leal 
1 a 
tion 
»ffi- 
fre- 
ost 
ons 
2x2 
0 a 
or 
the 
son 
). 
A M 
  
ind 
Ta- 
are 
the 
ble 
ne- 
ect 
of 
on- 
tart 
fer 
function and the break-off criterion was Imm/2 
mm/4mm. In both cases the root mean square of dif- 
ferences between reconstruction results and real sur- 
face was 13 mm (i.e. O.OT^/.. of flying altitude). 
In this special experiment the position of the Z-facets 
was chosen in a way, in which there was a coinci- 
dence between the ridge and the border of the 
Z-facets (resulting in 8x4 facets situated on each half 
of the roof), so that the reconstructed heights in 
each grid-point could be exactly compared with the 
heights on the real oject. The mean differences of the 
reconstructed heights from the real values on the 
object are equal with and without the application of 
the image pyramid. Thus, the quality of reonstruction 
is the same in both cases. 
5. Advantages of the Application of the Image Pyra- 
mid within FAST Vision with Respect to Radius 
and Rate of Convergence 
The advantages of the application of the image py- 
ramid within FAST Vision have to be investigated. 
For this pupose, a DTM and an orthophoto in the 
Dransfeld area was reconstructed. Several experi- 
ments were carried out with and without the appli- 
cation of an image pyramid. There were also diffe- 
rent regularization parameters and radiometric trans- 
fer functions chosen. Fig. 5.1 shows the number of 
iterations and the relative time for computation, until 
the break-off criterion was met. 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
regularization parameter a 
radiometric transfer funct 
with pyramid 8/4/8"* 1.8" 
constant 
no pyramid wrong 
AO with pyrarnid 12:577. 2.3 
linear 
no pvrarnid wrong 
radiornetric transfer funct 
with pyrarnid 8/4/4 16 
constant 
no pyrarnd ST 151 
A=1000 
2 with pyramid 73/4 1.0 
linear 
no pyramid 35 12.4 
radiometric transfer funct 
with pyramid 8/4/72 IO 
constant 
no pyramid 44 9.9 
X-8000 
with pyramid D T/3/4 1.5 
inear 
no pyramid 45 10.2 
wrong=convergence towards wrong heights 
**8/4/8 = 8 iterations on level 2 / 
4 on level 1 / 8 on level O 
*1.8 = computation time relative to === 
  
  
  
Fig.5.1: Comparison of FAST Vision with and 
without image pyramid: no. of iterations & 
CPU-times 
(image material: Dransfeld images, 
3 pyramid levels, 4x4 Z-facets) 
343 
As the start value for the height of 205 m was lower 
then the real heights in the area (bad start value), 
the application of the image pyramid resulted in an 
advantage of a factor of up to 10 in terms of compu- 
tational speed. Fig. 5. also shows, that convergence 
can be reached by applying the image pyramid in 
cases, in which it is not reached when not applied 
(v. first column of fig. 5.1: FAST Vision converges to 
wrong height values without application of image 
pyramid). 
6. Choice of Break-Off Criterion on Higher Levels of 
the Image Pyramid 
Regarding the number of iterations on the higher le- 
vels of the image pyamid (v. fig. 3.D, one realizes 
that it is generally greater on the higher levels of the 
image pyramid, which indicates that one does not 
have to choose the same break-off criterion on the 
higher level as on level O. This becomes especially 
clear when realizing, that the resulting heights on 
the higher levels are used as mere start values for 
the next lower ones. In order to investigate, if it is 
necessary to choose the same break-off criterion on 
each level of the image pyramid, the following ex- 
periment was carried out with two methods of choo- 
sing the break-off criterion on each level: 
a) The break-off criterion on each level is the same, 
b) the break-off criterion is doubled from one level 
to the next higher one. 
Doubling of the break-off criterion in b) has been 
chosen because of the proportionality of height errors 
with x-parallax errors, which are proportional to pixel 
size. 
Fig. 6.1 shows the number of iterations on each level 
of the image pyramid. They are equal for level O for 
a) and b), but the values are lower for b) on the 
higher levels. Therefore, the start values obtained 
from the higher levels are exact enough even if the 
break-off criterion is doubled from one level to the 
next higher one. On the other hand, as the time 
needed for an iteration on a higher level of the ima- 
ge pyramid is much lower than that on ievel O, the 
added advantage in terms of compuational time 
amounts to only 1% in case b) 
  
case| iterations | (level 3,2/1/0) 
a) 8/5/4/4 
b) 3/3/3/4 
  
  
  
  
  
Fig. 6.1: No. of iterations for equal break- 
oif criterion on each level of image 
pyramid (case a) and for break-off 
criterion doubled on each higher level 
(case b)