The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part Bl. Beijing 2008 
4. EVALUATION 
4.1 Test Setup 
The implemented algorithms have been tested using simulated 
data as well as the described traffic intersection setup (TIS). 
The interior orientation parameters of the simulated and the real 
traffic camera can be found in Table 2: 
Parameter 
SIM 
TIS 
in mm 
in mm 
x 0 
-0.001008 
0.848510 
Yo 
0.005275 
-0.875919 
c 
6.950257 
8.276964 
K1 
2.54744e-003 
3.16630e-003 
K2 
-7.83759e-005 
-2.17610e-005 
K3 
1.86310e-006 
-1.04590e-006 
PI 
3.08255e-005 
4.04520e-005 
P2 
-6.92956e-006 
3.37660e-005 
Bl 
-1.26747e-004 
4.03890e-004 
B2 
-1.08686e-004 
-1.15540e-004 
Pixel size 
0.00675 
0.0065 
Resolution 
768x488 px 
1024x768 px 
Table 2. Interior orientation parameters of used cameras 
In order to test the implementations with simulated data an 
array of 100 predefined control points is projected onto a virtual 
camera sensor. Hence the position of the projection center is 
predefined as well all values of this simulation setup are known 
with absolute accuracy. To derive an error behavior noise has 
been applied to the projected image points and defective control 
points are consecutively added to data space. The results are 
given as median values of 100 trials each. 
A camera of the VIDS setup at the traffic intersection Rudower 
Chaussee/ Wegedomstrasse has been used to test the algorithms 
in their designated environment. 48 ground control points were 
taken via DGPS. Their corresponding image points were 
clicked using a designed tool with sub-pixel accuracy. Two 
ground control points were subsequently used to define lines in 
the scene to aid comparability. Figure 3 shows an example 
image of the chosen camera: 
Figure 3. Image of a camera from the multi-camera VIDS 
4.2 Initial values 
When adding noise to the virtual image points, both DLT and 
the minimum space resection show a fast increasing rout mean 
square error (RMSE) when back-projecting the ground control 
points onto the virtual projection plane using the determined 
exterior orientation (Figure 5). The exterior orientation is 
unfeasible but the results of the minimum space resection 
suffice as initial values while the DLT seems too unstable. 
Sampling over random minimal point sets and taking the 
median value proves efficient when adding erroneous control 
points to the initial data set (Figure 6). When using 150 trials, 
both approaches prove resilient to the false input up to a certain 
percentage. The DLT can cope with up to 8% of erroneous 
points and the minimum space resection with up to 16% before 
the results are compromised. 
Applying both approaches to the traffic intersection setup 
emphasizes the simulation results. The DLT results with an 
RMSE of 16 pixel and fails completely with inaccurate input 
data while the minimum space resection yields an exterior 
orientation with a resulting RMSE of less then a pixel, even if 
40% of the input data set consist of erroneous control points 
(Figure 7). Table 4 shows the resulting estimations of the 
exterior orientation. While the calculated position of the DLT 
varies up to half a meter and the rotation angles up to 2° from 
the final result of an adjustment approach, the results of the 
minimum space resection are remarkably close. Never the less, 
both estimations suffice as initial values. 
DLT 
MSR 
GMM 
X 
399899.02m 
399899.51m 
399899.50m 
Y 
5809757.70m 
5809757.80m 
5809757.80m 
Z 
92.12 m 
92.10 m 
92.10 m 
CO 
33.81° 
35.68° 
35.67° 
<p 
69.58° 
70.62° 
70.62° 
K 
56.28° 
55.26° 
55.26° 
RMSE 
16,23 px 
0.36 px 
0.31 px 
Table 4. Exterior orientations deduced by DLT, minimum 
space resection and the Gauss Markov method 
4.3 Exterior Orientation 
The results of the application of the algorithms to the simulated 
data set and subsequently adding noise to the image control 
points are visualised in Figure 8. The approaches based on 
control points yield a RMSE of less than half a pixel even under 
high noise. The Newton and the Gauss Markov approach, both 
using trigonometric functions have the same results. Because 
both apply the same method to solve an overdetermined system 
of equations they perform equally. The fundamental difference 
of Gauss-Markov in contrast to the Newton approach is the 
ability to detect and exclude erroneous points which were 
absent in this scenario. Using quaternions results in a slight 
decrease of accuracy. This can be explained by the fact that due 
to this point no constraints were defined during the adjustment 
to ensure the orthonormality of the rotation matrix. This leads 
to a small deviation of the rotation angles derived from the 
matrix. Using lines as an input feature results in a rapidly 
decreasing accuracy. Further analysis points towards the 
problem of line representation using slope-intersect-form. The 
discrepancy between expected and true slope of a line increases 
with its steepness. Thus, steep slopes are unproportionally