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The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part Bl. Beijing 2008 
Figure 13. Planimetrie error vectors of first order rational 
functions 
Figure 14. Height error vectors of first order rational 
functions 
4 CONCLUSION 
For the analysis of dependence of rational functions and 
height distribution of control points, their accuracies were 
analyzed in three different cases of control points height 
distribution. At last we saw that rational functions are 
dependent to height distribution of control points and 
accuracies in under sampling are much degraded but because 
of the accuracies in over sampling and optimum sampling 
aren’t too different, using over sampling for rational functions 
are not necessary 
REFERENCES 
1- McGlone, C., 1996 :"Sensor modeling in image 
registration," Digital Pgotogrammetry : An Addendum 
(C. W. Greve, editor), American Society for 
Photogrammetry and Remote Sensing, Bethesda, 
Maryland, pp. 115-123. 
2- Paderes, Jr., F. C., Mikhail, E. M., Fagerman, J. A., 1989. 
Batch and on-line evalution of stereo SPOT imagery, 
Proceedings of the ASPRS-ACSM Convention, 
Baltimore, April, pp. 31-40. 
3- Yang, X., 2000 : "Accuracy of rational function 
approximation in photogrammetry," Proceedings of 
ASPRS Annual Convention, Washington D.C. May 22- 
26. 
4- Baltsavias, E., Pateraki, M., and Zhang, L., 2001, 
Radiometric and geometric evaluation of IKONOS Geo 
images and their use for 3D building modeling. 
Proceedings of Joint ISPRS Workshop High Resolution 
Mapping from Space 2001, 19-21 September (Hannover: 
International Society of Photogrammetry and Remote 
sensing (CD-ROM)), pp. 15-35. 
5- Toutin, T., Cheng, P., 2000. Demystification of 
IKONOS Earth Observation Magazine (EOM), 9(7): 17- 
21. 
6- OpenGIS Consortium, 1999. The OpenGIS Abstract 
Specification - Topic 7: The Earth Imagery Case, 
http://www.opengis.org/public/abstract/99-107.pdf. 
7- NIMA., 2000 : "The compendium of controlled 
extensions (CE) for the national imagery transmission 
format (NITF), version 2.1. 
8- Tao, C. V., Hu, Y., 2000: "A Comprehensive Study on 
the Rational Function Model for Photogrammetric 
Processing," Photogrammetric Engineering and Remote 
Sensing. 
9- Tao, C. V., Hu, Y., 2001a : "The rational function model 
- a tool for processing high-resolution imagery," Earth 
Observation Magazine (EOM), 10(1) : 13-16. 
10- Tao, C. V., Hu, Y., 2001b : "3-D Reconstruction 
Algorithms based on the Rational Function Model," 
Proceeding of Joint ISPRS Workshop on "High 
Resolution Mapping from Space 2001," Hannover, 
September 19-21. 
11- Madani, M., 1999 : "Real-time sensor-independent 
positioning by rational functions," Proceedings of ISPRS 
Workshop on "Direct versus indirect Methods of Sensor 
Orientation," 25-26 November, Barcelona, Spain, pp. 
64-75.