Classical correlation schemes, whereby the matched filter consists essentially of the Fourier transform of one harmonic of the stored pattern, are well known. Not always however, is the harmonic decomposition of the object applicable. In some instances a generalized spatial deformation harmonic should be defined, as presented in this paper. The duality between these harmonics and the circular harmonics when angular distortion is first proven, and then the case of tilt direction invariant pattern recognition is investigated. This example is followed by experimental results using computer simulations as well as real optical targets.