Journal of Circuits, Systems and Computers

In 1992, a new spatial temporal computing idea had been proposed, the CNN Universal Machine. It turned out that a new paradigm in computing on image flows, a Universal Machine on Flows, has ignited the intellect of hundreds of researchers. Today, visual microprocessors based on this idea can perform about TeraOPS computing power and 10 000 frames per second. In this paper, after a brief description of the history of the invention, architectural advances, physical implementation, algorithmic developments, as well as the biology relevance, theoretical aspects, mission critical applications, and new directions are reviewed.

The aim of this paper is to investigate synchronization phenomena in arrays composed of locally interconnected chaotic circuits. Such arrays are often considered as generalized Cellular Nonlinear Networks. In our computer experiments we study in particular the phenomena of formation of synchronized spatial clusters.

The stability and dynamics of a class of Cellular Neural Networks (CNNs) in the central linear part is investigated using the decoupling technique based on discrete spatial transforms, Nyquist and root locus techniques. The influence of the cell order and template neighborhood is discussed and computer simulations are presented. It is shown that, as in the case of Turing patterns, for 1D CNNs, the patterns predicted by the linear theory of the decoupling technique are often valid even when the nonlinearity has been reached.

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.

This paper further investigates a basic issue that has received attention in the recent literature, namely, the robustness of complete stability of standard Cellular Neural Networks (CNNs) with respect to small perturbations of the nominal symmetric interconnections. More specifically, a class of third-order CNNs with a nominal symmetric interconnection matrix is considered, and the Harmonic Balance (HB) method is exploited for addressing the possible existence of period-doubling bifurcations, and complex dynamics, for small perturbations of the nominal interconnections. The main result is that there are indeed parameter sets close to symmetry for which period-doubling bifurcations are predicted by the HB method. Moreover, the predictions are found to be reliable and accurate by means of computer simulations.

This paper presents new criteria for the existence of stable equilibrium points in the total saturation region for cellular neural networks (CNNs). It is shown that the results obtained can be used to derive some complete stability conditions for some special classes of CNNs such as positive cell-linking CNNs, opposite-sign CNNs and dominant-template CNNs. Our results are also compared with the previous results derived in the literature for the existence of stable equilibrium points for CNNs.

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.

This paper focuses on Discrete-Time Cellular Neural Networks (DTCNNs) for associative memories with application to pattern classification. At first, DTCNNs with a globally asymptotically stable equilibrium point are designed to behave as associative memories. The objective is achieved by considering feedback parameters related to circulant matrices and by satisfying frequency domain stability criteria. The approach, by generating DTCNNs where the input data are fed via external inputs rather than initial conditions, enables both hetero-associative and auto-associative memories to be designed. Numerical examples are reported in order to show the capabilities of the design tool. Successively, an application of DTCNNs to pattern classification is illustrated. Namely, it is shown that patterns belonging to the training set as well as patterns outside it can be reliably classified using the proposed design method. Comparisons with well-established classification techniques, such as signature technique and modified Fourier descriptor technique, clearly highlight the performances of the approach developed herein.

Recently a discrete-time cellular neural network (DT-CNN) is applied to many image processing applications such as compression and reconstruction, recognition and so on. Conventional image processing techniques such as the discrete cosine transformation (DCT) and wavelet transforms work as a simple filter and do not make good use of interpolative dynamics by the feedback A template, which is one of the significant characteristics of a cellular neural network (CNN). If CNN is applied to a filter by an only feedforward B template, one should make a model which consists of digital filters using high speed signal processing modules such as a high speed digital signal processor. This paper describes the nonlinear interpolative effect of the feedback A template, by showing the evaluation of image compression and reconstruction.

This paper describes parallel histogram modification techniques with embedded morphological preprocessing methods within the CNN-UM framework. The procedure is formulated in terms of nonlinear partial differential equations (PDE) and approximated through finite differences in space, resulting in coupled nonlinear ordinary differential equations (ODE). The I/O mapping of the system (containing both local and global couplings) can be calculated by a complex analogic (analog and logic) algorithm executed on a stored program nonlinear array processor, called the cellular nonlinear network universal machine (CNN-UM³). We describe and illustrate how the implementation of the algorithm results in an adaptive multi-thresholding scheme when histogram modification is combined with embedded morphological processing at a finite (low) number of gray-scale levels. This has obvious advantages if the further processing steps are segmentation and/or recognition. Experimental results processing real-life and echocardiography images are measured on different hardware/software platforms, including a 64 × 64 CNN-UM chip (ACE4k^6,17).

The CNN Universal Machine is generalized as the latest step in computational architectures: a Universal Machine on Flows. Computational complexity and computer complexity issues are studied in different architectural settings. Three mathematical machines are considered: the universal machine on integers (UMZ), the universal machine on reals (UMR) and the universal machine on flows (UMF). The three machines induce different kinds of computational difficulties: combinatorial, algebraic, and dynamic, respectively. After a broader overview on computational complexity issues, it is shown, following the reasoning related the UMR, that in many cases the size is not the most important parameter related to computational complexity. Emerging new computing and computer architectures as well as their physical implementation suggest a new look on computational and computer complexities. The new analog-and-logic (analogic) cellular array computer paradigm, based on the CNN Universal Machine, and its physical implementation in CMOS and optical technologies, proves experimentally the relevance of the role of accuracy and problem parameter in computational complexity. We introduce also the rigorous definition of computational complexity for UMF and prove an NP class of problems. It is also shown that choosing the spatial temporal elementary instructions, as well as taking into account the area and power dissipation, these choices inherently influence computational complexity and computer complexity, respectively. Comments related to relevance to biology of the UMF are presented in relation to complexity theory.

It is shown that algorithms using spatial-temporal continuous elementary instructions (α-recursive functions) represent not only a new world in computing, but also, a more general type of logic inference.