One-dimensional logarithmic harmonic synthetic discriminant function filters for shift-, scale-, and projection-invariant pattern recognition.

We introduce a new approach for shift-, scale-, and projection-invariant pattern recognition that combines the harmonic expansion and the synthetic discriminant function approaches by use of a synthetic discriminant function filter with equal-order one-dimensional logarithmic harmonic components. Because projection invariance in one direction is guaranteed by the harmonics, the required number of training images is much fewer than with classical synthetic discriminant function filters.