Bandpass filters for unconstrained target recognition and their implementation in coherent optical correlators
An up-dateable correlator is simulated which is based on the non-degenerate four wave mixing (NDFWM) interaction in the photorefractive material bismuth silicon oxide (Bi12SiO20). Specifically, it is shown that variable bandpass filters can be implemented directly in the correlator by adjusting the relative strengths of the signal and reference beams used to write the Fourier transform hologram into the photorefractive. The synthetic discriminant function (SDF) method of grey-level multiplexing is reviewed. A bandpass modification of this technique is used in the design of a multiplexed filter for the recognition of an industrial test component from a limited number of known stable state orientations when viewed from an overhead camera position. Its performance in this task when implemented in the up-dateable correlator is assessed through simulation. The conclusion of this work is that filter multiplexing must be used judiciously for orientation invariant recognition. Only a limited number of images, typically under ten, may be multiplexed into each filter since correlation peak heights and peak-to-sidelobe ratios inevitably progressively deteriorate as images are added to the filter. The effect of severe amplitude disruptions in the frequency plane on correlation peak localisation is examined. In two or higher dimensions simulations show the localisation is very robust to this disruption; an analysis is developed to indicate the reason for this. The effect is exploited by the implementation of an algorithm that locally removes the spatial frequencies that exhibit close phase matching between intra- and inter-class images. The inter-class response can be forced to zero while simultaneously improving the intra-class tolerance to orientation changes. The technique is assessed through simulation with images of two types of motor vehicle, in a variety of orientations, and shown to be effective in improving discrimination and intra-class tolerance for examples in which these were initially very poor. Bandpass filters are experimentally implemented in a joint transform correlator (JTC) based on a NDFWM interaction in Bi12SiO20. The JTC is described and its full bandwidth performance initially assessed. As anticipated from the previous considerations, inter-class discrimination was high but the intra-class tolerance very poor due to the high sensitivity of the filter. The difference of Gaussian approximation to a Laplacian of a Gaussian filter is described and its experimental implementation in the JTC detailed. Experimental results are presented for the orientation independent recognition of a car while maintaining discrimination against another car. An intra-class to inter-class correlation ratio of 7.5 dB was obtained as a best case and 3.6 dB as a worst case, the intra-class variation being at 11 ° increments in orientation at zero elevation angle. The results are extrapolated to estimate that approximately 80 filters would be required for a full 2 steradian orientation coverage. The implementation of the frequency removal technique and the Wiener filter in the JTC is briefly considered in conclusion to this work.