Incremental evaluation of BDD-represented set operators

In mathematical morphology set operators are described by a formal language, whose vocabulary is composed of dilations, erosions, complementation, union and intersection. They are called morphological operators when expressed in this form. Translation invariant and locally defined set operators are called W-operators. Decision diagrams have been used as an alternative representation for some 2-D and 3-D discrete W-operators. This paper shows that the reduced and ordered binary decision diagram (ROBDD) is a non-ambiguous scheme for representing W-operators and presents a method to compute the ROBDD of any W-operator from a corresponding morphological operator. This procedure of computing decision diagrams can be applied to the automatic proof of equivalence between morphological operators, since the W-operator they represent are equal if and only if they have the same ROBDD.