A Lattice-Based Minimal Gray-Scale Switching Algorithm for Obtaining the Optimal Increasing Filter from the Optimal Filter

Authors:
Edward R. Dougherty
Affiliations:
Department of Electrical Engineering, Texas A & M University, USA
Venue:
Journal of Mathematical Imaging and Vision
Year:
2004

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Abstract

For binary window-based filters, the optimal increasing filter is often derived from the optimal unconstrained (nonincreasing) filter by iteratively switching the filter values at pixels from 0 to 1 or from 1 to 0 so as to make the resulting filter be the optimal increasing filter. This paper gives a corresponding switching algorithm for gray-scale nonlinear filters, and it does so in the context of finite lattices, which makes the algorithm applicable to computational morphology on lattices. The algorithm is minimal in the sense that it involves a minimal search if one wishes to be certain to obtain the optimal increasing filter when beginning with the optimal unconstrained filter.