The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B4. Beijing 2008 
1317 
THE AFFINE PROJECTION MODEL AS A TOOL 
FOR RAPID GEO-CODING OF IRS-P5 SATELLITE IMAGERY 
F. Dadras Javan 3 *, A. Azizi b 
a Dept. of Geomatic Engineering, Faculty of Engineering, University of Tehran, Iran - fdadrasjavan@ut.ac.ir 
b Centre of Excellence for Disaster Management, Dept, of Geomatic Engineering, College of Engineering, University of 
Tehran, Iran - aazizi@ut.ac.ir 
KEY WORDS: High Resolution, Pushbroom, IRS-P5, Mapping, Sensor Modeling, Rational Function Model, 3D affine 
transformation, Hazards 
ABSTRACT: 
Nowadays, the information content of the satellite imageries as a means for the disaster forecasting and management has attracted the 
worldwide attention more than before. On the other hand, linear array satellite images such as Spot, Ikonos, QuickBird, IRS, etc., 
with their flexibility in acquiring stereo coverage over any part of the globe, have proven to be an excellent replacement for the other 
space-borne imaging systems such as digital frame cameras or whiskbroom technologies. The first step for using such data is Geo 
coding. High resolution data increase the need for higher accuracy data modeling. Up to now different models with different 
accuracy have been discussed. These models are divided into two main groups of the so called rigorous and non-rigorous models. 
The rigorous approaches are the most accurate but need crucial data such as satellite ephemeris and inner orientation parameters 
which are not always available. The non-rigorous models such as rational polynomials, DLT or 3D affine transformations on the 
other hand are less accurate but enjoy the advantage of being independent from the auxiliary information. In line with several other 
research works already performed by other researchers, this paper sets its main goal to compare the simple 3D affine model, as a 
replacement transformation for the more sophisticated rational function approach. The adopted strategy is based on generating virtual 
ground control points using rational polynomials intersection by means of available RPCs. The generated virtual GCPs provide a 
reliable data for estimating the degree of fitness of the 3D affine model to the rational polynomial transformation. This paper reports 
the result of the tests conducted on a high resolution stereo IRS-P5 satellite image. Other related issues including different methods 
for estimating initial values needed for the solution of the rational polynomials intersection, such as DLT, 3D affine and truncated 
rational polynomials are also presented and discussed. 
1. INTRODUCTION 
After the recent Tsunami and earthquake disasters with their 
devastating effects, the information content of the linear array 
satellite imageries as a means for the disaster forecasting and 
management has gained much more importance than before. 
One of the crucial preliminary stages after any natural disaster is 
the rapid mapping of the damaged areas using satellite 
imageries. This process entails a great deal of computations and 
field works which hinder the rapid response to the preliminary 
mapping demands. Two main approaches are used for geo 
coding of linear array imageries. The first approach is the so 
called rigorous model. This approach is based on the physical 
modeling of the linear array motion and attitude variations. 
However, this Method may not be appropriate for rapid 
mapping since it requires necessary orbital information as well 
as the sensor calibration parameters which may not be 
accessible. The second approach uses the rational polynomial 
model (RFM) as a replacement for the rigorous method. Again, 
the RFM coefficients are included in the metadata and may not 
be accessible in all circumstances. The solution of the RFM also 
requires the regularization and normalization. The RFM 
intersection is solved iteratively and hence demanding initial 
values for the object coordinates. Moreover, the solution may 
undergo computational collapse for a given dataset. These 
complications make these approaches non-optimal for rapid 
mapping applications. Taking into account the fact that high 
resolution satellite images inevitably have large focal length, it 
can be seen immediately that these imageries enjoy a very 
narrow field of view. The very small camera field of view 
makes the incoming signals almost parallel. This particular 
geometry provides a simple linear-parallel relationship between 
the image space and the object space and makes a simple eight 
parameters affine transformation optimum for geo referencing 
applications. Simplicity of the formulation (i.e. only eight affine 
parameters for the entire scene), few numbers of required 
GCP’s and the achieved accuracy makes this approach very 
attractive from the rapid mapping point of view. Nevertheless, 
in practice several unpredicted factors my influence the 
accuracy of the transformation. One of the major influential 
factors in this respect is the terrain relief undulations. This 
approach has been already evaluated by different researchers 
worldwide and reasonably accurate results have been reported 
using only few numbers of GCP’s (Fraser et al., 2004; Fraser et 
ah, 2003; Yamakawa et al 2004). The main task undertaken in 
this study is to investigate the fitness accuracy of the 3D affine 
model with the RFM, as far as the terrain independent scenario 
is concerned. The adopted strategy for the evaluation of the 
preliminary results is based on the generation of a network of 
the so called virtual GCP’s whose coordinates are obtained by 
the available RPC’s. Few number of well distributed virtual 
GCP’s serve as the reference data to determine the 
transformation parameters of the 3D affine transformation and 
the rest of the virtual ground points are considered as check 
points for the evaluation of the absolute accuracy. All accuracy 
figures are presented for the check points in the object space. 
This strategy for the accuracy evaluation adopts the accuracy of 
the virtual ground points generated by the RPCs as a criterion 
for the evaluation of the fitness accuracy of the affine model. 
In the sections that follow the basic concepts of the RFM and 
the 3D affine models are reviewed first. This is then followed 
by the review of the formulations of the RFM intersection. The