Optical EngineeringTranslation-invariant optical pattern recognition without correlation
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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.