An extension of an algorithm for finding sequential decomposition of erosions and dilations

An important problem in the field of designing automatically morphological operators is to study the transformation of standard morphological representations of the operators learned into other equivalent representations in order to make efficient implementations. In this paper, we study this problem restricted to decomposition of set translation invariant dilations (respectively, erosions) by arbitrarily shaped structuring elements into a minimum number of compositions of dilations (respectively, erosions) by smaller structuring elements that are subsets of the 3×3 square centered at the origin. In this work, we approach this problem by applying combinatorial optimization techniques and using algebraic and geometrical properties of Minkowski additions in order to find pruning strategies