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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