Abstract
Since its seminal publication in 1988, the Cellular Neural Network (CNN) (Chua & Yang, 1988) paradigm have attracted research community’s attention, mainly because of its ability for integrating complex computing processes into compact, real-time programmable analogic VLSI circuits (Rodríguez et al., 2004). Unlike cellular automata, the CNN model hosts nonlinear processors which, from analogic array inputs, in continuous time, generate analogic array outputs using a simple, repetitive scheme controlled by just a few real-valued parameters. CNN is the core of the revolutionary Analogic Cellular Computer, a programmable system whose structure is the so-called CNN Universal Machine (CNN-UM) (Roska & Chua, 1993). Analogic CNN computers mimic the anatomy and physiology of many sensory and processing organs with the additional capability of data and program storing (Chua & Roska, 2002). This article reviews the main features of this Artificial Neural Network (ANN) model and focuses on its outstanding and more exploited engineering application: Digital Image Processing (DIP).
TopBackground
In the following paragraphs, a definition of the parameters and structure of the CNN is performed in order to clarify the practical usage of the model in DIP.
The standard CNN architecture consists of an M × N rectangular array of cells C(i,j) with Cartesian coordinates (i,j), i = 1, 2, …, M, j = 1, 2, …, N. Each cell or neuron C(i,j) is bounded to a connected neighbourhood or sphere of influence Sr(i,j) of positive integer radius r, which is the set of all neighbouring cells satisfying the following property:
(1)This set is sometimes referred as a (2r +1) × (2r +1) neighbourhood, e.g., for a 3 × 3 neighbourhood, r should be 1. Thus, the parameter r controls the connectivity of a cell, i.e. the number of active synapses that connects the cell with its immediate neighbours.
When r > N /2 and M = N, a fully connected CNN is obtained, where every neuron is connected to every other cell in the network and Sr(i,j) is the entire array. This extreme case corresponds to the classic Hopfield ANN model (Chua & Roska, 2002).
The state equation of any cell C(i,j) in the M × N array structure of the standard CNN may be described mathematically by:
(2) where
C and
R are values that control the transient response of the neuron circuit (just like an
RC filter, typically set to unity for the sake of simplicity),
I is generally a constant value that biases or thresholds the state matrix
Z = {
zij}, and
Sr is the local neighbourhood of cell
C(
i,
j) defined in (
1), which controls the influence of the input data
X = {
xij} and the network output
Y = {
yij} for time
t.
This means that both input and output planes interact with the state of a cell through the definition of a set of real-valued weights, A(i, j; k, l) and B(i, j; k, l), whose size is determined by the neighbourhood radius r. The matrices or cloning templates A and B are called the feedback and feed-forward (or control) operators, respectively.
Key Terms in this Chapter
Transient: In electronics, a transient system is a short life oscillation in a system caused by a sudden change of voltage, current, or load. They are mostly found as the result of the operation of switches. The signal produced by the transient process is called the transient signal or simply the transient. Also, the transient of a dynamic system can be viewed as its path to a stable final output.
Feedback: The signal that is looped back to control a system within itself. When the output of the system is fed back as a part of the system input, it is called a feedback loop. A simple electronic device which is based on feedback is the electronic oscillator. The Phase-Locked Loop (PLL) is an example of complex feedback system.
Spatial Convolution: A term used to identify the linear combination of a series of discrete 2D data (a digital image) with a few coefficients or weights. In the Fourier theory, a convolution in space is equivalent to (spatial) frequency filtering.
Neuromorphic: A term coined by Carver Mead in the late 1980s to describe VLSI systems containing electronic analogue circuits that mimic neuro-biological architectures present in the nervous system. More recently, its definition has been extended to include both analogue, digital and mixed mode A/D VLSI systems that implements models of neural systems as well as software algorithms.
Piecewise Linear Function: A function f(x) that can be split into a number of linear segments, each of which is defined for a non-overlapping interval of x.
Template: Also known as kernel, or convolution kernel, is the set of coefficients used to perform a spatial filter operation over a digital image via the spatial convolution operator.
Artificial Neural Network (ANN): A system made up of interconnecting artificial neurons or nodes (usually simplified neurons) which may share some properties of biological neural networks. They may either be used to gain an understanding of biological neural networks, or for solving traditional artificial intelligence tasks without necessarily attempting to model a real biological system. Well known examples of ANN are the Hopfield, Kohonen and Cellular (CNN) models.
VLSI: Acronym that stands for Very Large Scale Integration. It is the process of creating integrated circuits by combining thousands (nowadays hundreds of millions) of transistor-based circuits into a single chip. A typical VLSI device is the microprocessor.