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The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Voi. XXXVII. Part B4. Beijing 2008 
than 0.4m in X, Y plane and 0.3m in height. The example 
projects of the ground control points showed on the (Figure 1). 
Two geometric correction variants have been used to correct 
Resurs DK-1 images. The analysis of the influence of number 
and distribution of the control points in boundary of the scene 
on the result of geometric correction was realized in each 
variant. First variant integrates all components of the viewing 
geometry and sensor as well as the Earth and cartographic 
projection. In this variant from 5 to 12 well identified and 
distributed control points was measured. Accuracy of the 
corrections has been checked on well defined check points. 
Results are shown in (Tab. 1). 
Number of control 
Number of check points 
RMSE on the check points in meters 
points for test area 
for test area 
Warsaw test area 
Cracow test area 
Warsaw/Cracow 
Warsaw/Cracow 
X 
Y 
X 
Y 
12 
16/12 
0.44 
0.46 
0.44 
0.46 
! 10 
18/14 
0.45 
0.47 
0.46 
0.44 
8 
20/16 
0.46 
0.48 
0.45 
0.46 
6 
22/18 
0.53 
0.48 
0.57 
0.53 
5 
23/19 
0.73 
0.82 
0.84 
0.92 
Table 1. Geometric correction results of the Resurs DK-1 images in first variant. 
Model of geometric correction of the Resurs DK-1 scenes based 
on first variant is sufficient for obtained results below half pixel 
of the source image. The accuracy on 8 independed check 
points was RMSE X = 0.45m and RMSE Y = 0.46m. Using the 
orbital parameters of the Resurs DK-1 satellite caused the 
limitation of measure of control points required for geometric 
correction. The results obtained in this variant show, what is 
influence of real orbital satellite parameters on the 
mathematical model of geometric correction of the Resurs DK- 
1 images. Obtainment of the results of geometrical correction 
below one pixel of the source image is possible thanks to use 
just 5 control points. Enlargement of the number of measured 
control points to 8 let’s get in this variant the optimum result. 
The second variant of the geometric correction uses a number 
of ground control points. Unknowns of Rational Polynomial 
Coefficients (RPC) were calculated on the basis of ground 
coordinates of control points measured in the field and on the 
image. The accuracy of RPC parameters depends on the 
number of control points, accuracy of their identification in the 
field and on the image, and their distribution on the scene. RPC 
data have been estimated independently from different number 
of control points. The results of geometric correction are 
shown in (Tab. 2). 
Number of 
control points 
Number of check 
points for test area 
Warsaw/Cracow 
Number of 
polynomial 
coefficient 
RMSE on the check points in meters 
Warsaw test area 
Cracow test area 
X 
Y 
X 
Y 
24 
4/0 
12 
0.32 
0.36 
0.37 
0.36 
22 
6/2 
11 
0.34 
0.32 
0.36 
0.38 
20 
8/4 
10 
0.40 
0.38 
0.39 
0.38 
18 
10/6 
9 
0.45 
0.45 
0.41 
0.44 
16 
12/8 
8 
0.52 
0.46 
0.48 
0.45 
14 
14/10 
7 
0.58 
0.62 
0.49 
0.55 
12 
16/12 
6 
0.76 
0.82 
0.69 
0.71 
10 
18/14 
5 
0.82 
0.90 
0.88 
0.97 
8 
20/16 
4 
1.04 
1.18 
1.22 
1.34 
Table 2. Geometric correction results of the Resurs DK-1 images in second variant. 
Delimitation of the optimum degree of the polynomial for 
estimation of the relationship between image matrix and 
geodesic coordinate system was the principle in analyzed 
variants. Obtainment of the result of the geometrical correction 
on the level of standard deviation of measure and identification 
of check points is possible during delimitation of 9 polynomial 
coefficients on the basis of measure 18 control points. 
Enlargement the number of control points needed for determine 
of RPC give the result of geometric correction RMSE X = 
0.32m and RMSE Y = 0.36m. However in this case the 
necessity of measurement as much as 4 control points disqualify 
this variant of geometrical correction. On the basis of results 
analysis in the individual variants of geometric correction was 
affirmed that obtainment of the accuracy below one pixel of the 
source image guarantees the measurement only 10 control 
points evenly distributed on the scene. Taking into account the 
economical aspect of geometrical correction of Resurs DK-1 
scenes in particular possibility to minimum of limitation of 
expensive field measurements it should to use the first variant 
exclusively. However his final choice is determined by the 
access to original orbital sensor data. Additionally analyzing a’ 
priority and a’ posterior errors on the control points it was