Technical Reports

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UBC CS TR-93-17 Summary

Multiresolution Geometric Algorithms Using Wavelets I: Representation for Parametric Curves and Surfaces, May 1993 L. M. Reissell, 75 pages

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, {\it 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.


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