Binarization methods and investigation of their influence on the fractal dimension of functional coatings


  • Anna Zhurba
  • Michail Gasik



binarization, binarization threshold, fractal dimension, upper threshold binarization method, lower threshold binarization method, double constraint binarization method, medium coverage binarization, functional coatings


An essential element of fractal analysis of functional coatings is the fractal dimension, which is an important quantitative characteristic. Typically, coating images are represented as colored or halftone, and most fractal dimension algorithms are for binary images. Therefore, an important step in fractal analysis is binarization, which is a threshold separation operation and the result of which is a binary image.
The purpose of the study is to study and program the methods of image binarization and to study the influence of these methods on the value of fractal dimension of functional coatings.
As a result of the binarization threshold, the image is split into two regions, one containing all pixels with values below a certain threshold and the other containing all pixels with values above that threshold. Of great importance is the determination of the binarization threshold.
The study analyzed a number of functional coating images, determined the fractal dimension of the image by the Box Counting method at different binarization thresholds and when applying different binarization methods (binarization with lower and upper threshold, with double restriction, and the average method for determining the optimal binarization threshold) images. The Box Counting method is used to depict any structure on a plane. This method allows us to determine the fractal dimension of not strictly self-similar objects. Each image binarization method is used for different types of images and for solving different problems.
As a result, the methods of image binarization were developed and implemented, the fractal dimension of binary images was calculated, and the influence of these methods on the value of fractal dimension of functional coatings was investigated.
The surfaces of composite steel structure, metallic porous materials, and natural cave structures are analyzed.


Zhurba A.O., Mikhalev O.I. Fractal characteristics of images of metal structures and features of their calculation // System technologies of modeling complex systems / Monograph under the general editorship of prof. A.I. Mikhaleva. - Dnipro: NMetAU-IVK “System Technologies”, 2016. - P. 299 - 327. ISBN 978-966-2596-19-9.

Zhurba A.O. Investigation of the influence of the parameters of fractal objects on their dimension / А.О. Zhurba, D.I. Zhurba // System technologies. Regional intercollegiate collection of scientific works. - Issue 1 (102). - Dnipropetrovsk. - 2016. - P. 125-131.

Zhurba A.O. Influence of threshold and binarization methods on fractal dimension of images of porous material surfaces / А.О. Zhurba // Adaptive automatic control systems. Interagency Scientific and Technical Collection. - Kyiv: National Technical University of Ukraine "Kyiv Polytechnic Institute". - 2015. - Issue 1 (26). - P. 198-201.