The object of research is the process of determining the position of objects on images that are segmented in digital frames. The purpose of the work is to increase the accuracy of estimating the position of objects in space based on digital images by developing new and improving known computational methods of segmentation and estimating the equatorial position of objects in space, which takes into account astronomical observations and specific of digital frames. The research methods are based on the use of numerical methods theory, morphological image processing, mathematical statistics theory, parametric estimation and optimization theory, which allowed to develop: computational methods of image segmentation of single, bright, long and compact group of objects on digital astronomical images; evaluation of the image parameters of the background substrate on digital images in the presence of anomalous pixels; method of estimating the angular position of objects in space with direct and inverse coordinate reduction of discrete images. The scientific novelty of the work is as follows: for the first time a computational method for segmenting images of single objects on digital images with the prior use of a smoothing digital low-pass filter and equalizing the brightness of the digital frame; for the first time a computational method of segmentation of long images of objects on digital images is proposed, which allows segmentation of input long images, where there are different types of images of local objects (single, compact group, long) at computational costs close to minimum; improved the method of estimating the parameters of the background substrate of the digital image of the object in the presence of anomalous pixels, which allows to take into account the conditions of astronomical observations to improve the accuracy of estimating the position of objects in space; computational methods for estimating the angular position of objects in space using direct and inverse coordinate reduction of discrete images were further developed, which improved the quality of aberration approximation for short-focus and long-focus optical observation systems and increased the overall accuracy of determining the coordinates of objects. The practical significance of the obtained results is that the developed computational methods have been tested in practice and implemented in the in-frame processing unit of the software complex for automated detection of asteroids and comets CoLiTec, one of the developers of which is the applicant. Developed computational methods of image segmentation have made it possible to select all types of objects on digital astronomical frames with computational costs close to the minimum. The computational methods of direct and inverse coordinate reduction proposed in the work allowed to significantly increase the accuracy of determining the equatorial positions of objects. For example, the obtained values of the standard deviation of the equatorial coordinates of the reference stars meet the requirements of the Center for Small Planets to accurately estimate the equatorial positions of asteroids in digital images. The developed computational methods can be used in various software systems for digital image processing for segmentation and equatorial positioning of objects with high accuracy (in particular, in software systems for stellar photometry, automated detection of asteroids and comets, space control software). The results of the dissertation research were used in the Odessa Astronomical Observatory Odessa-Mayaki (Mayaki village, Odessa region, Ukraine), in the space research laboratory at Uzhgorod National University, in the Western Ukrainian Center for Space Research of the State Space Agency of Ukraine (Mukachevo, Ukraine).
