Smooth Shape-Based Interpolation using the Conjugate Gradient Method

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• Publication Type: Technical Report
• Keywords: shape-based interpolation, conjugate gradient method, volume rendering

@techreport\{Csebfalvi-2002-SBICG,
  title =      "Smooth Shape-Based Interpolation using the Conjugate
               Gradient Method",
  author =     "Bal{\'a}zs Csebfalvi and Laszlo Neumann and Armin
               Kanitsar and Meister Eduard Gr{\"o}ller",
  year =       "2002",
  abstract =   "In this paper a novel technique for smooth shape-based
               interpolation of volume data is introduced. Previously
               simple linear interpolation of signed distance maps has been
               used in practice. As it will be shown, this approach results
               in artifacts, since sharp edges appear along the original
               slices. In order to obtain a smooth 3D implicit function
               generated by interpolating 2D distance maps, we use a global
               interpolation method instead of a higher order local
               technique. The global curvature of the implicit function
               representing an isosurface is minimized using an iterative
               conjugate gradient method. Because of the iterative approach
               the user can easily control the trade-off between the
               smoothness of the isosurface and the computational cost of
               the refinement. As opposed to previous techniques, like
               variational interpolation, our method can generate a
               reasonably good approximation of the ideal solution in a
               significantly                   shorter time.",
  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 =      aug,
  number =     "TR-186-2-02-10",
  keywords =   "shape-based interpolation, conjugate gradient method, volume
               rendering",
  URL =        "http://www.cg.tuwien.ac.at/research/publications/2002/Csebfalvi-2002-SBICG/",
}