Розроблення моделі синусоїдального перетворення темних тонів цифрових зображень

The object of the study is the technological process of sinusoidal transformation of dark tones into a digital image, used at the stage of preparation for printing. One of the most problematic areas is posterization, which occurs with traditional power-law gamma transformation, creating noticeable bands on the image that distort its quality and limit the capabilities of the operator, technologist, and printer. The study employed mathematical modeling and quantization of gradation characteristics to eliminate these shortcomings. A mathematical model of sinusoidal transformation was developed, describing the brightness of the image in the range of 0 ≤ L ≤ 255 levels. A structural scheme of the simulator model was also created in MATLAB: Simulink, allowing for the calculation and plotting of gradation characteristics, optical density, and contrast sensitivity for different transformation frequencies. As a result of the simulation, it was found that the sinusoidal transformation has significantly smaller initial quantization shifts (0.5–2 units) and first step lengths (1–2 levels) compared to the traditional gamma transformation (11–31 units and 10–15 levels, respectively). This eliminates posterization. The contrast sensitivity of the sinusoidal transformation increases up to 2.2, exceeding the constant value of 1 in the linear scale, which ensures improved tone perception. Thus, the proposed method demonstrates higher efficiency in reproducing images in both dark and light areas. The results obtained demonstrate the absence of posterization in the sinusoidal transformation of dark tones. This is due to the proposed approach having several features, including a steeper gradation characteristic at the beginning of the range, which eliminates posterization of dark tones without losses in highlights. This ensures the ability to obtain high-quality images with improved gradation characteristics. Compared to similar known methods, this provides advantages in the form of improved image quality and elimination of posterization, which is crucial for the quality preparation of images for printing. The results of the research and simulation modeling can be used to select optimal reproduction characteristics, ensuring improved perception of the printed image by the human visual system. This allows achieving high print quality without losses in detail and contrast, which is a significant advantage in the printing industry.