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The first part of this paper will analyze the computational complexity of the implementation of Mathematical Morphology operations on three different architectures: general-purpose serial systems, pipeline systems, and cellular systems. For each considered architecture, a different computing technique is devised, exploiting the specific system characteristics, and obviously reaching different throughputs. The second part will present an efficient algorithm for the computation of morphological operations (based on generic non-convex structuring elements) on cellular architectures, taking as an example the PAPRICA system. Finally some considerations on the optimization of the instruction set will conclude the paper.