Exploiting Eigenvalues of the Hessian Matrix for Volume Decimation

Information

• Publication Type: Technical Report
• Workgroup(s)/Project(s): not specified
• Date: October 2000
• Number: TR-186-2-00-19
• Keywords: Laplacian filter, Eigenvalues, Hessian matrix, Sparse data, Volume Rendering

Abstract

In recent years the Hessian matrix and its eigenvalues became important in pattern recognition. Several algorithms based on the information they provide have been introduced. We recall the relationship between the eigenvalues of Hessian matrix and the 2nd order edge detection filter, show the usefulness of treating them separately and exploit these facts to design a combined threshold operation to generate sparse data sets.

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BibTeX

@techreport{Hladuvka-2000-ExpX,
  title =      "Exploiting Eigenvalues of the Hessian Matrix for Volume
               Decimation",
  author =     "Ji\v{r}\'{i} Hlad\r{u}vka and Eduard Gr\"{o}ller",
  year =       "2000",
  abstract =   "In recent years the Hessian matrix and its eigenvalues
               became important in pattern recognition. Several algorithms
               based on the information they provide have been introduced.
               We recall the relationship between the eigenvalues of
               Hessian matrix and the 2nd order edge detection filter, show
               the usefulness of treating them separately  and exploit
               these facts to design a combined threshold                 
               operation to generate sparse data sets.",
  month =      oct,
  number =     "TR-186-2-00-19",
  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 =   "Laplacian filter, Eigenvalues, Hessian matrix, Sparse data,
               Volume Rendering",
  URL =        "https://www.cg.tuwien.ac.at/research/publications/2000/Hladuvka-2000-ExpX/",
}