Gradient Estimation in Volume Data using 4D Linear Regression

Information

• Publication Type: Technical Report
• Workgroup(s)/Project(s): not specified
• Date: February 2000
• Number: TR-186-2-00-03
• Keywords: Linear Regression., Gradient Estimation, Volume Rendering

Abstract

In this paper a new gradient estimation method is presented which is based on linear regression. Previous contextual shading techniques try to fit an approximate function to a set of surface points in the neighborhood of a given voxel. Therefore, a system of linear equations has to be solved using the computationally expensive Gaussian elimination. In contrast, our method approximates the density function itself in a local neighborhood with a 3D regression hyperplane. This approach also leads to a system of linear equations but we will show that it can be solved with an efficient convolution. Our method provides at each voxel location the normal vector and the translation of the regression hyperplane which are considered as a gradient and a filtered density value respectively. Therefore, this technique can be used for surface smoothing and gradient estimation at the same time.

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BibTeX

@techreport{Csebfalvi-2000-GELR,
  title =      "Gradient Estimation in Volume Data using 4D Linear
               Regression",
  author =     "L\'{a}szl\'{o} Neumann and Bal\'{a}zs Cs\'{e}bfalvi and
               Andreas K\"{o}nig and Eduard Gr\"{o}ller",
  year =       "2000",
  abstract =   "In this paper a new gradient estimation method is presented
               which is based on linear regression. Previous contextual
               shading techniques try to fit an approximate function to a
               set of surface points in the neighborhood of a given voxel.
               Therefore, a system of linear equations has to be solved
               using the computationally expensive Gaussian elimination. In
               contrast, our method approximates the density function
               itself in a local neighborhood with a 3D regression
               hyperplane.   This approach also leads to a system of linear
               equations but we will show that it can be solved with an
               efficient convolution. Our method provides at each voxel
               location the normal vector and the translation of the
               regression hyperplane which are considered as a gradient and
               a filtered density value respectively. Therefore, this
               technique can be used for surface smoothing and gradient
               estimation at the same time. ",
  month =      feb,
  number =     "TR-186-2-00-03",
  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 =   "Linear Regression., Gradient Estimation, Volume Rendering",
  URL =        "https://www.cg.tuwien.ac.at/research/publications/2000/Csebfalvi-2000-GELR/",
}