International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part Bl. Istanbul 2004 
  
difference between the ground point and the projection plane 
(Ah), the horizontal dislocation (AL) can be computed and 
respected (relief correction). In the case of the QuickBird 
Standard imagery the projection plane is not a plane with 
constant height level but the GTOPO30-DEM, so only the 
differences of both DEMs have to be used for the relief 
displacement.. Of course also a shift of the relief corrected 
scene to control points is required. 
If the height level of the projection plane is known, by theory 
only a shift to at least one control point is sufficient. If it is not 
known, the image scale in the CCD-line direction is not 
determined and has to be computed based on control points. 
the Hannover program RAPORI, based on the RPC and with 
the PCI satellite modelling, which is also based on RPCs as 
input values. In the program CORICON beside an affinity 
transformation (6 unknowns) also the view direction (2 
unknowns) can be adjusted. The unknowns are individually 
checked for significance and correlation. Not significant 
unknowns are marked and can be taken out of the adjustment. If 
the view directions cannot be determined because of missing 
geometric information, automatically they will be taken out of 
the adjustment to avoid errors of extrapolation. 
  
RMSX RMSY 
  
RAPORI, RPC + 6 affine parameters 5.30 m 0.98 m 
  
  
  
CORIKON, reconstruction of geometry | 5.33 m 0.86 m 
+ 6 affine parameters (6 unknowns) 
  
PCI satellite modeling (RPC + 6 affine | 5.85 m 0.82 m 
parameters) 
  
CORIKON, 8 unknowns (affine + view | 1.01 m 0.80 m 
direction) 
  
  
  
  
Table 1. root mean square discrepancies at 39 control points of 
the IKONOS orientation in Zonguldak, Turkey 
  
  
The first three results of the IKONOS scene orientation with 
different mathematical models listed in table 1 are very similar. 
Also the error vectors are going into the same direction. In 
relation to the pixel size of 1m it cannot be accepted. The root 
mean square difference between the first both solutions is just 
0.38m for X and also for Y. 
  
  
  
Figure 4. Influence of unknown height level of projection plane 
  
  
   
   
  
   
   
   
  
  
   
  
   
   
   
  
   
   
  
   
   
      
As it can be seen in figure 4, the unknown height level of the 
projection plane is influencing the scale in the sensor line 
direction (distances L1 and L2) while the distances in the orbit 
direction are nearly not changed because of the constant 
incidence angle. With an affinity transformation of the relief 
corrected level 1B-images to the control points this effect can 
be controlled. Of course also the view direction, that means for 
IKONOS the nominal collection elevation and azimuth can be 
adjusted based on three dimensional distributed control points. 
2.6 Other models 
Also some other models like the direct linear transformation 
(DLT) and other not polynomial interpolations are used but do 
not play an important role. The DLT requires a higher number 
of well distributed control points and does not reach the same 
accuracy level. 
3. EMPIRICAL RESULTS 
3.1 IKONOS 
In the area of Zonguldak, Turkey two IKONOS Geo scenes 
have been analysed with different methods. 39 control points 
determined by GPS, are located in an elevation between 217m 
and 652m above sea level. The mountainous area goes from the 
Black Sea up to 850m elevation. 
For one scene also the rational polynomial coefficients (RPC) 
are available. This scene has been adjusted with the Hannover 
program CORIKON, reconstructing the imaging geometry, with 
  
  
2: ét 
  
  
  
  
  
  
  
  
  
  
  
  
     
  
  
  
  
  
   
   
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
   
  
  
  
  
  
  
  
  
LE ES 
ASS ES EPA TM PC. 
rent Teg ah mR 
qu: Lune + 
eh Lp 
  
  
  
Figure 5. discrepancies at control points corresponding to 
IKONOS orientations listed in table 1 
Upper left: RAPORI (RPCs), right: CORIKON 6 unknowns 
Lower left: PCI satellite modelling, right CORIKON 8 
unknowns 
  
  
The orientation problems are obvious in this case, so with 
CORIKON also the nominal view direction and azimuth has 
been handled as unknown leading to a sub-pixel accuracy. The 
adjustment of the view direction resulted in a change of the 
nominal collection azimuth of 8.6° which is highly significant 
with a Student test value of 31. The nominal collection 
elevation has only changed 0.4°. This is also significant but 
only with a Student test value of 6.3. Only the affinity 
parameter 3 was not significant and could be taken out of the 
adjustment without any change at the discrepancies at the 
control points. A problem with the view direction has been 
seen also with a scene in Saudi Arabia, but not in other areas. In