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This paper develops a Lyapunov approach for studying convergence and stability of a class of differential inclusions termed differential variational inequalities (DVIs). The DVIs describe the dynamics of a general system evolving in a compact convex subset of the state space. In particular, they include the dynamics of the full-range (FR) model of cellular neural networks (CNNs), which is characterized by hard-limiter nonlinearities with vertical segments in the i-v characteristic. The approach is based on the following two main tools: 1) a set-valued derivative, which enables to compute the evolution of a Lyapunov function along the solutions of the DVIs without involving integrations, and 2) an extended version of LaSalle's invariance principle, which permits to study the limiting behavior of the solutions with respect to the invariant sets of the DVIs. Then, this paper establishes conditions for convergence (complete stability) of DVIs in the presence of multiple equilibrium points (EPs), global asymptotic stability (GAS), and global exponential stability (GES) of the unique EP. These conditions are applied to investigate convergence, GAS, and GES for FR-CNNs and some extended classes of FR-CNNs. It is shown that, by means of the techniques developed in this paper, the analysis of convergence and stability of FR-CNNs is no more difficult than that of the standard (S)-CNN5. In addition, there are significant cases, such as the symmetric FR-CNNs and the nonsymmetric FR-CNNs with a Lyapunov diagonally stable matrix, where the proof of convergence or global stability is much simpler than that of the S-CNNs. [ABSTRACT FROM AUTHOR]

Stable patterns that can be realized by a class of 1-D two-layer cellular neural networks (CNNs) are studied in this paper. We first introduce the notions of potentially stable pattern, potentially stable local pattern, and local pattern set. We then show that all of 256 possible sets can be realized as the local pattern set of the two-layer CNN, while only 59 sets can be realized as the local pattern set of the single-layer CNN. We also propose a simple way to optimize the template values of the CNN, which is formulated as a set of linear programming problems, and present the obtained values for all of 256 sets. [ABSTRACT FROM AUTHOR]

In this paper, a biologically inspired, CNN-based, multi-channel, texture boundary detection technique is presented. The proposed approach is similar to human vision system. The algorithm is simple and straightforward such that it can be implemented on the cellular neural networks (CNNs). CNN contains several important advantages, such as efficient real-time processing capability and feasible very large-scale integration (VLSI) implementation. The proposed algorithm also had been widely tested on synthetic texture images. Those texture images are randomly selected from the Brodatz textures database [1]. According to our simulation results, the boundaries of uniform textures can be detected quite successfully. For the nonuniform or nonregular textures, the results also indicate meaningful properties, and the properties also are consistent to the human visual sensation. The proposed algorithm also has been implemented on the CNN Universal Machine (CNN-UM), and yields similar results as the simulation on the PC. Based on the efficient performance of CNN-UM, the algorithm becomes very fast. [ABSTRACT FROM AUTHOR]

In this paper, the complete stability of cellular neural networks with time-varying delays is analyzed using the induction method and the contraction mapping principle. Delay-dependent and delay-independent conditions are obtained for locally stable equilibrium points to be located anywhere, which differ from the existing results on complete stability where the existence of equilibrium points in the saturation region is necessary for complete stability and locally stable equilibrium points can be in the saturation region only. In addition, some existing stability results in the literature are special cases of a new result herein. Simulation results are also discussed by use of two illustrative examples. [ABSTRACT FROM AUTHOR]

Lyapunov functionals and Lyapunov functions coupled with the Razumildiin technique are still the most popular tools in studying the stability of large-scale retarded nonlinear systems. However, it is generally difficult to construct Lyapunov functionals or functions that satisfy the strong conditions required in the classical stability theory. In this paper, we show that for some delay differential systems such as additive neural networks with delays, we can weaken the condition that the Lyapunov functional or function is positive definite, by using the equivalence between the state stability and the output stability. We apply our general theory to obtain some new stability conditions for cellular neural network models. It is represented that it is easy to construct Lyapunov functionals or functions satisfied conditions of our theorems. [ABSTRACT FROM AUTHOR]

In this paper, we show how a cellular nonlinear network with 1-bit weight programmability can be used for processing black and white image data. When using such a binary-programmable network, some templates need to be processed algorithmically, in other words, divided into subtasks that are processed consecutively. We classify templates into groups based on their properties and give guidelines as to how the division into subtasks (when applicable) is performed. A large collection of templates suitable for the proposed model is shown. We also describe one possible cell structure that realizes the binary-programmable model. The cell is modeled with Matlab and selected template simulations are shown. [ABSTRACT FROM AUTHOR]

