vestiftИзвестия Национальной академии наук Беларуси. Серия физико-технических наукProceedings of the National Academy of Sciences of Belarus. Physical-technical series1561-83582524-244XThe Republican Unitary Enterprise Publishing House "Belaruskaya Navuka"10.29235/1561-8358-2026-71-1-57-66vestift-928Research ArticleРАДИОЭЛЕКТРОНИКА И ПРИБОРОСТРОЕНИЕRADIOELECTRONICS AND INSTRUMENT-MAKINGСтатистический синтез байесовского алгоритма сегментации изображения и измерения координат воздушных объектовStatistical synthesis of a Bayesian algorithm image segmentation an d measurementof aerial object coordinateshttps://orcid.org/0009-0006-0080-4713ЦуприкС. В.TsuprikS. V.

Цуприк Сергей Викторович – кандидат технических наук, доцент кафедры автоматики, радиолокации и приемо-передающих устройств 

пр. Независимости, 220, 220057, Минск 

Sergey V. Tsuprik – Cand. Sci. (Engineering), Associate Professor of the Department of Automation, Radar and Transceiver Devices 

220, Nezavisimosti Ave., 220057, Minsk 

Serhio.Observer@yandex.ruСолонарА. С.SolonarA. S.

Солонар Андрей Сергеевич – кандидат технических наук, ведущий научный сотрудник отдела фундаментальных и прикладных исследований открытого акционерного общества 

пр. Партизанский, 64а, 220026, Минск 

Andrei S. Solonar – Cand. Sci. (Engineering), Professor of the Department of Automation, Radar and Transceiver Devices  

64a, Partizansky Ave., 220026, Minsk 

andssnew@yandex.ruhttps://orcid.org/0000-0003-3404-3917ХмарскийП. А.KhmarskiyP. A.

Хмарский Петр Александрович – кандидат технических наук, доцент, доцент кафедры информационных радиотехнологий 

ул. Петруся Бровки, 6, 220013, Минск 

Petr A. Khmarskiy – Cand. Sci. (Engineering), Associate Professor, Associate Professor of Information Radioengineering Department  

6, P. Brovka St., 220013, Minsk 

pierre2009@mail.ruВоенная академия Республики БеларусьMilitary Academy of the Republic of BelarusОАО «КБ Радар» – управляющая компания холдинга «Системы радиолокации»JSC “KB Radar” – Managing Company of “Radar Systems” HoldingБелорусский государственный университет информатики и радиоэлектроникиBelarusian State University of Informatics and Radioelectronics2026310320267115766Copyright © Цуприк С.В., Солонар А.С., Хмарский П.А., 20262026Цуприк С.В., Солонар А.С., Хмарский П.А.Tsuprik S.V., Solonar A.S., Khmarskiy P.A.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://vestift.belnauka.by/jour/article/view/928

Представлены результаты статистического синтеза алгоритма сегментации изображений воздушных объектов, основанного на байесовском критерии максимума апостериорной вероятности. Ключевой особенно­стью алгоритма является использование информации о начальном выборе объекта оператором для формирования априорного пространственного распределения координат, что позволяет эффективно учитывать геометрические огра­ничения на перемещение объекта между соседними кадрами видеопоследовательности. Разработан двухэтапный подход к решению задачи классификации пикселей и оценивания координат объекта, при котором пространственная информация интегрируется непосредственно в решающее правило сегментации через гауссову модель распределения вероятностей. Получены аналитические выражения для оптимального решающего правила в виде сравнения логарифма отношения правдоподобия, включающего яркостную и пространственную компоненты. Полученный алгоритм позволяет повысить качество сегментации и точность измерения координат в условиях изменяющегося освещения, что критически важно для систем автоматического сопровождения воздушных объектов в задачах мониторинга воздушного пространства и управления траекториями полета. 

This paper presents the results of a statistical synthesis of an algorithm for segmenting images of aerial objects based on the Bayesian criterion of maximum posterior probability. The key feature of the algorithm is the use of information about the operator’s initial choice of the object to form a priori spatial distribution of coordinates, which allows effectively taking into account geometric constraints on the movement of the object between adjacent frames of the video sequence. A twostage approach has been developed to jointly solve the tasks of pixel classification and object position estimation, in which spatial information is directly integrated into the segmentation decision rule through a Gaussian model of probability distribution. Analytical expressions for the optimal decision rule are obtained in the form of a threshold comparison of the log-likelihood ratio, which includes both intensity and spatial components. The resulting algorithm improves the quality of segmentation and the accuracy of coordinate measurements under varying lighting conditions, which is critically important for automatic tracking systems of aerial objects in the tasks of airspace monitoring and flight trajectory management. 

сегментация изображенийбайесовский алгоритмстатистический синтезвоздушные объектыавтоматическое сопровождениепространственное распределениеапостериорная вероятностьфункция правдоподобиякомпьютерное зрениемежкадровая обработкаоценка вектора состоянияклассификация пикселейimage segmentationBayesian algorithmstatistical synthesisaerial objectsautomatic trackingspatial distributionposterior probabilitylikelihood functioncomputer visioninterframe processingstate vector estimationpixel classificationавторы выражают благодарность А. С. Храменкову (УО «Военная академия Республики Бела­ русь») за неоценимую помощь в формулировках и корректировке концепции работы, а также за ценные рекомендации, которые способствовали улучшению качества исследования.the authors would like to thank A. S. 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The authors declare that there are no conflicts of interest present.