Bayesian switching algorithm for the optimal increasing binary filter

The optimal windowed, translation-invariant binary image operator depends on conditional probabilities p(Y|x), where Y is a pixel value in a window about the pixel. The switching algorithm derives an optimal increasing filter from the optimal operator by switching observation vectors in or out of the kernel in such a way as to obtain an increasing filter with minimal increase in error over the optimal operator. These operators are usually designed by estimating the conditional probabilities from observed ideal pairs of images. However, samples are typically too small to obtain good estimates of these probabilit ies. T his paper discusses the design of increasing optimal filters by the switching algorithm using prior distributions for the conditional probabilities.