Polynomial expansion for shift- and one- or two-dimensional scale-invariant pattern recognition

A polynomial expansion is suggested for achieving optical invariant pattern recognition. The expansion results in a real function and thus is theoretically able to be implemented under both coherent and spatially incoherent illumination. One obtains the expansion after applying the Gram–Schmidt algorithm on the Laurent’s series in order to achieve orthonormality. The initial Laurent term with which we apply the Gram–Schmidt procedure is chosen according to the desired expansion order. The use of the polynomial expansion is demonstrated for shift- and one-dimensional scale-invariant pattern recognition as well as for shift- and two-dimensional scale-invariant recognition.