Multiresolution Curve and Surface Representation: Reversing Subdivision Rules by Least-Squares Data Fitting

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dc.contributor.authorSamavati, Faramarz F.en_US
dc.contributor.authorBartels, Richard H.en_US
dc.date.accessioned2015-02-16T06:27:15Z
dc.date.available2015-02-16T06:27:15Z
dc.date.issued1999en_US
dc.description.abstractThis 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.en_US
dc.description.number2en_US
dc.description.seriesinformationComputer Graphics Forumen_US
dc.description.volume18en_US
dc.identifier.doi10.1111/1467-8659.00361en_US
dc.identifier.issn1467-8659en_US
dc.identifier.pages97-119en_US
dc.identifier.urihttps://doi.org/10.1111/1467-8659.00361en_US
dc.publisherBlackwell Publishers Ltd and the Eurographics Associationen_US
dc.titleMultiresolution Curve and Surface Representation: Reversing Subdivision Rules by Least-Squares Data Fittingen_US
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