Most optical pattern recognition techniques rely on correlation
that inherently achieves translation invariance. We introduce a significantly
different formulation for image recognition in which a set of inner
product operators are used to achieve translation-invariant pattern recognition.
Our formulation extends the distortion-invariant linear phase
coefficient composite filter family, developed by Hassebrook et al., into a
set of translation-invariant inner product operators. Translation invariance
is achieved by treating 2-D translation as distortion. The magnitudes
of the inner product operations are insensitive to translation,
whereas the phase responses vary, but are discarded. For large images
containing many objects, this method can be applied by tiling the 2-D
operators to the test image size, elementwise multiplying by the test
image, and then convolving with a binary rectangular window. Impressive
numerical efficiency, exceeding that of fast Fourier transform-based
techniques, is attained by the inner product operator approach. Examples
of our approach, distortion-invariant detection and discrimination
capabilities, idealized optical implementation, and comparison with conventional
matched filters are presented.
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