Design of monotonic binary-valued cellular neural networks

In order to be able to take full advantage of the great application potential that lies in cellular neural networks (CNNs) we need to have successful design and learning techniques as well. In almost any analogic CNN algorithm that performs an image processing task, binary CNNs play an important role. We observed that all binary CNNs reported in the literature, except for a connected component detector, exhibit monotonic dynamics. In the paper we show that the local stability of a monotonic binary CNN represents sufficient condition for its functionality, i.e. convergence of all initial states to the prescribed global stable equilibria. Based on this finding, we propose a rigorous design method, which results in a set of design constraints in a form of linear equalities. These are obtained from a simple local rules similar to that in elementary cellular automata without having to worry about continuous dynamics of a CNN. In the end we utilize our method to design a new CNN template for detecting holes in a 2D object.