Normalized Implicit Radial Models for Scattered Point Cloud Data without Normal Vectors

Abstract

We describe some new methods for obtaining a mathematical representation of a surface that approximates a scattered point cloud, {(x y z ) i N} i i i , , = 1,L, 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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Document Details

Document Type
Technical Report
Publication Date
Mar 23, 2009
Accession Number
ADA499959

Entities

People

  • Gregory M. Nielson

Organizations

  • Arizona State University

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Algorithms
  • Computational Science
  • Curve Fitting
  • Data Modeling
  • Data Sets
  • Eigenvalues
  • Eigenvectors
  • Equations
  • Images
  • Information Operations
  • Military Research
  • Point Clouds
  • Standards
  • Three Dimensional
  • Triangles

Fields of Study

  • Mathematics

Readers

  • Atmospheric Remote Sensing.
  • Calculus or Mathematical Analysis
  • Statistical inference.