In this paper, we present the theory and some new applications of linear, multivariate, sampling Kantorovich operators. By means of the above operators, we are able to reconstruct pointwise, continuous and bounded signals (functions), and to approximate uniformly, uniformly continuous and bounded functions. Moreover, the reconstruction of signals belonging to Orlicz spaces are also considered. In the latter case, we show how our operators can be used to approximate not necessarily continuous signals/images, and an algorithm for image reconstruction is developed. Several applications of the theory in civil engineering are obtained. Thermographic images, such as masonries images, are processed to study the texture of the buildings, thus to separate the stones from the mortar and finally a real-world case-study is analyzed in terms of structural analysis.
Multivariate sampling Kantorovich operators: approximation and applications to civil engineering
CLUNI, FEDERICO;COSTARELLI, Danilo;MINOTTI, ANNA MARIA;VINTI, Gianluca
2013
Abstract
In this paper, we present the theory and some new applications of linear, multivariate, sampling Kantorovich operators. By means of the above operators, we are able to reconstruct pointwise, continuous and bounded signals (functions), and to approximate uniformly, uniformly continuous and bounded functions. Moreover, the reconstruction of signals belonging to Orlicz spaces are also considered. In the latter case, we show how our operators can be used to approximate not necessarily continuous signals/images, and an algorithm for image reconstruction is developed. Several applications of the theory in civil engineering are obtained. Thermographic images, such as masonries images, are processed to study the texture of the buildings, thus to separate the stones from the mortar and finally a real-world case-study is analyzed in terms of structural analysis.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
