Template design methods for binary stable cellular neural networks

Abstract

SUMMARYStable cellular neural networks with binary outputs implement a non-linear mapping between sets of input and output images. Such a mapping is studied in detail. We prove two theorems: the ÿrst one yields a su cient condition in order that the non-linear mapping be well-deÿned; the second one yields a condition, that allows to describe the mapping through a simple algorithm based on the sign of the initial derivatives. Then we enunciate two additional theorems and two corollaries, that identify the class of templates satisfying the above condition: such a class is shown to be rather large and include, as particular cases, the monotonic templates, and several kinds of non-monotonic templates. Finally, a rigorous design procedure is proposed.

An improvement of the design method of cellular neural networks based on generalized eigenvalue minimization

“…In each application of CNNs, it is very important to find optimum values of the network parameters so that a CNN performs a desired task. So far, there have been many attempts to construct systematic ways of designing CNNs with space-invariant couplings for image processing tasks [2]- [5].…”

Design and synthesis methods for cellular neural networks

“…Proof: see 1231 We note that a particular case of Theorems 3 and 4 is a CNN that does not admit of configurations with adjacent active cells. We have the following corollaries: We remark that the sufficient conditions provided by Theorems 3 and 4 can be verified by examining a restricted number of configurations.…”