Smooth Shape-Based Interpolation using the Conjugate Gradient Method

Information

• Publication Type: Technical Report
• Workgroup(s)/Project(s):
  • ADAPT: Advanced Diagnosis, Analysis and Planning Tools (in Medicine)
• Date: August 2002
• Number: TR-186-2-02-10
• Keywords: shape-based interpolation, conjugate gradient method, volume rendering

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.

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BibTeX

@techreport{Csebfalvi-2002-SBICG,
  title =      "Smooth Shape-Based Interpolation using the Conjugate
               Gradient Method",
  author =     "Bal\'{a}zs Cs\'{e}bfalvi and L\'{a}szl\'{o} Neumann and
               Armin Kanitsar and 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.",
  month =      aug,
  number =     "TR-186-2-02-10",
  address =    "Favoritenstrasse 9-11/E193-02, A-1040 Vienna, Austria",
  institution = "Institute of Computer Graphics and Algorithms, Vienna
               University of Technology ",
  note =       "human contact: technical-report@cg.tuwien.ac.at",
  keywords =   "shape-based interpolation, conjugate gradient method, volume
               rendering",
  URL =        "https://www.cg.tuwien.ac.at/research/publications/2002/Csebfalvi-2002-SBICG/",
}