Розроблення моделі степенево-лінійного перетворення цифрових зображень для темних тонів

The object of research is the technological process of digital image processing using power transformation in pre-printing processes. A significant problem in preparing an image for printing is the phenomenon of posterization, which distorts the image and limits the possibilities of power transformation for correcting dark areas of the image. This is a disadvantage of power transformation, which is that at power indicators (r<0.45) and (r>1.5) power transformation is too sensitive to changes in black levels. The mathematical model of power-linear transformation of images for dark tones has been improved, which, unlike the known ones, involves the summation of power and linear transformation and includes a simulator of power-linear transformation of images. Taking into account the improved model, gradation characteristics, optical density dependences and contrast sensitivity were obtained, which quantitatively assess the perception of images by the human visual system. The validity of the improved model was verified by mathematical modeling using object-oriented programming and the MATLAB:Simulink software package. The results of mathematical modeling indicate that the development of the mathematical model allowed to further expand the possibilities of image correction. This is due to the fact that the length of the discrete gradation characteristics is 3–4 levels, which are not noticed by the human visual system (posterization is eliminated). The proposed model has significant advantages over image conversion methods used in printing. In particular, it expands the range of visual perception of images, eliminates the phenomenon of posterization, provides the ability to change (stretch and compress) contrast within wide limits. At the same time, it expands the functionality of power-law image conversion, and accordingly provides an increase in image quality when preparing it for printing. The results of the conducted research are recommended to be used at the stage of preparing images for printing and in workflows by operators and technologists.