282 
image and the refined second-order RFM orthorectified image 
are compared in Table 1: 
CKP 
Traditional RFM (RMS) 
Refined RFM (RMS) 
X 
Y 
Total 
X 
Y 
Total 
1 
11.392 
15.828 
19.502 
4.246 
6.032 
7.377 
2 
13.849 
9.316 
16.690 
4.813 
3.280 
5.824 
3 
3.718 
8.088 
8.902 
0.324 
2.107 
2.132 
4 
21.844 
15.692 
26.896 
7.588 
4.275 
8.709 
5 
28.153 
47.507 
55.222 
14.792 
16.377 
22.068 
6 
19.101 
35.256 
40.098 
14.011 
12.266 
18.622 
7 
8.078 
11.556 
14.100 
0.972 
4.136 
4.249 
8 
31.796 
14.616 
34.995 
9.228 
2.250 
9.498 
9 
15.372 
11.467 
19.178 
6.281 
1.374 
6.429 
10 
4.612 
36.583 
36.873 
0.876 
12.227 
12.258 
mean 
15.791 
20.591 
27.245 
6.313 
6.433 
9.717 
max 
31.796 
47.507 
55.222 
14.792 
16.377 
22.068 
Table 1: Residual errors table of CKPs (meter) 
Figure 8. RMS plot of CKPs based on refined RFM 
Figure 9 and Figure 10 illustrates the comparison of errors 
vector of CKPs using in different orthorectified methods. Figure 
9 illustrates errors vector map of CKPs based on traditional 
RFM; Figure 10 illustrates the errors vector map of CKPs based 
on refined RFM. Obviously, the geometric positioning accuracy 
of orthorectified image by using refined RFM has been greatly 
increased no matter in the direction or in the size. 
The residual errors of the traditional first-order RFM 
orthorectified image: in X direction, the mean of residual errors 
is 15.791m, and the maximum is 31.796m; in Y direction, the 
mean is 20.591m, and the maximum is 47.507m. The mean of 
total residual errors is 27.245m, and the maximum is 55.222m. 
The maximum residual error occurs at CKP 5, whose height is 
also maximum shown by DEM, while the chosen CKP 10, 20, 
23, 26 around the CKP 5 just lie out of the high area. With such 
GCPs involved in fitting, RFM does not consider the height 
change of the CKP 5 properly. The distribution of residual 
errors at each CKP is shown in Figure 7: 
According to the table analysis shows: compared to traditional 
RFM, the refined RFM has improved the accuracy considerably. 
Due to the increase of the number of GCPs from 6 to 15, the 
fitting of RFM becomes more reasonable, with the error limited 
in a certain range. Using the refined RFM to rectify the image 
can eliminate radiation distortion, tangential distortion, affine 
distortion, and the correlation such as translation and distortion, 
which results in a good improvement. Meanwhile, experimental 
data shows that: in X direction, the mean of residual errors is 
6.313m, and the maximum is 14.792m; in Y direction, the mean 
is 6.433m, and the maximum is 16.377m. The mean of total 
residual errors is 9.717m, and the maximum is 22.068m. The 
distribution of residual errors at each CKP is shown in Figure 8: 
Figure 9. Errors vector map of CKPs based on traditional RFM 
Figure 10. Errors vector map of CKPs based on refined RFM