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The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part Bl. Beijing 2008 
4000 
Figure 9. Ground control points distribution in over sampling 
Number of points that we have chose in over sampling are 185 
GCPs and 120 check points. 3D distribution of ground control 
points were shown in figure 9. 
Regards to table 5, accuracies of all models are more than 
optimum sampling. Other results are the same as optimum 
sampling 
4000 
Figure 10. Ground control points distribution in under sampling 
Number of points in under sampling are 60 GCPs and 245 
check points. Distribution of GCPs were shown in figure 10. 
Results of experiments were reported in table 6. Regards to this 
table, accuracies of models are much degraded on check points 
respect to over sampling and under sampling but accuracies are 
increased on GCPs. Other results are the same as other sampling 
cases. 
N.O.GCPs 
N.O.CKPs 
RMSECKPXYZ 
(cm) 
RMSECNPXYZ 
(cm) 
lorderRFM(P2^P4) 
185 
120 
4.680 
5.505 
2orderRFM(P2^P4) 
185 
120 
0.676 
0.976 
3 orderRFM (P2^P4) 
185 
120 
0.020 
0.022 
2orderRFM(P2=P4) 
185 
120 
2.150 
2.308 
3orderRFM(P2=P4) 
185 
120 
0.080 
0.086 
Inverse 1 orderRFM 
(P2#>4) 
185 
120 
60.705 
64.281 
Inverse 2orderRFM 
(P2#P4) 
185 
120 
2.202 
2.473 
Inverse 3 orderRFM 
(P2^P4) 
185 
120 
0.010 
0.010 
Table 5. Results obtained from aerial data in over sampling 
N.O.GCPs 
N.O.CKPs 
RMSECKPXYZ 
(cm) 
RMSECNPXYZ 
(cm) 
lorderRFM(P2^P4) 
60 
245 
14.919 
2.890 
2orderRFM(P2^P4) 
60 
245 
9.342 
0.520 
3orderRFM(P2^P4) 
60 
245 
0.613 
0.005 
2orderRFM(P2=P4) 
60 
245 
18.367 
0.990 
3orderRFM(P2=P4) 
60 
245 
1.129 
0.036 
Inverse 1 orderRFM 
(?2fP4) 
60 
245 
143.310 
17.596 
Inverse 2orderRFM 
(P2#>4) 
60 
245 
29.040 
0.980 
Inverse 3orderRFM 
(P2^P4) 
60 
245 
0.431 
0.004 
Table 6. Results obtained from aerial data in under sampling 
First order rational functions error vectors of X, Y and Z 
elements in optimum sampling, oyer sampling and under 
sampling were shown in figure 11 and 12. Some of these 
vectors were eliminated to the figures be more obvious. For 
aerial data like simulated data, rational functions’ errors in Z 
direction are much more than X and Y directions for all three 
sampling cases but the amounts of errors in X and Y directions 
are the same. As can be seen, maximum error is high but by 
regards prvious tables, check points average errors of first order