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Correlation may be applied following a regular grid or along those points found to be 
proper for correlation by an interest operator, e.g. the MORAVEC-algorithm (6). 
The selected points may be checked by a human operator and then measured by 
means of least squares correlation. While fracture surfaces tend to be very rough, 
the high accuracies and correlation coefficients given in (1) were not obtained, but, 
compared to cross correlation, the least squares correlation technique yielded a 
distinct improvement in accuracy of parallax measurement. 
The decision about the procedure (grid or interest operator) depends on the 
topography and the texture of the object surface as well as on the quality of the 
image data. With the SEM imagery this investigation is based on, the use of a grid 
proved to be of advantage. The MORAVEC-algorithm either yielded not enough 
points to ensure accurate interpolation or it turned out to be too costly if the 
corresponding point quantity was demanded. 
Because the resampled images are free of y-parallaxes, they can be processed by 
automatic one-dimensional correlation. First, approximate values for the homologue 
points are calculated by using the normalized cross correlation. With SEM data 
correlation coefficients frequently are less than 0.7, which is in general not 
considered a good matching result. But in most cases corresponding points are 
certainly found (fig. 4). 
    
       
     
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Fig. 4: 3D representation of cross correlation coefficient (left) 
and auto correlation coefficient (right) 
In a second step a least squares algorithm is applied to determine the x-parallaxes of 
corresponding points with increased accuracy. Up to now an affine transformation 
has been used in this algorithm, but regarding the complex geometry of fracture 
surfaces the application of higher transformations seems to be justified. 
135