2. Parameters, Image Material and Results 
Two sets of images were used for the FAST Vision 
experiments with and without the application of an 
image pyramid: 
a) three aerial pictures (1:12000, longitudinal overlap 
60%, focal length 153 mm) with low contrasts, 
taken in the Dankelshausen area in the vicinity of 
Dransfeld (near Göttingen, Lower Saxony, Germa- 
ny), showing a crossing of two paths in agri- 
cultural surroundings (fields). Surface heights are 
between 208m and 213m. 
b) two computer-generated pictures, rich of contrast 
(only noise due to truncation to integer grey 
values, 112000, longitudinal overlap 60%, focal 
length 153 mm) of an object similar to a saddle 
roof (two inclined planes meeting at a ridge). 
One plane (‘exposed to the sun) contains grey 
values from 128 to 255, the other one (in the 
shade) contains grey values from O to 12T. Surfa- 
ce heights are between 1003m and lOllm. 
In both cases, the area to be reconstructed had a size 
of 4O0mx4Om. The pictures had a size of 240x240 
pixels (pixel size: 20umx20um in image space). As 
the pictures were taken from an altitude of 1800m 
and with a base of 1350m, this pixel size corresponds 
to a minimum radius of convergence in Z-direction 
of 0.3 m, which is very small. It increases to 0.6 m 
on level | of the image pyramid, to 1.2 m on level 2 
and to 2.4 m on level 3. Break-off criterion was the 
maximum difference of heights between two iterati- 
ons. Convergence is assumed to be reached, when 
the differences of heights in all grid-points falls 
below the break-off criterion, which was chosen to 
be twice as high for the grid-points on the borders of 
the window to be evaluated (in comparison with 
interior grid-points) and four times as high for the 
four corner points (quoted in the result tables: bre- 
ak-off criterion interior / edge / corner). The number 
of iterations for each level of the image pyramid is 
given for each experiment (e.g. 4/3/8 iterations, i.e. 
4 iterations on level 2, 3 on level | and and 8 on 
level 0). The number of Z-facets (i.e. height facets) 
given in the parameters is that on level O of the 
image pyramid; the number of grey value facets per 
Z-facets remains constant for all levels. Regularization 
was achieved by minimizing curvature with a 
regularization parameter (regularization parameter 
O = no regularization). If not stated otherwise, the 
regularization parameter was chosen to be 1000 and 
the break-off criterion was 5cm/10cm/20cm. 
342 
3. Choice of Mask for Low-Pass Filtering 
There is no mask of finite dimension realizing ideal 
low-pass filtering. Therefore, the choice of such a 
mask has to be a compromise between approximation 
of ideal low-pass filtering and computational effi- 
ciency. A good approximation is characterized by 
almost complete elimination of higher signal fre- 
quencies while the lower ones have to be almost 
completely preserved. There are many suggestions 
for masks in literature reaching from a simple 2x2 
mean value filter (Li, 1989 / Weisensee, 1991) to a 
(e.g) 13x13 mask (Meer et. al, 1987). The latter 
one, which really is a Tx7 mask due to zero columns 
and rows, was used for low-pass filtering in the 
experiments in this paper. Fig.3.1 shows a comparison 
of this mask with two binomial masks (Jähne, 1989). 
  
  
filter mask |no. of computation time kernel 
iterations for filtering Crelative) no. 
3x3 8/6/5/9™ 1 
5x5 10/8/5/10 2.78 2 
13x13 15/1/5/9 5.44 
  
  
  
  
*8/6/5/9-8 iterations on level 3 / 6 on level 2 
5 on level 1 /9 on level O 
T 
  
kernel-a.a kernel 
no. 
  
a-O.25-C1,2,15 
a-0.0625<1,4,6,4,1) 2 
a-10-3<O,51.0.-87.0.298.475.298.0.-87,0,51,0) 
  
  
  
  
Fig. 3.1: Comparison of number of iterations and 
cornputation time for different filter masks 
(image material: Dransfeld images, 
4 pyramid levels, 8x8 Z-facets) 
A low number of iterations on level O of the image 
pyramid is desired for the reconstruction of larger 
DTMs. Fig. 3.1 shows, that this number is the lowest 
for the 13x13 mask, although it can be as low for a 
simpler binomial mask (v. 3x3 mask). But as the 
computaional cost for filtering is low compared with 
that of an additional iteration on level O, the 13xl3 
mask seems to be a good choice. Larger masks do 
not seem to be recommendable because of the large 
areas on the edges of the images, which cannot be 
filtered by them. 
4. Comparison of the Experimental Results with and 
without Image Pyramid 
It is necessary for the application of the image pyra- 
mid within FAST Vision, that the obtained results are 
of the same quality as those obtained without the 
application of an image pyramid. In order to be able 
to compare the results we chose computer-gene- 
rated images, because the exact heights of the object 
to be reconstructed are known. For the purpose of 
comparison a window of 8x8 Z-facets was recon- 
structed with and without image pyramid. The start 
value for all heights was lOOTm, see section 2b). 
There was no regularization, no radiometric transfer 
pute: del s A haut LM "iM ise m 
d$ uia. 
o7» RR eM 51 55 X.—2