Premium
Multiresolution Curve and Surface Representation: Reversing Subdivision Rules by Least‐Squares Data Fitting
Author(s) -
Samavati Faramarz F.,
Bartels Richard H.
Publication year - 1999
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/1467-8659.00361
Subject(s) - wavelet , subdivision , matrix decomposition , factorization , tensor product , multiresolution analysis , representation (politics) , computer science , algorithm , external data representation , matrix (chemical analysis) , mathematics , wavelet transform , artificial intelligence , discrete wavelet transform , pure mathematics , eigenvalues and eigenvectors , physics , materials science , archaeology , quantum mechanics , politics , political science , law , composite material , history
This work explores how three techniques for defining and representing curves and surfaces can be related efficiently. The techniques are subdivision, least‐squares data fitting , and wavelets . We show how least‐squares data fitting can be used to “reverse” a subdivision rule, how this reversal is related to wavelets, how this relationship can provide a multilevel representation, and how the decomposition/reconstruction process can be carried out in linear time and space through the use of a matrix factorization. Some insights that this work brings forth are that the inner product used in a multiresolution analysis in uences the support of a wavelet, that wavelets can be constructed by straightforward matrix observations, and that matrix partitioning and factorization can provide alternatives to inverses or duals for building efficient decomposition and reconstruction processes. We illustrate our findings using an example curve, grey‐scale image, and tensor‐product surface.