title: Optimisation of filters for optical correlation of noisy images
Creators: name: Shang, Lin
Publisher: name: University of Glasgow
Year: 1999
Subjects: subject: Electrical engineering

description: The capacity of an optical correlator to identify, recognise and locate a target object in a cluttered scene depends greatly upon the qualities of the spatial filter it uses to represent the reference image. Noise in the input scene degrades the discriminative powers of correlators in the several optical configurations that have been proposed and realised. That this loss might be ameliorated in the design of the spatial filter by trading-off the noise tolerance of the classical matched filter with the high spatial resolution yielded by the phase alone filter is examined herein. Spatial discriminant function filters so designed are evaluated by simulations of their performance that account for distortions of the target object, the discrimination of the target from a nearly similar object and noise corrupting the input scene. Criteria are established for the purposes of this evaluation, including measures of the signal to noise ratio, the spatial discrimination of the correlation peak in the correlation plane and the ease of its detection. A cosine-wave joint transform correlator is proposed, an alternate to the binary joint transform correlator, and is evaluated by simulations of its performance when presented at its input with multiple objects contained in noisy scenes. The design strategy seeks an optimisation that values the sharp spatial discrimination contributed by the high spatial frequency components and the tolerance to noise imparted by the low frequency components of the spatial filter. Chapter 3 examines the trade-off between these characteristics by applying a filter composed with two difference of Gaussian, band-pass filters - one passing in a high frequency band the other passing in a low frequency band - to a matched filter. An optimisation of the spatial discrimination of the correlation peak that accounts for noise in the input scene is found by systematically varying the two pairs of parameters that define the composite filter. The primary effect of the optimal filter is to cut the low frequency spectrum of the matched filter in a sharply defined band centred on its zero order. The high frequency spectrum is little affected. This is a significant result, for the optimisation across four parameters is complex and computationally slow. The design of the more demanding spatial discriminant function (SDF) filters might then proceed by variation of a single parameter in a function that attenuates the low frequency end of the spectra of the training set of images. A single parameter function is adopted in the optimisation of SDFs reported in Chapter 4, which introduces the weighted amplitude SDF. This design balances the sharpness of the correlation peak against the filter's capacity to distinguish between similar target objects as the signal to noise ratio deteriorates. Though the location of the correlation peak produced by the optimal filter is never left in doubt, in light of the results of Chapter 3 the chosen weighting function is considered to be less effective than a sharp, low cut filter might have been. Notwithstanding the sensitivity to noise of phase encoded filters, a SDF filter synthesised from phase-encoded images and correlating phase-encoded images is examined in Chapter 5 because this scheme can be realised in real time, using current phase modulating spatial light modulators. The general case for this form of phase-phase correlation is not proved by the results of the simulations performed, but value is to be found in this scheme whenever the optical efficiency is at a premium. Although the design goal is unchanged, the design objective in the case of the joint transform correlator is to extract information directly from the joint power spectrum rather than to modify the spectrum of the reference image. A scheme is devised that is similar to even function correlation of the phase information in the spatial frequency spectra of the input and reference images. When an object in the input scene coincides with the reference image the inversion of the cosine-wave term extracted from the JPS generates a pair of delta functions in the output plane, being spaced apart by a distance con-esponding to the relative displacement of the object and the reference images. The performance of the cosine-wave JTC is superior to that of the binary JTC and more especially so when multiple targets are presented in a low contrast, noisy scene. However, the thresholding function JTC is entirely comparable with the cosine-wave scheme. It remains for future work to examine the relative sensitivity to noise of these competing systems. In prospect a JTC is capable of real time correlation that accommodates distortion of the input object and the depredations of noise through the use of cosine-wave extracting SDF filters.