C. Vincent Tao 
  
IMAGE RECTIFICATION USING A GENERIC SENSOR MODEL — RATIONAL FUNCTION MODEL 
C. Vincent TAO, Yong HU 
Department of Geomatics Engineering, The University of Calgary, Canada 
> 
J. Bryan MERCER, Steve SCHNICK 
Intermap Technologies Ltd., Canada 
2 
Yun ZHANG 
Department of Geodesy and Geomatics Engineering, University of New Brunswick, Canada 
WG IV/4 
KEY WORDS: Sensor Model, SAR, Polynomial Model, Rational Function Model, Rectification. 
ABSTRACT 
The Rational Function Model (RFM) has been considered as a generic sensor model. Compared to polynomial models 
widely used, RFM is essentially a more generic and expressive form. The RFM is technically applicable to all types of 
sensors such as frame, pushbroom, whiskbroom and SAR etc. With the increasing availability of the new generation 
imaging sensors, accurate and fast rectification of digital imagery using a generic sensor model becomes of great 
interest to the user community. In this paper, the technical viability of use of the RFM is examined. This paper firstly 
presents a brief overview of the geometric models used for the rectification of digital imagery. These models are the 
collinear equations based differential rectification model, the polynomial model, the projective transform model, the 
extended direct linear transform model and the RFM. The remarks on their properties, and the advantages and 
disadvantages for different models are discussed so that one will have a better understanding of the generic nature of the 
RFM. The two solution methods to the RFM, namely direct solution and iterative solution, are then provided. In fact, 
iterative solution is more rigorous in theory but requires many iterative steps to achieve the solution. Finally, the test 
results using real-world data sets are described. Comprehensive experiments have been carried out to evaluate the 
viability of the RFM solutions. 
1 BACKGROUND 
Sensor models are required to restitute the functional relationships between the image plane and the ground space. They 
can be grouped into two classes, physical sensor models and generalized sensor models. Physical sensor models are 
more rigorous and normally provide better accuracies since the model parameters employed represent the physical 
imaging process of sensors. However, building of a physical sensor model requires information of the physical sensor 
and its imaging model. It is realized that this information is not always available, especially for images from 
commercial satellites (e.g., IKONOS). The generalized sensor models are independent on sensor platforms as well as 
sensor types. Such properties have made generalized sensor models very popular in the remote sensing community. The 
typical generalized sensor models are polynomial-based ones. Their capabilities have been widely tested and examined. 
The RFM is essentially a generic form of polynomial models. However, there are few publications that address its 
viability, accuracy and stability. In Tao and Hu (2000), the numerical properties of the RFM and its detailed least square 
solutions are investigated and documented. The RFM solution has been tested using various data sets including 
simulated data, aerial photogrammetry data as well as SPOT data. In this paper, we describe results of the recent tests 
conduced in conjunction with the Intermap Technologies Corporation, Canada. 
The objective of this work is to test the viability of the use of RFM to image rectification using Intermap SAR 
(synthetic aperture radar) imagery and DEMs obtained from Intermap STAR-3i system. STAR-3i is an X-band, 
interferometric airborne SAR system that is owned and commercially operated by Intermap Technologies. The system 
is able to produce DEMs with sample spacing of 2.5 meter and with vertical accuracy at the meter to sub-meter level 
(Bryan and Schnick, 1999). The System can also produce ortho-rectified SAR magnitude imagery (ORIs) by using 
direct GPS/INS georeferencing technology. In fact, both DEMs and ORIS are created simultaneously as part of STAR- 
3i processing. With the utilization of the ORIs and DEMS, the image rectification process can be simplified since the 
  
  
874 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000.