Development of methods and algorithms for processing images and other types of ordered data on the basis of Trained Markov Models 

(RFBR Grant  16-07-01039 )

Project objectives: development of mathematical methods, as well as fast, easily parallelized and low computational cost algorithms for solving a number of applied image and other types of ordered data processing tasks on the basis of a unified mathematical framework of Trained Markov Models.

Problem formulation

In this work we will use a generalization of the Bayesian approach to the image analysis

                                The ultimate aim of processing can be represented as a transformation of the original image , defined on a subset of the two-dimensional discrete space  , into a secondary array , which would be defined on the same argument set and take values from a set depending on the problem
We will consider an analyzed imageAnalyzed Imageand processing result Resultas, respectively, the observed and hidden components of the two-component random field (X, Y ).

Problem Reformulation Criterion

Examples of image processing problems


Relative Computation Time of Various Image Processing Techniques (sec)

Relative computational time

Computation Time Comparison

Computation Time Comparison
Computation time of Guided filter, fast Guided filter (with s = 2), fast Guided filter (with s = 4)
and our algorithm for processing of images of different sizes


  1. B.H. Chen, A. Kopylov, S.C. Huang, O. Seredin, R. Karpov, S.Y. Kuo, K.R. Lai, et al. Improved global motion estimation via motion vector clustering for video stabilization. //Engineering Applications of Artificial Intelligence. – 2016. – Т. 54. – С. 39-48.
  2. Грачева Инесса Александровна, Копылов Андрей Валериевич, Середин Олег Сергеевич, Кушнир Олеся Александровна, Ларин Александр Олегович. Background-Invariant Robust Hand Detection Using One Class Color Segmentation and Skeleton Description. // Интеллектуализация обработки информации: 11-я международная конференция. Барселона, Испания, 10 – 14 октября 2016 г.: Тезисы докладов. Москва: ТОРУС ПРЕСС, 2016. С. 102-103.
  3. А.В. Копылов, О.С. Середин, О.А. Кушнир, И.А. Грачева, А.О. Ларин. Устойчивое детектирование ладони на изображениях на основе комбинирования информации о цвете и форме // Известия Тульского государственного университета. Технические науки. Вып.11. Ч.1. Тула: Изд-во ТулГУ, 2016. С.24–40.
  4. Pham Cong Thang, Andrey V. Kopylov. Parametric procedures for image denoising with flexible prior model// Proceedings of the Seventh International Symposium on Information and Communication Technology, Ho Chi Minh City, Vietnam, December 8-9, 2016. ACM International Conference Proceeding Series, ISBN 978-1-4503-4815-7, P. 294-301. 
  5. Thang, P. C., Kopylov, A. V., and Dvoenko, S. D.: Edge–Preserving Denoising Based on Dynamic Programming on The Full Set Of Adjacency Graphs, Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci., XLII-2/W4, 55-60, doi:10.5194/isprs-archives-XLII-2-W4-55-2017, 2017.
  6. Inessa Gracheva and Andrey Kopylov. Image Processing Algorithms with Structure Transferring Properties on the Basis of Gamma-normal Model. 5th International Conference, AIST 2016, Yekaterinburg, Russia, April 7-9, 2016, Revised Selected Papers. Communications in Computer and Information Science, Vol. 661, Springer International Publishing AG, 2017 г., pp 257-268 
  7. Грачева И.А., Копылов А.В. Алгоритм передачи структуры объектов на изображении на основе модифицированного способа аппроксимации графа смежности. Известия ТулГУ. Технические науки. Вып. 10, стр. 30-39, 2017
  8. Грачева И.А., Копылов А.В. Алгоритм обработки изображений на основе диагональной аппроксимации графа смежности элементов изображения. Математические методы распознавания образов: 18-я Всероссийская конференция, г. Таганрог, 9–13 октября 2017г.: Тезисы докладов. —М.: Торус Пресс, стр. 80-81, 2017
  9. Andrey Kopylov, Oleg Seredin, Olesia Kushnir, Inessa Gracheva and Aleksandr Larin. Background-Invariant Robust Hand Detection Using One-Class Color Segmentation and Skeleton Description. ICPRAM-2018. International Conference on Pattern Recognition Applications and Methods, Funchal, Madeira - Portugal, January 16 - 18, 2018 (In printing)