Introduction to Univariate Subdivision Schemes for Noisy Data

Applications and Limitations of Univariate Subdivision Schemes

Abstract

We introduce and analyse univariate, linear and stationary subdivision schemes for refining noisy data by using geometrical applications. Sub divisions schemes are presented that are based on univariate polynomials. Subdivision is a process of recursively refining discrete data using a set of subdivision rules (called subdivision scheme) which generates a continuous or even smooth limit. Subdivision schemes are multi-resolution methods used in computer-aided geometric design to generate smooth curves or surfaces.