1- INTRODUCTION 
SPOT-1 
followed by 
the two 
synchronous 
was launched in February 1986 and 
SPOT-2 in January 1990. Each one of 
satellites circles the Earth in a 
orbit (altitude 832 km) and repeats 
its coverage every 26 days. SPOT-1 and SPOT-2 
carry an identical push-broom sensor system. 
This sensor system includes two identical 
optical instruments, the HRV1 and HRV2 (High 
Visible Resolution). SPOT's sensor produces 
images in two modes; the panchromatic mode (P) 
with a single spectral band (0.51 um to 0.73 um) 
and a ground resolution of 10 m and the 
multispectral mode (XS) with three spectral 
bands (between 0.5 um to 0.84 um) and a ground 
resolution of 20 m. 
The reflected radiation picked up by the 
optical instrument, for each spectral band, is 
measured by an array of detectors (6000 for the 
^P' mode, 3000 for each of the spectral bands of 
the ^"XS' mode) which forms .rows of the image 
perpendicular to the satellite track (60 km on 
the ground). The scenes dimension parallel to 
the satellite .track is achieved by movement of 
the satellite along its orbit. Each SPOT scene 
covers 60 km by 60 km. 
in front of the HRV 
modification of the look 
an across-track angle with the 
reach +27 degrees. So, it is 
images of the same ground 
look angles from different 
a stereoscopic pair from any two 
situated 
allows 
making 
A mirror 
instrument 
direction 
vertical that can 
possible to record 
area at different 
orbits forming 
of such images. 
SPOT stereoscopic 
used to extract 3-dimensional 
information by using conventional 
photogrammetric methods. In the first method, a 
stereomodel was formed by an analytical relative 
orientation. Model coordinates, then, were 
fitted into ground coordinates using 
3-dimensional affine and polynomials 
transformations. In the second method of 
stereoscopic analysis, ground coordinates, in 
three dimensions, of check points are computed 
by space intersection. In this case, the 
exterior orientation elements of each image is 
determined, first, by space resection and then 
used to orient left and right rays through image 
In this 
pair Was 
investigation a 
points to intersect in the ground position of 
any point. A variable number of ground control 
points is used to determine the transformation 
and orientation parameters in each case. A 
special polynomial was used to correct computed 
heights derived from the second method. 
Residuals and their root mean squares in a 
number of check points were determined and 
analysed. 
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2- THE MATHEMATICAL MODELS 
Conventional photogrammetrical mathematical 
models were used in this investigation to 
perform stereoscopic analysis of the SPOT data. 
There are two well known analytical methods for 
extracting 3-dimensional ground coordinates from 
a stereo pair of images. In the first method, a 
stereomodel is formed and ,then, computed model 
coordinates are transformed into ground 
coordinates by a mathematical model for absolute 
orientation. There are a number of ways to solve 
the problem of relative orientation ,coplanirity 
equation, analytically. In this investigation, 
the method of fixing the left hand image is 
adopted and, accordingly, the relative 
orientation mathematical model can be written 
as: 
{x y z)Le]| 0 -Bz By 
Bz O0 -Bx 
-By Bx O0 
  
X 
ER sly 
z 
  
r 
where (x y z)L and (x y z)r are the image 
coordinates of any point at the left and right 
images respectively and Bx is an arbitrary scale 
factor for the formed stereomodel. The five 
orientation parameters are; the base component 
in Y-direction ’By’, the base component in 
Z-direction ’Bz’ and the three rotation elements 
which define the orthogonal rotation matrix 'R'. 
For images collected by scanners, the relative 
orientation parameters may change along the 
track direction and polynomials may be 
considered to represent these changes. In this 
study, changes .in the base components 'By' and 
?Bz* are taken into consideration and 
represented by polynomials. 
after 
orientation 
coordinates 
overlapping 
computed. 
coordinates 
coordinates are: 
determining the relative 
elements, 3-dimensional model 
of any image point in the 
area between the two images can be 
The mathematical models used for model 
transformation into ground 
(i) The three-dimensional transformation in the 
form:- 
E = al + a2.Xm + a3.Ym + a4.Zm, 
N - bil * b2.Xm + b3.Ym + b4.Zm, and 
Haz clat:c2.Xm + cS: ¥Ynitocd.Zm 
(ii) The three-dimensional second order 
polynomials in the form:- 
E = al + a2.%m * a3.Ym t ad.Zm t a5.Xm**2 + 
a6.Ym**2 t a7.Xm.Ym, 
N = bi + b2.Xm | bs5.Ym 4 b4.7m t b5.Xmt**2 * 
b6.Ym**2 + b7.Xm.Ym and 
H = cl t c2.YXm | c5.Ym * cd.7m t c5.Xm**2 + 
c6.Ym**2 * c7»Xm.Ym. 
(E,N,H), (Xm,Ym,Zm) are, respectively, the 
ground and model coordinates of any reference 
point and the remaining elements are the 
transformation parameters or cxonstants. This 
method, some times, is called ’the two steps 
orientation’ 
where