In this paper I present a novel analysis of the signal-to-noise ratio (SNR) for the complex output of a correlator obtained by Fourier filtering an input image with a binary phase-only filter (BPOF). Rather than defining the output variance as being the variance of the real and imaginary components added together, it is defined as being the variance of the complex magnitude. An expression for the complex magnitude variance is obtained using a Taylor series expansion in which higher order terms are discarded. The variance is found to be related to the ratio of eveness to oddness of the BPOF, which in turn is related to the choice of threshold line angle. For a purely even BPOF, the correlator output is real, hence the variance is the same as for the conventional case. As the degree of oddness increases the higher frequency complex amplitudes of the noise are rotated out of phase with the dc component. Consequently, the complex magnitude variance decreases. For a BPOF that is odd the variance is a minimum as the higher frequency noise variations are orthogonal to the dc component. Furthermore, the SNR for the BPOF in this case is an order of magnitude greater than that obtained with a phase-only filter (POF). This last result contradicts the perceived wisdom that the SNR ratio for a BPOF and POF is in the range 4/π2→1. The analysis results are confirmed through simulation.
A robust least squares motion detection algorithm was evaluated with respect to target size, contrast and sensor noise. In addition, the importance of robust motion estimation was also investigated. The test sequences used for the evaluation were generated synthetically to simulate a forward looking airborne sensor moving with translation parallel to a flat background scene with an inserted target moving orthogonal to the camera motion. For each evaluation parameter, test sequences were generated and from the processed imagery the algorithm performance measured by calculating a receiver-operating-characteristic curve. Analysis of the results revealed that the presence of small amounts of noise results in poor performance. Other conclusions are that the algorithm performs extremely well following noise reduction, and that target contrast has little effect on performance. The system was also tested on several real sequences for which excellent segmentation was obtained. Finally, it was found that for small targets and a downward looking sensor, the performance of the basic least squares was only slightly inferior to the robust version. For larger targets and a forward looking sensor the robust version performed significantly better.
Mutual information-based image registration has been verified to be quite effective in many clinical applications. However, when calculating the mutual information between two working images, we need to estimate the grey values of the transformed image by interpolation on the reference image, which introduces regular artefacts in the registration function. In this paper, we analyse the underling mechanism of the artefacts, and present a new statistical interpolation, which will not introduce new intensities. In addition, it also breaks the conformity of the interpolation points, which is considered as a major contributing factor to the artefacts in commonly used interpolations. These characteristics make the registration function much smoother, enabling easier convergence to a global extreme. Experimental results on clinical images verify these advantages.
Several designs for a reduced resolution optical correlator are proposed. The design of reduced resolution filters by multiresolution wavelet analysis (MWA) or by downsampling is extended to spatial light modular with fill-factors less than one. A reduced resolution optical correlator is constructed based on one of the above designs, and a comparison of MWA and downsampling filters is performed for different size targets. The experimental results show good qualitative agreement with simulation; however, the first-order correlation peaks were found to be greater for the experimental results. A possible reason for this is suggested and a new technique for measuring the fill-factor is proposed.
In conventional approaches to the design of binary phase-only synthetic discriminant function filters the filters are trained on discrete Fourier transforms (DFTs) of the training image, even though DFTs are in fact downsampled approximations of the continuous optical Fourier transform (FT) that is generated in an optical correlator. The justification for this is that one can completely reconstruct the training image from its DFT. In this work however, we show, by use of a realistic correlator simulation, that filters designed by the conventional approach do not give the correct results when implemented in a real correlator. It is shown that multiresolution wavelet analysis approximations (MWA) of the training image FTs should be used for correct filter design. Furthermore, we show that it is possible to design filters whose resolution is reduced with respect to the conventional case, but whose performance is comparable, using the MWA approach. Finally, the performance of the filters trained on MWA approximations was found to be vastly superior in nearly all cases to the equivalent filters trained on conventional downsampled approximations.
The effect of reducing the resolution of a phase-only filter (POF) with respect to the target Fourier transform, while maintaining a constant filter bandwidth, is investigated. An existing procedure for the optimal design of filters with constrained complex amplitude values is modified by imposing an additional constraint on the filter resolution, and is used to design an optimal POF under such restrictions. A simple analysis is performed for an idealized target, which shows that the correlation peak magnitude significantly decreases when the filter resolution, in terms of number of subregions (pixels), falls below the target size, measured in terms of the number of smallest resolvable elements (pixels), in the input. The applicability of this analysis for real IR imagery is verified by simulation. The dependence of the correlation peak degradation, with filter resolution, on the nature of the imagery is also investigated, and it is shown that, for a given image size, high-pass filtered images are marginally more robust to filter resolution reduction than normal imagery. Finally, the effectiveness of the optimizing procedure is demonstrated by comparing the amount of filter resolution reduction that can be achieved by this procedure with that achieved by an existing nonoptimal technique.
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