Low-pass filtering of power transformation of light tones of images

  1. Home
  2. Archive
  3. № 1 (68)
Author(s) Collection number Pages Download abstract Download full text
Янчинський А. В. № 1 (68) 145-152 Image Image

A mathematical model of the normalized power transformation with a low-pass filter of digital images, given by the number of gray levels in the range [0, 255], within which gray tones are found, is developed. For the study, three typical variants of the power-gamma transformation are set, the tone of which is set by the power indicator r1 = 0.3; r2 = 0.45; r3 = 0.6. A low-pass filter is proposed, the input of which is fed with a power transformation of the image. The filter is described by a first-order transfer operator with a constant of 5 levels. To evaluate the filtered digital images, the differences between the filtered and input images are determined.

To solve the problem, object-oriented programming in the MATLAB package: Simu­link is used, a structural diagram of the simulator model of typical variants of the filtered power transformation of images is developed, which simultaneously calculates and builds the gradation input characteristics L1, L2, L3 of the power transformation and filter Lr1, Lr2, Lr3 and their differences and visualizes the simulation results. The results of modeling the gradation characteristics of the power transformation of images, which are convex curves with 50, 40, 20 levels at the beginning of the range, respectively, which causes posterization in the dark areas of the images, are presented. Instead, the gradation characteristics of the filtered images at the beginning of the range have a much lower slope, which eliminates posterization in the dark areas of the image and does not affect the tonal reproduction of the images in the worlds. The graphs of the differences between the filtered and the power transformation of the images are presen­ted, which at the beginning of the range are 43, 22, 13 levels, after which they quickly decrease, and at the middle tones the deviation is 1(2%), so the filter practically does not affect the tonal transmission of the images in the middle range and in It is found that the two-fold increase of the filter is not critical for the filtering of digital images systems for selecting the optimal gradation characteristics of reproduction during the preparation of images for printing.

Keywords: simulation, low-pass filter, power transformation, digital images, simulator, gradation characteristics, parameters, quality.

doi: 10.32403/1998-6912-2024-1-68-145-152


  • 1. Baranovskyi, I. V., & Yakhymovych, Yu. Ya. (1998). Polihrafichna pererobka obrazotvorchoi informatsii. Kyiv-Lviv : IZMN (in Ukrainian).
  • 2. Vorobel, R. A. (2012). Loharyfmichna obrobka zobrazhen. Kyiv : Naukovo-vyrobnyche pidpryiemstvo «Vydavnytstvo «Naukova dumka» NAN Ukrainy» (in Ukrainian).
  • 3. Havrysh, B. M., Durniak, B. V., Tymchenko, O. V., & Yushchyk, O. V. (2016). Vidtvorennia zobrazhen rastrovymy prystroiamy. Lviv : UAD (in Ukrainian).
  • 4. Lotoshynska, N. D., & Ivakhiv, O. V. (2014). Teoriia koloru ta kolorotvorennia. Lviv : Vydav­nytstvo Lvivskoi politekhniky (in Ukrainian).
  • 5. Lutskiv, M. M. (2016). Tsyfrovi tekhnolohii drukarstva. Lviv : UAD (in Ukrainian).
  • 6. Martyniuk, V. T. (2009). Osnovy dodrukarskoi pidhotovky obrazotvorchoi informatsii : K. 2. Osnovy opratsiuvannia obrazotvorchoi informatsii. Kyiv : Universytet «Ukraina» (in Ukrainian).
  • 7. Yushchyk, O. V. (2009). Osnovy tsyfrovoi obrobky zobrazhen. Lviv : UAD (in Ukrainian).
  • 8. Panak, J., Ceppan, M., Avonka, V., Karpynski, L., Kovdos, P., Mikula, M., & Jakucewiz, S. (2009). Poligrafia: procesy i technika. COBRPE. Warszawa (in Polish).
  • 9. Gonzales, C., & Woods, E. (2008). Digital image Processing: International Version 3rd Edition, Inc publishing as Prentice Hall. Copyright (in English).