### Abstract

In this paper, we develop a common cellular neural network framework for various adaptive non-linear filters based on robust statistic and geometry-driven diffusion paradigms. The base models of both approaches are defined as difference-controlled non-linear CNN templates, while the self-adjusting property is ensured by simple analogic (analog and logic) CNN algorithms. Two adaptive strategies are shown for the order statistic class. When applied to the images distorted by impulse noise both give more visually pleasing results with lower-frequency weighted mean square error than the median base model. Generalizing a variational approach we derive the constrained anisotropic diffusion, where the output of the geometry-driven diffusion model is forced to stay close to a pre-defined morphological constraint. We propose a coarse-grid CNN approach that is capable of calculating an acceptable noise-level estimate (proportional to the variance of the Gaussian noise) and controlling the fine-grid anisotropic diffusion models. A combined geometrical-statistical approach has also been developed for filtering both the impulse and additive Gaussian noise while preserving the image structure. We briefly discuss how these methods can be embedded into a more complex algorithm performing edge detection and image segmentation. The design strategies are analysed primarily from VLSI implementation point of view; therefore all non-linear cell interactions of the CNN architecture are reduced to two fundamental non-linearities, to a sigmoid type and a radial basis function. The proposed non-linear characteristics can be approximated with simple piecewise-linear functions of the voltage difference of neighbouring cells. The simplification makes it possible to convert all space-invariant non-linear templates of this study to a standard instruction set of the CNN Universal Machine, where each instruction is coded by at most a dozen analog numbers. Examples and simulation results are given throughout the text using various intensity images.

Original language | English |
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Pages (from-to) | 375-423 |

Number of pages | 49 |

Journal | International Journal of Circuit Theory and Applications |

Volume | 26 |

Issue number | 4 |

Publication status | Published - Jul 1 1998 |

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### Keywords

- Adaptive non-linear filters
- CNN Universal Machine
- Geometry-driven diffusion
- Non-linear cellular neural networks
- Robust statistic filters

### ASJC Scopus subject areas

- Electronic, Optical and Magnetic Materials
- Computer Science Applications
- Electrical and Electronic Engineering
- Applied Mathematics

### Cite this

*International Journal of Circuit Theory and Applications*,

*26*(4), 375-423.