0 
  
Fig. 4.15 Surface 4 with area of constant grey value: 
standard deviation of heights s 
FAST Vision with adaptive regularization 
  
Fig. 4.16 Surface 4 without area of constant grey value: 
standard deviation of heights sZ 
FAST Vision with adaptive regularization 
5. Reconstruction with Aerial Pictures 
One purpose of the experiments in this chapter is a 
comparison of the two regularization methods. The other 
is to study the different results of surface reconstruction 
using 2, 3 and 4 pictures. In order to achieve that, a set 
of aerial pictures with a longitudinal and lateral overlap 
of 60% was chosen. These were taken in a rural part of 
southeast Lower Saxony, a state in Northern Germany. 
The area to be reconstructed consists of fields and 
woods. The contrasts in the images are low. The scan- 
technique described in chapter 3 was used in order to 
limit the size of the systems of normal equations set up 
by FAST Vision. Table 51 shows the numerical results 
of the experiments, which were carried out with both 
regularization methods, with 2, 3 and 4 pictures and 
With regularization parameters A-2000, A-4000 and 
\=6000. The area to be reconstructed was divided into 
4 stripes of a size of 25x9 Z-facets. The numerical results 
for all experiments and all stripes are given in table 51. 
The values to be compared for different regularization 
methods, different regularization parameters and different 
numbers of pictures are: 
So standard deviation of unit weight. 
5 mean standard deviation of heights. 
As in the experiments with computer-generated pictures, 
the standard deviations of unit weight were equal or 
lower, if adaptive regularization was used (only excep- 
tion: stripe 4, A-6000, 4 pictures). In general, the mean 
815 
standard deviation of heights also was equal or higher, 
if one chose regularization by curvature minimization 
(exceptions: stripe 3, A-4000, 3 pictures ; stripe 3, 
\=6000, 3 pictures ; stripes 3 and 4, A-6000, 4 pictu- 
res). As the differences in these values were only mar- 
ginal, the surface can be expected to have been smooth, 
so that the assumption of smoothness implied in regula- 
rization by curvature minimization is true. Standard 
deviation of unit weight and mean standard deviations 
slightly increase with increasing regularization parameter 
A, which shows, that À should be chosen as low as 
possible in order to get good reconstruction result. But 
on the other hand it has to be chosen high enough to 
guarantee, that the break-off criterion is met. As the dif- 
ference in the numerical results does not depend very 
much on the choice of A, this choice is not a crucial 
point, which again indicates, that the surface is smooth. 
  
  
  
  
  
  
  
  
  
  
regularization 
gt | curvat. min. adaptive 
"ol X Ino. So Sz nil Sg sz ni 
2 |2000 | 1 16.6 | 0.065 4 16.3 | 0.062 | 17 
2 12000 | 2 } 7.0 | 0.051 4 16.6 | 0.049 | 10 
2 | 2000 | 3 | 7.8 |0.064 | 12 17.6 | 0.062 | 11 
2 | 2000 | 4 | 8.4 | 0.074 | 12 | 8.1 | 0.070 | 50 
2 | 4000 | 1 1 6.7 | 0.055 4 | 6.5 | 0.053 6 
2 | 4000 | 2 | 7.0 | 0.043 4 | 6.7 | 0.041 6 
2 |4000 | 3! 7.9 | 0.054 | 12 | 7.6 | 0.052 } 16 
2 | 4000 | 4 | 8.5 | 0.063 | 12 | 8.3 | 0.061 | 20 
26000 | 1 | 6.7 0.050 4 | 6.5 | 0.048 6 
2 | 6000 | 2 | 7.0 } 0.038 4 16.8 | 0.037 6 
2 |6000 | 3 | 7.9 |0.049 | 12 17.6 | 0.047 | 16 
216000/418.5 10.056 | 12 18.3 | 0.055 | 20 
3 | 2000 | 1 | 4.3 | 0.045 3 | 4.2 | 0.045 5 
3 | 2000 | 2 | 4.5 | 0.035 3 | 4.4 | 0.035 7 
3 | 2000 | 3 | 5.1 | 0.044 4 5.1 | 0.043 | 50 
3 | 2000 | 4 15.6 | 0.052 3 |5.5 | 0.049 | 50 
3 | 4000 | 1 | 4.3 | 0.038 3.14.3 | 0.038 4 
3 | 4000 | 2 | 4.6 | 0.029 3 | 4.5 | 0.029 6 
3 |400G | 3} 3.2 | 0.037 4 | 5.1 | 0.038 7 
3 | 4000 | 4 | 5.6 | 0.043 3 15.5 | 0.041} 50 
3 | 6000 | 1 | 4.3 | 0.034 3 14.2 | 0.033 4 
3 |6000 | 2 14.6 | 0.026 3 14.5 | 0.026 4 
3 |6000 | 3 | 5.2 | 0.033 3 |5.1 | 0.034 5 
3 |6000 | 4 1 5.6 | 0.039 3 45.60.0374 50 
4 12000 | 1 | 4.0 | 0.042 3 | 4.0 | 0.041 5 
4 | 2000 | 2 | 4.4 | 0.034 3 14.2 | 0.033 7 
4 | 2000 | 3 ( 5.0 | 0.043 4 15.0 | 0.043 3 
4 | 2000 | 4 | 5.4 | 0.049 3 15.3 | 0.048 44 
4 | 4000 | 1 | 4.0 | 0.035 3 | 4.0 | 0.035 3 
4 | 4000 | 2 | 4.5 | 0.028 7 14.310.027 6 
4 | 4000 | 3 5.0 | 0.036 3 15.0 | 0.036 7 
4 | 4000 | 4 | 5.4 | 0.041 | 14 (5.2 | 0.041 | 50 
4 | 6000 | 1 | 4.0 | 0.032 3 | 4.0 | 0.032 3 
4 | 6000 | 2 | 4.5 | 0.026 3 | 4.3 | 0.024 6 
4 16000 | 3 | 5.0 | 0.032 3 | 5.0 | 0.033 5 
4 | 6000 | 4 | 5.4 | 0.037 | 13 | 5.5 | 0.040 3 
  
  
  
  
  
  
  
  
  
  
  
Table 5.1 Numerical results of surface reconstruction with 
2, 3 and 4 aerial pictures (n=number of pic- 
tures, n;=number of iterations, n;=50 => con- 
vergence criterion was not met in 50 iterati- 
ons, St.no. - No. of stripe)