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

TL;DR

This paper explores how a class of discrete operators can approximate curves, with implications for computer graphics and image processing, supported by graphical examples and applications in curve reconstruction.

Contribution

It introduces a new approach to curve approximation using discrete operators, extending classical scalar function methods to curves with practical applications.

Findings

Effective approximation of curves demonstrated through graphical examples

Applications in image reconstruction and computer graphics discussed

Potential for improved curve modeling in digital image processing

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.