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DIGITAL IMAGE PROCESSING OF REMOTE SENSING IMAGERY: 
A COMPARATIVE STUDY ON DIFFERENT OBJECTIVE FUNCTIONS 
IN CORRELATION PROCESS 
MANFRED EHLERS 
Institut fiir Photogrammetrie 
Universitat Hannover 
D - 3000 Hannover 1 
ABSTRACT 
In this paper five different objective functions for correlation process have 
been compared in an empirical test on identical images with added random noise 
in varying magnitudes. The accuracy of the correlation function is computed on 
20 correlation points for each image. One result is that phase correlation 
turns out to be relative undistortable against low signal-to-noise-ratio. On 
the other hand a careful selection of correlation points according to the vari- 
ances is of great influence in accuracy and sharpness of the objective function. 
INTRODUCTION 
In recent years digital correlation turns out to be a useful tool to detect 
identical points in different images for rectification of remote sensing image- 
ry (Gópfert 1980). Even in images of natural landscape like tidal lands digital 
correlation methods have been applied successfully (Ehlers and Dennert-Moller 
1981). 
Tidal lands of the German North Sea coast are the test sites of the 'Sonder- - 
forschungsbereich' (SFB) 149, a special research organization for ‘Surveying 
and Remote Sensing at Coasts and Oceans'. One great disadvantage for digital 
correlation in images of this terrain is the very low signal-to-noise-ratio 
(SNR) which leads to inaccurate parallaxes (Ehlers and Wrobel 1980). 
So preprocessing of the images, i.e. twodimensional digital filtering is one 
method to increase correlation accuracy (Ehlers 1982, Fórstner 1982). 
On the other hand the linkage between accuracy and objective function in corre- 
lation process has not been investigated systematically although different 
functions for this purpose have been presented (Ehlers and Wrobel 1980, 
Gópfert 1980, Kuglin et al. 1979, Makarovic 1980). 
In the following we present the results of a test series to answer this ques- 
tion. The test computations have been executed on the image processing system 
MOBI-DIVAH of the SFB 149 (MOBI, DIVAH-Handbuch ). 
OBJECTIVE FUNCTIONS 
The correlation concept of the SFB 149 is based on a modular structure. 50 it 
allows an easy exchange of different objective functions for the correlation 
process. Five of them have been tested: 
a) The 'normal' product moment correlation coefficient, 
b) the correlation intensity coefficient that has been derived out of coherent- 
optical considerations (Gópfert 1980). The image signals are mapped on the 
complex plane and the intensity of the complex correlation function is com- 
puted. The coefficient is weighted by a parameter Py which depends on the 
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