Octahedral Filters for 3D Image Processing
Reiner Lenz · 2009
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. We demonstrate filtering of three-dimensional volumes as application examples of its representation theory. We summarize properties of the octahedral group and basic results from its representation theory. Linear filter systems are defined as projection operators and symmetrybased filter systems are generalizations of the Fourier transforms. The algorithms are implemented in Maple/Matlab worksheets and functions. We illustrate the nature of the different types of filter systems, their invariance and transformation properties.