The projection-slice synthetic discriminant function (PSDF) filter is introduced and proposed for distortion-invariant pattern-recognition applications. The projection-slice theorem, often used in tomo-graphic applications for medical imaging, is utilized to implement a distortion-invariant filter. Taking M projections from one training image and combining them with (N - 1)M projections taken from another N - 1 training image accomplishes this. With the projection-slice theorem, each set of these M projections can be represented as M one-dimensional slices of the two-dimensional Fourier transform of the particular training image. Therefore, the PSDF filter has the advantage of matching each of the training images with at least M slices of their respective Fourier transforms. This filter is theoretically analyzed numerically simulated, and experimentally implemented and tested to verify the simulation results. These tests show that the PSDF filter significantly outperforms the matched-filter and the basic synthetic discriminant function technique for the particular images used. # 1997 Optical Society of America
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