Modeling and analysis of fractal transformation of distorted images of the Earth's surface obtained by optoelectronic surveillance systems

The results of a study of methods for processing optoelectronic images of the Earth’s surface are presented. The application of fractal transformations to solve the problems of automated and automatic analysis of terrain images, ensuring the separation of natural and anthropogenic objects without the use of machine learning, is shown. The analysis of existing works has shown the absence of studies linking the result of fractal transformation with the image quality recorded in real conditions of optoelectronic photography. There is no justification for choosing a specific fractal transformation for the applied processing of images with certain typical distortions. The purpose of this work was to identify the dependence of the signal-to-noise ratio of fractal dimension on the quality of the source images, to determine the type of fractal transformation that is most resistant to the effects of the considered negative factors. Methods of fractal transformations for thematic image processing are defined, which include the prism method and the differential cube counting method, and their description is presented. To study the selected methods, real images of the Earth’s surface were used, simulating distorted images of the terrain. Image distortions determined by the instability of shooting conditions and the properties of the optoelectronic complex are considered: defocusing, smudging and noise. The mathematical models used to describe them are summarized. A technique for analyzing the signal-to-noise ratio of fractal transformation is described, involving the processing of reference and distorted images of the terrain. The aspects of distortion modeling and indicators characterizing the level of image distortion are indicated. To implement the experiment, images of the area were selected characterized by various plots. For each plot, the dependences of the signal-to-noise ratio on the indicators characterizing the studied distortions are obtained. By estimating the signal-tonoise ratio, the analysis of the influence of distorting factors on the fractal dimension field being formed was performed. The results of the experiment confirmed the possibility of using fractal transformations for thematic processing of distorted optoelectronic images. It is shown that the dependence of the signal-to-noise ratio on the distortion index has a pronounced nonlinear character. It is established that for distortions of the defocusing and smearing type, the prism method is mor