Error Bounds and Optimal Neighborhoods for MLS Approximation

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dc.contributor.authorLipman, Yaronen_US
dc.contributor.authorCohen-Or, Danielen_US
dc.contributor.authorLevin, Daviden_US
dc.contributor.editorAlla Sheffer and Konrad Polthieren_US
dc.date.accessioned2014-01-29T08:14:02Z
dc.date.available2014-01-29T08:14:02Z
dc.date.issued2006en_US
dc.description.abstractIn 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 stabiliten_US
dc.description.seriesinformationSymposium on Geometry Processingen_US
dc.identifier.isbn3-905673-24-Xen_US
dc.identifier.issn1727-8384en_US
dc.identifier.urihttps://doi.org/10.2312/SGP/SGP06/071-080en_US
dc.publisherThe Eurographics Associationen_US
dc.subjectCategories and Subject Descriptors (according to ACM CCS): I.3.3 [Computer Graphics]: Surface approximation, Point clouds, Meshes, Differential quantities estimationen_US
dc.titleError Bounds and Optimal Neighborhoods for MLS Approximationen_US
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SGP06: Eurographics Symposium on Geometry Processing