Cellular Neural Network Simulation and Modeling
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About the CNN in general
In 1988 papers from Leon O. Chua introduced the concept of the Cellular Neural Network. CNNs can be defined as “2D or 3D arrays of mainly locally connected nonlinear dynamical systems called cells, whose dynamics are functionally determined by a small set of parameters which control the cell interconnection strength” (Chua). These parameters determine the connection pattern, and are collected into the so-called cloning templates, which, once determined, define the processing of the whole structure.
Basic Characteristics of the CNN
The CNN can be defined as an M x N type array of identical cells arranged in a rectangular grid. Each cell is locally connected to its 8 nearest surrounding neighbors.
Each cell is characterized by uij, yij and xij being the input, the output and the state variable of the cell respectively.
Modeling and simulation of the CNN architecture
Simulation plays an important role in the design of the CNN cloning templates.
Therefore, it has to be fast enough to allow the design phase of various templates be accomplished in reasonable time.
At the same time, the simulation has to be accurate enough, to reflect the behavior of the analog circuitry correctly.
In practice, the simulation of the CNN involves a trade-off between accuracy and computation time.
The functional model of the CNN architecture (2)
As a closed form for the solution of the above equation cannot be given, it must be integrated numerically.
For the simulation of such equations on a digital computer, they must be mapped into a discrete-time system that
emulates the continuous-time behavior,
has similar dynamics
and converges to the same final state.
The error committed by this emulation depends on the choice of the method of integration, i. e. the way in which the integral is calculated.
Handling special cases for increasing performamce
What can be considered a special case from a programming point of view?
special templates (A, B)
To gain significant speed improvements, the case of special templates should be examined.
It is not uncommon within templates that extract local properties of the image (like edge detectors) to use a fully zero A template.
I have discovered, that revisiting the state equation when the A template is fully zero, significant improvements in speed can be achieved.
functional modeling (mathematical calculation according to the state-equation)
based on functional model
written in C++ programming language