Shift- and scale-invariant anamorphic Fourier correlator

Abstract

A new method of shift- and scale-invariant matched filtering in an anamorphic image processor is proposed. It consists in matching the nonsymmetrical Fourier spectrum of an analyzed scene with the symmetrical filter of a target through a wedge mask. A scene object is transformed with two cylindrical lenses of focal lengths fx and fy > fx in the x and y directions, respectively. In the Fourier plane of the correlator a classical Vander Lugt matched filter is placed, which has been prepared for a basic-sized target by means of a spherical lens of focal length f = fx. The spectrum for a basic-sized target in the analyzed scene perfectly matches the filter along the x axis. The spectrum of a similar object, which is magnified by a factor S = fy/fx, perfectly matches the filter along the y axis. For similar objects of intermediate sizes matched filtering occurs along intermediate directions. Results of the computer experiment are presented, and limitations of the method are discussed.