On the controllability of a two-cell CNN

Physics Letters A, 2005

A Cellular Nonlinear Network (CN N) based on uncoupled nonlinear oscillators is proposed for image processing purposes. It is shown theoretically and numerically that the contrast of an image loaded at the nodes of the CN N is strongly enhanced, even if this one is initially weak. An image inversion can be also obtained without reconfiguration of the network whereas a gray levels extraction can be performed with an additional threshold filtering. Lastly, an electronic implementation of this CNN is presented.

International Journal of Circuit Theory and Applications, 2005

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 deÿned 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 su cient 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 conÿrmed. 394 E. BILGILI,İ. C. G OKNAR AND O. N. UCAN CNN stability is analysed for the standard activation function as in References , (v) global exponential stability conditions of CNN via a new Lyapunov function are stated in Reference [9]. It is well known that the standard uncoupled CNN single-layer structures, extremely useful for realizing Boolean functions, are not capable of classifying linearly nonseparable data. The parity is a binary function of the inputs, which returns a high output if the number of inputs set to 1 is odd and a low output if that number is even. Therefore, for n inputs, the parity problem consists of being able to divide the n-dimensional input space into disjoint decision regions such that all input patterns in the same region yield the same output and, thus is linearly non-separable. Uncoupled CNN can only classify linearly separable data, that is can only separate the input space with hyper-planes [10]. Recently, a single perceptron-like cell with: (i) double threshold, (ii) implemented using only ÿve MOS transistors, (iii) capable of classifying data which are not linearly separable has been reported in References .

1991

IEEE Transactions on Circuits and Systems I: Regular Papers, 2004

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.

2010 12th International Workshop on Cellular Nanoscale Networks and their Applications (CNNA 2010), 2010

Approaching the limits of scaling down of CMOS circuits where transistors can switch faster and faster transmitting information between different areas of an integrated circuit has great importance. The speed of signals are determined by the physical properties of the medium therefore the distance between the elements should be decreased to improve performance. Array processors are a good candidate to solve this problem. Similar approach is required on today high performance field programmable logic devices where wire delay dominates over gate (LUT) delay. Centralized control unit of a configurable accelerator might become a performance bottleneck on the current state-of-the-art FPGAs. In the paper a process network inspired approach is given to create distributed control units. The advantage of the proposed method will be shown by designing a complex multi-layer array computing architecture to emulate the operation of a mammalian retina in real time.

In this contribution, we propose the use of Cellular Neural Networks as an application for the image segmentation of cinematographic image sequences. The proposed approach is based on a Cellular Neural network cost function that takes into account motion and colour. Cellular Neural Networks are of particular interest for hardware implementation due to the inherent parallelism and initial results using an FPGA simulator are also presented.

IEEE Transactions on Very Large Scale Integration (VLSI) Systems, 2000

The resonant tunneling diode (RTD) has found numerous applications in high-speed digital and analog circuits due to the key advantages associated with its folded back negative differential resistance (NDR) current-voltage (I-V) characteristics as well as its extremely small switching capacitance. Recently, the RTD has also been employed to implement high-speed and compact cellular neural/nonlinear networks (CNNs) by exploiting its quantum tunneling induced nonlinearity and symmetrical I-V characteristics for both positive and negative voltages applied across the anode and cathode terminals of the RTD. This paper proposes an RTD-based CNN architecture and investigates its operation through driving-point-plot analysis, stability and settling time study, and circuit simulation. Full-array simulation of a 128 128 RTD-based CNN for several image processing functions is performed using the Quantum Spice simulator designed at the University of Michigan, where the RTD is represented in SPICE simulator by a physics based model derived by solving Schrödinger's and Poisson's equations self-consistently. A comparative study between different CNN implementations reveals that the RTD-based CNN can be designed superior to conventional CMOS technologies in terms of integration density, operating speed, and functionality. Index Terms-Resonant tunneling diode (RTD), cellular neural/ nonlinear network (CNN), full array simulation, settling time analysis. I. INTRODUCTION S INCE its invention by Chua and Yang in 1988 [1], [2], the cellular neural/nonlinear network (CNN) has been much acclaimed as a powerful back-end analog array processor, capable of accelerating various computation-intensive tasks in image processing, pattern formation and recognition, motion detection, robotics, and various other real-time problem solving that requires complex computation [3]. In such real-world applications, massively parallel computation of spatial data over a 2-D surface is needed to process data in real-time, albeit computational functions are rather simple algebraic operations and each array element concurrently performs identical operation. The features of CNN that make it an easily implementable parallel computing architecture relative to fully connected neural networks are mentioned in [4] but reiterated here:

IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 2003

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.

IEEE Circuits and Systems Magazine, 2001

The paradigm of Cellular Neural Networks (CNNs)is going to achieve a complete maturity. In fact, from a methodological point of view, important results on their digitally programmable analog dynamics have been gained, completed with thousands of application routines. This has encouraged the spreading of a great number of applications in the most different disciplines. Moreover, their structure, tailor made for VLSI realization, has led to the production of some chip prototypes that, embedded in a computational infrastructure, have produced the first analogic cellular computers. This completes the framework and makes it possible to realize complex spatio-temporal and filtering tasks on a time scale of microseconds. In this paper some sketches on the main aspects of CNNs, from the formal to the hardware prototype point of view, are presented together with some appealing applications to illustrate complex image, visual and spatio-temporal dynamics processing

