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Replaced by vucini_2008_rnp.

Abstract

We present a method for non-uniform reconstruction of 3D scalar data. Typically, radial basis functions, trigonometric polynomials or shift-invariant functions are used in the functional approximation of 3D data. We adopt a variational approach for the reconstruction and rendering of 3D data. The principle idea is based on data fitting via thin-plate splines. An approximation by B-splines offers more compact support for fast reconstruction. We adopt this method for large datasets by introducing a block-based reconstruction approach. This makes this method practical for large data sets. Our reconstruction will be smooth across blocks. We give reconstruction measurements as error estimations based on different parameter settings and also an insight on the computational effort. We show that the block size used in reconstruction has a negligible effect on the reconstruction error. Finally we show rendering results to emphasize the quality of this 3D reconstruction technique.

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BibTeX

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@techreport{TR-186-2-08-02,
  title =      "Efficient Reconstruction from Non-uniform Point Sets",
  author =     "Erald  Vu{\c c}ini and Torsten M{\"o}ller and Meister
               Eduard Gr{\"o}ller",
  year =       "2008",
  abstract =   "We present a method for non-uniform reconstruction of 3D
               scalar data. Typically, radial basis functions,
               trigonometric polynomials or shift-invariant functions are
               used in the functional approximation of 3D data. We adopt a
               variational approach for the reconstruction and rendering of
               3D data. The principle idea is based on data fitting via
               thin-plate splines. An approximation by B-splines offers
               more compact support for fast reconstruction. We adopt this
               method for large datasets by introducing a block-based
               reconstruction approach. This makes this method practical
               for large data sets. Our reconstruction will be smooth
               across blocks. We give reconstruction measurements as error
               estimations based on different parameter settings and also
               an insight on the computational effort. We show that the
               block size used in reconstruction has a negligible effect on
               the reconstruction error. Finally we show rendering results
               to emphasize the quality of this 3D reconstruction
               technique.",
  address =    "Favoritenstrasse 9-11/186, A-1040 Vienna, Austria",
  institution = "Institute of Computer Graphics and Algorithms, Vienna
               University of Technology",
  note =       "human contact: technical-report@cg.tuwien.ac.at",
  month =      jan,
  number =     "TR-186-2-08-02",
  keywords =   "3D Object Modeling, Non-uniform Reconstruction, Variational
               Approximation, B-splines",
  URL =        "http://www.cg.tuwien.ac.at/research/publications/2008/TR-186-2-08-02/",
}