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The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B4. Beijing 2008 
where v, = residuals of height Z 
Z H n 
Z H = unknown height of object point H 
X H s Y H = unknown coordinates of object point H 
constant coordinates of MOLA DTM 
mesh point 
X M > ^ M ■> Z M 
d = Mesh width of MOLA DTM 
{d = X u -X u _ =Y U _ -Y u ) 
With this approach an improvement of the height (Z) can be 
expected. An improvement in planimetry (X, Y) can only be 
determined if there are different local terrain slopes at the 
MOLA surfaces. Figure 4 demonstrates a situation before 
bundle adjustment: 
trajectory 
orientation 
points 
Figure 4. Situation before bundle adjustment 
After bundle adjustment the differences (red lines) between 
HRSC points and MOLA DTM are reduced (see Figure 5): 
trajectory 
orientation 
points 
The adjustment can be divided into two steps which are called 
Relative and Absolute Orientation here: In the first part the ray 
intersections are improved by estimating the pitch and yaw 
angles at the orientation points. For geometric reasons the roll 
angle can only be determined with poor accuracy. In this step 
points are eliminated which are considered erroneous on the 
basis of their residuals of the image coordinates. In the second 
part the point cloud is adjusted to the MOLA DTM for absolute 
positioning. For that purpose biases for the three parameters of 
position and one drift for the height component are estimated. 
The angles are determined at the orientation points like in the 
first step. Additionally, the roll angle is calculated which was 
not possible in the first step. 
For the stochastic model the observed image coordinates are 
considered to be uncorrelated and with equal accuracy. For 
estimation of the Absolute Orientation the stochastic model is 
altered that the ray intersections from the Relative Orientation 
are kept unchanged. Only translations, a tilting in the height 
component and the roll angle are effectively carried out. Also 
in this step HRSC points are eliminated by taking into account 
the differences between the HRSC and the MOLA points. 
Single HRSC points are eliminated which exhibit major 
residuals to the MOLA DTM. Generally, these are no errors 
from matching but points which are not visible in the MOLA 
dataset because of its lower resolution (e.g. small craters). The 
bundle adjustment approach is described in more detail in 
Spiegel (2007a) and Spiegel (2007b). 
4. RESULTS 
In order to evaluate the developed approach results are 
presented which are obtained from a test dataset of 45 chosen 
test orbits. Image quality varies from very good to images 
whose contrast and sharpness have been blurred by dust in the 
atmosphere. All kinds of topography is contained in the data 
set: diverse landscapes with many craters, areas of erosion and 
textureless regions. Valley networks with steep and hillsides 
with continuous height changes can be found. The resolution of 
the prerectified images varies from 13 m to 60 m. 
The ray intersections of the matching points are evaluated with 
a bundle adjustment for all 45 test orbits. In addition to the 
scheme of chapter 3 the accuracy of the a priori image 
coordinates is adapted in an iterative way. The bundle 
adjustment is repeated until a value of 1.0 is obtained for the 
standard deviation of the weights o 0 . This assures that the 
standard deviations of different orbits are comparable with each 
other. Figure 6-8 show the standard deviations of the ray 
intersections for all 45 test orbits before and after bundle 
adjustment. The values apply to a local coordinate system 
where X (along flying direction) and Y (across flying direction) 
indicate the horizontal position and Z the height component. 
* .** 
ÌsssssISÌIÌÌIssskÌ; 
45 Test Orbits 
♦ Before « After 
- ^ CN ? $ tn S œ 
Figure 6: Standard deviations [m] of the ray intersections for all 
45 test orbits in X (along flying direction) before and after BA 
45 Test Orbits 
♦ Before .s. After 
Figure 7: Standard deviations [m] of the ray intersections for all 
45 test orbits in Y (across flying direction) before and after BA 
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