Introduction to Normal Multiresolution Approximation

Abstract

A multiresolution analysis of a curve is normal if each wavelet detail vector with respect to a certain subdivision scheme lies in the local normal direction. In this paper we give an introduction to the analysis of normal approximations in [3]. We define the normal approximation in its basic form and show simplified proofs of the method’s convergence, approximation quality and stability. We also explain how higher order approximations can be constructed using subdivision operators and give a brief summary of the corresponding results for these more general schemes.