A rigorous design method for binary cellular neural networks

Abstract

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 the form of linear inequalities. These are obtained from 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. © 1998 John Wiley Sons, Ltd.

A new cell output nonlinearity for dense cellular nonlinear network integration

“…It was observed in [13] that almost all the templates reported in the literature that process bipolar initial values and produce bipolar outputs introduce monotonic evolution of the cell outputs in time. The only exception found was the connected component detector (CCD) template in [14].…”