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.

Non-linear coupled CNN models for multiscale image analysis / Corinto, Fernando; Biey, Mario; Gilli, Marco. - In: INTERNATIONAL JOURNAL OF CIRCUIT THEORY AND APPLICATIONS. - ISSN 0098-9886. - STAMPA. - 34:(2006), pp. 77-88. [10.1002/cta.343]

Non-linear coupled CNN models for multiscale image analysis

CORINTO, FERNANDO;BIEY, MARIO;GILLI, MARCO
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 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.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11583/1675960
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