control points. Graphical representations of the Empirical error measures: 
dependence of these precision values are shown in : Nr. 
Figure 6, Figure 7, and Figure 8 for coordinates xyz As we had 105 ground control points and only a part of 
respectively. These plots make it evident that not much of them was introduced into the adjustment, the rest GCP 
increase in precision can be gained by increasing the has been used as check points. Their ground coordi- b S 
number of ground control points beyond 30. nates were treated as unknowns in the adjustment. Aft- D 
erwards the rms-differences of the computed and the 
8 measured ground coordinates were calculated. The D emos 
result is shown in Figure 9. The trends are similar to 40 
= all zones | those of the theoretical standard deviations. Of course, [T 
5 5 the values may be influenced much by the distribution 
s : E 
= and the number of the check points. 30 
34 E 
© 
5 14 n 
s? 20 
7 12 e 
o 
s? [740 
3 ii p 
1 
o 8 
o LI———— 
0 % 4 
9 10 20 30 40 50 60 70 %0 90 100 ES E 
: number of GCPs 
Figure 6. Averaged theoretical standard deviations for 4 Table 
coordinate x in dependence on the number of 2 D. 
ground control points 
3.00 0 
0 10 20 30 40 so 60 70 80 90 100 e f 
number of GCPs 
5 Figure 9. Empirical rms-errors in check points in depend- $n 
$ 2.00 ence on number of ground control points The p 
= whole 
= 1.50 about 
> accur 
o 
= 1.00 Table 
2 zone 
~ 0.50 contr 
Some more values on the empirical accuracy of the too fo 
0.00 final DEM were derived by comparing it to an already 
O 10 20 39 40 50 60 70 80 90 100 available DEM of the Bavarian Survey of that region. 
number of GCPs This was acquired from the Bayerisches Landesver- 
Figure 7. Averaged theoretical standard deviations for messungsamt. Its accuracy is about 2 m and the values 14- 
coordinate y in dependence on the number of are given as a grid with 50m . 50m spacing. In order to 
ground control points compare our irregularly distributed results the com- 124 
puted Gauß-Krüger coordinates were taken and bilinear 
  
  
  
  
  
  
  
  
9- interpolation used to obtain the corresponding height 104 
8- — values of the DEM of the Survey. Let us concentrate o 
gk all zones first on the case with 99 ground control points. o 
$74 -*- zone 2 Straightforward calculation of the rms differences leads 5 2 
= to the first row in Table 4. = 
o 6- 9 64 
> However, besides the interpolation errors and the E 
s5- errors in x,y-position this comparison suffers from the 4] 
Sal fact, that objects found by automatic image matching 
= will include tops of trees and houses. Thus, the number 2] 
= 3- of conjugate points where the computed height is larger 
d. than the height derived from the Survey DEM should 0 
= be higher than the number of points with lower height. a 
1- This is shown clearly in the last two columns of 
Table 4. Looking at points with height differences larg- 
o T 2 50 2 50 pa 75 2D 90 ado er than 20m (points excluded in the second row of Figure 
number of GCPs Table 4) we found that for a substantial number of 
these points (516 out of 596) the computed height value 
was larger than the height value in the Survey DEM. A 
manual classification of these points with height differ- 
ences larger 20m gave the following result: 
Figure 8. Averaged theoretical standard deviations for 
coordinate z in dependence on the number of 
ground control points 
74