Normal multiresolution approximation of curves
type: Item
instance of: scholarly article
title: Normal multiresolution approximation of curves
zbMATH Open document ID: 1051.42025
author: Ingrid Daubechies
author: Olof Runborg
author: Wim Sweldens
published in: Constructive Approximation
publication date: 2004-10-28T00:00:00Z
review text: Subdivision is a powerful procedure for iteratively creating smooth curves and surfaces. Combined with wavelet methods, subdivision can be used to approximate functions, curves, and surfaces. The authors discuss the multiresolution approximation of a plane curve \(\Gamma\) in detail. A multiresolution approximation of \(\Gamma\) is called normal if all wavelet detail vectors align with a locally defined normal direction which only depends on the coarser levels. Here normal direction means a normal onto an approximation of \(\Gamma\). This notion is very useful for compression applications. In this interesting paper, the authors study properties as convergence, speed of convergence, regularity, and stability of a normal multiresolution approximation of \(\Gamma\). It is shown that these properties critically depend on the underlying subdivision scheme and that in general the convergence of normal multiresolution approximation of \(\Gamma\) equals the convergence of the underlying subdivision scheme. The central idea is to study the normal multiresolution approximation of \(\Gamma\) as a perturbation of a linear subdivision scheme.
reviewed by: Manfred Tasche
Mathematics Subject Classification ID: 42C40
Mathematics Subject Classification ID: 65D10
Mathematics Subject Classification ID: 65D17
Mathematics Subject Classification ID: 65T60
Mathematics Subject Classification ID: 68U07
zbMATH DE Number: 2111592
zbMATH Keywords: subdivision scheme
zbMATH Keywords: multiresolution approximation
zbMATH Keywords: plane curve
zbMATH Keywords: approximation of curves
zbMATH Keywords: convergence
zbMATH Keywords: regularity
zbMATH Keywords: stability
MaRDI profile type: Publication
full work available at URL: s00365-003-0543-4
OpenAlex ID: W2043440570
DOI: 10.1007/S00365-003-0543-4
description: scientific article; zbMATH DE number 2111592