Международная студенческая научно-практическая конференция «Инновационное развитие государства: проблемы и перспективы глазам молодых ученых». Том 3

Makrenko R.O., Baybuz O.G., Atanova M.Y.

Oles Honchar Dnipropetrovsk National University, Ukraine


Currently, digital image processing systems are used in computer vision, systems of making decisions and in many other industries.

Using segmentation, we can identify significant areas of an image, to conduct a preliminary analysis of the image, make an assumption about the patient's diagnosis (X-ray image etc.).

In this work the computing schemes of image segmentation on the basis of  K-means and methods for the isolation boundaries in the image were developed and implemented. Kirsch’s, Wallace’s, Roberts’s, Laplace’s, and Sobel’s methods, a statistical method and the high-frequency filtering based on polynomial splines were used to highlight the borders of the image. The methods of linear smoothing and low-frequency filtering based on polynomial splines were used to smooth the images.

While considering the methods of image filtering the concept of filter aperture is used. The filter aperture is the size of the window (image), in which filter is working at this time. This window is gradually moving through the image from the left to the right and from the top to the bottom by one pixel. So, the next step, the filter is working with the window, which consists not only of the elements from the original image, but also of the elements from the previous transformation.

Also, all discussed methods work with the brightness at each point, which may be considered by the formulas:



so, it is equal to converting an image to a grayscale.

Along with the conversion to the grayscale, we can use the brightness value of the YCbCr color scheme:



From the considered methods of image filtering which work with an aperture, Roberts method is the easiest, the fastest, and even one of the most effective of the presented methods.

This method works with an aperture of 2x2:





The evaluating formula for each value:



The usage of splines, closed to interpolation in average, the problems of filtering and multiply-scale analysis is made according to work [1].

To build a filter for the averaged values ​​of some two-dimensional function формула given by uniform partitioning, a functional based on polynomial approximation is offered in [1]



where формула– real coefficients.



For one-dimensional splines based on B-splines, closed to interpolation in average, the following expression is right:





The better results were obtained for the segmentation of complex images with many details by using YCbCr color space than using the space RGB. The recommendations how to use low-and high-frequency filters for different types of images for the best results were described.

The results may be used in computer vision systems, medicine and other fields, which require borders allocation or separate parts of the image and for further processing and image analysis by the user or by the another program.


1. Приставка П.О. Поліноміальні сплайни при обробці даних / П.О. Приставка. – Дніпропетровськ, 2004. – 236 с.

2. Мандель И.Д. Кластерный анализ / И.Д. Мандель. – М.: Финансы и статистика, 1988. – 176 с.