Robustness of cellular neural networks in image deblurring and texture segmentation

Template parameters of cellular neural networks (CNNs) should be robust enough to random variability of VLSI tolerances and noise. Using the CNN for image processing, one of the main problems is the robustness of a given task in a real VLSI chip. It will be shown that very different tasks such as 2D or 3D deconvolution and texture segmentation can be solved in a real VLSI CNN environment without significant loss of efficiency and accuracy under low precision (about 6–8 bits) and random variability of the VLSI parameters. The CNN turns out to be very robust against template noise, image noise, imperfect estimation of templates and parameter accuracy. The parameters of a template are tuned using genetic learning. These optimized parameters depend on the precision of the architecture. It was found that about 6–8 bits of precision is enough for a complicated multilayer deconvolution, while only 4 bits of precision is enough for difficult texture segmentation in the presence of noise and parameter variances. The tolerance sensitivity of template parameters is considered for VLSI implementation. Theory and examples are demonstrated by many results using real-life microscopic images and natural textures.     

Complete stability of feedback CNNs with dynamic memristors and second‐order cells

The paper considers a feedback cellular neural network (CNN) obtained by interconnecting elementary cells with an ideal capacitor and an ideal flux‐controlled memristor. It is supposed that during the analogue computation of the CNN the memristors behave as dynamic elements, so that each dynamic memristor (DM)‐CNN cell is described by a second‐order differential system in the state variables given by the capacitor voltage and the memristor flux. The proposed networks are called DM‐CNNs, that is CNNs using a dynamic (D) memristor (M). After giving a foundation to the DM‐CNN model, the paper establishes a fundamental result on complete stability, that is convergence of solutions toward equilibrium points, when the DM‐CNN has symmetric interconnections. Because of the presence of dynamic memristors, a DM‐CNN displays peculiar and basically different dynamic properties with respect to standard CNNs. First of all a DM‐CNN computes during the time evolution of the memristor fluxes, instead of the capacitor voltages as for a standard CNN. Furthermore, when a steady state is reached, the memristors keep in memory the result of the computation, that is the limiting values of the fluxes, while all memristor currents and voltages, as well as all currents, voltages, and power in the DM‐CNN vanish. Instead, for standard CNNs, currents, voltages, and power do not drop off when a steady state is reached. Copyright © 2016 John Wiley & Sons, Ltd.     

On the universe of stable cellular neural networks

A cellular neural network (CNN) is a novel analogue circuit architecture with many desirable features. This paper extends previous stability results of CNNs to include classes of strictly sign-symmetric and acyclic templates. We show that most of the 3×3 strictly sign-symmetric templates are stable almost everywhere, with the unknown templates reduced to three classes. We also introduce template graphs and CNN graphs and utilize them to obtain results concerning stability and irreducibility of CNN templates.     

A rigorous design method for binary cellular neural networks

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.     

Cellular neural networks based on resonant tunnelling diodes

Resonant tunnelling diodes (RTDs) have intriguing properties which make them a primary nanoelectronic device for both analogue and digital applications. We propose two different types of RTD‐based cells for the cellular neural network (CNN) which exhibit superior performance in terms of complexity, functionality, or processing speed compared to standard cells. In the first cell model, the resistor of the standard cell is replaced by an RTD, which results in a more compact and versatile cell which requires neither self‐feedback nor a non‐linear output function, and allows three stable equilibrium points. If a resonant tunnelling transistor (RTT) is used instead of the RTD, the dynamics can be controlled through its gate voltage as an additional network parameter. In a majority of CNN applications, bistable cells are sufficient. Utilizing RTD‐based bistable logic elements to store the state of the cell, switching occurs almost instantaneously as virtually no charge transfer is necessary, and it is possible to implement non‐linear connections in a straightforward manner. Hence, it turns out that RTD‐based CNNs are tailor‐made for the implementation of extremely fast bipolar operations and non‐linear templates. The ideas presented in this paper may also be beneficially applied to other types of circuits and systems such as A/D converters or sigma‐delta modulators. Copyright © 2001 John Wiley & Sons, Ltd.     

Robot vision with cellular neural networks: a practical implementation of new algorithms

Cellular neural networks (CNNs) are well suited for image processing due to the possibility of a parallel computation. In this paper, we present two algorithms for tracking and obstacle avoidance using CNNs. Furthermore, we show the implementation of an autonomous robot guided using only real‐time visual feedback; the image processing is performed entirely by a CNN system embedded in a digital signal processor (DSP). We successfully tested the two algorithms on this robot. Copyright © 2006 John Wiley & Sons, Ltd.     

Watermarking on CNN‐UM for image and video authentication

In this paper a new approach to fragile watermarking technique is introduced. This problem is particularly interesting in the field of modern multimedia applications, when image and video authentication are required. The approach exploits the cellular automata suitability to work as pseudorandom pattern generators and extends the related algorithms under the framework of the cellular non‐linear networks (CNNs). The result is a novel way to perform watermarking generation in real time, using the presently available CNN‐universal chip prototypes. In this paper, both the CNN algorithms for fragile watermarking as well as on‐chip experimental results are reported, confirming the suitability of CNNs to successfully act as real‐time watermarking generators. The availability of CNN‐based visual microprocessors allows to have powerful algorithms to watermark in real time images or videos for efficient smart camera applications. Copyright © 2004 John Wiley & Sons, Ltd.     

