GVU Technical Report Number:
GIT-GVU-91-14
Title:
Multi-Dimensional Two-Scale Dilation Equations
Authors:
Marc A. Berger
Yang Wang
Abstract:
This work involves the study of multidimensional scaling functions.
These functions satisfy a two-scale dilation equation, just as the 1-D
scaling functions which are used to construct 1-D wavelets. Two
frameworks are presented for studying these dilation equations. Fourier
methods are used to analyze existence, uniqueness, and regularity of
solutions. Expansions with infinite matrix products are used to derive
an iterated function system (IFS) algorithm for generating the scaling
function. Application to subdivision schemes for surface generation is
presented, as a genuine multidimensional example where scaling functions
arise and the IFS algorithm can be applied.
Keywords:
Multidimensional scaling, fourier methods, expansions, IFS algorithm
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