Image resampling using generalized series Whittaker-Kotelnikov-Shannon
DOI:
https://doi.org/10.15587/1729-4061.2013.12758Keywords:
Discretization, interpolation image, samples of signal, fractal dimensionAbstract
The operation scaling leads to search for information about the pixels that are not on the original image. The conventional approach to digital signal processing is based on sampling theorem, which solves the problem of interpolation samples only of function on an infinite time interval. But the assumption made in sampling theorem, and complexity of calculations to restore function numerical series does not allow to get rid of the disadvantages associated with unlimited range of real stochastic signals.
Generalized series of Whittaker-Kotelnikov-Shannon, based on the atomic functions. They satisfy all the requirements of the sampling theorem and they have better convergence in the case of discontinuous and local time signals. The computation uses end product and there is an exact decomposition.
The image zoom adds the new information into original image and so it contains new information. It is necessary to identify how the entropy of new image matches the original. The similar elements as such as lines and squares are always in image. That reduces them to fractals. Then we can calculate the fractal dimension of the original and the source image and apply the metric PSNR.
This approach was tested for the interpolation of the field vectors in the problem of motion estimation between frames video sequence and showed better results compared to known algorithms interpolationReferences
- . Shai, Avidan. Seam Carving for Content-Aware Image Resizing [Текст] / Shai Avidan, Ariel Shamir // Proceedings of SIGGRAPH 2007. — ACM Transactions on Graphics. — Vol. 26, no. 3. — 2008. — С. 16.1-16.10.
- Leitao, J. A. Content-Adaptive Video Up-Scaling for High-Definition Displays / J.A. Leitao, M. Zhao and G. de Haan // Proceedings of the SPIE. — 2003. — Vol. 5022. — С. 612-622.
- Turkowski, Ken. Filters for Common Resampling Tasks [Tекст] / Ken Turkowski // Graphics gems I. — Academic Press Professional, Inc. — 1990. — C. 147-165.
- Аветисян, Д. О. О представлении непрерывных функций одного класса дискретным множеством их значений [Текст] / Д.О. Аветисян // Проблемы передачи информации. — 1984. — Т. 20, Вып. 3. — С. 94-96.
- Джерри, А. Дж. Теорема отсчетов Шеннона, ее различные обобщения и приложения [Текст] / Дж. Джерри // Обзор. ТИИЭР. — 1977. — Т. 65, № 11. — С. 53-89.
- Petre, Stoica. Spectral analysis of signals [Tекст] / Petre Stoica, Randolph L. Moses. — Pearson Prentice Hall. 2005. — 452 c.
- Кравченко, В.Ф. Лекции по теории атомарных функций и некоторым их приложеним[Текст] / В.Ф. Кравченко. — М.: Радиотехника, 2003.— 512 с.
- Спектральные свойства атомарных функций в задачах цифровой обработки сигналов [Текст] / В. Ф. Кравченко, М. А. Басараб, Х. Перес-Меана // Радиотехника и электроника. — 2001. — Т.46, №5. — С. 534-552.
- Fractals and the Fractal Dimension [Електронний ресурс] // Vanderbilt University official website. — Режим доступу: www/ URL: http://www.vanderbilt.edu/AnS/psychology/cogsci/chaos/workshop/Fractals.html/ —22.11.2012.
- Shezafs, N., Abramov-Segals, H., Sutskovers, I. Adaptive low complexity algorithm for image zooming at fractional scaling ratio [Електронний ресурс]// The Signal and Image processing Lab.—Режим доступу:www/ URL:http://www-sipl.technion.ac.il/new/Teaching/Projects/Zoom_Article.pdf/ — 10.11.2012.
- Avidan, S., Shamir, A. (2008). Seam Carving for Content-Aware Image Resizing. Proceedings of SIGGRAPH 2007, ACM Transactions on Graphics. vol. 26(3), 16.1-16.10.
- Leitao, J.A., Zhao, M., & de Haan, G. (2003). Content-Adaptive Video Up-Scaling for High-Definition Displays.
- Proceedings of IVCP 2003, vol. 5022, January 2003. 612-622.
- Turkowski, K. (1990). Filters for Common Resampling Tasks. Graphics gems I, Academic Press Professional, Inc., 1990, 147-165.
- Avetisyan D.O. (1984). On the representation of continuous functions of a class of discrete set of values. Problems of Information Transmission, vol. 20(3), 94-96.
- Jerry, J.A. (1977). The Shannon Sampling Theorem — Its Various Extension And Application: Tutorial Review. Review. TIIER, vol. 65, (11), 53-89.
- Stoica, P., Moses R.L. (2005). Spectral Analysis of Signals. Pearson Prentice Hall, 452.
- Kravchenko, V.F. (2003). Lectures on the theory of atomic functions and their applications. Мoscow: Radiotechnika, 512.
- Kravchenko, V.F., Basarab, M.A., & Peres-Meana, X. (2001). Spectral properties of the atomic functions in problems of digital signal processing. Radio engineering and electronic, vol. 46(5), 534-552.
- Fractals and the Fractal Dimension (2012). Vanderbilt University official website, http://www.vanderbilt.edu/AnS/psychology/cogsci/chaos/workshop/
- Fractals.html.
- Shezafs, N., Abramov-Segals, H., Sutskovers, I. (2012). Adaptive low complexity algorithm for image zooming at fractional scaling ratio. The Signal and Image processing Lab, http://www-sipl.technion.ac.il/new/Teaching/Projects/
- Zoom_Article.pdf.
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