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

We 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.     

Compact CMOS implementation of a low‐power,current‐mode programmable cellular neural network

We report on the design and characterization of a full‐analog programmable current‐mode cellular neural network (CNN) in CMOS technology. In the proposed CNN, a novel cell‐core topology, which allows for an easy programming of both feedback and control templates over a wide range of values, including all those required for many signal processing tasks, is employed. The CMOS implementation of this network features both low‐power consumption and small‐area occupation, making it suitable for the realization of large cell‐grid sizes. Device level and Monte Carlo simulations of the network proved that the proposed CNN can be successfully adopted for several applications in both grey‐scale and binary image processing tasks. Results from the characterization of a preliminary CNN test‐chip (8×1 array), intended as a simple demonstrator of the proposed circuit technique, are also reported and discussed. Copyright © 2001 John Wiley & Sons, Ltd.     

A novel approach to propagation prediction in confined and diffracting rough surfaces

Modern wireless systems operating in the millimetre waves bands are now to be used in complex confined media such as mining environment. System designs require that multipath, fading and diffraction effects be accounted for in a suitable model. This paper presents a new propagation prediction method that can be used in mine corridors, buildings, underground roads, galleries with rough surfaces and others complex sub‐surface installations. A method named cascade impedance method (CIM) is used in combination with the segmental statistic method (SSM) in mine tunnels having considerable wall roughness and bending forms. Two (2D)‐ and three (3D)‐dimensional profiles of the radio waves are simulated and compared with available measurements at 2.45 and 18 GHz. Copyright © 2003 John Wiley & Sons, Ltd.     

External inputs,stable equilibria and complete stability of CNNs

We construct two cellular neural networks (CNNs) of three cells to show that a CNN can have stable equilibria, but is not completely stable and that the complete stability of CNN depends on the choice of external inputs. These phenomena cannot occur for two‐cell CNNs. Copyright © 2003 John Wiley & Sons, Ltd.     

New designs of low/high‐pass and mid‐pass/stop FIR digital filters

New designs of highly efficient low/high‐ and mid‐pass/stop (centre‐symmetric band‐pass/stop) FIR non‐recursive digital filters are presented. The designs are based on the modulation property of DFT, applied to the already presented MAXFLAT halfband low‐pass filters. The presented filters have explicit formulas for their tap‐coefficients, and therefore are very easy to design. They have highly smooth frequency response and wider transition regions like MAXFLAT filters. The design formulae are modified to give new classes of low/high‐ and mid‐pass/stop filters, for which, like in equiripple filters, the transition bandwidth can be reduced by increasing the size of ripple on magnitude response. It is shown, with the help of design examples, that the performance of these filters is comparable to that of equiripple filters. Copyright © 2001 John Wiley & Sons, Ltd.     

Cellular neural network with trapezoidal activation function

This paper presents a cellular neural network (CNN) scheme employing a new non‐linear activation function, called trapezoidal activation function (TAF). The new CNN structure can classify linearly non‐separable data points and realize Boolean operations (including eXclusive OR) by using only a single‐layer CNN. In order to simplify the stability analysis, a feedback matrix W is defined as a function of the feedback template A and 2D equations are converted to 1D equations. The stability conditions of CNN with TAF are investigated and a sufficient condition for the existence of a unique equilibrium and global asymptotic stability is derived. By processing several examples of synthetic images, the analytically derived stability condition is also confirmed. Copyright © 2005 John Wiley & Sons, Ltd.     

Fabrication of high‐quality two‐dimensional photonic crystals based on porous alumina

We fabricated porous alumina templates with a well‐ordered pore array by a pre‐triggered anodization method. The arrangement of pores in the fabricated templates was set by a Ni‐dot stamper. The structure of the templates was analyzed by field emission scanning electron microscopy (FESEM), two‐dimensional Fourier transformation of FESEM images and optical means. It was found that the porous alumina templates have a high‐quality, extended, two‐dimensional hexagonal lattice, which can be used in the fabrication of two‐dimensional magnetophotonic crystals (2D‐MPCs). © 2007 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

