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.