The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B4. Beijing 2008 
Number of 
RMSE 
RMSE 
RMSE 
RMSE 
GCLs 
(P) 
(a) 
(X) 
00 
fi 
6 
0.56m 
0.049 0 
0.91m 
1.26m 
parameters 
10 
0.34m 
0.052° 
1.03m 
1.06m 
15 
0.30m 
0.052° 
1.03m 
1.04m 
8 
parameters 
6 
0.50m 
0.061° 
1.10m 
1.34m 
10 
0.48m 
0.066° 
1.17m 
1.03m 
15 
0.47m 
0.066° 
1.15m 
1.03m 
DLT 
10 
0.94m 
0.042° 
2.16m 
1.73m 
15 
0.90m 
0.045° 
1.77m 
1.01m 
Table 1. RMSE for check-lines and check-points 
In order to test the stability of the estimated parameters, another 
experiment is conducted using the 6 parameters transformation 
model with different sets of GCLs. For each experiment, the 
transformation parameters are computed. Results in table 2 
shows the minimum, maximum, and mean values of the 
calculated transformation parameters. In addition, table 2 shows 
the transformation parameters calculated using the point-based 
6 parameters transformation model with all the 12 GPS points 
used as GCPs. The table shows that the differences between the 
mean values of the transformation parameters and the point- 
based transformation parameters are insignificant. Table 3 
shows the statistics for the differences in the parameters of the 8 
parameters transformation model using different sets of GCLs 
and the values computed using the point-based transformation 
model. 
Min 
Max 
Mean 
Point- 
based 
al 
0.8840 
0.8811 
0.8827 
0.8827 
a2 
-0.0020 
-0.0075 
-0.0041 
-0.0043 
a3 
0.6913 
-1.3231 
0.0163 
0.000 
a4 
0.0529 
0.0514 
0.0522 
0.0520 
a5 
0.9150 
0.9131 
0.9138 
0.9146 
a6 
0.1972 
-0.4049 
0.0319 
0.000 
Table 2. Statistics for the differences in the parameters of the 6 
parameters transformation model using different sets 
of GCLs 
Min 
Max 
Mean 
Point- 
based 
al 
0.881 
0.883 
0.882 
0.882 
a2 
-0.007 
-0.001 
-0.004 
-0.004 
a3 
-1.283 
0.685 
0.025 
0.431 
a4 
0.051 
0.530 
0.052 
0.052 
a5 
0.913 
0.914 
0.913 
0.914 
a6 
-0.516 
0.332 
0.023 
0.074 
a7 
0.000 
0.000 
0.000 
0.000 
a8 
0.000 
0.000 
0.000 
0.000 
Table 3. Statistics for the differences in the parameters of the 8 
parameters transformation model using different sets 
of GCLs 
5. CONCLUSIONS 
This research presents the potential of using straight lines to 
rectify a single panchromatic IKONOS image. The research 
showed the process of developing the line-based 2D 
transformation models. In addition, the research investigates the 
use of the line-based 6-parameters, 8-parameters, and DLT 
transformation models to rectify panchromatic IKONOS images. 
Results showed less than 1.5 meters RMSE in the horizontal 
direction using 6 to 15 GCLs. Moreover, the results showed that 
the computed parameters are stable and equivalent to the 
parameters computed using the point-based transformation 
models and the differences are insignificant. The results suggest 
the use of linear features to rectify IKONOS images and other 
high-resolution satellite images such as QuickBird. This will 
allow reducing the number of ground control points and will 
eventually reduce the time and cost of the surveying effort. 
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