The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part Bl. Beijing 2008 
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blue one, so the rectification accuracy in X direction is relative 
high for flat terrain. The trend and value of yellow line is 
closed to the red on, but the yellow one is the direction of Z, 
which has the highest requirement of accuracy, Z direction for 
flat terrain not absolutely reach the requirement of accuracy 
when the numbers of GCLs increase to 50. 
For the hilly terrain, the maximum RMS error for the three 
directions is less than 10m, this value is in the requirement of 
tolerance for X and Y directions. Only the numbers of GCLs 
from 4 to 8, the various of the trends line of three directions are 
relative sharp, and the various for Z direction is relative 
obvious, the RMS errors can less than 4m on all the three 
directions when the numbers of GCLs more than 24. As shown 
in Figure 5b, the lowest line is also the blue one when the 
GCLs number less than 48, but when the numbers over 48, the 
smallest error is the Z direction. The RMS errors for all the 
three directions are in tolerance until the numbers of GCLs 
over 20. 
20.00 
15.00 
10.00 
5.00 
0.00 
4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 
(a) Results of flat terrain 
4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 
(b) Results of hilly terrain 
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 
(c) Results of mountainous terrain 
Figure 5: Effects of the number and the slope of the GCLs on 
the three conditions of terrain accuracy of the assumed data 
using 3D affine LBTM 
For the mountains terrain shown in Figure 5c, the maximum 
RMS error for the three directions is over 40m, this value is 
higher than the requirement of tolerance. For X direction, the 
maximum RMS errors is less than 10m, in the requirement of 
tolerance for mountainous terrain. For the Y direction, when 
the numbers of GCLs from 4 to 8, the variety of the trend line 
is sharp, and the maximum value of RMS error is about 25m. 
After the GCLs numbers reach to 8, the trend become mild and 
has high accuracy. The various for Z direction is violent, the 
maximum error is over 40 when use 8 ground control line. 
Until the numbers of GCLs reach to 36, the RMS error reaches 
to a perfect value for the accuracy of rectification. Because of 
the difference of elevation for mountainous terrain is over 
1000m, the elevation influence for accuracy of the model is 
higher than the other two directions. 
4.3 Compare of different conditions of terrain 
For different conditions of terrain, the accuracy influences will 
have some differences. This section will compare and discuss 
the accuracy differences of three conditions of terrain in three 
ground directions. The comparing of various trends for terrain 
condition in X, Y and Z direction is shown in Figure 6 
respectively. 
As presented in Figure 6a, b and c, the trend lines of RMS 
errors of flat and hilly terrains are nearly overlapping in all the 
ground directions, it is to say when the errors range influence 
of coordinates in object space and stereo image space are 
similar to each other, the accuracy of rectification for flat and 
hilly terrain have little difference until the numbers of GCLs 
reach to standard numbers. 
12.00 
10.00 
8.00 
6.00 
4.00 
2.00 
0.00 
25. 00 
20. 00 
w 15 - 00 
£ io. oo 
5. 00 
0. 00 
4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 
(a) Results of X direction 
mL 
s. 
=*_|E 
4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 
(b) Results of Y direction 
50.00 
40.00 
M 30.00 
V) 
ffS 20.00 
10.00 
0.00 
4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 
(c) Results of Z direction 
Figure 6: Effects of the number and the slope of the GCLs on 
the three directions on the ground accuracy of the assumed data 
using 3D affine LBTM 
And the trend lines of RMS errors of mountainous terrain are 
higher than the other two, the accuracy of rectification is higher 
when the maximum difference of ground elevation is over 
1000m and the slope of GCLs is increasing. The trend various 
speed of the mountainous terrain is slower than flat and hilly 
terrain, so the mountainous terrain needs more GCLs to reach 
to the requirement. On the other hand, because of the same 
errors range for original artificial data, the mountainous and 
hilly might higher in the real data sets. 
5. CONCLUSIONS 
After computation and analysis above, the conclusions on the 
result from artificial data can be obtained as followed: 
1) 3D affine LBTM can be used as rectification model for 
different conditions of terrain when the GCLs density 
reach to 50 every 10x10 square kilometers area, the