Optimum filter for detection of a target in nonoverlapping scene noise

Intensity invariant nonlinear correlation filtering in spatially disjoint noise

We analyze the performance of a nonlinear correlation called the Locally Adaptive Contrast Invariant Filter in the presence of spatially disjoint noise under the peak-to-sidelobe ratio (PSR) metric. We show that the PSR using the nonlinear correlation improves as the disjoint noise intensity increases, whereas, for common linear filtering, it goes to zero. Experimental results as well as comparisons with a classical matched filter are given.

Signal-to-noise-ratio analysis for nonlinear N-ary phase filters

The problem of recognizing targets in nonoverlapping clutter using nonlinear N-ary phase filters is addressed. Using mathematical analysis, expressions were derived for an N-ary phase filter and the intensity variance of an optical correlator output. The N-ary phase filter was shown to consist of an infinite sum of harmonic terms whose periodicity was determined by N. For the intensity variance, it was found that under certain conditions the variance was minimized due to a previously undiscovered phase quadrature effect. Comparison showed that optimal real filters produced greater signal-to-noise-ratio values than the continuous phase versions as a consequence of this effect.

Reduction of the correlation sensitivity to the changes of the input illumination by a post processing based on the correlation statistics

Linear-correlation amplitude changes when the intensity level of the input image is modified. As recognition is often based on the correlation-peak level, a change of the input illumination may result in a false recognition. We propose an illumination-change compensation by a post processing of the correlation distribution that is based on statistical measures of the correlation histograms. The theoretical background and simulation results are provided in the frame of an actual application in biology.

Nonlinearity optimization in nonlinear joint transform correlators

Three types of nonlinear transformations of the joint spectrum in nonlinear joint transform correlators (NLJTC's) are investigated with the purpose of achieving the highest discrimination capability in target location in a cluttered background: logarithmic transformation and the (1/k)th law transformation in combination with the limitation of the signal dynamic range and binarization by thresholding. By computer simulation carried out on a set of test images, it is shown that application of these transformations in NLJTC's may considerably improve the correlator's capacity to locate and recognize properly small objects on a cluttered background, provided there is proper selection of nonlinearity parameters. It is also shown that a moderate blur of the joint spectrum in such NLJTC's before nonlinear transformation is permissible, which simplifies the requirements of correlator optical alignment, the resolution power of correlator electronic components, or both.

Optimum rotation-invariant filter for disjoint-noise scenes

We introduce an optimum matched filter for rotation-invariant pattern recognition in scenes with disjoint noise. The optimum filter maximizes the ratio between the correlation-peak intensity and the correlation-output energy; in order to ensure rotation invariance, we assume the filter to take the form of a circular-harmonic function. The performance of this new filter is tested by computer simulations with a variety of natural and artificial backgrounds. The results obtained from these tests show an excellent performance much better than the classical circular-harmonic function (the filter that maximizes the signal-to-noise ratio while maintaining rotation invariance).

Reduction in correlation-filter sensitivity to background clutter by the automatic spatial frequency selection algorithm

We propose an automatic spatial frequency selection correlation filter that reduces the sensitivity to nonoverlapping noise or background clutter. This is achieved by inclusion of distorted versions of the reference images surrounded by nonoverlapping background clutter. Furthermore, we impose that the window functions of the reference images give response zero-correlation amplitudes. Simulation results are provided in the case of a two-class pattern-recognition problem and show that the results are appreciably increased. The results are compared with a normal automatic spatial frequency selection.