### 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 |
---|---|

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 1998 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Electrical and Electronic Engineering

### Cite this

*International Journal of Circuit Theory and Applications*,

*26*(4), 375-423.

**CNN-based difference-controlled adaptive non-linear image filters.** / Rekeczky, Csaba; Roska, T.; Ushida, Akio.

Research output: Contribution to journal › Article

*International Journal of Circuit Theory and Applications*, vol. 26, no. 4, pp. 375-423.

}

TY - JOUR

T1 - CNN-based difference-controlled adaptive non-linear image filters

AU - Rekeczky, Csaba

AU - Roska, T.

AU - Ushida, Akio

PY - 1998/7

Y1 - 1998/7

N2 - 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.

AB - 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.

KW - Adaptive non-linear filters

KW - CNN Universal Machine

KW - Geometry-driven diffusion

KW - Non-linear cellular neural networks

KW - Robust statistic filters

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UR - http://www.scopus.com/inward/citedby.url?scp=0032116248&partnerID=8YFLogxK

M3 - Article

VL - 26

SP - 375

EP - 423

JO - International Journal of Circuit Theory and Applications

JF - International Journal of Circuit Theory and Applications

SN - 0098-9886

IS - 4

ER -