orward
“nadir
Fig. 6 Track of the border pixels of two different lines
So it is getting more difficult for the match algorithm to
identify points correctly. The probability of wrong match
results increases. This is especially important for highly
elliptical satellite orbits.
Shading caused by the optical components of the system
(cos*-law) influences the signal-to-noise ratio of the data.
This ratio is not only determined by the field of view, but by
the stereo angle as well. Consequently the bigger the
stereo angle, the smaller the signal-to-noise ratio. And
again it becomes more difficult for the match program, to
find conjugated points.
Besides there is still another point. The larger the stereo
angle, the more it becomes probable that certain areas on
the surface are invisible for a CCD-line.
The last three effects plead for a small stereo angle.
These counteracting processes are responsible for the for-
mation and definition of an “optimal” stereo angle we want
to find.
3. INVESTIGATIONS
The value of this optimal value of the stereo angle was
determined in dependence on the following parameters
(Börner, A., 1995):
- elevation dynamic of the observed terrain
- ground resolution of the camera.
3.1. Influence of elevation dynamic
Elevation dynamic in this contents means the standard
deviation of the original elevations given as a grid of sam-
ples. The distance of these samples should be equivalent
to the ground resolution of the camera.
In order to have comparable conditions one area of the
Mars was selected. The existing terrain model was modi-
fied in the following way:
The DTM was compressed by factor 5 once and exagge-
rated by factors 3,4 and 5. The simulated ground resolu-
tion is about 1 km and resulted from 256 pixels per line, a
field of view of 80 degrees and a flight height of 150 km.
This value corresponds to the resolution of the original
DTM of Mars (U.S. Geological Survey, 1992).
For the evaluation of the results the following criterions
were selected:
- accuracy of single reconstructed points
- number of matched points
- accuracy of the whole reconstructed DTM.
A measure for both accuracies is the standard deviation of
the elevation errors. The results of the investigation are
28
shown in Fig. 7 to Fig. 9. In Fig. 7 the standard deviation of
the elevation errors of all matched points is drawn in
dependence on the exaggeration factor and the stereo
angle. It could be established that up to a value of about
15 degrees for the stereo angle the determination of the
elevation of single points is getting more accurate. After
that there is no improvement of the results. So it makes no
sense to make the stereo angle greater than this value. A
stereo angle smaller than 10 degrees yields too large
errors.
The second curve shows the number of matched points in
dependence on the stereo angle and the exaggeration fac-
tor. The more the original DTM was exaggerated the less
the number of conjugated points could be found. Also the
number of matched points decreases with an increasing
stereo angle. In the previous section was tried to explain
the reasons for this effect. The exaggeration factor causes
an increase of the local elevation dynamic. Since the used
match algorithm evaluates the local image correlation, it is
clear that a strong local elevation dynamic causes a rapid
change of the local image correlation even for small
changes of the viewing direction. An extreme example for
such a kind of areas are urban terrains. The nadir line just
sees the roofs and no walls, the other lines have a totally
different impression.
Even for flat areas the number of conjugated points
decreases drastically for stereo angles greater than 40
degrees.
Fig. 9 is the result of the two previous curves. It shows the
standard deviation of elevation errors of the whole DTM,
i.e. the interpolated points were taken into consideration.
For all exaggeration factors a minimum of these curves
exists. The bigger the factor the more the minimum
becomes expressed. For flat areas the stereo angle
doesn't play any important role. But for terrains with a big
local elevation dynamic the range of permissible stereo
angles gets smaller. The parts of the curves can be
explained with the results shown in Fig. 7 and Fig. 8. Up to
a value of about 15 degrees for the stereo angle the stan-
dard deviation becomes smaller. After that the influence of
the interpolation algorithms increases, because the
number of conjugated points decreases.
The large deviations of the measured values from the
curves in the plots even for great exaggeration factors indi-
cate an essential dependence of the results on the choice
of the starting points of the matching algorithm.
To sum up, there are permissible ranges of the stereo
angle in dependence on the elevation dynamic of the
observed area. But the application of an stereo angle
between 15 and 20 degrees enables a sufficient accuracy
in determining single point elevations as well as a suffi-
cient number of conjugated points in two images.
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B1. Vienna 1996
