Susumu Hattori 
  
ORIENTATION OF HIGH-RESOLUTION SATELLITE IMAGES BASED ON 
AFFINE PROJECTION 
Susumu Hattori, Tetsu Ono*, Clive Fraser** and Hiroyuki Hasegawa*** 
Fukuyama University, Japan, Dept. of Computer Science 
hattori@fuip.fukuyama-u.ac.jp 
*Kyoto University, Japan, Dept. of Global Engineering 
ono@jf.gee.kyoto-u.ac.jp 
**Melbourne University, Australia, Dept. of Geomatics 
c.fraser@eng.unimelb.edu.au 
***Geonet Inc., Japan 
hasegawa@geonetz.com 
KEY WORDS: Satellite images, affine projection, sensor orientation, SPOT, MOMS-2P 
ABSTRACT 
This paper discusses an orientation method for high-resolution satellite images based on the affine projection 
model. The conventional central projection model can lead to over-parameterisation due to the narrow field 
of view of the optics, which in turn can cause instability in the orientation. It is shown that the affine model 
offers a solution to this problem since it can absorb linear distortions in orientation parameters while at the 
same time stabilising the orientation /triangulation process. The assumption is made with the affine model that 
the satellite travels in a straight path at uniform velocity within the model space, where the chosen datum is 
the Gauss-Krueger projection (or UTM). The affine model has been validated through experiments conducted 
with both SPOT and MOMS-2P stereo imagery, and the results of practical tests are reported. These show 
that the affine approach, which needs no prior knowledge of sensor trajectory or a precise camera model, can 
yield sub-pixel ground point triangulation accuracies, while displaying a high level of solution stability. 
1 INTRODUCTION 
High-resolution satellite imaging sensors feature very long focal lengths and narrow fields of view. This imaging 
geometry can lead to over-parameterisation in orientation/triangulation if the conventional central projection 
model is adopted for restitution. The problem becomes more acute as the field of view narrows. If sensor interior 
orientation is known, and high precision navigation sensors are available to provide position and attitude data for 
the satellite line scanner, either all or some of the exterior orientation parameters can be constrained to suppress 
over-parameterisation and thus stabilise the orientation/triangulation process. As an alternative restitution 
approach, a model based on affine projection can be considered. The late Professor Okamoto proposed such an 
approach (Okamoto, 1981,1988; Okamoto & Akamatsu, 1992a;b) and over recent years efforts have been made to 
investigate the geometric and algebraic properties of affine projection, and to formulate and evaluate alternative 
sensor orientation and triangulation models for satellite line scanner imagery (Okamoto et al.,1998;1999). 
The present paper integrates the theories and procedures of affine-based orientation for satellite line scanner 
imagery and shows through experimental results that the method can produce a precise and stable algorithm for 
exterior orientation of satellite imagery. Moreover, the affine model exhibits some advantages over conventional 
central projection approaches and these become more pronounced with narrower fields of view of the sensor. 
The reported experiments utilised stereo images of SPOT and MOMS-2P, where ground control points (GCPs) 
and check points were recorded to sub-metre accuracy by aerial photogrammetry and GPS surveying. 
2 CATEGORIES OF ORIENTATION METHODS 
The imaging systems of high-resolution satellites are typically linear, push-broom scanners. Orientation methods 
developed to date for satellite imagery, typically SPOT images, may be classified into two groups. The first 
involves the formulation of a strict central projection model, with the trajectory and orientation of the satellite 
sensor being described in a 3D Cartesian coordinate system (Kratky, 1989; Gugan, 1988; Westin, 1990; Trinder, 
1988). The second approach involves the formulation of a projection model which simulates conventional stereo 
photogrammetric restitution for frame imagery, using collinearity equations. With this method, restitution 
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000. 359