A. Optical Correlators
As mentioned before, the basics behind the optical correlation techniques studied in this project are correlators based on a "4f" setup, a comparison between test and reference images and peak detection on correlation plane. Thus, there are two main architectures used for correlators known as the Joint Transform Correlator or JTC and the Vander Lugt Correlator or VLC.
First introduced by Weaver and Goodman around 1966[3], where they set the basis and conditions for implementing optical methods to obtain, and display on a plane, the correlation between a target image and a reference sample (extracted from a established database). Later on, the JTC architecture was improved and optimized by means of the "4f" setup and the binarization of the spectrum by making use of a SLM modulator, which can be enhanced even more by introducing a non-linearity in the Fourier plane, which is located in the middle of the two lenses at their focal planes.[1]
The main characteristic of the JTC set up is that both the target and the reference image are located at certain distance from each other on the input plane, thus, the correlation function shows three main peaks representing the self-correlation of each sample for the central one and the cross-correlation for the outer peaks. Therefore, the montage and diagram of how the correlator works, is shown below (taken from Afalou et. al).
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Subsequently, the ideal result on the correlation plane is to get sharp and bright peaks with no noise, which is attempted by application of the non-linearity on the Fourier plane, employing certain types of SLM modulators or other techniques. Although some of these various settings contribute to have better discrimination on the result, they can suffer from major drawbacks. As an example of one of these issues, consider a non-linear joint transform correlator (JTC-NL) where two SLM modulators are put into use, one of them placed at the input plane to lay out both images at the time, the other modulator is located at the Fourier plane to read the joint spectrum. The inconvenient that arises for this setup, is related to resolution dependence on the modulators quality and on the other hand, the lenses to be used also require some restrictions [1].
As a final note on the JTC architecture, is worth mentioning that there are some applications for the correlator on the facial recognition field, with different variations of the architecture. However, the main focus of the project will be on the VLC correlator which is described bellow.
Just as the JTC, the Vander Lugt Correlator is based on a "4f" setup and uses the spectrum of target and reference images to obtain a result in a corralation plane that dictates how similar they are. Nevertheless, the VLC settings and performance features still differ drastically from the JTC, mainly because in the former the input plane only contains the target image.
Perhaps the most important characteristic of the VLC architecture is the usage of correlation filters, which are usually constructed from a group of reference images and are meant to be applied to the test image spectrum. Afterwards, a second Fourier transform is computed and finally the result appears in the correlation plane as a single peak, which ideally, when the images coincide, must be sharp, bright and as centered as possible. For the physical montage, the idea is to use a linearly polarized parallel beam as a light source to illumine the input plane, after which the test image FT is performed thanks to a lens, next the chosen filter is applied employing a SLM modulator on the Fourier plane. Finally a second lens performs yet another FT and the resulting correlation plane is to be displayed on a CCD camera [1]. The basics of the VLC montage settings and a diagram of how it works are presented bellow (taken from Afalou et. al).
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As was mentioned before, the correlation filters play a huge role when it comes to the VLC architecture, therefore is necessary to construct an appropriate filter to obtain the most favorable result possible.
Now, the main goal of this project was to design a computational algorithm capable of performing an accurate facial verification process based on a purely optical fashion represented by the computational simulation of a Vander Lugt correlator as well as the inclusion of two types of linear filters (MACE and BCOM). Thus, once a certain filter is built, its implementation on the VLC correlator is really straightforward.
The information concerning to the filters construction and implementation is well described on the subsequent section Linear Filters