Interleaved Dimension Decomposition

Manfred Kopp, Werner Purgathofer
Interleaved Dimension Decomposition
TR-186-2-98-03, January 1998 [ paper]
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Abstract

Wavelets in 2D or higher dimensions are often generated by a decomposition scheme from 1D wavelets. There are two decomposition schemes called the standard and the nonstandard decomposition which are used in most applications of higher dimensional wavelets. This paper introduces a new decomposition method, the interleaved dimension decomposition and compares its advantages and disadvantages with the other decompositions. Based on the properties of the interleaved dimension decomposition, applications to computer graphics are sketched including multiresolution painting, morphing in 2D and 3D, and image compression.

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@techreport{Kopp-1998-IDD,
  title =      "Interleaved Dimension Decomposition",
  author =     "Manfred Kopp and Werner Purgathofer",
  year =       "1998",
  abstract =   "Wavelets in 2D or higher dimensions are often generated by a
               decomposition scheme from 1D wavelets. There are two
               decomposition schemes called the standard and the
               nonstandard decomposition which are used in most
               applications of higher dimensional wavelets. This paper
               introduces a new decomposition method, the interleaved
               dimension decomposition and compares its advantages and
               disadvantages with the other decompositions. Based on the
               properties of the interleaved dimension decomposition,
               applications to computer graphics are sketched including
               multiresolution painting, morphing in 2D and 3D, and image
               compression.",
  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-186-2-98-03",
  keywords =   "Wavelets, morphing, multiresolution painting, image
               compression",
  URL =        "http://www.cg.tuwien.ac.at/research/publications/1998/Kopp-1998-IDD/",
}