ISPRS Commission III, Vol.34, Part 3A , Photogrammetric Computer Vision*, Graz, 2002 
  
The consequence is that GCPs will always be required in order 
to precisely orient images with pixel accuracy. 
SAR images have a significant advantage over optical images. 
Due to the image generation process, based on distance 
measurements, image orientation is independent from sensor 
attitude angles (Renouard and Perlant, 1993). Provided that an 
accurate orbit is available, together with precise SAR 
processing parameters, images are already precisely oriented 
and GCPs are not required. That is the case of ERS SAR 
imagery, which have a geo-location accuracy of 10 m (Mohr 
and Madsen, 2001). 
Mixed sensor image pairs, composed by a SAR and an optical 
image, provide a strong parallax effect from where heights can 
be determined (Raggam et al., 1994, Toutin, 2000). Provided 
that precise orientation is known for both images, heights of 
conjugate points can be determined by applying an intersection 
algorithm. If only the approximate orientation is known for 
SPOT then parallaxes will be systematically affected. 
The essential point of the methodology proposed here for the 
improvement of SPOT image orientation is that using altimetric 
ground control points, the relation between parallaxes and 
heights can be calibrated, allowing for the determination of 
heights for a set of SAR-SPOT tie points. Using the precise 
SAR image orientation and the heights of the tie-points, 
planimetric coordinates can be calculated, thus transforming the 
SAR-SPOT tie points into actual GCPs. These GCPs can then 
be used in the standard SPOT image orientation procedure. 
1.2 Study area and available data 
The methodology proposed in this paper was tested with a 
SPOT and a SAR scene of Portugal. The area is mountainous, 
with a height range of 1000 m. 
The SPOT scene is of panchromatic mode, with an incidence 
angle of 25.5? to west of the trajectory. It was acquired in 
August 1991, by SPOTI. 
A Radarsat image, covering almost all of the area, was 
available. It is of the standard mode, with a pixel size of 12.5 m 
and was acquired in August 1997, in the ascending pass of the 
orbit, with an incidence angle of 44°. Figure 1 represents the 
location of the two images. 
  
SPAIN 
  
  
  
41°} j pepe 
/ | PORTUGAL 
  
  
  
  
Figure 1 — Location of the Radarsat and SPOT images used 
An ERS-2 image of northern Portugal was also available but 
with a very small overlap with the SPOT image. An ERS SAR 
image would have been preferable, due to the better geolocation 
information. For Radarsat, the orbit accuracy is known to be of 
the order of 100 m (Rufenacht et al, 1997). 
The verification of SAR image orientation was done with digital 
topographic map data. A hydrographic network, digitised from 
topographic maps of scale 1:25,000, was used. A set of 13 
check-points uniformly distributed on the image were surveyed 
with GPS and used to assess the SPOT image orientation. 
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2. SPOT IMAGE ORIENTATION 
2.1 SPOT sensor model 
Optical line scanners on board of satellites acquire strips of 
images composed of consecutive image lines. Each line is 
generated by a central projection, which is represented by the 
co-linearity equations, as for aerial photography but with the 
difference that exterior orientation parameters are functions of 
time. Figure 2 represents the image formation process and the 
sensor coordinate system (x,y,z). 
    
Platform motion 
Figure 2 — Image acquisition by a linear array scanner 
The relation between ground and image coordinates, in a linear 
sensor, is established by the co-linearity equations. A detailed 
description of these equations for SPOT is given by Westin 
(1990). 
The exterior orientation parameters of a SPOT scene describe 
the satellite trajectory and the sensor attitude, and are all 
functions of time. Usually only 4 orbital parameters are 
required, all corresponding to the instant of the first image line 
(Gugan and Dowman, 1988, Westin, 1990). Their variations in 
time are predicted by the orbital perturbation theory. 
The attitude angles at the time of first image line (roll, cy, pitch, 
% and yaw, kp) are also exterior orientation parameters. Their 
variations in time can be predicted by the onboard 
measurements of attitude variation (Westin, 1990). In this case a 
total of 7 parameters are required to orientate a SPOT scene. 
Other authors prefer to model the attitude variations in time by 
linear or quadratic functions, introducing the derivatives of 
attitude angles as additional orientation parameters. In this case 
the number of parameters becomes 10 or more. 
The determination of all the parameters (space resection) 
requires a number of GCPs greater or equal to half the number 
of parameters. In order to achieve a strong solution in the least 
squares adjustment, some redundancy is required. 
The number of parameters, and consequently the number of 
GCPs, can be reduced if an accurate orbit is known, as in the 
case of SPOT4. Anyway, the precise modelling of sensor 
attitude always requires the use of accurate GCPs. 
Once the precise orientation of a sensor is established, it is 
possible to do object-to-image projection and image-to-object 
projections. The latter requires the height of the point above the 
reference ellipsoid (77). The line defined by the sensor equations 
is intersected with the surface of constant height, which can be 
approximated by an ellipsoid of semi-axis a--H and b+H 
(Curlander, 1982): 
XY dz Q) 
(a-HyY (b+H) 
where a and b are the semi-major axis of the reference ellipsoid. 
These projections can then be expressed as (Olander, 1998):