JAMC
Estimating the Parameters of Vortex and Ship Wakes in Images
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Abstract
International schools-conferences of young scientists on problems of geophysics in Russia attract the attention of mature mathematicians and editors of major scientific journals. The problems of the analysis of vortex formations in remote sensing were posed by K.V. Pokazeev and S.P. Perov. Another impetus to the creation of methods of Gradient Morphology was the rethinking of the usual Image Morphology by Pytiev Yu.P., Chulichkov A. I. and the well-known Wiener-Kotelnikov sampling theorem. In our Finite-Dimensional Sampling Theorem (FDST) operations of mathematical analysis (differentiation and integration of non-integer order with interpolation without the use of finite-difference schemes and integral sums) and field theory are implemented with the accuracy of the mantissa. The image is associated with its vector gradient field. The analysis of vector fields with the help of single-length vector templates made it possible to localize (indicate) object in the image by calculating the main parameters of the object: position and size. The proposed method of indicating local objects using gradient fields turned out to be highly precision and noise-immunity.
References
[1] Karev, V.I., Pokazeev, K.V., Chaplina, T.O. (2018). Modern issues of geophysics and geomechanics. PROCESSES IN GEOMEDIA, № 4, 1150–1156, (in Russian).
[2] Pytiev, Yu. P., Chulichkov, A. I. (2010). Methods of morphological analysis of images, Moscow,FIZMATLIT, (in Russian).
[3] Terentyev, E.N., Terentyev, N.E. (2016). PROCESSES IN GEOMEDIA. No. 4(9), pp. 355-362 (in Russian).
[4] Terentiev, E.N., García-Magariño, I., Shilin-Terentyev, N.E., Prikhodko, I. N., Farshakova, I.I. (2018). The Method of False Vortices in Designation Problems of Targets, Road Signs, Facial Features and Real Vortices in Space Images, Information and Computer Security Volume 1, doi:10.24294/ics.v1i1.1025
(http://systems.enpress-publisher.com/index.php/ICS/article/view/ 1025).
[5] Kuznetsov, N.A., Sinitsyn, I.N. (2009). Development of the Kotelnikov sampling theorem, UFN, 179 216–218 (in Russian).
[6] Terentiev, E.N., Shilin–Terentyev, N.E., Prikhodko, I.N., Farshakova, I.I. (2018). Vector operations for accurate indication of local objects in images, Scientific Notes of the Physics Faculty of Moscow University, (5): 1850308–10, (in Russian).
[7] Terentiev, E.N., Prikhodko, I.N., Farshakova, I.I. Kuznetsov, I. D., Shilin-Terentiev, N.E. (2019). Localization of the Vortices and Road Sings in Images, https://link.springer.com/chapter/10.1007/978-3-030-11533-3_30.
[8] Terentiev, E.N., Prikhodko, I.N., Farshakova, I.I. (2019). Problems of accurate localization objects in imagers, AIP Conference Proceedings 2171, 110009
https://doi.org/10.1063/1.5133243.
[9] Terentiev, E.N., Prikhodko, I.N., Farshakova, I.I. (2019). Applications of finite dimensional sampling theories, AIP Conference Proceedings 2195, 020019;
https://doi.org/10.1063/1.5140119.
[10] Terentiev, E.N., Prikhodko, I.N., Aleshin, P.E. (2022). Gradient Morphology in Estimating the Parameters of Vortex Formations and Ship Wakes in Images, Eight International Scientific Conference-School for Young Scientists Physical and Mathematical Modeling of Processes in Geomedia, Moscow, IPMECH RAS, October 12-14, 2022, Proceedings, pp. 23-26.
[11] Terentiev, E.N., https://orcid.org/0000-0003-1024-2575.
How to cite this paper
Estimating the Parameters of Vortex and Ship Wakes in Images
How to cite this paper: Evgeni Nikolaevich Terentiev, Irina Nikolaevna Prikhodko, Pavel Evgenievich Aleshin. (2023) Estimating the Parameters of Vortex and Ship Wakes in Images. Journal of Applied Mathematics and Computation, 7(2), 234-242.
DOI: http://dx.doi.org/10.26855/jamc.2023.06.004
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