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The article developed the mathematical model for the synthesis of ornamental images and implemented the software editor of ornamental images, based on symmetry theory. The paper shows the fundamental role of symmetry. It is analyzed that the symmetry theory methods are used in physics, chemistry, biology, and engineering. It was found that symmetry is based on transformation and storage. In addition, the symmetrical system is based on a set of invariants that are built according to certain rules.

Contemplating the works of monumental art that surround us in everyday life, you always see the numerous sculptural decorations of Lviv houses, carefully look at the wall paintings of temples, catch the glare of coloured stained glass windows. And the city itself, which has not been subjected to crushing destruction, not only has a considerable number of monumental architectural objects but also acts as a large complex representing the philosophy of different historical periods of society's existence. We see all this almost daily.

In the article were researched the principles of building systems for observation and recognition of objects. Also we have given the classification of human faces recognition methods. Authors have analized the features of operetion for the progressive calibration network (PCN) for human face recognition. And finally has been created and tested the developed face recognition algorithm as the realized software system.

The images are one of the most used kinds of the information in modern information company. Therefore actual problems is the organization of protection from unauthorized access and usage. An important characteristic of the image is the presence of contours in the image. The task of contour selection requires the use of operations on adjacent elements that are sensitive to change and suppress areas of constant levels of brightness, that is, contours are those areas where changes occur, becoming light, while other parts of the image remain dark.

The article deals with the correlation between the notions of symbol and image. The main attention is paid to the interpretation of symbol and image in various areas of Humanities, which allows to reveal substantial features of these terms. The terms “symbol” and “image” in semiotics and cultural studies have been analyzed. The interrelation of the terms “artistic symbol” and “artistic image” in literary theory has been discovered. According to the approaches to the study of linguistic terms, their terminological variability is substantiated.

In this article, a system of handwritten or printed text recognition in the image has been developed. Empirical methods of image processing and statistical models of machine learning and simulation are being developed in two directions: the detection of text on the image and the recognition of the text. Thus, in this paper, algorithmic software tools that combine these two areas in the software created for the operating systemiOS 11.0 or later for devices of the company Apple – iPhone, iPad that support this operating system are developed.

 A new method for rapid automatic detection values of crossing-over operations in the of the image preprocessing tasks, which based on the divergence matrix operators. Experimental results shown high resistance of method to image processing with fluctuation of intensity function. Comparing the results of the proposed method with the results for the existing, showed acceleration automatically select the crossover factor that significantly reduces the necessary computing power for its operation. This leads to the possibility of he effective usage in preprocessing of large-size images.

Досліджено особливості інтелектуальних компонент інтегрованих автоматизо- ваних систем управління. Розглянуто створення інтелектуальної компоненти ІАСУ для енергетичних систем. Запропоновано нейромережні методи прогнозування споживання електроенергії підприємством на основі машини геометричних перетворень. Наведено результати проведених експериментів.

In this article the methods of image superresolution based on machine learning are
investigated. The work of different groups of these methods are analyzed. Basic features of this
methods are describing. On the basis of practical experiments comparative analysis (by the
criterion PSNR) of the superresolution methods in the case of one input image from different
classes were conducted. Experimentally found that the best results are obtained in case of
using the method based on the convolutional neural network. Despite the requirement on the

Для кодування зображень на відміну від використання методів, заснованих на класичній двійковій системі числення, пропонується опрацьовувати за допомогою вейвлет-перетворення утворені форми графіків