METRIC INFORMATION EXTRACTION FROM SPOT IMAGES 
AND THE ROLE OF POLYNOMIAL MAPPING FUNCTIONS 
Emmanuel P. Baltsavias, Dirk Stallmann 
Institute of Geodesy and Photogrammetry 
Swiss Federal Institute of Technology 
ETH-Hoenggerberg, CH-8093 Zurich, Switzerland 
Tel.: +41-1-3773042, Fax: +41-1-3720438, e-mail: manos@p.igp.ethz.ch 
  
Commission IV 
ABSTRACT 
This paper handles the aspect of metric information extraction from SPOT images and focuses mainly on sensor 
modelling and the geometric accuracy potential of polynomial mapping functions, and secondly on the use of 
these functions for automated derivation of DTMs and generation of digital orthophotos. 
The sensor modelling is based on V. Kratky's strict geometrical model. First, an accuracy analysis is provided 
based on points of varying definition quality covering the whole image format and having a height range of 1700 
m. Different computation versions and an accuracy comparison is presented. Kratky also provides polynomial 
mapping functions to transform from image to image, object to image, and image to object space. The mapping 
functions are much faster, easier to implement, and almost equally accurate as compared to strict 
transformations. The accuracy of these functions will be assessed. This is crucial, since these polynomial 
functions are subsequently used for automatic DTM and orthophoto generation. 
The automatic DTM generation is based on a modified version of the Multiphoto Geometrically Constrained 
Matching (MPGC). The polynomial functions for the image to image transformation are used to define geometric 
constraints in image space. Thus, the search space is reduced along almost straight epipolar lines and the success 
rate and reliability of matching increase. The deviation of the epipolar lines from straight lines will be analysed 
for different image positions, heights and height approximations. The generation of digital orthophotos is fully 
automated and is based on polynomial functions modelling the object to image transformation. Aspects 
  
  
  
  
regarding speed and accuracy will be analysed. 
KEY WORDS: remote sensing, SPOT, geometrical accuracy, constrained matching, DEM, orthophoto 
1. INTRODUCTION 
SPOT data is extensively used because of its geometric 
resolution and secured availability, and the stereo 
capability of the sensor. This data can supply substantial 
topographic and thematic information to GIS. Today, 
problems exist firstly in the extraction of the appropriate 
information from satellite images, especially in an 
automated manner, and secondly in the integration of this 
information into GIS. The geometric accuracy of SPOT 
has been extensively investigated during the last years. 
Different models of varying complexity, rigour and 
accuracy have been developed (Kratky, 1989a; Westin, 
1990; Konecny et al., 1987; Toutin, 1985, Gugan, 1987) 
up to SPOT block adjustment (Veillet, 1990). Various 
tests have proven that the geometric accuracy potential of 
SPOT is below 10 m in both planimetry and height. 
However, strict transformations from image to image, 
object to image, and image to object space are 
computationally very intensive and pose problems on the 
implementation of real-time positioning in analytical 
photogrammetric instruments. Kratky, 1989b, proposed 
the use of polynomial mapping functions (PMFSs) that are 
much faster and almost equally accurate (maximum error 
less than 1 m in object and 1 jum in image space) as 
compared to the strict transformations. The aim of this 
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paper is to test the geometric accuracy of PMFs and 
check their usefulness for automated DTM and 
orthophoto generation. Since the PMFs are derived using 
the results of the strict SPOT model, their accuracy 
depends on the accuracy of the latter. Thus, 
investigations on the accuracy of Kratky's strict model 
and ways to improve it will also be presented. 
2. KRATKY'S SPOT MODEL 
Kratky's model processes single and stereo panchromatic 
level 1A and 1B SPOT images. It is an extended bundle 
formulation considering in a rigorous way all physical 
aspects of satellite orbiting and of earth imaging, together 
with geometric conditions of the time-dependent 
intersection of corresponding imaging rays in the model 
space. The ephemeris data (position and attitude) are not 
necessary but they may be used optionally. Orbital 
perturbations are taken into account by allowing the 
SPOT orbital segment to be shifted with respect to its 
expected nominal position. The total number of 
unknowns per image is 14 - 6 elements of exterior 
orientation, linear and quadratic rates of change for the 
rotation angles, a change A f for the camera constant, and 
a quadratic distortion in x (corresponding to a shift of the 
principal point along the CCD sensor). The quadratic