C(xoyo) 7 E,E, Cay) - gQxox, 2yo:y) Y 
with : 
C(xo yo) = "correlation" function 
g(x,y) = density at x,y (the image) 
X9 Yo = position of the symmetry point 
Without interpolation, the correlation function can 
be evaluated on a grid with half pixel intervals. To 
obtain subpixel accuracy a 2-dimensional second 
order polynomial is fitted to a matrix of 3 by 3 
datapoints of the correlation function. In this way 
the correlation function is approximated in an area 
the size of a pixel. The position of the minimum of 
the function gives the best estimate of the position 
of the symmetry point. The value of the minimum 
is an indication for the density noise in combination 
with the (lack of) symmetry present in the image. 
To assure convergence of the matching procedure, 
apart from a relatively accurate position, the scale 
of the target should be approximated. In our 
experiment the scale of the targets could differ a 
factor 10 partly due to differences in photoscale, 
partly because of three different sizes of targets 
were used. 
An indication for the scale is obtained through the 
autocorrelation procedure described above: the size 
of the so-called correlation window (circular area 
for which the autocorrelation function is evaluated) 
is chosen in such a way that a symmetry-criterion 
and a contrast-criterion is met. The measure for 
symmetry is defined by the minimum of the 
correlation function relative to the assumed 
emulsion noise. The contrast-criterion ensures a 
minimum size of the correlation window. Starting 
from a maximum size correlation window 
(depending on photoscale and size of the targets 
used) the size is decreased until both criteria are 
met. In this way the correlation window is fitted to 
the symmetric part of the target. 
The standard deviation of the position using the 
autocorrelation method described above was 
estimated between 1% and 3% of a pixel for good 
quality images. The diameter of the correlation 
window generaly was between 30 and 50 pixels. 
The estimated emulsion noise was between 2% and 
4% of the average density. These estimates are 
optimistic because the correlation between neigh- 
bouring density measurements, due to pixel over- 
N 
lap (effective size at least 13 x 13 um depending on 
focus and only 10 pm intervals), was neglected. 
Template matching. Apart from the position of the 
target the scale is also provided with a first 
estimate. This facilitates convergence of the least 
squares template matching. 
The template is an artificial digital image based on 
the target design. It contains only the circle and the 
ring of a target. The template image is smoothed 
with a 3 by 3 averaging filter to simulate 
convolution with the Point Spread Function. For 
target images the P.S.F. is wider than for 
reseaucrosses (P.S.F. of the emulsion only) due to 
the influence of the lenssystem, atmosphere and 
defocussing. These effects differ between different 
targets. The same holds for the photoscale. The 
template is designed for the image of a slightly 
defocused target with average photoscale. The 
template and a sample image are shown in figure 4. 
  
figure 4: template and target image 
The eight parameter model for the least squares 
matching can be written as follows: