Non‐linear coupled CNN models for multiscale image analysis
Fernando Corinto, Mario Biey, Marco Gilli · International Journal of Circuit Theory and Applications · 2006
Abstract A CNN model of partial differential equations (PDEs) for image multiscale analysis is proposed. The model is based on a polynomial representation of the diffusivity function and defines a paradigm of polynomial CNNs, for approximating a large class of non‐linear isotropic and/or anisotropic PDEs. The global dynamics of space‐discrete polynomial CNN models is analysed and compared with the dynamic behaviour of the corresponding space‐continuous PDE models. It is shown that in the isotropic case the two models are not topologically equivalent; in particular, discrete CNN models allow one to obtain the output image without stopping the image evolution after a given time (scale). This property represents an advantage with respect to continuous PDE models and could simplify some image preprocessing algorithms. Copyright © 2006 John Wiley & Sons, Ltd.