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«THE BULLETIN OF IRKUTSK STATE UNIVERSITY». SERIES «MATHEMATICS»
«IZVESTIYA IRKUTSKOGO GOSUDARSTVENNOGO UNIVERSITETA». SERIYA «MATEMATIKA»
ISSN 1997-7670 (Print)
ISSN 2541-8785 (Online)

List of issues > Series «Mathematics». 2022. Vol 39

Displacement Field Construction Based on a Discrete Model in Image Processing Problems

Author(s)
Elena D. Kotina1, Ekaterina B. Leonova1, Viktor A. Ploskikh1

1Saint-Petersburg State University, Saint-Petersburg, Russian Federation, e.kotina@spbu.ru

Abstract
The problem of a displacement field calculation for an image sequence based on a discrete model is being solved. Algorithms for velocity field (displacement field) construction are in demand in various image processing tasks. These methods are used in motion detection, object movement tracking, analysis of complex images, movement correction of medical diagnostic images in nuclear medicine, radiology, etc. An optimization approach to the displacement field construction based on a discrete model is developed in the paper. The approach explores the possibility of taking into account the brightness change along the trajectories of the system. A linear model is considered. Directed optimization methods based on the analytical representation of the functional gradient are constructed to search for unknown parameters. The algorithm for displacement field construction with image partitioning into regions (neighborhoods) is proposed. This algorithm can be used to process a variety of image sequences. The results of the algorithm operation on test radionuclide images are presented.
About the Authors

Elena D. Kotina, Dr. Sci. (Phys.–Math.), Prof., St. Petersburg, State University, St. Petersburg,199034, Russian Federation,e.kotina@spbu.ru

Ekaterina B. Leonova, Postgraduate, St. Petersburg State University, St. Petersburg, 199034, Russian Federation, st062324@student.spbu.ru

Viktor A. Ploskikh, Cand. Sci. (Phys.–Math.), Assoc. Prof., St. Petersburg State University, St. Petersburg, 199034, Russian Federation, v.ploskikh@spbu.ru

For citation
Kotina E. D., Leonova E. B., Ploskikh V. A. Displacement Field Construction Based on a Discrete Model in Image Processing Problems. The Bulletin of Irkutsk State University. Series Mathematics, 2022, vol. 39, pp. 3–16. https://doi.org/10.26516/1997-7670.2022.39.3
Keywords
discrete systems, displacement field, functional variation, optimization, image processing
UDC
519.6
MSC
65K10
DOI
https://doi.org/10.26516/1997-7670.2022.39.3
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