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

In this paper, we develop a common cellular neural network framework for various adaptive nonlinear filters based on robust statistic and geometry-driven diffusion paradigms. The base models of both approaches are defined as difference-controlled nonlinear 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 analyzed primarily from VLSI implementation point of view, therefore all nonlinear cell interactions of the CNN architecture are reduced to two fundamental nonlinearities, to a sigmoid-type and a radial basis function. The proposed nonlinear characteristics can be approximated with simple piecewise-linear functions of the voltage difference of neighboring cells. The simplification makes it possible to convert all space invariant nonlinear 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.