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Normalized implicit eigenvector least squares operators for noisy scattered data: radial basis functions

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Abstract

We describe some new methods for obtaining a mathematical representation of a surface that approximates a scattered point cloud, {(x i , y i , z i ) i = 1, . . . , N} without the use or need of normal vector data. The fitting surface is defined implicitly as the level set of a field function which is a linear combination of trivariate radial basis functions. Optimal approximations are based upon normalized least squares criteria which lead to eigenvalue/eigenvector characterizations. The normalized aspect allows for the exclusion of the need of normal vector estimates which is one of the unique features of this new method. Localizing techniques are introduced to allow for the efficient application of these new methods to large data sets. The use of a variety of radial basis functions are introduced through various examples that illustrate the performance and efficiency of the new methods.

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Authors and Affiliations

  1. Arizona State University, Tempe, AZ, USA

    Gregory M. Nielson

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  1. Gregory M. Nielson
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Correspondence to Gregory M. Nielson.

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Communicated by C. H. Cap.

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Nielson, G.M. Normalized implicit eigenvector least squares operators for noisy scattered data: radial basis functions. Computing 86, 199–212 (2009). https://doi.org/10.1007/s00607-009-0054-7

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  • DOI: https://doi.org/10.1007/s00607-009-0054-7

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