Weyl group orbit functions in image processing. (English) Zbl 1335.42003
Kielanowski, Piotr (ed.) et al., Geometric methods in physics. XXXIII workshop, Białowieża, Poland, June 29 – July 5, 2014. Cham: Birkhäuser/Springer (ISBN 978-3-319-18211-7/hbk; 978-3-319-18212-4/ebook). Trends in Mathematics, 189-194 (2015).
It is known that in the standard digital data processing, a convolution of the image and a spatial filter is used to change a brightness value in each point, while the Fourier transform changes the convolution into a simple multiplication of Fourier images. Recently, the authors of this paper found an application in spatial image filtering of a generalized Fourier transform and a related convolution based on Weyl group orbit functions. In this paper, via the family of \(E\)-orbit functions, the authors further present an example of such a filtering.
For the entire collection see [Zbl 1329.00214].
For the entire collection see [Zbl 1329.00214].
Reviewer: Wen Yuan (Beijing)
MSC:
| 42B10 | Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type |
| 43A75 | Harmonic analysis on specific compact groups |
| 94A08 | Image processing (compression, reconstruction, etc.) in information and communication theory |
References:
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