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The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B4. Beijing 2008 
45 Test Orbits 
♦ Before i After 
Figure 8: Standard deviations [m] of the ray intersections for all 
45 test orbits in Z (height component) before and after BA 
Table 1 shows the standard deviations of the ray intersections 
averaged over all 45 test orbits. The respective left column 
shows the value before adjustment using the nominal exterior 
orientation. The right column shows the result of the bundle 
adjustment (labelled “BA”). Results for Cross Correlation only 
and LSM are given. 
blunders is about 10% including the points eliminated which do 
not fit to MOLA and that 10000-60000 points per strip have 
been found. 
Next, in the second step the HRSC object points are tied to the 
MOLA DTM. For this task, the a priori accuracy of the exterior 
orientation has been introduced into the bundle adjustment with 
a value of 1000 m for the position and 25mdeg for the attitude 
at the orientation points. The MOLA DTM is introduced with 
an accuracy of 100 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 the ground of HRSC is up to 12 m compared to 
the MOLA surface footprint of about 168 m. Regarding local 
areas, the MOLA data describe the surface less detailed as 
HRSC object points. 
The root-mean-square (RMS) differences between the HRSC 
and the MOLA DTM is reduced significantly in the bundle 
adjustment. Hence, there is a high consistency between HRSC 
points and the MOLA reference system after the bundle 
adjustment. This is clearly visible in Figure 9 which shows the 
height differences between the HRSC object points and the 
MOLA DTM of orbit 2063 before and after bundle adjustment. 
Method 
X 
X„ A 
Y 
Y ra 
Z 
ZßA 
CC 
15.6 
7.3 
12.2 
5.5 
55.5 
25.6 
LSM 
14.5 
4.5 
11.3 
3.4 
50.9 
15.8 
-• 
i 
Table 1. Standard deviations [m] of the 
averaged over all 45 test orbits 
ray intersections 
Due to a small convergence angle of the HRSC the height 
component cannot be determined as precisely as planimetry. 
Before bundle adjustment the points derived from LSM are 
slightly more accurate. The points derived from CC can be 
improved by a factor of 2.2 by bundle adjustment whereas the 
points derived from LSM have been improved by a factor of 3.2 
With respect to an average resolution of 30 m of the prerectified 
images a very high accuracy has been achieved. In the next 
table the a posteriori standard deviations of the image 
coordinates and the percentage of rays of the tuples have been 
verified: 
> 80 m 
Method 
Accuracy 
of image 
coordinates 
2-ray 
[%] 
3-ray 
[%] 
4-ray 
[%] 
5-ray 
[%] 
CC 
0.32 
8.0 
9.6 
8.7 
73.7 
LSM 
0.19 
8.5 
9.6 
8.4 
73.5 
Table 2. A posteriori standard deviations [pixel] of the image 
coordinates and the percentage of rays of the tuples 
averaged over all 45 test orbits 
It can be seen that with CC a high accuracy of 1/3 pixel has 
been attained. With LSM an increased accuracy of 1/5 pixel 
has been achieved. For a stable bundle adjustment a high 
percentage of 5-ray points is desirable and the percentage of 2- 
ray points should be as small as possible because they are 
omitted in the bundle adjustment. About 3/4 of all tuples 
consist of all five rays and the remaining values are below 10%. 
This means that matching delivers rather strong geometric 
blocks. Finally, it should be noted that the percentage of