Towards all-numerical implementation of correlation

Interestingly, the past 20 years have provided us many examples of optical correlation methods for pattern recognition, e.g. VanderLugt correlator (VLC). In recent years, hybrid techniques, i.e. numerical implementation of correlation, have been also considered an alternative to all-optical methods because they show a good compromise between performance and simplicity. Moreover, these correlation methods can be implemented using an all-numerical and reprogrammable target such as the graphics processor unit (GPU), or the field-programmable gate array (FPGA). However, this numerical procedure requires realizing two Fourier Transforms (FT), a spectral multiplication, and a correlation plane analysis. The purpose of this study is to compare the performances of a numerical correlator based on the fast Fourier transform (FFT) with that relying on a simulation of the Fraunhofer diffraction. Different tests using the Pointing Head Pose Image Database (PHPID) and considering faces with vertical and horizontal rotations were performed with the code MATLAB. Tests were conducted with a five reference optimized composite filter. The receiving operating characteristics (ROC) curves show that the optical FT simulating the Fraunhofer diffraction leads to better performances than the FFT. The implications of our results for correlation are discussed.