Abstract
In this second part of a two-part study, the lattice-based computational representational structure is applied to image operators. The computational representations are first applied to some common non-linear window (vector) operators used in image processing — for instance, flat erosion, flat dilation, fuzzy erosion, and flat filters, in general. For these, application of the representations is direct. Representations are then developed for gray-to-binary and gray-to-gray image operators. In all cases, images are assumed to be lattice-valued. It is shown that under appropriate circumstances the representations can be viewed as structural generalizations of classical representations. Flat (stack) filters are treated in their own fight (as operators on lattice-valued images) and it is seen that for these the lattice representations can be interpreted in terms of threshold decomposition.
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