A theorem for calculating the local histograms of a gray-scale input image by means of convolution of input-image binary slices with a binary kernel is presented and proved. The calculation of the local histograms of a gray-scale image for all resolution cells and its arbitrary neighborhoods is optically implemented in a shadow-casting correlator. The choice of different rank-order values from the local histograms can lead to a wide spectrum of nonlinear filtration algorithms.
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