
recovery of the interior orientations and the additional
camera parameters, and also ensures that spatial positioning
with the vision system yields homogeneous coordinates at
different distances in front of the van (of course, there is a
limit due to the narrow intersection angles of light rays for
points that are far away from the van).
The image coordinates of eleven control and six tie-
points were measured manually on the computer screen
with an estimated accuracy of 1/4 pixel in the digital
images. The base-length was determined by theodolite
intersections. The bundle-triangulation (including the
constraints mentioned above) was computed twice, with
and without additional camera parameters, to demonstrate
their contribution to the positioning accuracy.
The results are combined in table 1. It shows the
aposteriori standard deviation Go, which corresponds to the
mean accuracy of the measured image coordinates both in
pixels and millimeters. The additional parameters
improved the accuracy by a factor of two, so that it
corresponds to about 1/3 of a pixel on the sensor, which is
consistent with our assumptions (manual measurement).
The principal points and focal lengths of both cameras were
always treated as unknowns. The tie-point coordinates
computed by the bundle triangulation were compared to
their known coordinates at the wall to show the potential
point positioning accuracy (Sx, Sy, sz), if object control is
available.
Then we used the computed orientation parameters in
an intersection to determine object coordinates from image-
coordinate pairs. This corresponds to the positioning of
points with the stereo-vision system on the van,
independent of any control in object space. This test was
done independently for each stereo-pair, and for all points
that appear in a stereo-pair. Again, the coordinates of the
targets of the test-field were used for comparison. The
results are displayed in table 2, showing the RMS errors for
each stereo-pair for the two types of calibrations computed
before.
One can see that the additional parameters improve the
positioning accuracy, and that all derived values are
consistent or better than our estimates. It is fair to state that
the positioning accuracy of the stereo-vision system is
within 10 cm for objects closer than 20 m in front of the
van.
To determine the absolute positioning accuracy we
measured the image coordinates of the targets on the wall
in two stereo-pairs that were not used for the vision system
calibration (image pairs 6, 7). The object coordinates were
computed by point intersections applying the orientation
parameters derived previously. Additional camera
parameters were always applied in the intersection. As a
result we obtained the object coordinates in two separate
local systems. Both were transformed into a common
coordinates system to be able to compare the positioning
accuracy of the stereo-vision system. Table 3 shows the
RMS difference between the point positioning determined
from image-pair 6 and those of image-pair 7.
calibration Co Co Sx Sy Sz
[mm] [pixels] i [cm] [cm] [cm]
without additional parameters : 0.0063 10.68 1.95 1.09 7.79
with 6 additional parameters {0.0034 10.37 0.42 0.55 2.09
Table 1: Comparison of a calibration of the stereo-vision system with and without
additional parameters. The standard deviation of unit weight (6,) corresponds to the
mean accuracy of image coordinate measurement. The RMS error in object space at four
of the tie-points (which were available in all stereo-pairs and used as check-points) is
given by sy, sy, s;.
stereo- calibration with or i object Sx Sy Sz Oz
pair without additional i distance | [cm] [cm] [cm] [cm]
parameters [m]
1 without 19.0 31 2.0 8.9 9.3
2 without 11.8 1.3 1.9 4.2 3.6
3 without 9.2 13 0.7 3.9 2.5
1 with 19.0 2.1 12 6.2 93
2 with 11.8 0.4 1.1 3.4 3.6
3 with 9.2 0.4 0.5 1.3 2.2
Table 2: Intersection of conjugate image points to evaluate the positioning accuracy
without object control. The RMS errors (sy, Sy, 82) are computed for each stereo-pair. In
the last column the theoretical accuracy limit in the driving direction (6;) is displayed. It
was computed by: 6,- ZZ I
pe
f=. Opx (Opx= 3 pixel).
