A behavioural modelling technique for visual microprocessor mixed‐signal VLSI chips

We describe a novel cellular connectionist neural network model for the implementation of clustering-based Bayesian image segmentation with Gibbs random-field spatial constraints. The success of this algorithm is largely due to the neighborhood constraints modeled by the Gibbs random field. However, the iterative enforcement of the neighborhood constraints involved in the Bayesian estimation would generally require tremendous computational power. Such computational requirement hinders the real-time application of the Bayesian image segmentation algorithms. The cellular connectionist model proposed aims at implementing the Bayesian image segmentation with real-time processing potentials. With a cellular neural network architecture mapped onto the image spatial domain, the powerful Gibbs spatial constraints are realized through the interactions among neurons connected through their spatial cellular layout. This network model is structurally similar to the conventional cellular network. However, in this new cellular model, the processing elements designed within the connectionist network are functionally more versatile to meet the challenging needs of Bayesian image segmentation based on the Gibbs random field. We prove that this cellular neural network does converge to the desired steady state with a properly designed update scheme. Examples of CT volumetric medical image segmentation are presented to demonstrate the potential of this cellular neural network for a specific image segmentation application.

Complex behavior of polynomial FitzHugh–Nagumo cellular neural network model

The paper considers the full-range (FR) model of cellular neural networks (CNNs) with ideal hard-limiter non-linearities that limit the allowable range of the neuron state variables. It is also supposed that there is a concentrated delay (D) in the neuron interconnections. Due to the presence of multivalued nonlinearities the D-FRCNN model is mathematically described by a retarded differential inclusion. The main result is a rigorous proof that, in the case of nonsymmetric cooperative (nonnegative) interconnections, and delayed interconnections, the semiflow generated by D-FRCNNs is monotone, and that monotonicity implies some basic restrictions on the long-term behavior of the solutions. The result is compared with recent results in the literature on semiflows generated by cooperative standard CNNs, with and without delays.

In this paper we show cellular neural network (CNN) models of some basic types of cells characterized by diverse spiking patterns. After presenting some preliminary models (ion channels, neurons), CNN models of action potential generation are given, followed by an analysis of the rate-coding capabilities of the models. Furthermore, we show CNN models of synaptic connections. Finally, CNN models of neurons with diverse intrinsic firing patterns are presented.

In the present work an adaptation of the cellular neural network (CNN) model to grey scale image processing is proposed. This task is performed programming the network to work as a classical spatial filter, taking advantage of the neural network structure in order to improve the filtering effects. This enhancement is carried out by the inclusion of the feedback of the state variables and the adaptation of the input bias of every neuron based on the brightness of the image. A proper choice of the gain of the output function may also improve some of the network capabilities.

A model of cellular neural networks with mixed delays is proposed. Applying contraction mapping fixed point theorem and differential inequality technique, several sufficient conditions are derived to ensure the existence and exponential stability of weighted pseudo anti‐periodic solutions for the proposed neural networks. Finally, a numerical simulation example is given to illustrate the effectiveness of the obtained results.

There are many cases where image processing is performed using the neural network. The content of this Chapter is implementation of CNN (Cellular Neural Network) on a chip in a new original digital approach. First, testing of some features of the proposed cell of the neural network is evaluated. Then the design of the basic circuit containing the cell for the CNN will be introduced. The idea is to use it for a more complex chip with image processing application. CNN have been extensively used in various image processing applications. One of the most important problems in signal processing is noise removal. The input signals mostly arrive from the real world and therefore they contain relatively high amounts of noise. The CNN circuits are capable of removing this noise partly. The possibility of noise removing depends on the template (weight) coefficients between the cells. CNN networks are based on relatively simple principles, very similar to biological neurons. The input signals are multiplied by appropriate weights, the weight matrix being given intuitively, as it is typical for CNN networks. Then they are added and multiplied by the transfer function. We describe also the settings of weights coefficients. CNN have been extensively used in various image processing applications ( Matsumoto & Yokohama, 1990 ) or ( Sziranyi & Csicsvari, 1993 ). The main problem of CNN implementations on a chip is the chip area consumption. The most area is reserved for the multiplexer, so we looked for alternative multiplications. We describe the achieved results with the designed chip. During the creation of the chip architecture we proposed and introduced special original coding for the weight coefficients. After simulations we recognized that the results were better with rounding than without it, but we found that the rounding during multiplication was not as important as we previously expected. Therefore we decided – instead of a hardware multiplexer – to use multiplication realized by simple gate timing of the special signal. The circuit was designed as a digital synchronized circuit. For the design and simulation we used the Xilinx tool. The cell is based on sub-circuits as it will be shown in detail. The Chapter describes the designed circuit. We introduce also our novel simulator for the CNN using the program tool Visual Basic for Application, and its algorithm which was based on the same principle as the planned designed circuit. The network can process the patterns with 400 points of recognition. O pe n A cc es s D at ab as e w w w .ite ch on lin e. co m

The paper discusses the detection of weaknesses and defects on photolithographic masks by cellular neural networks. The detection by cellular neural networks is performed with the advantages of their massive parallel architecture. First a survey is given of actual methods for the detections of weaknesses and defects. Then the relations between the structures of the mask layouts and the real structures of the masks are defined by local design rules. These local design rules can also indirectly be used to detect most weaknesses and defects. After that, the design of the operators for the detection of weaknesses and defects are executed on the basis of the local design rules, using the method of Galias that is practicable by cellular neural networks. Then some examples of weakness and defect detections on real mask images by cellular neural networks are presented. Finally the results and future aims are discussed. >

