13 April 2009 Nonlinear Fourier correlation
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Abstract
Fourier correlators perform space-invariant linear filtering on all input points, so they can identify and locate patterns in parallel. Each output point is a weighted sum of components of the Fourier transform of the input, so the discriminants used are inherently linear. As most practical problems are not linearly discriminable, that causes a problem. This paper describes a quite general solution involving nonlinear combining of nonlinearly processed outputs from multiple Fourier masks. The design of the masks and nonlinearities allows very powerful nonlinear discrimination that preserves the space-invariant feature that makes Fourier correlators attractive. Given a set of target-class images, henceforth referred to as the training set or trainers, the algorithm developed herein computes an ordered set of classifier filters - Generalized Matched Filters (GMFs) threshold values. An unlabeled image is applied to the classifier filter set, hereafter referred to as super-generalized matched filter (SGMF). If the peak response of any of the classifier filters (GMFs) to the unlabeled test image exceeds the threshold level the decision is made in favor of labeling the image as target-class otherwise it is labeled non-target- class.
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Kaveh Heidary, Kaveh Heidary, H. John Caulfield, H. John Caulfield, } "Nonlinear Fourier correlation", Proc. SPIE 7340, Optical Pattern Recognition XX, 73400A (13 April 2009); doi: 10.1117/12.818256; https://doi.org/10.1117/12.818256
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