International Archives 
of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B2. Istanbul 2004 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
The results show that, the use of 3D polynomial 
transformations, obtained on the basis of ground survey points, 
appears to be an unreliable approach, especially when applied 
for large territories. Its use for smaller regions with insignificant 
relief variations, when having sufficient number of control and 
check points, gives considerably better results. 
5.3. Use of Rational Polynomial Coefficients (RPC), supplied 
by QuickBird, with further polynomial transformations 
With the cooperation by RACURS Co. relatively good results 
are obtained in the range of the entire image. The software was 
upgraded, which gives the opportunity to include RPC, 
submitted together with the satellite image. They are such an 
empirical coefficients that, the obtained functions represent 
approximation of the rigorous sensor model. Their use is an 
alternative to application of accurate physical model of the 
sensor, especially for relatively flat terrain. 
The following approach is used: 
° Transformation by use of the RPC is made. 
. The precision of the obtained result is increased by means 
of 3D polynomial transformations of the basis of points, 
measured by GPS. 
For the experiment 8 control and 15 check points, normally 
distributed within the range of the image, are used. The 
obtained obtained maximal displacement and RMS error in 
position of the check points are 2.56 and 1.40 m. respectively. 
The errors in X and Y directions, as well as the location of 
points are given in Table 2 and Figure 2. 
  
  
  
  
Residuals in control points | Residuals in check points 
Ne | Point dx dy Ne |Point| dx dy 
Pixels Pixels Pixels Pixels 
1. 111 -0.456| -0.755 l. 14| -0.287] -0.813 
2 3 0.1084 0306] 2 15] 1.043] -1.081 
3. 60| -0.003] -2708|- 3. 152) 0.297}: 3.408 
4.0 1132} 0.10] 1018 41 321 0442 0771 
5. 991 221 2.7421]. S4 . 331. 1.9921 0209 
6. 114! -0.268/ 1.301} 6. 1541 2.035] -0.519 
7. 46| 0.466| 0.322 | 92] 0.808] -0.548 
8] 301; 0.443] -0.164|] 8. s500| 0250| -1.612 
91 509 0.555) 0750) 9) SG2| 0.0175] .0 741 
10. 159! 0.007] -0.849| 10. 508| 0.767| -0.296 
IE 160] 0.598] -0.126] 11.| 156] 0.706] 0.848 
12. 85| 0.044] -1.580[ 12.| 162] 1.044] -1.451 
13. 100| -0.495| -0.641| 13.| 163| 0.981 1.375 
14. 106] 0.681| -0.774| 14.1 165| -0.019| 0.947 
15. 107} -0016] 2337] 151 103 -0.012) 0.918 
16. 133} 08051 0.525( 16.1 1111 03181 1:005 
17.1. 115. 0.1778 1.700 
18.1 116 -0.898| -0.404 
19. 117] -0.087] -0.825 
RMS: 0.49 1.40 |RMS: 0.80 1.01 
MAX: 0.86 2.74 |MAX: 2.04 1.70 
Approximate ground Approximate ground 
displacement [m] displacement [m] 
RMS: 0.92 RMS: 0.82 
MAX: 1.78 MAX: 1.64 
  
  
  
Table I. The residuals in control and check points 
60 BJ 
1145 
107 5 
  
  
154 
1154103 2 
AIS 
09 bd 
500 À 
162 A 
1132 pd 
uj 
£502 
163 A4 
154 4 A a7 
5159 
53501 
10653 117 As 160 
& Control point 
ix 
116 4117 
133 
à Check point 
  
  
Figure 1. Points location within the imagery 
The accuracy is verified also by superimposition of vector 
objects from the available cadastral information over the 
orthorectified image. The differences are within the obtained 
maximal displacement and RMS error. 
388 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
Residuals in control points | Residuals in check points 
(o | Point dx dy Ne | Point dx dy 
Pixels Pixels Pixels Pixels 
= 011 -0.030| -1.464 l.|| 04| -1.205| -2.700 
2. 02}. 0086) 0835} 2 7| -0.5355] -0.598 
3 03] 0.044 -1.553| 3.1 08/0040) -1328 
4. 031 0014. 0561). 41 09% -0.559| -0.402 
S. 06|..-0.063] .4.323] | .5. 131. 0.772 0979 
6. Li 0.0281 1.0251 6, 141 -0.258| -2.342 
7. 15; -0.181}: 0.072 16| -1.101| -0.369 
8. 22} 0.160$--0325} 8 17} 1.350} -3.238 
9. 19] 0.5421° -0.820 
106.1 20] —2.052| 1.334 
b 21]. 2316].-1.521 
12.| - 23] 210.290} 2.606 
13.0 24} -2603] 2388 
14.1 25] -0.3891 2010 
IS] -20[| 0.9971 22387 
RMS: 0.10 1.03 |RMS: 1.26 1.89 
MAX: 0.18 1.56 |MAX: 2.61 3.24 
Approximate ground Approximate ground 
displacement [m] displacement [m] 
RMS: 0.64 RMS: 1.40 
MAX: 0.97 MAX: 2.56 
  
  
  
  
  
  
Table 2. The residuals in control and check points 
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