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S. Numerical Experiments Of FAST Vision With Adaptive 
Regularization 
In this paper only introducing experiments are presented. 
However, in another paper at this congress a series of 
different examples is given, see KAISER et al. 1992. 
In order to compare the methods of regularization the 
experiment of chapter 3 is carried out again. The second 
pair of images (with a section of constant grey value) 
was used. The photogrammetric and FAST Vision 
parameters are the same as in chapter 3. An image 
pyramid with two levels was applied. The results of the 
experiments in fig. 5.1 - 5.3 correspond to those in chapter 3; 
see fig. 3.2 for explanation. 
  
  
  
  
X So rms( dZ) $2 D 
6000 3.914 0.152 0.0279 12 
2000 3.910 0.154 0.0373 12 
2000 3.901 0.200 0.0368 66 
6000 3.917 0.158 0.0279 ll 
2000 3.911 0.152 0.0373 11 
2000 3.906 0.182 0.0369 65 
  
  
  
  
  
  
  
Fig. 5.1: Experimental results: exclusively self adaptive 
regularization (above), combined self adaptive 
and pyramid assisted regularization (below) 
Results: 
e The quality of reconstruction is definitely better than 
with curvature minimization, fig. 3.2, at the same number 
of iterations! The true errors dZ at the roofline have the 
same magnitude as everywhere, with the exemption of 
the region with constant grey values. This region is not 
correctly reconstructed (nothing else had to be expected 
because of lacking deterministic grey values) But in 
these experiments the differences between the true and the 
reconstructed object are smaller than with curvature 
minimization (v. fig. 52 and fig. 5.3). This indicates a 
better interpolation in that region, due to the use of 
approximated curvature values from surface pyramid, 
being closer to reality than in the case of regularization 
by curvature minimization. So, FAST Vision with adaptive 
regularization shows up remarkable edge preserving 
characteristics. 
e Às predicted by theory in section 41, see (33), the 
results of true errors dZ and standard error so practically 
do not differ with different regularization weight P, = À, 
fig. 5.1. 
e Also, the impact of different iteration numbers n, is 
confirmed as predicted. The reconstructed surface 
becomes rougher with increasing n,. The true errors dZ are 
distributed more stochasticallly - as they should do 
(cf. white image noise) - than with low iteration numbers ni. 
This effect results from the smoothing influence of the 
additional observation equations (see chapter 4.1), which 
decreases with n;. 
830 
   
  
  
Fig. 5.2: Reconstructed roofline: self adaptive regulariza- 
tion (lefÜ. and dZ-graph (right) 
\= 6000, dZmax = +0.873m and dZmin = -0.195 m, 
12 iterations (above) 
À » 2000, dZmax » +1.059m and dZmin= -0.647m, 
56 iterations (below) 
e However, the mean but not the maximum difference 
between true and reconstructed obiect gets larger with 
increasing number of iterations. This seems to be a 
paradoxical result, but it corresponds to the special shape of 
the object, which consists of two planes. Therefore, this 
result probably cannot be generalized to other surfaces. 
e The results of self adaptive and of pyramid assisted 
regularization can be compared in region of constant 
grey values, v. fig. 5.2 and 5.3. They do not differ much 
in that experiment. The average standard error s. does 
not agree with the corresponding rms of true errors. This 
discrepancy could be removed, if the refinement 
procedure for standard errors, see section 4.2, step 3, is used 
subsequently. 
  
   
  
  
   
  
Fig. 5.3: Reconstructed roofline: combined self adaptive 
and pyramid assisted regularization (left) and 
dZ-graph (right): 
À = 6000, d7maz = +0.892 m and dZmin = -0.201 m, 
11 iterations (above) 
À = 2000, dZmax = +0.819 m and dZmin = -0.639m, 
65 iterations (below) 
  
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