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Chapter 18:
Binary Image Decompositions for Nonlinear Optical Correlations
The inherent parallelism of optical systems is a useful property for optical information processing. Most optical processing techniques are based on the linear operations of convolution and correlation. Although linear filtering is easy to accomplish by means of optical correlators, nonlinear image processing may alleviate some of the limitations of linear filtering. Nonlinear filtering can also have very useful properties for removing noise and for preserving edges. There are many ways to introduce nonlinearities in optical processing. One way is to use a spatial light modulator (SLM) to introduce nonlinearities in the input plane, the output plane, or the Fourier plane. Nonlinear functions are also involved in visual communication and in photodetectors used for the output of optical processors. Nonlinear operations are frequently introduced in optical correlators by introducing a nonlinearity in the Fourier plane, thus establishing a nonlinear matched filter. The aim of such filters is usually to obtain well-defined and sharp correlation peaks. Some nonlinearities are obtained by introducing a threshold in the Fourier plane in order to improve discrimination and to reduce false alarms. Some nonlinear filtering techniques are based on an optimum nonlinear processor that optimizes discrimination in the presence of target variations. The joint transform correlator (JTC) is a widely used processor for optical pattern recognition. Its discrimination may be increased by introducing nonlinearities in the joint power spectrum (JPS). The above methods introduce a nonlinear function in a linear optical processor. Nonlinear filtering or morphological filtering can be performed by means of convolution and threshold. Although optical thresholding devices have been proposed, their speed and number of pixels still are not competitive with electronics. So, linear optical systems can best perform nonlinear filtering if they are complemented with electronics to carry out the nonlinear thresholding operation.
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