With the exception of the first two ones and the latter 
one, the parameters chosen for the experiments of 
chapter 4 and chapter 5 were the same: The image 
pyramid consisted of 3 levels. Each Z-facet had a size 
of 2mx2m and contained 4x4 G-facets,which yielded 
approx. 2x2 pixels per G-facet. In the experiments 
with computer-generated images (chapter 4) the 
window used for reconstruction had a size of 12412 
Z-facets (= 24mx24m in object space = 48x48 G-fa- 
cets). The difference of heights between two iterations 
was used as break-off criterion with 0.02m / 0.04m / 
0.08m for interior grid heights, border heights and 
corner heights, respectively. 
For the experiments with aerial pictures (chapter 5) 
windows with a different shape were used (v. chap- 
ter 3): Their size was 25x9 Z-facets (= 50mxl8m = 
100x36 G-facets). Break-off criterion: 010m / 020m / 
0.40m. In these experiments the differences concer- 
ning the grey values the pictures 
modelled by a linear radiometric transfer function. 
Such a function was not utilized in the experiments 
with computer-generated pictures, because there were 
no such differences to be modelled. 
between were 
3. A Scan-Technique for the Reconstruction of larger 
areas 
The number of variables of the system of normal equa- 
tions set up by FAST Vision increases with the number 
of Z- and G-facets in the object window to be recon- 
structed and even more so does computation time for 
solving that system of equations. If the window contains 
Ixs Z-facets and pxq G-facets, the total number of un- 
knowns will amount to (r+1)x(s+1)+(p+1)x(q+l). Thus, if 
the reconstruction of a larger surface with a fine resolu- 
tion Cie. small distances between the facets) is required, 
a scan-technique can be used. The window will be 
partitioned into smaller windows, which overlap each 
other. An especially efficient way of doing this is the 
use of so-called ‘stripes’, which are windows being very 
narrow in one direction. The application of a scan-tech- 
nique using stripes results in a narrow band in the 
doubly bordered band diagonal coefficient matrix of the 
system of normal equations. In the experiments described 
in chapter 5 of this paper, stripes with 50% overlap 
were used. 
4. Reconstruction with Computer-Generated Pictures 
In order to be able to compare the results of reconstructi- 
on with the exact heights of a known object, which had 
to be reconstructed, several pairs of images were genera- 
ted from various computer-generated surfaces (in the 
following denoted as original surfaces), which posessed 
certain geometric features. Four objects were generated: 
810 
- surface 1 (rfpar.=roof with a parallel ridge): a gable 
roof consisting of two planes with an inclination of 
20° meeting at a ridge, which is parallel to the X- 
coordinate axis and is the border between Z-facets. 
Thus curvature is O everywhere with the exception of 
the ridge. Fig. 4.9a shows an almost perfect recon- 
struction of this surface. 
surface 2 (r£rot-roof with rotated ridge): a ‘gable roof’ 
of the same shape, but the ridge forms an angle of 
11.3° with the X-coordinate axis, see fig. 4.13a. 
surface 3 (cyl.par=cylinder with parallel arc): a 'ey- 
linder, which in fact is a surface generated by mo- 
ving a parabola along a horizontal straight line. Cur- 
vature of this surface is O in direction of the X-axis of 
the object coordinate system. Fig. 4.6a gives an idea, 
how the original surface looks like. 
surface 4 (cylrot-cylinder with rotated arc): another 
cylinder, looking like the before-mentioned surface, 
which is rotated in the X-Y-plane by 11.3? (see fig. 
4.23). 
The grey values on the ‘gable roof ranged from O to 127 
on the ‘shady plane’ of the roof and from 128 to 255 on 
the the ‘plane exposed to the sun. Two computer-gene- 
rated pictures of this surface can be seen in (Wrobel et 
al 1992a,b). The texture on the ‘cylinder is very similar, 
but here the grey values range from O to 255. 
Additionally to these grey values on the object surface 
there was an area of constant grey values (size: 8mx6m 
= 43 Z-facets) 
marked in the figures. It was introduced to study the 
behaviour of FAST Vision in areas, where grey values 
on the object surface do not contain any information, 
which can be used for reconstruction. It is 
especially interesting to see, how the two types of 
regularization - regularization by curvature minimization 
and adaptive regularization - are able to 'bridge' such 
areas of constant grey values. Otherwise, the matrix of 
normal equations set up by FAST Vision can become 
singular, if the objects contain such areas and no stabi- 
lizing functional is added (Wrobel et al., 1992a,b). 
The computer-generated pictures of the above mentioned 
objects were taken with a standard deviation of 4 grey 
values (white noise). À pair of images was generated for 
each object. 
on some of the surfaces. This area is 
surface 
As there are four surfaces and two types of texture on 
the surface of each object (with and without area of 
constant grey value), 8 pairs of images were generated. 
Of these, 7 were used for the reconstruction experiments. 
Surface | containing the area of constant grey values 
was not used, because similar experiments are shown in 
(Wrobel et al, 1992a,b). Multiplying these 7 data sets 
with two types of regularization, the number of experi- 
ments amounts to 14. These and the respective figures 
were numbered as follows: