The padding consists of placing the N by N image into a bed of zeros.
That is, the matrix values in the resultant image, f'ij, are all zero
except the N by N center portion which contains the original image.
This padded image, when Fourier transformed, provides a matrix which
is always smooth over two pixels in both directions. A standard
Cooley-Tukey Fast Fourier Transform (FFT) algorithm is used to provide
F'ij, the Fourier transform of the reference image.
The normal correlation is performed by taking the product of Fij
and Gij point by point. This product is performed using real or
double precision real numbers and provides more than adequate dynamic
range. In addition to a normal correlation, the simulation software
includes a pre-processing option. This permits the reference image to
be modified using a frequency emphasis or phase-only filter. In the
frequency emphasis option, the frequency plane values are multiplied
by a real valued coefficient based on the emphasis desired. In the
experiments shown in this report, the frequency emphasis applied is a
gradient filter. That is, the weight of each frequency component is
equal to the radius of that component. Because the reference image
must account for the filter effect for both the reference and the test
image, the actual filter applied is the square of the desired filter
response. In this case the gradient squared is known as a Laplacian
filter or radius-squared weighting.
Another pre-processing technique possible in the ideal correlation
simulation is the phase-only filter. In this option, the magnitude at
each location is set to one while the angle of each complex value is
left intact. This is accomplished by dividing the real and imaginary
components by the magnitude. This normalizes the pattern such that