Morphology provides the algebraic means to specify operations on images. Discrete-time cellular neural networks (DT-CNN's) mechanize the execution of operations on images. The paper first shows the equivalence between morphological functions and DT-CNN's. Then, the argument is extended to the synthesis of optimal DT-CNN structures from complex morphological expressions. It is shown that morphological specifications may be freely derived, to be subsequently transformed and adopted to the needs of a specific target technology. This process of technology mapping can be automated along the well-trodden path in CAD for microelectronics.