Wavelet Multiresolution Representation of Curves and Surfaces

✍ Scribed by L.-M. Reissell

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 567 KB
• Volume: 58
• Category: Article
• ISSN: 1077-3169
• DOI: 10.1006/gmip.1996.0017

✦ Synopsis

We develop wavelet methods for the multiresolution representation of parametric curves and surfaces. To support the pression method, selected scaling coefficients of the surface representation, we construct a new family of compactly supyield a compact hierarchical surface representation using ported symmetric biorthogonal wavelets with interpolating ''natural'' surface building blocks.

scaling functions. The wavelets in these biorthogonal pairs have

A new family of wavelets, pseudocoiflets, is constructed properties better suited for curves and surfaces than many for use in these applications. Pseudocoiflets are symmetric, commonly used filters. We also give examples of the applicacompactly supported biorthogonal [8] wavelets with an tions of the wavelet approach: these include the derivation of interpolating scaling function. 1 The scaling functions are compact hierarchical curve and surface representations using functions of the type first described by Deslauriers and modified wavelet compression, the identification of smooth sec-Dubuc [12]. The interpolation property enables us to use tions of surfaces, and a subdivision-like intersection algorithm curve or surface samples directly as initial coefficients in for discrete plane curves.