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DEM Determination from SPOT 
C. Angleraud 
K. Becek, and J.C.Trinder 
School of Surveying, University of NSW 
2033 Sydney, Australia 
P.O. Box 1, Kensington, 
ABSTRACT 
Software developed for computation of DEM's is based on a satellite orientation model 
which varies according to polynomials as a function of spacecraft position. The 
determination of digital elevation models (DEM) from the digital data incorporates this 
satellite model for the computation of ground coordinates from the two overlapping 
digital images. The process of computing the matched image points has been divided 
into two steps. The first is based on the extraction of features on the two images, while 
the second is based on grey level matching using the pixel intensity values within 
windows on the two images. The process is based on a triangulated network which 
progressively densifies points within each triangle. Results of accuracy tests using this 
method are presented in this paper. 
KEY WORDS: DEM, Image Matching, Image Processing, 3D. 
1. INTRODUCTION 
SPOT satellite images are the first data that can be considered 
suitable for mapping at small and medium scales. Tests in 
several locations around the world indicate that SPOT images 
are well suited to mapping and map revision at 1:50,000 and 
1:100,000 (Dugan and Dowman 1988, Murray and Farrow 
1988). The suitability of the images for mapping depends on 
the two primary requirements which must be satisfied; they 
are, the geometric accuracy of features extracted from the 
images, and the interpretation of adequate features from the 
images for specific map scales. Generally it has been found 
that the geometric accuracy of the data extracted from the 
images can satisfy larger map scales than can be satisfied by 
the number of features interpreted from the data. Mapping 
and the determination of digital elevation models (DEM) from 
SPOT images can be based on analogue images produced 
from the digital data using analytical stereoplotters (normally 
level 1A or IAP images are preferred), or the digital images 
themselves. Both types of data have been investigated by the 
authors but this paper will concentrate on the development of 
software for the computation of DEM's. 
The choice of whether to observe analogue images on an 
analytical stereoplotter, for the derivation of DEM's or 
compute DEM's from digital data, ultimately rests on the 
assessment of the time and cost of manual observations, 
versus the cost of the computations from digital data. Based 
on an observation rate for a human observer, of one height 
observation every 5 to 10 seconds, the time required to 
Observe a grid of points over a complete SPOT stereo-pair, 
even at an interval of 250m, can amount to several weeks. 
The cost of such an operation is likely to be very high, while 
the sheer boredom for the operator in observing many 
thousands of points is likely to affect the accuracy. Software 
to carry out this process on the digital data requires 
considerable time to develop because of its complexity and 
will most likely require some interaction from the operator in 
difficult terrain cases. However, once the software has been 
developed to a high level of automation, it will not require 
continuous monitoring from the operator. The cost of the 
process is therefore likely to be significantly less than if the 
DEM is derived by manual means. A test of the accuracy of 
the manual observations of a Wild-Leitz BC2 compared with 
2m contours of the area indicated results of approximately 
5m. The same DEM's will be compared with that derived by 
the software using the digital images. 
969 
1.1 SATELLITE MODEL 
The satellite model that has been used for the mapping and 
computation of DEM's is based on an image to ground 
relationship shown in equations (1) and (2), and as 
demonstrated in Figure 1. Because of the nature of the linear 
array or push-broom scanner which is used to acquire the 
SPOT images, a separate set of collinearity equations must be 
written for each scan-line. 
m11(Xj - Xp) + m12(Yj - YP) + m13(Zj - 25) 
  
Fxj=xj +f 3 c 
m3](X;j - X) * m32(Yj - YO + m33(Zj - Zo 
  
$ Eng X) *m22(Yj - Y) * m23(Zj -Z5- 
yi^ =0 
m31(Xj - XD + m32(Yj - Y) + m33(Z; - ZU 
Equations (1) and (2) 
where x} xe zt are the coordinates of the perspective 
centre for line k of the image 
f is the effective focal length 
m1], m12, ..., m33 are the elements of the rotation 
matrix of the sensor for line k 
Xi, Y. Zj are the object coordinates of point j. 
Figure 1 shows the image space/object space geometry for a 
point 'j' for a linear array image. Taking the image x-axis to 
be at right-angles to the satellite path, the projective 
relationship exists only in the x-z plane of the image space. 
Thus, the resulting collinearity equations for a line 'k' are 
given in equations 1 and 2. A set of these equations is written 
for each line of the image with its own perspective centre and 
attitude. The parameters of the perspective centre and attitude 
are modelled by polynomials in terms of the y-image 
coordinate, with the position parameters following second 
order polynomials and the tilts following first order 
polynomials. The solution of the orientation of two 
overlapping SPOT images involves a total of 30 unknowns. 
Ephemeris data derived from the image header file can also be 
used as input for the modelling of the polynomials. This