International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part Bl. Istanbul 2004 
  
— image coordinates of 5270 tie points, obtained by 
automated image matching in the HRS1, HRS2 and the 
THR images (o = 0.5 pixel, see figure 3), 
— horizontal object coordinates of 19 control points 
(c = 2.5 m, corresponding to the ground sample distance 
of the THR-channel, which is limiting the point 
identification accuracy), 
— heights of 19 control points (c = 2.2 m = 2 x Oprm). 
The supplied look angles, ephemeris, velocity and attitude 
parameters enter as constants and not as observations. 
3.4.3 Results 
In order to get rid of correlation effects between external and 
internal orientation, the 24 CPC for the external orientation 
parameters were fixed in a first step and only 24 CPC for the 
look angles are estimated. Later in a second step, i.e. after the 
set of significantly determinable CPC (for the look angles) 
has been found, this set together with the 24 CPC for the 
external orientation parameters are estimated simultaneously. 
3.4.3.1 Bundle adjustment using HRS and HRG data 
In a series of adjustment runs those CPC are consecutively 
fixed, whose estimated values are small compared to their 
estimated standard deviations. Simultaneously it is 
monitored, whether the fixing of the CPC provokes a 
systematic alignment or an increase of the residual vectors of 
the control points both in image and in object space. If there 
is an increase or a systematic, the CPC is not fixed, even if 
the relation between value and standard deviation is small. 
After a series of adjustment runs it turned out, that 15 of the 
24 CPC can be fixed and consequently 9 CPC are determined 
more or less significantly. In table 2 their estimated values 
(x), the estimated standard deviations (oy), their significance 
(x/o,) and the maximum effect (E) in pixel at the edges of 
the CCD-array are listed. 
error of approximately 2 meters in Easting (dE), Northing 
(dN) and Height (dH). Table 4 lists the statistics on the 
differences between the 5235 estimated tie point heights and 
their interpolated DTM heights. The respective histogram is 
shown in figure 4. The higher frequency of positive height 
differences is due to tie points lying on top of the vegetation 
or artificial objects, which actually must not be compared 
directly to the DTM heights. If these points would be filtered 
out, the statistics would improve. 
MIN. MEAN MAX. RANGE RMS. o [m] 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
Channel Ax Bx |Cx|Dx| Ay |By Cy Dy 
X |5.3E-06/1.0E-06 2.8E-05 
THR |_ 9 7.8E-06]1.1E-07 3.3E-06 
Xo: 0.7. 1.99 | 86 
Ei 18 | 42 9.5 
x {49 1.5E-05| |-4.2E-07|-6.9E-08 
Hrg1|-0*_|1-3E-05 5.6E-06| | 4.7E-07 | 9.1E-08 
xlox| 04 26 09 08 
E | 04 24 26 | 5 
X -4.6E-07 |-7 4E-08 
non. x 4.8E-07 | 9.6E-08 
xlox 1.0 0.8 
E 28.] 25 
  
  
  
  
  
  
Table 2: Estimated CPC (x) for look angles, standard 
deviations (0,), significance (x/o,) and maximum 
effect (E) [pixel]. A,-D, apply in scan direction, 
A,-D, in flight direction 
Table 3 shows the statistics on the differences of the 
coordinates at the 17 check points, indicating an empirical 
dE -4.40 -2.07 1.39 5.79 2.0^ 1.74 
ON -—6.0G 0.81 3.654: 9.74 2.331 2.25 
dH -4.435 0.19 3.46 6.89 1.95 1.95 
Table 3: Statistics on coordinate differences of the 17 check 
points 
MIN. MEAN MAX. RANGE RMS. c [m] 
OH -/2.24 2.10 63.30°87,54 65.11 5.74 
Table 4: Statistics on height differences between 5235 tie 
points and the reference DTM 
  
  
700 
600 
500 
4go |... dq. uk 
300 | ; + \ - 
200 = 
100 
o 
  
Frequency 
  
  
  
  
  
  
  
  
  
  
  
-20 -15 -10 -5 o 5 10 15 20 25 $0 
dH [m] 
Figure 4: Histogram of height differences between tie points 
and the reference DTM 
  
The adjustment employing also CPC for the position and 
attitude parameters in addition to the 9 CPC for the look 
angles did not show a significant improvement. Thus, it was 
concluded not to correct the attitude and position parameters, 
i.e. to apply the 9 estimated CPC to the look angles only. 
3.4.3.2 Bundle adjustment using HRS data only 
HRG imagery is not available for all SPOTS stereo data sets. 
Therefore an additional adjustment is done considering pure 
SPOT-5 HRS data. It turned out, that without HRG data none 
of the CPC can be determined significantly. This is not that 
astonishing, since the effect of the estimated CPC for the 
HRS1 and HRS2 channels proved to be very small (less than 
3 pixels maximum, see table 2). Consequently, an adjustment 
with all CPC fixed to value 0 was calculated, whose results 
are listed in tables 5 and 6: 
MIN. MEAN MAX. RANGE RMS. o [m] 
dE 5.02 -1.569 6.10 11.12: 3.823.352 
dN 5.02; 0.515.123 -10.45..2.92. 2.96 
dH 2.76 0.26 4.17 6.93 2.08 1.90 
Table 5: Statistics on coordinate differences of the 17 check 
points after the adjustment of HRS data only, all 
CPC fixed 
MIN. MEAN MAX. RANGE  RMS. o [m] 
dH —22.07 2.65 00.55 382.47 6.61 6.05 
Table 6: Statistics on height differences between 5233 tie 
points and the reference DTM after the adjustment 
of HRS data only, all CPC fixed 
   
  
    
    
  
   
     
    
  
       
       
          
    
   
   
    
    
    
  
  
  
  
  
   
   
  
    
    
   
    
     
    
    
   
     
    
      
    
    
     
   
       
   
    
    
  
   
   
    
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