On the rectangular grid representation of general CNN networks

Although the cellular neural net (CNN) paradigm in its original form provides a suitable framework for investigating problems defined on arbitrary regular grids, the neural chips available or under design and the available simulators are all restricted to a rectangular structure. It is not at all self-evident, however, that the rectangular structure is the most suitable to represent every practical problems. In this paper we demonstrate that several CNNs of various regular grids can be mapped onto the typical eight-neighbour rectangular one, by applying weight matrices of periodic space-variance. By adopting this option, the applicability of cellular neural chips and simulators can be extended to investigate problems of essentially arbitrary grid structures