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J. Álvaro Fernández (University of Extremadura, Badajoz, Spain)

DOI: 10.4018/978-1-59904-849-9.ch007

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TopThe 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 sphere of influence *S _{r}*(

This set is referred as a (2*r* +1) × (2*r* +1) neighbourhood. The parameter *r* controls the connectivity of a cell. When *r* > *N* /2 and *M* = *N*, a fully connected CNN is obtained, a case that corresponds to the classic Hopfield ANN model.

The state equation of any cell *C*(*i*,*j*) in the *M* × *N* array structure of the standard CNN may be described by:

where *C* and *R* are values that control the transient response of the neuron circuit (just like an *RC* filter), *I* is generally a constant value that biases the state matrix *Z* = {*z _{ij}*}, and

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 *r*. The cloning templates *A* and *B* are called the feedback and feed-forward operators, respectively.

An isotropic CNN is typically defined with constant values for *r*, *I*, *A* and *B*, implying that for an input image *X*, a neuron *C*(*i*, *j*) is provided for each pixel (*i*, *j*), with constant weighted circuits defined by the feedback and feed-forward templates *A* and *B*. The neuron state value *z _{ij}* is adjusted with the bias parameter

Dynamic Range: A term used to describe the ratio between the smallest and largest possible values of a variable quantity.

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.

Chebyshev Polynomial: An important type of polynomials used in data interpolation, providing the best approximation of a continuous function under the maximum norm.

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.

FPGA: Acronym that stands for Field-Programmable Gate Array, a semiconductor device invented in 1984 by R. Freeman that contains programmable interfaces and logic components called “logic blocks” used to perform the function of basic logic gates (e.g. XOR) or more complex combination functions such as decoders.

Bionics: The application of methods and systems found in nature to the study and design of engineering systems. The word seems to have been formed from “biology” and “electronics” and was first used by J. E. Steele in 1958.

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.

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