Octahedral Transforms for 3D Image Processing
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comunitat-uji-handle2:10234/7038
comunitat-uji-handle3:10234/8634
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Title
Octahedral Transforms for 3D Image ProcessingDate
2009Publisher
Institute of Electrical and Electronics EngineersISSN
1057-7149Type
info:eu-repo/semantics/articleVersion
info:eu-repo/semantics/submittedVersionAbstract
The octahedral group is one of the finite subgroups
of the rotation group in three-dimensional Euclidean space and
a symmetry group of the cubic grid. Compression and filtering
of three-dimensional volumes are given ... [+]
The octahedral group is one of the finite subgroups
of the rotation group in three-dimensional Euclidean space and
a symmetry group of the cubic grid. Compression and filtering
of three-dimensional volumes are given as application examples
of its representation theory. We give an overview over the
finite subgroups of the three-dimensional rotation group and
their classification. We summarize properties of the octahedral
group and basic results from its representation theory. Widesense
stationary processes are processes with group theoretical
symmetries whose principal components are closely related to
the representation theory of their symmetry group. Linear filter
systems are defined as projection operators and symmetry-based
filter systems are generalizations of the Fourier transforms.
The algorithms are implemented in Maple/Matlab functions
and worksheets. In the experimental part we use two publicly
available MRI volumes. It is shown that the assumption of widesense
stationarity is realistic and the true principal components
of the correlation matrix are very well approximated by the
group theoretically predicted structure. We illustrate the nature
of the different types of filter systems, their invariance and
transformation properties. Finally we show how thresholding in
the transform domain can be used in three-dimensional signal
processing. [-]
Is part of
IEEE Transactions on Image Processing, vol. 18, no. 12 (2009), p. 2618-2628Rights
http://rightsstatements.org/vocab/CNE/1.0/
info:eu-repo/semantics/openAccess
info:eu-repo/semantics/openAccess
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