THE AFFINE PROJECTION MODEL FOR SENSOR ORIENTATION: 
EXPERIENCES WITH HIGH-RESOLUTION SATELLITE IMAGERY 
T. Yamakawa, C.S. Fraser 
Department of Geomatics, University of Melbourne, Melbourne VIC 3010, Australia 
yamakawa(@sunrise.sli.unimelb.edu.au, c.fraser@unimelb.edu.au 
Commission I, WG V/5 
KEY WORDS: Sensor orientation, high resolution satellite imagery, affine projection, IKONOS, QuickBird 
ABSTRACT: 
Accompanying the successful deployments of the IKONOS and QuickBird high-resolution satellite imagery (HRSI) systems have 
been a number of investigations into the utilisation of HRSI for the extraction of precise 3D metric information. 
Among the 
promising ‘alternative’ sensor orientation models investigated has been an approach based on affine projection. This model has 
previously been reported as performing well in experiments with stereo configurations of IKONOS imagery. In situations where 
precise sensor and orbital information is not fully accessible, empirical sensor orientation models requiring only a modest number of 
ground control points become an attractive proposition. This paper briefly summarises the theory and validity of the affine model as 
configured for application to sensor orientation and geopositioning for HRSI. The results of experiments with three HRSI stereo 
scenes are also presented, in which sub-pixel accuracy was achieved from both IKONOS and QuickBird imagery. 
1. INTRODUCTION 
The determination of sensor orientation models to support 
photogrammetric exploitation of satellite imagery has been an 
active research topic for around two decades. As the most 
rigorous approach, collinearity-based mathematical models 
have in the past been proposed and successfully applied for 
medium-resolution imaging systems such as SPOT, MOMS and 
IRS. These models describe the rigorous geometry of the 
scanner, utilising knowledge of the satellite trajectory and 
sensor calibration data. Therefore, access to the camera model 
and orbit ephemeris data is indispensable for their successful 
application. In circumstances where the policy of the HRSI 
vendor does not permit access to the camera model and orbital 
data, the collinearity-based approach is generally not a viable 
proposition. 
As a substitute for rigorous sensor models, a number of 
‘alternative’ or ‘replacement’ models have been proposed. The 
best known and currently most widely utilised of these is the 
rational function model (also termed rational polynomial 
camera model or rational polynomial coefficients, and 
abbreviated to RFM, RPC or RPCs). A set of polynomial 
coefficients provided by the satellite imagery vendor is 
accurately computed from the rigorous sensor model. RPCs 
have gained popularity as a replacement for the rigorous sensor 
model for HRSI (Fraser & Hanley, 2004; Grodecki & Dial, 
2003). A further alternative sensor orientation model is based 
on affine projection. This was initially applied with success to 
the orientation of SPOT and MOMS-2P imagery (Hattori et al., 
2000; Okamoto et al., 1998; 1999), and it has characteristics 
that indicate suitability for HRSI. 
The authors have been involved in a number of investigations 
centred upon assessment of the affine sensor orientation model 
for HRSI (Hanley et al., 2002; Fraser et al., 2002; Fraser & 
Yamakawa, 2004). The overall results have indicated that the 
affine model achieves sub-pixel to l-pixel level accuracy for 
Reverse-scanned IKONOS stereo configurations and even for 
IKONOS  multi-strip configurations. In spite of these 
encouraging results, there have always been several concerns 
about the applicability of the model. These especially focus 
upon its lack of rigour and its likely shortcomings when the 
satellite imaging system does not perform in a linear manner. 
Justifiable questions therefore remain about how universally 
applicable the affine model is for HRSI sensor orientation. 
In this paper we summarize recent experiences with the affine 
model for sensor orientation and geopositioning from IKONOS 
and QuickBird imagery. The paper is divided into two parts. 
The first part covers important issues involved in sensor 
orientation modelling based on affine projection. The second 
presents results of experimental application with one IKONOS 
Geo and two QuickBird Basic stereo image pairs. These will 
highlight both advantages and shortcomings of the affine model 
approach. 
2. THEORY OF AFFINE PROJECTION 
The standard formulation of the affine model is expressed as a 
linear transformation from 3D object space (X, Y, Z) to 2D 
image space (x, y): 
x= AX + A1 + 0,2 + À, 
y= A X + AY + A,£ + 4 
(1) 
where A, — As = parameters describing rotation (3), translation 
(2) and non-uniform scaling and skew distortion (3) 
X, y — coordinates in line and sample direction 
X, Y, Z 7 object coordinates