Abstract

A new approach to composite filter design is presented in which the filter is the weighted sum of training samples with the complex weights being of unit magnitude and linear phase. The LPCC filters are based on the fact that when the N training images are uniformly sampled in in-plane rotation, the resulting N×N correlation matrix (CM) is Toeplitz. The training set for out-of-plane rotation is chosen so that its CM most closely resembles the Ideal CM for in-plane rotation. The eigenvectors of the ideal CM are used to obtain the coefficients needed to generate the LPCC filters. The elements of these eigenvectors are complex exponentials which have unit magnitude and linear phase. The resulting magnitude response from such filters is constant (equal to the associated eigenvalue). The outputs of these filters are combined into a filter bank response based on the Bayes minimum probability of error criterion.

© 1988 Optical Society of America