Curves defined by a class of discrete operators: approximation result and applications

Abstract

In approximation theory classical discrete operators, like generalized sampling, Sz\'{a}sz-Mirak'jan, Baskakov and Bernstein operators, have been extensively studied for scalar functions. In this paper, we look at the approximation of curves by a class of discrete operators and we exhibit graphical examples concerning several cases. The topic has useful implications about the computer graphics and the image processing: we discuss applications on the approximation and the reconstruction of curves in images.