Fig. 4.2 The semi-synthetic image strip of the nadir 
channel 
Random errors with different standard deviations in 
position (o, = 0.4 m, 1.0 m, 2.0 m) and attitude (o, — 
0.08 mgrad, 0.2 mgrad, 0.4 mgrad) were added to the 
elements of exterior orientation for every 10th line. The- 
se errors can be regarded as originating from interpola- 
tion errors in the flight path. 
4.2 Pyramid structure 
For each image strip and for the DTM a pyramid struc- 
ture was generated. Level 0 contained 256 * 256 pixels 
in 16 * 16 DTM meshes, the next level 128 * 128 pixels 
in 8 * 8 DTM meshes and so on. Level 4 contained 
16 * 16 pixels in one DTM mesh. In the levels 5 and 6 
only the number of pixels was reduced. For level 7 the 
number of pixels and of DTM meshes remained con- 
stant, but the size of the object surface elements was 
doubled in each direction. The same was done again for 
level 8. The details of the pyramid structure can be seen 
in table 4.1. 
4.3 Results and conclusions 
  
Matching was performed through the pyramid as descri- 
bed. The elements of exterior orientation (straight flight 
path and disturbed flight path respectively) were intro- 
duced as constant values in all cases. For the initial 
height values a horizontal plane was used. Starting 
heights between 1500 and 4000 m all yielded the same 
result. This shows that the convergence radius, which 
amounts to only a few pixels in image space for least 
squares matching without image pyramids, can be exten- 
ded nearly arbitrarily. 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
poramid | sumberof number of| size of object 
: DTM | surface elements 
level pixels heli: [m2] 
8 4*4 1 800 * 800 
7 4*4 1 400 * 400 
6 4*4 1 200 * 200 
5 8*8 1 100 * 100 
4 16 * 16 1 50 * 50 
3 32 * 32 2*2 28 * 28 
2 64 * 64 4*4 125: 125 
1 128 * 128 8*8 6.25 * 6.25 
0 256 * 256 16 * 16 3.125 * 3.125 
  
  
292 
Table 4.1: Pyramid structure 
Table 4.2 shows the results in detail. In the ideal case (1) 
a standard deviation of 1.22 m between the known and 
the derived DTM was obtained. This corresponds to 0.1 
pixel (1 um in image space) or 50 us in the image strip. 
It is caused by errors during the generation of the semi- 
synthetic images. It can also be seen that the radiometric 
noise does not influence the matching results to a large 
extend. The noise of well calibrated CCD sensors, case 
(2), can be neglected. Even in case (3) the results are still 
acceptable. 
Errors in exterior orientation can be directly related to 
locations in image space. In case (4) and (5) they induce 
an error of about 0.5 pixel, in (6) and (7) about 1 pixel 
and in (8) and (9) about 2 pixels standard deviation. The 
derived errors in height show, how sensitive the ap- 
proach is towards errors in the exterior orientation. 
Therefore in any practical application it should be de- 
termined simultaneously with the DTM heights. The 
additional introduction of grey value noise has only mi- 
nor effects onto the results. 
The algorithm was further tested with a very rough but 
exactly known flight path. In this flight path deviations 
of up to 10 m in position and 5 mgrad in attitude within 
10 image lines (= 31.25 m in object space) occurred. 
New image strips were generated using this flight path. 
The matching results were exactly the same as for the 
straight flight path, case (1). Thus a rough flight path 
does not pose a problem as long as it is exactly known. 
  
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