The choice of a higher regularization parameter \=4000 
shows, that regularization by curvature minimization is 
more sensitive to an increase in A, if the surface con- 
tains edges: rms(dZ) is distinctively lower for adaptive 
regularization in the case of reconstruction of the sur- 
faces | (rfpar) and 2 (rfrot). The reconstruction of the 
smooth surface 3 (cylpar.) again yields only marginal 
differences in the rms(dZ)-values for both regularization 
methods. The experiments 1-4 also show, that recon- 
struction with regularization by curvature minimization 
is closer to the original surface, if A=4000 is chosen. 
But compared with A=2000, the gap between the 
rms(dZ)-values of both regularization methods has be- 
come closer. 
In regularization by curvature minimization, the implied 
assumption of smoothness of a surface yields smooth 
reconstructed surfaces, which can be seen in fig. 4.2a, 
fig. 4.6a, fig. 48a, fig. 4.10a and fig. 412a (all surfaces 
reconstructed with A-2000). 
If the surface to be reconstructed itself is smooth, the 
reconstructed one shows great similarity to the original 
one. But if it is not, the surface edges will not be pro- 
perly reconstructed, especially if a high regularization 
parameter À is chosen. 
All experiments show, that both regularization methods 
are capable of ‘bridging’ areas of low contrasts in image 
grey values. 
Fig. 4.15 shows the standard deviation of heights for the 
reconstruction of surface 4 (cylrot) containing an area 
of constant grey value, fig. 4.16 shows the standard de- 
viation of heights for the reconstruction of the same sur- 
face, which does not contain such an area. Adaptive 
regularization was used in both cases. The distribution of 
standard errors looks very similar in both cases, with 
one exception: in the area of constant grey value the 
standard deviations of heights are higher in fig. 415 
than those in the respective area in fig. 416. In that 
experiment the area to be 'bridged is small, only 4x3 
Z-facets. The increase of 84. is low, accordingly. But 
principally, these values can be used for the detection 
of regions of insufficient grey value information. Such 
areas could be marked in the reconstruction result, in 
order to inform a human operator of this situation. 
area of constant grey value 
Z-axis 
1010 ; 
1008 
1010 
  
9090 
Fig. 4.1a Surface 4 with area of constant grey value: 
reconstructed surface 
FAST Vision with adaptive regularization 
area of constant grey value 
        
    
     
    
  
  
    
    
     
| 
e 
m ONERE R 
ZEN 
0,5 
   
Fig. 4.1b Surface 4 with area of constant grey value: 
differences between original and reconstructed surface 
FAST Vision with adaptive regularization 
Z-axis 
1010 
1008 
Fig. 4.2a Surface 4 with area of constant grey value: 
reconstructed surface S 
FAST Vision with regularization by curvature minimization 
, 05 
-0,5 
dZmin=-0.029 m 09 
X-axis 
9099 
Fig. 4.2b Surface 4 with area of constant grey value: 
differences between original and reconstructed surface 
FAST Vision with regularization by curvature minimization 
Z-axis 
1010 
  
9080 
Fig. 4.6a Surface 3 without area of constant grey value: 
reconstructed surface 
FAST Vision with regularization by curvature minimization 
812