The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B5. Beijing 2008 
760 
Figure 4. DLT with first 3th order parameter 
Figure 1. 3D plot of object points 
* C»V 4* fijX 4» 
* C t X + 4* fjS 4* 1 ( 1 ) 
*r» 4* 
- t*Y 4* C>-+* I 
6î.J4» g,y 4» Cî -4* 4- 6 r F 3 ■»> 4> 
r * - fV + r ,X + + egT l ~ c^Z i - 1 (2 ) 
t _ (¡ijC 4 &§I 4" 4“ &$T‘ 4 4” &■ 
f 4 f »J* «♦» f 4* •4 f * 4» f ^ *4 lk 
As we see in table 1 residuals of measured point decrease with 
added parameters. This decrease in RMSE may be from adding 
new parameters. But with attention to Figure 3 and Figure 4 we 
can understand that this parameters decrease the effect of radial 
lens distortion. 
By adding new special parameters to DLT function the problem 
of camera calibration could be eliminate linearly. These 
parameters could satisfy lens distortion deformation. The 
decrease in RMSE is shown in graphic plot in Figure 5. 
4. CONCLUSION 
In this paper we analyse radial lens distortion with this 
parameters. It could be examine with other camera parameters 
such as tangential lens distortion and finding principal point. 
The intersection model of rational function could be very useful 
and simple procedure if the model computing solved. This idea 
is a good issue in this area. 
ACKNOWLEDGEMENTS 
We would acknowledge National Cartographic Centre (NCC) 
of Iran for supports in photographs and other technique we need. 
Figure 2. One sample of images 
Image 1 
Image 2 
Image 3 
DLT 
1.49 
1.63 
1.65 
First step 
0.75 
0.90 
1.02 
Second step 
0.71 
0.84 
0.91 
Third step 
0.53 
0.68 
0.82 
Table 1. List of residuals derive from four stages 
Figure 3. DLT without any added parameters applied to points 
REFERENCES 
Madani, M., 1999. Real-time sensor-independent positioning by 
rational functions. Proceeding of ISPRS Workshop on 
‘‘Direct versus Indirect Methods of Sensor Orientation", 
25-26 November, Barcelons, Spain, pp. 64-75. 
Tao, C.V., and Y. Hu, 2001. A comprehensive study of the 
rational function model for photogrammetric processing. 
Photogrammetric Engineering & Remote Sensing, 67(12), 
pp. 1347-1357.