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Invariant characterizations and pseudocharacterizations of finite multidimensional sets based on mathematical morphology

This paper outlines a methodology for characterizing finite subsets of (eta) d where (eta) is the set of integers and integer d >= 1. The schemes are based on the lattice-based mathematical morphology and on the notion of a pseudo-complement. Three different schemes for multidimensional objects are presented, two of which provide only pseudo- characterizations, while the third scheme provides a complete characterization of objects. The performance of the proposed pseudo-characterizations has been shown to be superior to the similar existing algorithms. The proposed methods lend themselves to efficient implementation on parallel machines.