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Modelirovanie i Analiz Informatsionnykh Sistem, 2020, Volume 27, Number 1, Pages 96–107
DOI: https://doi.org/10.18255/1818-1015-2020-1-96-107
(Mi mais706)
 

Discrete mathematics in relation to computer science

The determination of distances between images by de Rham currents method

S. N. Chukanov

Sobolev Institute of Mathematics, SB RAS, Omsk branch, 13 Pevtsova str., Omsk 644043, Russia
References:
Abstract: The goal of the paper is to develop an algorithm for matching the shapes of images of objects based on the geometric method of de Rham currents and preliminary affine transformation of the source image shape. In the formation of the matching algorithm, the problems of ensuring invariance to geometric image transformations and ensuring the absence of a bijective correspondence requirement between images segments were solved. The algorithm of shapes matching based on the current method is resistant to changes of the topology of object shapes and reparametrization. When analyzing the data structures of an object, not only the geometric form is important, but also the signals associated with this form by functional dependence. To take these signals into account, it is proposed to expand de Rham currents with an additional component corresponding to the signal structure. To improve the accuracy of shapes matching of the source and terminal images we determine the functional on the basis of the formation of a squared distance between the shapes of the source and terminal images modeled by de Rham currents. The original image is subjected to preliminary affine transformation to minimize the squared distance between the deformed and terminal images.
Keywords: pattern recognition, image matching, de Rham current, affine transformations.
Funding agency Grant number
Russian Foundation for Basic Research 18-07-00526_а
18-08-01284_а
Siberian Branch of Russian Academy of Sciences I.5.1., проект № 0314-2019-0020
This work was supported by the Russian Foundation for Basic Research, projects № 18-07-00526 and № 18-08-01284. This work was supported by the Basic Research Program of the Siberian Branch of the Russian Academy of Sciences № I.5.1., Project № 0314-2019-0020.
Received: 01.02.2020
Revised: 27.02.2020
Accepted: 28.02.2020
Document Type: Article
UDC: 004.932.2
MSC: 68U10
Language: English
Citation: S. N. Chukanov, “The determination of distances between images by de Rham currents method”, Model. Anal. Inform. Sist., 27:1 (2020), 96–107
Citation in format AMSBIB
\Bibitem{Chu20}
\by S.~N.~Chukanov
\paper The determination of distances between images by de Rham currents method
\jour Model. Anal. Inform. Sist.
\yr 2020
\vol 27
\issue 1
\pages 96--107
\mathnet{http://mi.mathnet.ru/mais706}
\crossref{https://doi.org/10.18255/1818-1015-2020-1-96-107}
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    Моделирование и анализ информационных систем
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