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).
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)
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
}, and Sr
is the local neighbourhood of cell C
) defined in (1
), which controls the influence of the input data X
} and the network output Y
} 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.