This study employed the use of Cellular Neural Networks (CNN) for Edge Detection in images due to its high operational speed. The process of edge detection is unavoidable in many image processing tasks such as obstacle detection and satellite picture processing .The conventional edge detector models such as Sobel Operator, Robert Cross, among which Canny is the best, have high computational time. The CNN Model is a class of Differential Equation that has been known to have many application areas and high operational speed. The work investigated four parameters: resolutions, processing time, false alarm rate, and usability for performance evaluation. The CNN Model was modified by using hyperbolic tangent (tanh x) and Von Neumann Neighborhood. The modified CNN Model and enhanced Canny Model were implemented using MATLAB 7.0 running on Pentium III and 128 MB RAM Personal Computer. A series of images served as input for both Canny and modified CNN Model. With several images tested, the overall results indicated that the two models have similar resolutions with average computational time of 1.1078 seconds and 2.293 seconds for CNN-based and Enhanced Canny Model respectively. The hyperbolic entry a 22 of the cloning template A made our work fully controllable since max(tanh x) = +1 and min(tanh x) = -1. A consideration of the set of digital images showed that edge maps which result from Canny Model have adjacent boundaries that tend to merge. The CNN model obviously produced the optimum edge map with edges that are one-pixel wide and unbroken. The false alarm rate of noise variance probability     2  F P for which an edge detector can easily declare an edge pixel given that there is no edge, showed the value 0.8525 for CNN Model and 0.4595 for Canny Model. The CNN parameters can be adjusted and modeled to solve Partial Differential Equations and Maximum likelihood problems for edge detection while Canny Model cannot be easily adjusted for any other functionality. The CNN-based edge detector performed better than the popular canny operator in terms of the computational time required, usability, and false alarm rate.

This paper deals with the obtention of robust parameter configurations for DT-CNNs and for a class of CT-CNNs (here called CT-CNNs with Discrete Configurations, DC-CT-CNN), in the presence of additive and multiplicative implementation errors. Expressions that characterize the tolerance to both multiplicative and additive errors caused by circuit inaccuracies in DT-CNNs and DC-CT-CNNs VLSI implementation are first deduced. Taking into account those expressions it is proposed to obtain robust parameter configurations, by using a design process based on local rules, as the solution of a single linear programming problem. The process is applied to the generation of robust configuration for some tasks. The tolerance to errors of these configurations has been corroborated by simulations. The differences in parameter values and tolerance to errors, between the robust configuration obtained for solving a particular task in DT-CNNs and that obtained in DC-CT-CNNs, are given. 1.-INTRODUCTION The Cellular Neural Network model proposed by L. O. Chua and L. Yang [1] has been widely used for image processing tasks [2]. The time evolution of the state of a cell (neuron or pixel) c in an NxM-cell CNN is described by the differential equation [1]: where n denotes a generic cell belonging to the neighbourhood of cell c, N R (c), with radius equal to R (for example, N 1 (c) is the set of 3x3 cells centred on c, N 1 (c)={ c-N-1, c-N, c-N+1, c-1, c, c+1, c+N-1, c+N, c+N+1}). x c is the state of cell c, y n and u n are the output and the input, respectively, of the cell n, I is an offset term, and the matrices A and B are called feedback and control templates respectively. Some authors have proposed [3] a discrete-time (DT) version of CNN obtained by applying the Euler integration algorithm to discretise the cell state equation. The state of a cell c in an NxM-cell DT-CNN is described

2018

This paper presents implementation of a chaotic Cellular Neural Network (CNN) on Field Programmable Gate Array (FPGA). The network has two non-autonomous cells and exhibits chaotic behavior. In the implementation stage, Verilog Hardware Description Language (HDL) is used and discrete time model of the network is coded on Xilinx ISE Design Suite 13.2. It seems that the chaotic attractor can be used as entropy source or short key (seed) of chaos based random number generator design.

ISRN Machine Vision, 2012

An artificial cell is comprised of the most basic elements in a hierarchical system, that has minimal functionality, but general enough to obey the rules of "artificial life." The ability to replicate, organize hierarchy, and generalize within an environment is some of the properties of an artificial cell. We present a hardware artificial cell having the properties of generalization ability, the ability of self-organization, and the reproducibility. The cells are used in parallel hardware architecture for implementing the realtime 2D image convolution operation. The proposed hardware design is implemented on FPGA and tested on images. We report improved processing speeds and demonstrate its usefulness in an image filtering application. O16 [0 : 31] Conv out [0 : 31] Status Fltr 3 × 3 Figure 4: The hierarchical cell architecture for 2D convolution operator.

Nonlinear Analysis: Real World Applications, 2010

It is well known that one-dimensional cellular neural networks (1-D CNNs) with the template A = [1, 2, −1] can perform connected component detection (CCD). However this has been confirmed only by numerical and laboratory experiments. In this paper, sufficient conditions for 1-D CNNs to perform CCD are obtained through theoretical analysis. Main result shows that a wide class of templates including A = [1, 2, −1] can be used for CCD.

2011

An artificial cell is comprised of the most basic elements in a hierarchical system, that has minimal functionality, but general enough to obey the rules of "artificial life." The ability to replicate, organize hierarchy, and generalize within an environment is some of the properties of an artificial cell. We present a hardware artificial cell having the properties of generalization ability, the ability of self-organization, and the reproducibility. The cells are used in parallel hardware architecture for implementing the realtime 2D image convolution operation. The proposed hardware design is implemented on FPGA and tested on images. We report improved processing speeds and demonstrate its usefulness in an image filtering application.