Most optical pattern recognition techniques rely on correlation that i
nherently achieves translation invariance. We introduce a significantl
y different formulation for image recognition in which a set of inner
product operators are used to achieve translation-invariant pattern re
cognition. Our formulation extends the distortion-invariant linear pha
se coefficient composite filter family, developed by Hassebrook et al.
, into a set of translation-invariant inner product operators. Transla
tion invariance is achieved by treating 2-D translation as distortion.
The magnitudes of the inner product operations are insensitive to tra
nslation, whereas the phase responses vary, but are discarded. For lar
ge images containing many objects, this method can be applied by tilin
g 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 trans
form-based techniques, is attained by the inner product operator appro
ach. Examples of our approach, distortion-invariant detection and disc
rimination capabilities, idealized optical implementation, and compari
son with conventional matched filters are presented, (C) 1996 Society
of Photo-Optical Instrumentation Engineers.