AM  Vol.5 No.3 , February 2014
Weyl Group Orbit Functions in Image Processing
ABSTRACT

We deal with the Fourier-like analysis of functions on discrete grids in two-dimensional simplexes using C- and E-Weyl group orbit functions. For these cases, we present the convolution theorem. We provide an example of application of image processing using the C-functions and the convolutions for spatial filtering of the treated image.


Cite this paper
G. Chadzitaskos, L. Háková and O. Kajínek, "Weyl Group Orbit Functions in Image Processing," Applied Mathematics, Vol. 5 No. 3, 2014, pp. 501-511. doi: 10.4236/am.2014.53049.
References
[1]   R. C. Gonzalez and R. E. Woods, “Digital Image Processing,” Addison Wesley Longman, Inc., Reading, 1992.

[2]   H. G. Granlund and H. Knutsson, “Signal Processing for Computer Vision,” Kluwer Academic Publisher, Dordrecht, 1995.

[3]   N. X. Thao, V. A. Kakichev and V. K. Tuan, “On the Generalized Convolutions for Fourier Cosine and Sine Transforms,” East-West Journal of Mathematics, Vol. 1, 1998, pp. 85-90.

[4]   J. Hrivnák and J. Patera, “On Discretization of Tori of Compact Simple Lie Groups,” Journal of Physics A: Mathematical and Theoretical, Vol. 42, 2009, Article ID: 385208.

[5]   J. Hrivnák and J. Patera, “On E-Discretization of Tori of Compact Simple Lie Groups,” Journal of Physics A: Mathematical and Theoretical, Vol. 43, No. 16, 2010, Article ID: 165206.

[6]   A. Klimyk and J. Patera, “Orbit Functions,” SIGMA (Symmetry, Integrability and Geometry: Methods and Applications), Vol. 2, 2006, p. 6.

[7]   A. Klimyk and J. Patera, “Antisymmetric Orbit Functions,” SIGMA (Symmetry, Integrability and Geometry: Methods and Applications), Vol. 3, 2007, 83 p.

[8]   A. Klimyk and J. Patera, “E-Orbit Functions,” SIGMA (Symmetry, Integrability and Geometry: Methods and Applications), Vol. 4, 2008, 57 p.

[9]   L. Háková, J. Hrivnák and J. Patera, “Six Types of E-Functions of the Lie Groups O(5) and G(2),” Journal of Physics A: Mathematical and Theoretical, Vol. 45, No. 12, 2012, Article ID: 125201.

[10]   R. V. Moody, L. Motlochová and J. Patera, “New Families of Weyl Group Orbit Functions,” arXiv:1202.4.

 
 
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