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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004 
and 2 show the results for the cases of using the 3D and 2D 
affine LBTMs, respectively. The results reveal that the 
accuracy level of about 2 m in X and Y directions can be 
achieved by applying 12 GCLs to the 3D affine LBTM. 
However, the accuracy declined to about 5 m in X and 9 m in Y 
when using the 2D affine LBTM and the same number of 
GCLs. This last finding is consistent with our expectations and 
the results obtained from applying the 2D affine LBTM to the 
simulated data because the effects of the terrain elevation 
differences (about 450 m in this study area) are not considered. 
In this case, the results in the X direction are better than the 
results in the Y direction (when using the 2D affine LBTM) 
because of the along track capturing techniques. In general, the 
results are comparable to what was achieved by using the 3D 
affine model and GCPs in Shi and Shaker, 2003. In addition, 
the results suggest that the developed LBTM is applicable to 
and reveals an accurate performance for high-resolution satellite 
imagery rectification. 
  
  
Figure 4. GCLs and checkpoints distribution of the Hong Kong 
data set. 
4. CONCLUSIONS AND FURTHER WORK 
The Line Based Transformation Model is proposed for the 
rectification of high-resolution satellite imagery. This is an 
attempt to establish a new model, which can deal with linear 
features and/or linear features with a number of GCPs. In this 
model, most of the problems encountered in previous models 
using linear features have been overcome. In addition, sensor 
calibration and satellite orbit information, which are withheld 
from the user community for most of the new high-resolution 
satellites, are not required. 
The underlying principle of the new model is that the line unit 
vector components of a line segment could replace the point 
coordinates in the representation of the ordinary 3D/2D affine 
and conformal models. Any two points along a line segment 
could be measured in image and object spaces to calculate the 
line unit vector. It is noteworthy that the two line segments in 
image and object spaces are not required to be the same, but are 
required to be segments of conjugate lines. Experiments with 
synthetic and real data have been conducted and the results 
prove the applicability of the new model for image rectification. 
The analysis of the results obtained from the LBTM indicates 
that the slope values of GCLs, which are based on the 
differences in terrain elevations along the line and the line 
length, significantly affect the accuracy of the results. The 
lower the slopes of GCLs are, the higher accuracy can be 
855 
attained, and visa versa. No significant differences in the results 
could be recorded for flat terrain. 
Currently, the applicability of the developed model for the 
rectification of images produced by several high-resolution 
satellites such as IRS-1D, SPOT-5 and QuickBird is under 
study. In addition, the effects of the sensor inclination angles on 
the performance of the model and possible limitations of the 
model are examined. Finally, we are also investigating the 
possibility of extending the use of the new model for frame 
cameras. 
ACKNOWLEDGMENTS 
This project is fully supported by the Hong Kong Polytechnic 
University (project no. G-W129). The Ikonos image for Hong 
Kong used in this study is from CERG project ‘Optimum 
Compression of One-Meter Satellite Images for mapping 
purposes.” The author would like to acknowledge Dr. Bruce 
King for his invaluable contributions to the work. He also 
expresses his gratitude to Dr. John Shi. 
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