Minimum-Variance Synthetic Discriminant Functions,
CARNEGIE-MELLON UNIV PITTSBURGH PA DEPT OF ELECTRICAL AND COMPUTER ENGINEERING
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The conventional synthetic discriminant functions SDFs determine a filter matched to a linear combination of the available training images such that the resulting cross-correlation output is constant for all training images. We remove the constraint that the filter must be matched to a linear combination of training images and consider a general solution. This general solution is, however, still a linear combination of modified training images. We investigate the effects of noise in input training images and prove that the conventional SDFs provide minimum output variance when the input noise is white. We provide the design equations for minimum-variance synthetic discriminant functions MVSDFs when the input noise is colored. General expressions are also provided to characterize the loss of optimality when conventional SDFs are used instead of optimal MVSDFs. Keywords Reprints Optical image recognition.