Back
 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.

 
 
Top