In this paper, we extend the linear cellular neural network (CNN) paradigm by introducing temporal derivative diffusion connections between neighboring cells. Our proposal results in an analog network topology for implementing general continuous-time discrete-space mixed-domain 3-D rational transfer functions for linear filtering. The network connections correspond one-to-one to the transfer function coefficients. The mixed-domain frequency response is treated as a temporal frequency-dependent spatial function and we show how nonseparable properties of the spatio-temporal magnitude response can be derived from the combination of: 1) sinusoidal functions of spatial frequencies and 2) polynomials of the continuous-time frequency in the 3-D frequency response expression. A generic VLSI-compatible implementation of the network based on continuous-time integrators is also proposed. Based on our proposed CNN extension, the analysis of a spatio-temporal filtering example originated from analytical modeling of receptive fields of the visual cortex is presented and a spatio-temporal cone filter is designed and presented with numerical simulation results. [ABSTRACT FROM AUTHOR]

In this paper, an on-chip implementation of the active contour technique called pixel-level snakes is proposed. This is based on an optimized cellular neural network (CNN) algorithm with capabilities to support changes in the contour topology. The entire algorithm has been implemented on a 64 × 64 CNN universal machine chip-set architecture for which the results of the time performance measurements are given. To illustrate the validity and capabilities of the proposed implementation some on-chip experiments are also included. [ABSTRACT FROM AUTHOR]

Linear cellular neural networks (CNNs) are capable of performing efficient spatiotemporal filtering operations as re- cursive infinite impulse response (IIR) filters. Particularly, linear CNNs can be characterized as a spatial frequency-dependent recursive temporal filter with complex coefficients. Based on a modified version of the CNN paradigm recently proposed by the authors, nonseparable spatiotemporal bandpass filters with tunable spatiotemporal passband volumes are synthesized. The filters reported here qualitatively resemble spatiotemporal receptive field models for the primary visual cortex. Numerical simulation results confirm the bandpass characteristics of our filtering network. [ABSTRACT FROM AUTHOR]

We propose a programmable architecture for a single instruction multiple data image processor that has its foundation on the mathematical framework of a simplicial cellular neural networks. We develop instruction primitives for basic Image processing operations and show examples of processing binary and gray scale images. Fabricated in deep submicron CMOS technologies, the complexity of the digital circuits and wiring in each cell is commensurate with pixel level processing. [ABSTRACT FROM AUTHOR]

Cellular neural networks (CNNs) are dynamical systems, described by a large set of coupled nonlinear differential equations. The equilibrium-point analysis is an important step for understanding the global dynamics and for providing design rules. We yield a set of sufficient conditions (and a simple algorithm for checking them) ensuring the existence of at least one stable equilibrium point. Such conditions give rise to simple constraints, that extend the class of CNNs, for which the existence of a stable equilibrium point is rigorously proved. In addition, they are suitable for design and easy to check, because they are directly expressed in term of the template elements. [ABSTRACT FROM AUTHOR]

The design of a large-neighborhood cellular nonlinear network (LN-CNN) with propagating connections is proposed. The propagating connections are utilized to achieve large-neighborhood templates in the shape of diamonds. Based on the propagating connections, each LN-CNN cell can only be connected to neighboring cells without interconnections to farther cells. Thus, it is suitable for very large scale integration implementation. The LN-CNN functions of diffusion, deblurring, and Muller-Lyer illusion are successfully verified. Meanwhile, the functions of erosion and dilation are expanded with the diamond-shaped LN templates. Furthermore, the simple N- and P-type synapses stop all the static current paths so that the dc power dissipation can be reduced to only 0.7 mW on standby and 18 mW in operation. An experimental LN-CNN chip with a 20 x 20 array has been fabricated using 0.18-μm CMOS technology. With the proposed LN-CNN chip, more applications and LN-CNN templates can be studied further. [ABSTRACT FROM AUTHOR]

For decades, numerous scientists have examined the following questions: "How do humans see the world?" and "How do humans experience vision?" To answer these questions, this study proposes a computer fovea model based on hexagonal-type cellular neural network (hCNN). Certain biological mechanisms of a retina can be simulated using an in-state-of-art architecture named CNN. Those biological mechanisms include the behaviors of the photoreceptors, horizontal cells, ganglions, and bipolar cells, and their co-operations in the retina. Through investigating the model and the abilities of the CNN, various properties of the human vision system can be simulated. The human visual system possesses numerous interesting properties, which provide natural methods of enhancing visual information. Various visual information enhancing algorithms can be developed using these properties and the proposed model. The proposed algorithms include color constancy, image sharpness, and some others. This study also discusses how the proposed model works for video enhancement and demonstrates it experimentally. [ABSTRACT FROM AUTHOR]