Wavelet multiresolution representation of curves and surfaces

ID
TR-93-17
Authors
L.-M. Reissell
Publishing date
May 1993
Length
75 pages
Abstract
We apply wavelet methods to the representation of multiscale digitized parametric curves and surfaces. These representations will allow the derivation of efficient multiresolution geometric algorithms. In this report, we outline the definitions and basic properties of the resulting surface and curve hierarchies, and discuss the criteria on wavelets used in geometric representation. We then construct a new family of compactly supported symmetric biorthogonal wavelets, pseudo-coiflets, well suited to geometric multiresolution representation: these wavelets have coiflet-like moment properties, and in particular, the reconstructing scaling functions will be interpolating. The methods have been implemented in C/C++ software, which have been tested on geographic image data and other examples, comparing different choices of underlying wavelets.