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No. of type of type of type of 
experiment surface texture — regularization 
1 surface 4 (cylrot) wogv adaptive 
2 surface 4 (cylrot) wogv curv.min. 
3 surface 4 (cylrot) ncgv adaptive 
4 surface 4 (cylrot.) ncgv curv.min. 
5 surface 3 (cylpar) ncgv adaptive 
6 surface 3 (cylpar) ncgv curv.rnin. 
T surface 3 (cyl.par) wogv adaptive 
8 surface 3 (cyl.par.) wcgv curv.min. 
9 surface 1 (rfpar) ncgv adaptive 
10 surface | (rf.par) ncgv curv.min. 
11 surface 2 (rfrot.) wcgv adaptive 
12 surface 2 (rf.rot.) wogv -curv.min. 
13 surface 2 (rfrot.) ncgv adaptive 
14 surface 2 (rf.rot.) ncgv curv.min. 
(wcgv = with constant grey value, ncgv = no constant 
grey value, adaptive = adaptive regularization, curv.min. 
= regularization by curvature minimization). 
Table 4.1 shows seme numerical results of these experi- 
ments, which were carried out using two different regu- 
larization parameters À for each regularization method: 
A=2000 and A=4000. The shown values from the expe- 
riments are: 
So standard deviation of unit weight of the digital 
image grey values, 
5, mean standard deviation of heights Z, 
rms(dZ) root mean square of the differences between 
original surface and reconstructed surface, 
dZmax maximum value of dZ, 
dZmin minimum value of dZ. 
dZmax and dZmin are the extreme values of the diffe- 
rences in the grid-points forming the grid of Z-facets 
with the exception of those grid-points situated on the 
borders of the window in object space, which was used 
for reconstruction. 
[3-2000] 
  
  
  
  
  
  
  
Exper.| so $, |rms(dZ) dZmax dZmin 
No. metres | metres [metres | metres 
cyl.rot. = surface 4 
1 4.3 | 0.029 0.082 | 0.218 | -0.322 
2 4.3 | 0.029| 0.041 | 0.074 | -0.029 
3 4.3 | 0.028| 0.062 | 0.206 | -0.145 
4 4.4 | 0.028| 0.040 | 0.075 | -0.056 
cyl.par. = surface 3 
5 3.9 | 0.025| 0.089 | 0.133 | -0.163 
6 4.0 | 0.026| 0.093 | 0.134 | -0.127 
7 3.9 | 0.0261 0.092 | 0.131 | -0.164 
8 4.0 | 0.027| 0.093 | 0.132 | -0.124 
rf.par. = surface l 
9 3.9 | 0.033| 0.063 | 0.121-| -0.181 
10 4.11 0.035] 0.100 | 0.275 | -0.176 
rf.rot. = surface 2 
11 4.0 | 0.034| 0.108 | 0.276 | -0.411 
12 4.2 | 0.035| 0.114 | 0.472 | -0.160 
13 4.1 | 0.034| 0.096 | 0.173 | -0.390 
14 4.3 | 0.035| 0.092 | 0.251 | -0.166 
  
  
  
811 
[A=4000] 
  
  
Exper.| sg §, |rms(dZ)| dZmax dZmin 
No. metres| metres |metres| metres 
cyl.rot = surface 4 
1 4.3 | 0.024| 0.062 | 0.148 | -0.241 
2 4.4 | 0.025| 0.044 | 0.060 | -0.036 
3 4.3.1.0.023]. 0.051 1 0.147 | -0.106 
4 4.4 | 0.024] 0.045 | 0.060 | -0.044 
cyl.par. = surface 3 
5 3.91.0.021/|. 0.091 | 0.130 | -0.177 
6 4.0 | 0.022| 0.099 | 0.133 | -0.118 
7 3.9./.0.022| 0,094 | 0.129 |.-0.183 
8 4.0 | 0.023| 0.099 | 0.134 | -0.118 
rf.par. = surface 1 
9 3.9| 0.028| 0.063 | 0.109 | -0.207 
10 4.2| 0.030| 0.128 | 0.349 | -0.215 
rf.rot. = surface 2 
11 4.0 | 0.028| 0.099 | 0.287 | -0.340 
12 4.3 | 0.030| 0,136 | 0.512 | -0.220 
13 4.11 0.028: 0.087 | 0.136 | -0. 342 
14 4.4| 0.030| 0.115 | 0.319 | -0.219 
  
  
  
  
  
  
  
  
Table 4.1 Numerical results of reconstruction experiments 
1-14 with two different regularization parame- 
ters À (For comparison: 5,= Ol8m corresponds 
to OlŸoo of flying altitude’) 
Comparing the two regularization methods, it has to be 
noticed, that adaptive regularization yielded equal or 
lower standard deviations of unit weight and equal or 
lower standard errors of heights in all experiments. But 
which regularization method yields lower rms(dZ) de- 
pends very much on the surface to be reconstructed 
and on the regularization parameter À chosen. As it had 
to be expected from theory and from the experiments in 
(Wrobel et al, 1992a,b), the ridge in surface ! (rf.par.) 
is reconstructed best by adaptive regularization. The 
same is true for surface 3 (cyl.par.). In both cases the 
largest curvature of the original surface can be found at 
the borders between Z-facets and thus the smoothing 
effect of regularization by curvature minimization causes 
larger differences between original and reconstructed 
surface. However, it has to be said, that the advantage 
for adaptive regularization is only marginal, if surface 
3 (cyl.par.) is reconstructed with reconstruction parame- 
ter A-2000. With the same choice of A, the reconstruc- 
tion results of surface 2 (rfrot) are very similar for 
both regularization methods. If there is no area of con- 
stant grey value on the surface, the reconstructed surfa- 
ce is marginally closer to the original one when using 
regularization by curvature minimization. If surface 2 
(rfrot) contains an area of constant grey value, the 
opposite is true. And the difference between original 
and reconstructed surface is clearly higher for adaptive 
regularization, when surface 4 (cylrot) is reconstructed 
using A=2000.