Improvement of grayscale images in the basis of orthogonal transformations of fuzzy sets type_2 characteristics

Abstract

Inaccuracies and ambiguities in the original image appear as dark shadows, light-stuck areas, spots, and intensity gradients that alter the true brightness values. This increases the complexity of the automatic calculation of numerical parameters based on the images brightness characteristics analysis. One of the ways of improving the quality of images and the reliability of their analysis is based on the transition to a new space of informative features.
The usage of fuzzy sets due to nonlinearity allows to enhance the influence of variations in the brightness properties of the analyzed images and eliminate ambiguity in the initial data. Fuzzy sets of type_1 (T1) allow converting uncertainty into a membership function and eliminating gray ambiguity. Fuzzy sets of type_2 (T2) allows considering problems with a higher degree of uncertainty. Currently, image processing algorithms using T2 have been proposed for solving clustering, filtering, edge detection, and image classifica-tion problems.
The article is devoted to the description of a grayscale images brightness parameters improving algorithm using fuzzy sets T2 to take into account the uncertainty in the initial data and comparing the information capabilities of the resulting characteristics obtained by different orthogonalization methods: singular value decomposition, Gram-Schmidt and fuzzy principal components for membership functions T2 (FPT2 ) at the defuzzification stage.
The proposed method consists of the following steps: scaling the original image to the range ; preprocessing, which was made on the basis of adaptive power-law brightness correction and local background subtraction; forming of "lower" and "upper" membership functions T1 and MFT2; applying the orthogonal transformation for an ensemble of images obtained by preprocessing and membership functions, which gives a transition to a new space of features; automatic selection of the most significant features after applying the orthogonal transformation; forming of the output image based on the weighted sum of the most significant features.
The proposed method was tested on various grayscale images. As an example of such a snapshot, the article presents an optical microscopic image of a phosphorus-containing alloy Fe–2%P–0.042%C sample with a magnification of x250, obtained on a metallographic microscope GX-51 with a digital image analysis system of the “Olympus” company. This image has a light-stuck area, an irregular background, noise, insufficient contrast level for reliable analysis.
Experimental studies have shown that the usage of fuzzy sets T2 allows a transition to a multidimensional space for grayscale images and makes it possible to use multidimensional analysis methods for their processing; the proposed algorithm allows to improve the visual characteristics of optical microscopic images; the diagnostic significance of the obtained characteristics is determined by the initial data and the purpose of the analysis.