Membrain: A cellular neural network model based on a vibrating membrane

This paper introduces the Membrain model describing a neural network architecture which is similar to the architecture underlying the class of cellular neural networks (CNNs). the main difference pertains to the characteristic processing equation, which is based on a wave equation instead of a heat equation. Within the CNN framework, a cellular Membrain model may be obtained by replacing the neuron output function by a first-order state equation. Furthermore, the network-cloning templates are chosen such that the CNN behaves like a system of coupled harmonical oscillators. Since the energy of such a system is bounded, the piecewise linear neuron characteristic function may be chosen such that it always operates in the linear regime. Our starting point is the analytical and general solution for forced vibrations with damping. This solution applies to a Membrain neural network whose functional architecture is based on the specialized solution for a network of coupled harmonic oscillators. In particular, we present a Membrain CNN (MCNN) having a toroidal connection structure such that the natural modes of vibration of the net are translation-invariant. Moreover, depending on the point group of the network, some rotation invariance can also be obtained. Identifying the input of such a network with the initial state of the oscillators gives rise to an output which is in essence a transversally travelling wave made up of components which are coupled harmonic neuronal oscillators; that is, the wave is a superposition of natural modes of vibration of the network. the temporal wave pattern may be transformed into a one-dimensional temporal signal which is invariant under translation of the initial deflection pattern of the MCNN. the amplitudes of the components in the temporal signal correspond to the power spectrum of the natural vibration modes in the MCNN. Interpreting the initial deflection pattern as a grey-level image, the temporal signal can be viewed as a modulation of a translation-invariant ‘fingerprint’ of the image. the signal may be sampled such that the modulated ‘fingerprint’ can be classified using some of the traditional neural network models. In particular we show that (1) a self-organizing feature map clusters correlated images and (2) a back-propagation neural network extracts position-invariant features.     

Multi‐template approach to realize central pattern generators for artificial locomotion control

Biologically inspired control of artificial locomotion often makes use of the concept of central pattern generator (CPG), a network of neurons establishing the locomotion pattern within a lattice of neural activity. In this paper a new approach, based on cellular neural networks (CNNs), for the design of CPGs is presented. From a biological point of view this new approach includes an approximated chemical synapse realized and implemented in a CNN structure. This allows to extend the results, previously obtained with a reaction‐diffusion‐CNN (RD‐CNN) for the locomotion control of a hexapod robot, to a more general class of artificial CPGs in which the desired locomotion pattern and the switching among patterns are realized by means of a spatio‐temporal algorithm implemented in the same CNN structure. Copyright © 2002 John Wiley & Sons, Ltd.     

A method for the approximate synthesis of cellular non‐linear networks—Part 2: Circuit reduction

In this paper, we face the problem of model reduction in piecewise‐linear (PWL) approximations of non‐linear functions. The reduction procedure presented here is based on the PWL approximation method proposed in a companion paper and resorts to a strategy that exploits the orthonormality of basis functions in terms of a proper inner product. Such a procedure can be favourably applied to the synthesis of the resistive parts of cellular non‐linear networks (CNNs) to reduce the complexity of the resulting circuits. As an example, the method is applied to a case study concerning a CNN for image processing. Copyright © 2003 John Wiley & Sons, Ltd.     

EVALUATION OF CNN TEMPLATE ROBUSTNESS TOWARDS VLSI IMPLEMENTATION

In this paper a method for the evaluation of static robustness towards random variations in cellular neural network (CNN) templates is proposed. From this evaluation, circuit accuracy specifications for a VLSI implementation are derived which allow the designer to optimize the performance. Moreover, from this evaluation method, guidelines for robust template designs are derived and parametric testing templates are developed.     

Guiding a mobile robot with cellular neural networks

We show how cellular neural networks (CNNs) are capable of providing the necessary signal processing needed for visual navigation of an autonomous mobile robot. In this way, even complex feature detection and object recognition can be obtained in real time by analogue hardware, making fully autonomous real‐time operation feasible. An autonomous robot was first simulated and then implemented by simulating the CNN with a DSP. The robot is capable of navigating in a maze following lines painted on the floor. Images are processed entirely by a CNN‐based algorithm, and navigation is controlled by a fuzzy‐rule‐based algorithm. Copyright © 2002 John Wiley & Sons, Ltd.     

CNN-based difference-controlled adaptive non-linear image filters

In this paper, we develop a common cellular neural network framework for various adaptive non-linear filters based on robust statistic and geometry-driven diffusion paradigms. The base models of both approaches are defined as difference-controlled non-linear CNN templates, while the self-adjusting property is ensured by simple analogic (analog and logic) CNN algorithms. Two adaptive strategies are shown for the order statistic class. When applied to the images distorted by impulse noise both give more visually pleasing results with lower-frequency weighted mean square error than the median base model. Generalizing a variational approach we derive the constrained anisotropic diffusion, where the output of the geometry-driven diffusion model is forced to stay close to a pre-defined morphological constraint. We propose a coarse-grid CNN approach that is capable of calculating an acceptable noise-level estimate (proportional to the variance of the Gaussian noise) and controlling the fine-grid anisotropic diffusion models. A combined geometrical–statistical approach has also been developed for filtering both the impulse and additive Gaussian noise while preserving the image structure. We briefly discuss how these methods can be embedded into a more complex algorithm performing edge detection and image segmentation. The design strategies are analysed primarily from VLSI implementation point of view; therefore all non-linear cell interactions of the CNN architecture are reduced to two fundamental non-linearities, to a sigmoid type and a radial basis function. The proposed non-linear characteristics can be approximated with simple piecewise-linear functions of the voltage difference of neighbouring cells. The simplification makes it possible to convert all space-invariant non-linear templates of this study to a standard instruction set of the CNN Universal Machine, where each instruction is coded by at most a dozen analog numbers. Examples and simulation results are given throughout the text using various intensity images. © 1998 John Wiley & Sons, Ltd.