<title>Distortion-invariant optical pattern recognition without correlation</title>

Abstract

Most distortion-invariant optical pattern recognition techniques rely on correlation which inherently achieves translation-invariance. We introduce a new formulation for image recognition where only 'vector inner product' (assuming 2D images are lexicographically converted to vectors) operations are used to achieve distortion-invariant pattern recognition. Our formulation expands the linear phase coefficient composite filter family, developed by Hassebrook et.al., into a set of translation- and distortion-invariant vector inner product operators. The set of vector inner products are optimal in numerical efficiency because they represent a Karhunen Loeve expansion. Translation- invariance is achieved by embedding 2D translation into the training set as two additional distortion parameters. The magnitude of the vector inner product results in a response insensitive to translation and distortion, where as the phase response varies, but is discarded. For large images containing many objects this method can be applied by tiling the vector inner product operators to the test image size. Examples of our approaches, distortion-invariant detection/discrimination capabilities, numerical efficiency, and tradeoffs between conventional correlation are presented.