Ondřej Kajínek's research while affiliated with Czech Technical University in Prague and other places

Publications (4)

Article
Full-text available
The study of the evolution process of our visual system indicates the existence of variational spatial arrangement; from densely hexagonal in the fovea to a sparse circular structure in the peripheral retina. Today’s sensor spatial arrangement is inspired by our visual system. However, we have not come further than rigid rectangular and, on a minor...
Article
Full-text available
The study of the evolution process of our visual system indicates the existence of variational spatial arrangement; from densely hexagonal in the fovea to a sparse circular structure in the peripheral retina. [...]
Article
Full-text available
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.
Chapter
We present the first attempt to use the C-orbit functions in image processing. For the image processing we perform a Fourier-like transform of the image. Then we define a convolution on C-orbit functions and we apply the simplest spatial linear filters on several examples. Finally we compare the results with filtering via an ordinary Fourier transf...

Citations

... Furthermore, the actualized coincidence between the (anti)symmetric trigonometric and Fourier-Weyl transforms offers tools for connection and transfer of the discrete Fourier methods [11,19]. The successful interpolation tests for the 2D and 3D (anti)symmetric trigonometric functions [2,9,10,12] indicate matching interpolation behavior of the corresponding Fourier-Weyl transforms as well as relevance of both types of transforms in data processing methods [20]. In particular, the vast pool of recursive algorithms for fast computation of the (multivariate) trigonometric transforms [11] becomes linked to the central splitting of the discrete Fourier-Weyl transforms [21,22] and vice versa. ...
... As applications, cubature rules [28,41,76] and discretizations of tori of compact simple Lie groups [38,40,42] were studied by this school. Furthermore they studied discrete orbit transforms [10,16,39] but did not make the connection to the algebraic signal processing theory and hence could not derive fast algorithms for their calculation. ...