Nonlinear correlation of two images based on their Fourier phases using binary joint transform correlation

Abstract

The correlation performance of the binary joint transform correlator (JTC) is dependent on the threshold that is used to binarize the joint power spectrum in the Fourier plane.1 One type of threshold function is the sum of the power spectrum of the reference signal and the power spectrum of the input scene.1 Applying this threshold function in the binary JTC removes the Fourier magnitudes of both the reference signal and the input image. In other words, the Fourier magnitudes of the input signal and the reference signal are set to unity. It results in a nonlinear correlation between two images based on their Fourier phases only. This nonlinear correlator is different from the phase-only filter technique in which only the Fourier magnitude of the reference signal is set to unity. The thresholding function provides an optimal correlation performance by maximizing the autocorrelation peak intensity and eliminating the even-order harmonic terms in the output plane. Computer simulation and experiment results will be presented to illustrate the optimal correlation performance of the binary JTC using the thresholding function. Several different thresholding methods are also described and compared in the presentation.