Rational Functions and Potential for Rigorous Sensor Model Recovery

Abstract

achieve a higher accuracy and to be effective for implementaRational functions (RFs) have been applied in photogrammetry tion. Madani (1999) discussed advantages and disadvantages of and remote sensing to represent the transformation between RFs compared with rigorous sensor models. He tested the accuthe image space and object space whenever the rigorous model racy of the RF solution using 12 SPOT Level 1A scenes of the is made unavailable intentionally or unintentionally. It at- Winchester area in Virginia. Using two stereo image pairs with tracts more attention now because Ikonos high-resolution 50 ground (control/pass) points, the RMS error of the planimetimages are being released to users with only RF coefficients. ric coordinates estimated from the differences between the This paper briefly introduces the RF for photogrammetric known and computed ground coordinates is 0.18 m. The RMS processing. Equations of space intersection with upward RF error of the Z coordinate is about 10 m. It is concluded that the are derived. The computational experimental result with one- RF expressed the SPOT scenes very well and that properly meter resolution Ikonos Geo stereo images and other airborne selected RFs can be used in operations of digital photogramdata verified the accuracy of the upward RF-based space metric systems. Tao and Hu (2000; 2001b) and Tao et al. (2000) intersection. We demonstrated different ways to improve the gave a least-squares solution for RF parameter generation and geopositioning accuracy of Ikonos Geo stereo imagery with assessed the fitting accuracy using simulated DEM data, a SPOT ground control points by either refining the vendor-provided scene, and an aerial image. In their comprehensive investigaIkonos RF coefficients or refining the RF-derived ground tion, various scenarios with different polynomial orders and coordinates. The accuracy of 3D ground point determination different forms of the denominators were tested and compared. was improved to 1 to 2 meters after the refinement. Finally, It was found that RFs are sensitive to the distribution of control we showed the potential for recovering sensor models of a points (CPs). If CPs are well distributed, RFs normally perform frame image and a linear array image from the RF. much better than regular polynomials (no denominator). Hu and Tao (2001) proposed two methods to update solutions of