Non-linear coupled CNN models for multiscale image analysis

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 nonlinear isotropic and/or anisotropic PDEs. The global dynamics of spacediscrete polynomial CNN models is analyzed and compared with the dynamic behavior 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.