Design of Morphological Set Operators by Statistical Optimization

The design of operators (e.g. filters) for Signal or Image Processing requires an algebraic decomposition structure, to represent the family of operators considered, and statistical optimization techniques, defined over the space of operator decompositions or over another isomorphic structure. This paper surveys a technique for designing set operators based on Mathematical Morphology decompositions and optimization algorithms over Boolean lattices. This technique has an intrinsic discrete nature and usually depends on combinatorial optimization algorithms. Its most remarkable quality is the conjunction of formality and pragmatism. In fact, it is both a strong Mathematical theory and a powerful computational tool.