This paper develops and validates through a series of presentable examples, a comprehensive high-precision, and ultrafast computing concept for solving nonlinear ordinary differential equations (ODEs) and partial differential equations (PDEs) with cellular neural networks (CNN). The core of this concept is a straightforward scheme that we call "nonlinear adaptive optimization (NAOP),” which is used for a precise template calculation for solving nonlinear ODEs and PDEs through CNN processors. One of the key contributions of this work is to demonstrate the possibility of transforming different types of nonlinearities displayed by various classical and well-known nonlinear equations (e.g., van der Pol-, Rayleigh-, Duffing-, Rössler-, Lorenz-, and Jerk-equations, just to name a few) unto first-order CNN elementary cells, and thereby enabling the easy derivation of corresponding CNN templates. Furthermore, in the case of PDE solving, the same concept also allows a mapping unto first-order CNN cells while considering one or even more nonlinear terms of the Taylor's series expansion generally used in the transformation of a PDE in a set of coupled nonlinear ODEs. Therefore, the concept of this paper does significantly contribute to the consolidation of CNN as a universal and ultrafast solver of nonlinear ODEs and/or PDEs. This clearly enables a CNN-based, real-time, ultraprecise, and low-cost computational engineering. As proof of concept, two examples of well-known ODEs are considered namely a second-order linear ODE and a second order nonlinear ODE of the van der Pol type. For each of these ODEs, the corresponding precise CNN templates are derived and are used to deduce the expected solutions. An implementation of the concept developed is possible even on embedded digital platforms (e.g., field programmable gate array (FPGA), digital signal processor (DSP), graphics processing unit (GPU), etc.). This opens a broad range of applications. Ongoing works (as outlook) are using NAOP for deriving precise templates for a selected set of practically interesting ODEs and PDEs equation models such as Lorenz-, Rössler-, Navier Stokes-, Schrödinger-, Maxwell-, etc.

The effect of the boundary conditions on the global dynamics of cellular neural networks (CNNs) is investigated. As a case study one dimensional template CNNs are considered. It is shown that if off-diagonal template elements have the same sign (i.e. the CNN is completely stable), then the qualitative dynamics is not influenced by the boundary conditions. If the off-diagonal template elements have opposite sign, then the boundary conditions behave as bifurcation parameters and can give rise to a very complex dynamic behavior. In particular they determine the equilibrium point patterns, the transition from stability to instability and the occurrence of several bifurcation phenomena leading to strange and/or chaotic attractor.

A Cellular Neural Network (CNN) is a highly-parallel, analog processor that can significantly outperform von Neumann architectures for certain classes of problems. Here, we show how emerging, beyond-CMOS devices could help to further enhance the capabilities of CNNs, particularly for solving problems with non-binary outputs. We show how CNNs based on devices such as graphene transistors -- with multiple steep current growth regions separated by negative differential resistance (NDR) in their I-V characteristics -- could be used to recognize multiple patterns simultaneously. (This would require multiple steps given a conventional, binary CNN.) Also, we demonstrate how tunneling field effect transistors (TFETs) can be used to form circuits capable of performing similar tasks. With this approach, more exotic device I-V characteristics are not required -- which should be an asset when considering issues such as cell-to-cell mismatch, etc. As a case study, we present a CNN-cell design that employs TFET-based circuitry to realize ternary outputs. We then illustrate how this hardware could be employed to efficiently solve a tactile sensing problem. The total number of computation steps as well as the required hardware could be reduced significantly when compared to an approach based on a conventional CNN.

Theoretic design of differential minimax controllers for stochastic cellular neural networks

An accelerated-time simulation of car traffic on a motorway using a CAS

Currently, the mechanical dynamics of soft tissue deformation is achieved by numerical time integrations such as the explicit or implicit integration; however, the explicit integration is stable only under a small time step, whereas the implicit integration is computationally expensive in spite of the accommodation of a large time step. This paper presents a cellular neural network method for stable simulation of soft tissue deformation dynamics. The non-rigid motion equation is formulated as a cellular neural network with local connectivity of cells, and thus the dynamics of soft tissue deformation is transformed into the neural dynamics of the cellular neural network. Results show that the proposed method can achieve good accuracy at a small time step. It still remains stable at a large time step, while maintaining the computational efficiency of the explicit integration. The proposed method can achieve stable soft tissue deformation with efficiency of explicit integration for surgical simulation.

This paper presents a novel class of cellular neural networks (CNNs), where output of a cell in the CNN is given by the piecewise-linear (PWL) function having multiple constant regions or a quantization function. CNNs with one of these output functions allow us to extend CNNs to image processing with multiple gray levels. Since each cell of the original CNN has the PWL output function with two saturation regions, the image-processing tasks are mainly developed for black and white output images. Hence, the proposed architecture will extend the promising nature of the CNN further. Moreover, the hysteresis characteristics are introduced for these functions, which make tolerance to a noise robust. It is demonstrated mathematically that under a mild assumption, the stability of the CNN, which has an output function with hysteresis characteristics, is guaranteed, and the impressive simulation results are also presented.