Grown Control Points - Georeferentiation 
Image 229 - 079 
GPS (WGS 84) Coordinates to Gauss - Kiiger 
Rectification - Errors 
Data 
G. C. P. 
Grown C. 
Points 
Gauss - Krüger Coordinates 
Image Pixel Coordinates 
Residual Error 
R.M.S. 
(Root Mean Error) 
Column 
Row 
X(nord) 
Y (est) 
X 
Y 
X 
Y 
9 
7.056.623,949 
4.440.205,522 
857,328 
5.451,453 
0.363 
0.127 
0.385 
10 
7.047.704,583 
4.523.857,638 
3.609,141 
5.600,547 
0.089 
-0.029 
0.039 
12 
7.001.107,811 
4.437.845,464 
1.071,516 
3.657.547 
-0.936 
0.055 
0.938 
8 
6.963.367,212 
4.437.000,970 
1.241,734 
2.439,920 
0.239 
-0.033 
0.241 
6 
6.897.860,137 
4.401.211,035 
427,266 
149,859 
0.286 
-0.177 
0.336 
4 
6.908.868,274 
4.538.027,734 
4.793,281 
1.215,844 
-0.267 
0.356 
0.445 
13 
6.947.852,357 
4.555.307,808 
5.148,672 
2.557,453 
0.028 
-0.206 
0.208 
11 
6.978.417,342 
4.578.022,819 
5.723,031 
3.656,969 
0.314 
0.052 
0.319 
7 
7.016.618,837 
4.597.134,886 
6.141,391 
4.983,703 
-0.116 
-0.145 
0.185 
Errors in Pixels 
Root Mean Square in X 
0,16510 
Root Mean Square in Y 
0,38572 
Total Root Mean Error 
0.41956 
TABLE 3 
If the rectification process, with the calculated transformation 
matrix gives a R.M.S. lower than !4 pixel, the program enter 
to the rectification dialog box. To calculate these errors, the 
system, with the trasnformation matrix calculated, obtains the 
rectificated coordinates of all the GCPs used, then carries out 
an inverse transformation and compare the pixel coordinates 
obtained (x r ,y r ) with the original pixel coordinates of any point 
(Xi.y,), 
With the expression 
>l( x r -*>)’+O', -y,Y 
Total R.M.S. = ^R a 2 +R/ 
the R.M.S. for any point is obtained , also : 
(See Tables 2 and 3) 
R¡ =VxR, 2 + YR, 2 
In the Rectification Dialog Box, it is possible to 
choose the resample method and the pixel size of 
the rectificated image to be obtained. 
where 
Ri = Root Mean Square of the Grown Control Point “i" 
XR| = residual in X of the GCP T 
YR| = residual in Y of the GCP “i" 
To calculate the R.M.S. in X and Y, and the Total RMS, the 
following expressions are used: 
The resample method is the program procedure 
to establish the digital levels (DL) to asign to the 
resultant image pixels. The software offers 3 
alternative methods: 
1. - Nearest Neighbour 
2. - Bilineal Interpolation 
3. - Cubic Convolution 
We selected Nearest Neighbour that the software 
offers as default. This method places in any grid 
location of the corrected image, the DL of the