optical and digital, tend to suffer from two types of difficulties.
They tend to be too sensitive to differences likely to occur in the
desired pattern. These differences are termed "within-class
variations." Second, they tend to be too insensitive to differences
between real and false targets. These are "between-class variations."
While other deformations in the object condition are possible in
specific applications, translation, rotation, and scale are the most
common in pattern recognition whether it is accomplished optically or
digitally.
Deformation Invariant Optical Pattern Recognition
The basic operation performed in an optical processor is a two-
dimensional Fourier transform. Matched spatial filters are used to
perform correlations between an input image and a reference pattern.
While the reference pattern may exist in the input image, it may be
deformed by scale, rotation or geometrical distortion. The Fourier
transform is invariant to shift in two dimensions (see equation 2.6).
It is not however invariant to scale or rotation, and a dramatic loss
in signal-to-noise ratio (3 to 30 dB) occurs for small scale changes
(2%) or rotation (3.50).44
In some applications it is desirable to give up translation or
shift invariance in substitution for some other deformation
invariance. The technique described by Casasent and Psaltis45
involves a space variant coordinate transformation to convert the
deformation under consideration to a shift in the new coordinate
system. Because the optical processor performs two-dimensional
transforms, it is insensitive to shifts in two dimensions. Thus, two
separate invariances can be accommodated. Scale can be converted to a