Information
- Publication Type: Technical Report
- Workgroup(s)/Project(s): not specified
- Date: October 1999
- Number: TR-186-2-99-21
- Keywords: volume rendering, Fourier transform, Hartley transform
Abstract
The Fast Hartley Transform (FHT), a discrete version of the Hartley
Transform (HT), has been studied in various papers and shown to be
faster and more convenient to implement and handle than the
corresponding Fast Fourier Transform (FFT). As the HT is not as
nicely separable as the FT, a multidimensional version of the HT
needs to perform a final correction step to convert the result of
separate HTs for each dimension into the final multi-dimensional
transform. Although there exist algorithms for two and three
dimensions, no generalization to arbitrary dimensions can be found
in the literature. We demonstrate an easily comprehensible and
efficient implementation of the fast HT and its multi-dimensional
extension. By adapting this algorithm to volume rendering by the
projection-slice theorem and by the use for filter analysis in
frequency domain we further demonstrate the importance of the HT in
this application area.
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BibTeX
@techreport{Theussl-1999-MDH,
title = "The Multi-Dimensional Hartley Transform as a Basis for
Volume Rendering",
author = "Thomas Theu{\ss}l and Robert F. Tobler and Eduard
Gr\"{o}ller",
year = "1999",
abstract = "The Fast Hartley Transform (FHT), a discrete version of the
Hartley Transform (HT), has been studied in various papers
and shown to be faster and more convenient to implement and
handle than the corresponding Fast Fourier Transform (FFT).
As the HT is not as nicely separable as the FT, a
multidimensional version of the HT needs to perform a final
correction step to convert the result of separate HTs for
each dimension into the final multi-dimensional transform.
Although there exist algorithms for two and three
dimensions, no generalization to arbitrary dimensions can be
found in the literature. We demonstrate an easily
comprehensible and efficient implementation of the fast HT
and its multi-dimensional extension. By adapting this
algorithm to volume rendering by the projection-slice
theorem and by the use for filter analysis in frequency
domain we further demonstrate the importance of the HT in
this application area.",
month = oct,
number = "TR-186-2-99-21",
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 = "volume rendering, Fourier transform, Hartley transform",
URL = "https://www.cg.tuwien.ac.at/research/publications/1999/Theussl-1999-MDH/",
}