Efficient DTCNN implementations for large-neighborhood functions

Most image processing tasks, like pattern matching, are defined in terms of large-neighborhood discrete time cellular neural network (DTCNN) templates, while most hardware implementations support only direct-neighborhood ones (3×3). Literature on DTCNN template decomposition shows that such large-neighborhood functions can be implemented as a sequence of successive direct-neighborhood templates. However, for this procedure the number of templates in the decomposition is exponential in the size of the original template. This paper shows how template decomposition is induced by the decomposition of structuring elements in the morphological design process. It is proved that an upper bound for the number of templates found in this way is quadratic in the size of the original template. For many cases more efficient and even optimal decompositions can be obtained