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The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part Bl. Beijing 2008 
When we use under sampling there isn’t ground control points 
in all places of high slope and height distributions of control 
points are restricted. Number of ground control points are 44 
and number of check points are 52. Figure 5 shows distribution 
of control points. 
Figure 5. Ground control points distribution in under sampling 
Results of the experiments were shown in table 3. Regards to 
this table we can conclude: 
• Accuracies of check points have decreased in all 
models because control points hanven’t good height 
distribution and all points are placed in low height 
levels. This shows that in under sampling case 
accuracies for check points aren’t high. 
• Approximately accuracies of control points have 
improved in all models because all control points are 
nearly in the same height level and fitting of rational 
functions to these points was better. 
• By increasing rational functions’ order, their accuracies 
have improved such that third order rational functions 
P2& F4 
( ) have the best accuracy. 
N.O.GCPs 
N.O.CKPs 
RMSECKPXYZ 
(cm) 
RMSECNPXYZ 
(cm) 
lorderRFM(P2#>4) 
44 
52 
8.410 
5.235 
2orderRFM(P2^P4) 
44 
52 
50.041 
0.960 
3orderRFM(P2#>4) 
44 
52 
1.407 
0.006 
2orderRFM(P2=P4) 
44 
52 
21.059 
1.329 
3orderRFM(P2=P4) 
44 
52 
6.707 
0.021 
Inverse lorderRFM 
(P2*P4) 
44 
52 
1935.72 
98.689 
Inverse 2orderRFM 
(P2^P4) 
44 
52 
1014.16 
2.496 
Inverse 3orderRFM 
(P2#>4) 
44 
52 
Table 3. Results obtained from simulated data in under sampling 
For the better analysis of residuals, first order rational functions 
error vectors of X, Y and Z elements in optimum sampling, over 
sampling and under sampling were shown in figure 6 and 7. For 
seeing error vectors more obvious, some of these vectors were 
shown. In all cases of sampling, rational functions’ errors in Z 
direction are much more than X and Y directions, but the 
errors in X direction are the same as Y direction. Regarding 
these figures it can be see that maximum error is high, but we 
saw in previous tables, the average error of first order ational 
functions is approximately 6cm for optimum sampling and over 
sampling and the error is nearly 10cm for under sampling. 
(a) 
(c) 
Figure 6. Planimetric error vectors of first order rational functions in a) optimum sampling b) over sampling c) under sampling