Abstract
This paper analyzes the computational complexity of methods of digital filtering of images by linear spatial filters. A comparison of the direct method of realization of two-dimensional filtering and the method of realization of two-dimensional filters by Winograd is carried out. It is shown that the best result using the Winograd method is obtained for averaging Gaussian filters and for symmetrical filters of a general form with different coefficients. The Winograd method application for Gauss filter reduces the number of multiplication operations 3 times at an increase of several addition operations 1.84 times. For symmetric general filters with different coefficients, multiplication operations are reduced to 2.12 at a rise in the number of addition operations 2 times.
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Acknowledgements
The authors would like to thank the North-Caucasus Federal University for supporting in the contest of projects competition of scientific groups and individual scientists of the North-Caucasus Federal University. The work is supported by North-Caucasus Center for Mathematical Research under agreement â„– 075-02-2021-1749 with the Ministry of Science and Higher Education of the Russian Federation.
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Lyakhov, P., Abdulsalyamova, A. (2022). On the Algorithmic Complexity of Digital Image Processing Filters with Winograd Calculations. In: Tchernykh, A., Alikhanov, A., Babenko, M., Samoylenko, I. (eds) Mathematics and its Applications in New Computer Systems. MANCS 2021. Lecture Notes in Networks and Systems, vol 424. Springer, Cham. https://doi.org/10.1007/978-3-030-97020-8_8
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DOI: https://doi.org/10.1007/978-3-030-97020-8_8
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