format by the nature of its scan pattern. Whether accomplished by the
sensor scan or by a coordinate transformation, the logarithmic
coordinate transformation is equivalent to resampling an image at
logarithmically spaced intervals. An increase in space bandwidth
(number of samples) is caused by the oversampling which takes place at
small values of the input coordinate. This increased sampling at the
input is a cause for concern in a practical correlator design. In
such a system, the resolution required at the highest sampling rate
fixes the design of the entire system. This may cause the space-
bandwidth product required for adequate correlation to exceed the
capability of the sensor. However, Anderson and Callary51 showed
that previous researchers52 had overestimated the space-bandwidth
requirement and that practical Mellin-Fourier correlators were
possible.
Synthetic Discriminant Functions
Another technique for recognizing multiple orientations and
conditions is to cross-correlate with many different reference images
in parallel. The test image can be transformed by many lenses at
once, with each Fourier transform falling on an array of reference
filters chosen to give reasonable correlation to all conditions. By
the proper choice and location of the inverse transform lens, the
correlations of all the filters can coincide in one common plane.
This parallel setup has been extensively studied by Leib et al.53
They showed that with a memory bank of 23 views of a tank, an optical
correlator could obtain a 98% probability of detection and 1.4% false
alarm rate in scenes exhibiting both scale and rotation variations.