stanbul 2004
ge
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1 must be lin-
ore, approxi-
ect points are
' used in a si-
1€ unknowns.
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tes of the ob-
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ns containing
shows a band
blem, several
as control in-
approach de-
control infor-
vestigates the
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"t have to be
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| information
points lie on
this approach
ts but interpo-
is that the ef-
nts is reduced
hlhof, 1994),
1ssical GCPs,
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B4. Istanbul 2004
too. Here, as control information they use irregular arranged ter-
rain points which don't have to be identified in the images. Trans-
ferred to case of Mars Express (Spiegel et al., 2003), the role of
terrain points corresponds to the role of the MOLA track points.
However, the HRSC tie points must be acquired in such a way,
that at least HRSC points are arranged in the surrounding of each
MOLA track point. The HRSC object points would define small
surface patches, each containing a MOLA track point.
In principle, these are two viable alternative ways to combine
HRSC points and MOLA points. The first approach is to use the
terrain surface derived by MOLA DTM points and fit the matched
HRSC points into the MOLA surface. The second approach is to
use a terrain surface defined by HRSC points and adapt this sur-
face to the MOLA track points which serve as control informa-
tion. The first alternative is suited better if there are more MOLA
points than HRSC points. The second is more reasonable if there
are more HRSC points than MOLA points.
The comparison of the matched HRSC tie points and the MOLA
data shows that in all investigated areas more MOLA points than
matched HRSC tie points are available. Therefore, in the fol-
lowing investigations the first approach will be applied. This
approach will be described more in detail now. It uses a least
squares adjustment with additional conditions to get a relation
between a DTM and the HRSC points. As already mentioned,
the HRSC points have to lie on a bilinear surface defined by four
neighboring MOLA DTM points, which enclose the HRSC point
(see Fig. 6). This condition can be formulated as a constraint on
the vertical distance d from the HRSC point to the bilinear sur-
face. Furthermore, this constraint can be substituted by a fictive
observation, used as additional observation in the bundle adjust-
ment.
d
M4.4: MOLA DTM mesh derived
from MOLA points
H: HRSC point
d: distance between HRSC point
and MOLA DTM-surface
Figure 6: Fitting HRSC point in bilinear surface defined by
MOLA DTM
The mathematical model for this observation equation is given in
(Equation (2)).
da + d = f(Xn,Yn, Zn, X mis Ym,> ZM;) @)
For each equation the number of unknowns is three
(XH, Yu, Zu). lt contains one observation (d = 0) and
twelve constants (Xu, Yu, ZM;, i — 1..4) The standard
deviation c4 will be determined by the standard deviations of
four MOLA DTM points M;, My, Ma, and Ma. Thus, the
implementation of the least squares adjustment with observation
equations only is quite easy.
With this approach an improvement of the height (Z) can be ex-
pected, of course. An improvement in planimetry (X, Y) can only
be determined, if there are different local terrain slopes at the dif-
ferent MOLA surfaces.
UA
4 PROCESSING OF HRSC IMAGERY
This section is divided in two parts. Section 4.1 describes the
results of bundle adjustment without control information. The
results of bundle adjustment with the MOLA DTM as control in-
formation is presented in Section 4.2. In both cases the a priori
accuracy has been introduced into the bundle adjustment with a
value of 1000 m for the position and 28 mgon for the attitude.
One whole trajectory of the orbiter is considered to be very sta-
ble. Therefore, only a bias over the whole trajectory will be
improved. The MOLA DTM is introduced with an accuracy of
100 m instead of 10 m in order to cope with differences between
HRSC object points and MOLA track points due to the limited
spatial resolution of MOLA. As mentioned before, the resolution
on ground of HRSC is up to 12 m compared to the MOLA surface
spot size of about 168 m. Regarding local areas, the MOLA data
describe the surface less detailed as HRSC object points. The
orbits 18, 22, and 68 will be analysed.
4.4 Bundle adjustment without DTM
In order to evaluate the quality of the matched image coordinates,
the ray intersections of the tie points are analysed. First the ob-
served values of the exterior orientation are fixed in the bundle
adjustment, i.e., they are regarded as error free, and no DTM as
control information is introduced. This can be considered as a
forward intersection. The obtained values are then compared to
the results calculated by the bundle adjustment improving ¢ and
&. More precisely, a constant bias is modelled for both angles
along the entire orbit. In all orbits the number of HRSC points is
very high. Thus, it is possible to use only 3-ray points in the bun-
dle adjustment. With 3-ray points the redundancy for each HRSC
object point is high and gross errors of image coordinates are vis-
ible. These errors can be eliminated by a robust adjustment.
In Table 2 the accuracies of the object coordinates derived from
the ray intersections are shown for the selected orbits. The left
value is the accuracy of the ray intersections keeping the observed
exterior orientation fixed. The right value shows the achieved
accuracy of the ray intersections after improving « and «, i.e.,
after estimating the bias in ¢ and &.
orbit | altitude [km] | cx [m] | ev [m] | ez [m]
18 275 - 347 11/59 | 13/66 | 34/18
22 311 - 941 13/78 | 18/92 | 427/22
68 269 - 505 30/10 | 27/11 | 49/18
Table 2: Object point accuracies of ray intersections
The accuracies of the object points for all processed orbits are in
a range of about 6 to 11 m in X and Y, depending on different
imaging altitudes. Z accuracies for all orbits are about 18 - 22 m.
The standard deviations of the ray intersections are improved by
a factor of 2 and a final accuracy of about 0.4 pixel on the ground
in X and Y and 0.8 pixel in Z is achieved. The generated tie
points are evenly distributed over the whole image block except
for areas with a lack of texture (see Fig. 7). Black points are 2-ray
points and gray points are 3-ray points. White areas are without
tie points.
4.2 Bundle adjustment with DTM
The second part of the results shows the evaluation after HRSC
object points have been fitted to the MOLA DTM. Here, all six
parameters of the exterior orientation (Xo, Yo, Zo, ¢,w, kK) have
been improved along the trajectory. The reliability is very high
because the coordinates of one point is determined on two ways.
