s. In 
nain 
ence 
t up 
lasi- 
ross- 
h is 
ated 
age 
lies 
ified 
face. 
rea- 
des 
ad- 
ing 
> of 
iod 
7 in 
1th- 
ics, 
[WO 
rith 
tat 
the 
im- 
re- 
| of 
rive 
ges, 
ned 
1A 
are 
ges 
ace- 
per- 
oth 
By 
‘ace 
ent 
' re- 
  
        
     
  
  
  
  
Left 
Image A LIS 
Reference 
Points ce 
Ephemeris Ephemeris 
Data L Data R 
1 
Satellite *' Satellite 
Parameters Parameters 
Estimation . Estimation 
  
  
  
  
  
  
1 1 
  
  
Geometric Correction 
| ' and : 
 Epipolar Resampling 
Geometric Correction 
| and 
_Epipolar Resampling 
  
  
  
  
  
  
  
  
       
  
  
       
    
      
Left Image 
Right Image 
Library 
Library 
  
Top Down 
Area Matching 
   
Match 
Control 
Points 
  
  
  
  
1 
  
D.E.M. 
generation 
  
  
  
Fig. 1 : Matching Process 
2. THE GEOMETRIC CORRECTION MODEL 
2.1. SPOT Imaging Characteristics 
The SPOT satellite is an earth resource satellite espe- 
cially designed for cartographic applications. Its sensor 
package consists of two High Resolution Visible (HRV) 
imaging instruments. Each HRV is made up of a lin- 
ear array of Charged Coupled Devices (CCD), i.e. 6000 
detectors for the panchromatic mode, accounting for a 
spatial resolution on the ground of 10m. Images are 
obtained by using the 'pushbroom' scanning tech- 
nique, whereby each line is scanned by the CCD-array 
and successive lines are produced as a result of the 
satellite's movement along its orbit (Chevrel et al, 
1981). As for panchromatic images, lines are scanned 
at a sample interval of 1.504 milliseconds. Each HRV 
has a pointable mirror, which allows off-nadir view- 
ing in the cross-track direction over a range of X27? rel- 
ative to the vertical. 
2.2. Rectification Method 
Before the matching algorithm can be applied, both 
stereoimages should be resampled in a cartographic 
reference plane (by preference an epipolar registration 
473 
so that relief displacements are confined to the x-direc- 
tion). Thereby, all image distortions such as satellite 
orbit and attitude variations, earth shape and rotation, 
effects of sensor geometry, panoramic effect, etc. 
should be removed. A precision rectification of SPOT 
imagery when only a few reference points are known, 
requires modelling the satellite motion and attitude in 
a rigorous way (Pattyn, 1991). 
In order to calculate the intersection point of the 
image vector pointing towards the earth (i.e. vector 
from the satellite's perspective centre towards a detec- 
tor in the CCD-array) and the reference ellipsoid, one 
has to know at any time the position and orientation 
of the satellite along its orbit and the viewing direc- 
tion of the CCD-array in the HRV-instrument. The 
nominal position and orientation of the satellite at 
moment t is derived from the Ephemeris data, sup- 
plied with each SPOT scene. At sample intervals of 1 
minute satellite's position and velocity vectors are 
given in a geocentric reference system. By applying a 
7th degree Lagrange interpolation polynomial, satel- 
lite position coordinates are generated at equally 
spaced time intervals of 5 lines within the time span 
of the acquisition of one scene (i.e. 9 seconds). These 
points are then described by a second degree polyno- 
mial in function of time, which is convenient for 
scenes smaller than 300 km (Hottier and Albattah, 
1990) : 
X, 2 Zi 
= X 
7° = a +at+at + y2 
S t 3 
with [X, Y. Z.] the satellite's position and X, £, X4 po- 
sition errors along its orbit. The three axes defining 
the nominal orientation of the satellite at moment t 
are also derived from the Ephemeris position and ve- 
locity vectors, forming the orthogonal matrix R,. 
Satellite attitude drift rates are measured every 125 ms 
during image scanning. The relative attitude angles 
Aw A¢ Ax are calculated by numerical integration. 
Since the attitude offset (wy $9 ky) is not known, rota- 
(1) 
tion angles w ¢ x are obtained using reference points in 
the adjustment phase. 
ot) = ag * Ao(t (roll) 
$(0 2 dy * AQ(0 (pitch) 
k(t) = Kg * AK(t) (yaw) Q) 
These attitude rotation angles are then used to form 
the orthogonal matrix R,. 
Assuming a principle distance of 1, a rectangular sen- 
sor coordinate system is formed. The components of 
the viewing vector (i.e. vector from the centre of per- 
spective to a detector in the CCD-array) are derived by 
linear interpolation between the normalised vectors 
of the look angles for the detectors at each end of the