Methods of filtering the graph images of the functions

Бурса, А. Г. Комплекс методов фильтрации сканированных изображений графиков функций / А. Г. Бурса, В. С. Молчанова // Вісник Приазовського державного технічного університету : зб. наукових праць / ПДТУ. – Маріуполь, 2016. – Вип. 33. – С. 159–168. – (Серія : Технічні науки).Рассмотрен теоретический аспект очистки растровых изображений сканированных графиков функций от цифрового хроматического и яркостного шума с применением методов машинной графики. Предложен комплекс методов подавления полутонового шума, обеспечивающий высокое качество изображений графиков функций.Розглянуто теоретичний аспект чищення сканованих растрових зображень графіків функцій від цифрового хроматичного і яскравісного шуму із застосуванням методів машинної графіки. Запропоновано комплекс методів приглушення напівтонового шуму, що забезпечує високу якість зображень графіків функцій.The theoretical aspects of cleaning raster images of scanned graphs of functions from digital, chromatic and luminance distortions by using computer graphics techniques have been considered. The basic types of distortions characteristic of graph images of functions have been stated. To suppress the distortion several methods, providing for highquality of the resulting images and saving their topological features, were suggested. The paper describes the techniques developed and improved by the authors: the method of cleaning the image of distortions by means of iterative contrasting, based on the step-bystep increase in image contrast in the graph by 1%; the method of small entities distortion restoring, based on the thinning of the known matrix of contrast increase filter (the allowable dimensions of the nucleus dilution radius convolution matrix, which provide for the retention of the graph lines have been established); integration technique of the noise reduction method by means of contrasting and distortion restoring method of small entities with known σ-filter. Each method in the complex has been theoretically substantiated. The developed methods involve treatment of graph images as the entire image (global processing) and its fragments (local processing). The metrics assessing the quality of the resulting image with the global and local processing have been chosen, the substantiation of the choice as well as the formulas have been given. The proposed complex methods of cleaning the graphs images of functions from grayscale image distortions is adaptive to the form of an image carrier, the distortion level in the image and its distribution. The presented results of testing the developed complex of methods for a representative sample of images confirm its effectiveness