Error bounds and optimal neighborhoods for MLS approximation

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In recent years, the moving least-square (MLS) method has been extensively studied for approximation and reconstruction of surfaces. The MLS method involves local weighted least-squares polynomial approximations, using a fast decaying weight function. The local approximating polynomial may be used for approximating the underlying function or its derivatives. In this paper we consider locally supported weight functions, and we address the problem of the optimal choice of the support size. We introduce an error formula for the MLS approximation process which leads us to developing two tools: One is a tight error bound independent of the data. The second is a data dependent approximation to the error function of the MLS approximation. Furthermore, we provide a generalization to the above in the presence of noise. Based on the above bounds, we develop an algorithm to select an optimal support size of the weight function for the MLS procedure. Several applications such as differential quantities estimation and up-sampling of point clouds are presented. We demonstrate by experiments that our approach outperforms the heuristic choice of support size in approximation quality and stability.
Original languageEnglish
Title of host publicationSGP '06: Proceedings of the fourth Eurographics symposium on Geometry processing
Place of PublicationGoslar, Germany
PublisherEurographics Association
Number of pages10
ISBN (Electronic)978-3-905673-36-4
StatePublished - 2006
Event4th Eurographics symposium on Geometry processing, SGP 2006 - Cagliari, Sardinia, Italy
Duration: 26 Jun 200628 Jun 2006
Conference number: 4

Publication series

NameSymposium on Geometry Processing
PublisherEurographics Association
ISSN (Electronic)1727-8384


Conference4th Eurographics symposium on Geometry processing, SGP 2006
Abbreviated titleSGP 2006
CityCagliari, Sardinia


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