ISPRS Commission II, Vol.34, Part 3A „Photogrammetric Computer Vision“, Graz, 2002 
(col,row)=F(A,0,H) (3) 
(4,9) G(col, row, H) (4) 
where (4,9,H) are the geodetic coordinates of the point and 
(col,row) are the pixel column and row position. Similar 
operations can be done for a SAR image. 
2.2 Orientation parameters from the image header 
Approximate orbit and attitude parameters can be extracted 
from the SPOT image header data. The accuracy of these 
orientation parameters was assessed with the points surveyed in 
the field using GPS (sub-meter accuracy). Applying the image- 
to-object projection for these points, errors in longitude and 
latitude (converted to distances) were found to have the 
following mean values: 
AA — 360m 
AgQ- 594m 
The methodology proposed significantly improves this figures, 
using only one altimetric control point. 
3. SAR IMAGE ORIENTATION 
3.1 SAR sensor model 
The relation between ground and image coordinates in a SAR 
image is given by the Doppler and range equations (Curlander, 
1982): 
2 (s - P).(S- P) 
fel cm. (5) 
A. |s-P| 
p=|s-P| 
where  /fpc- Doppler shift 
A= Wavelength 
p= Slant range 
S,$ = Satellite position and velocity vectors 
P,P = Imaged point position and velocity vectors 
    
  
start 
Figure 3 - Point being imaged in a SAR image processed at zero 
Doppler 
The exterior orientation is established by the sensor trajectory, 
which can be known with high accuracy. From the SAR 
processing, fpc is known for any point on the image. The 
projection of a point P onto image space consists of solving 
equations (522) in order to determine range (p) and time (7). 
Knowing the start and end time of image acquisition and the 
near and far range, row and column coordinates can be 
calculated from 1 and p, respectively. Frequently SAR images 
are acquired at zero-Doppler (fpc=0). In this case the problem is 
only to find the instant for which relative position and velocity 
vectors are perpendicular. Figure 3 represents the search for the 
instant of perpendicularity. 
Orbit data, as well as reference range and time information, 
required to calculate pixel coordinates of a point on the image 
space, are extracted from the image header data. 
3.2 SAR image orientation using header data 
The orbit data and the reference time and range were extracted 
from the image header. In order to assess their accuracy, 3D 
digital map data were projected onto image space and 
superimposed on the images. As map data is in a local map 
reference system they had to be converted to WGS84. 
There are advantages in using linear features instead of check- 
points. Individual points are difficult to find in SAR images and 
frequently their location cannot be defined with very good 
accuracy. Boundaries of water features are very well defined 
and are an alternative to check SAR image orientation. 
In the case of the available ERS-2 image a very good 
coincidence of river margins could be observed throughout the 
entire image. Figure 4 represents a portion of the ERS-2 image 
where the river Douro, in the city of Porto, can be identified and 
the vector data. 
This ERS-2 image is appropriate for the methodology proposed. 
Unfortunately it has a very small overlap with the SPOT image. 
     
    
        
Figure 4 - Portion of an ERS-1 image (300 by 150 pixels) with 
superimposed vector data corresponding to the river 
margins, projected onto the image space. 
The same procedure was used with the Radarsat image. A 
systematic shift of the vector data could be clearly detected. 
Figure 5 represents a portion of the Radarsat image with the 
superimposed vector data. The displacement was of 5 pixels 
(approx. 60 m) in range and only 1 pixel in azimuth-time 
direction. 
ERR REC Te He LM " 
Figure 5 — Portion of the Radarsat image (300 by 150 pixels) 
with superimposed vector data. 
This shift is within the Radarsat standard of image geolocation, 
which is 100 m (Rufenacht et al., 1997). However, this is not 
A - 127