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

Abstract

In approximation theory, classical discrete operators, like generalized sampling, Szasz-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.