Single Cellular Neural Network Research Articles

NXOR- or XOR-based robust template decomposition for cellular neural networks implementing an arbitrary Boolean function via support vector classifiers

Robust template design for cellular neural networks (CNNs) implementing an arbitrary Boolean function is currently an active research area. If the given Boolean function is linearly separable, a single robust uncoupled CNN can be designed preferably as a maximal margin classifier to implement the Boolean function. On the other hand, if the linearly separable Boolean function has a small geometric margin or the Boolean function is not linearly separable, a popular approach is to find a sequence of robust uncoupled CNNs implementing the given Boolean function. In the past research works using this approach, the control template parameters and thresholds are usually restricted to assume only a given finite set of integers. In this study, we try to remove this unnecessary restriction. NXOR- or XOR-based decomposition algorithm utilizing the soft margin and maximal margin support vector classifiers is proposed to design a sequence of robust templates implementing an arbitrary Boolean function. Several illustrative examples are simulated to demonstrate the efficiency of the proposed method by comparing our results with those produced by other decomposition methods with restricted weights.

Preprocessor embedding in cellular neural network

Cellular neural network (CNN) is a highly parallel analog circuit suitable for real‐time image processing. However, the needs of preprocessors in real‐world applications usually destroy the parallel processing nature of CNN. In this paper, we propose methods to embed the function of a preprocessor into a single CNN universal machine (CNN‐UM) such that the novel CNN contains the functions of both the preprocessor and the original CNN. The embedding processes are divided into three categories according to the structure of the B template in CNN. In the general case of nonzero B template (Case 1), an unbiased method and three approximation methods are proposed. The unbiased method is equivalent to its sequential counterpart, although templates of twice the neighborhood size should be used. Among the three approximation methods, AM III shows the least deviation from the unbiased method. In some experiments, AM II and AM III even outperform the unbiased method in noise‐elimination. In the two degenerated cases of Case 2 and Case 3 CNN, the embedding process can be fulfilled with templates of the original size. An exact solution can be derived for Case 2 while an approximate solution is developed for Case 3. The deviation due to the approximation in Case 3 is minor and the assumption made can even assist in noise elimination.

An efficient paradigm for wavelet‐based image processing using cellular neural networks

AbstractWe propose a novel paradigm for cellular neural networks (CNNs), which enables the user to simultaneously calculate up to four subband images and to implement the integrated wavelet decomposition and a subsequent function into a single CNN. Two sets of experiments were designated to test the performance of the paradigm. In the first set of experiments, the effects of seven different wavelet filters and five feature extractors were studied in the extraction of critical features from the down‐sampled low‐low subband image using the paradigm. Among them, the combination of DB53 wavelet filter and the r=2 halftoning processor was determined to be most appropriate for low‐resolution applications. The second set of experiments demonstrated the capacity of the paradigm in the extraction of features from multi‐subband images. CNN edge detectors were embedded in a two‐subband digital wavelet transformation processor to extract the horizontal and vertical line features from the LH and HL subband images, respectively. A CNN logic OR operator proceeds to combine the results from the two subband line‐edge detectors. The proposed edge detector is capable of delineating more subtle details than using typical CNN edge detector alone, and is more robust in dealing with low‐contrast images than traditional edge detectors. The results demonstrate the proposed paradigm as a powerful and efficient scheme for image processing using CNN. Copyright © 2008 John Wiley & Sons, Ltd.

REALIZATION OF BOOLEAN FUNCTIONS VIA CNN WITH VON NEUMANN NEIGHBORHOODS

Recently, an effective method for realizing linearly separable Boolean functions via Cellular Neural Networks (CNN), called the threshold bifurcation method, was introduced, with a CNN gene bank of four variables established [Chen & Chen, 2005]. Based on this success, the present paper is to further explore the realization of all linearly separable Boolean functions of five variables via CNN with von Neumann neighborhoods. This paper provides: (i) important and essential relations among the genes (or templates) and the offsets of an uncoupled CNN as well as the basis of the binary input vectors set, (ii) a neat truth table of uncoupled CNN with five input variables, (iii) 94572 linearly separable Boolean functions (LSBF) in the family of 225 = 4.294967296 × 109 Boolean functions of five variables, realizable by a single CNN, and (iv) all 94572 CNN linearly separable Boolean genes (LSBG), which can be determined to form the CNN gene bank of five variables.

CHARACTERISTIC OF MUTUALLY COUPLED TWO-LAYER CNN AND ITS STABILITY

This paper presents some interesting image processing applications with the mutually coupled two-layer Cellular Neural Networks (CNNs). We found that the two-layer CNNs are very useful compared to single layer CNNs in some applications such as center point detection, skeletonization, and so on. We also focus our discussions on both their transients and operations. In addition, the stability of the two-layer CNNs with mutually coupled symmetric templates is also discussed based on those of decoupling CNN technique.

BIFURCATIONS AND CHAOS IN CELLULAR NEURAL NETWORKS

The dynamic behavior of first-order autonomous space invariant cellular neural networks (CNNs) is investigated. It is shown that complex dynamics may occur in very simple CNN structures, described by two-dimensional templates that present only vertical and horizontal couplings. The bifurcation processes are analyzed through the computation of the limit cycle Floquet's multipliers, the evaluation of the Lyapunov exponents and of the signal spectra. As a main result a detailed and accurate two-dimensional bifurcation diagram is reported. The diagram allows one to distinguish several regions in the parameter space of a single CNN. They correspond to stable, periodic, quasi-periodic, and chaotic behavior, respectively. In particular it is shown that chaotic regions can be reached through two different routes: period doubling and torus breakdown. We remark that most practical CNN implementations exploit first order cells and space-invariant templates: so far only a few examples of complex dynamics and no complete bifurcation analysis have been presented for such networks.

Self-organization in a two-layer CNN

In this work, it is shown that a two-layer cellular neural network (CNN) with constant templates is suitable for generating self-organizing patterns and, therefore, it is able to model complex phenomena. The dynamic behavior of the single two-layer linear CNN cell is studied and the global behavior of the whole CNN is discussed. Different nonlinear phenomena are generated, including autowaves and spirals. Finally, the sensitivity with respect to parametric uncertainties and noise is investigated.