maisМоделирование и анализ информационных системModeling and Analysis of Information Systems1818-10152313-5417Yaroslavl State University10.18255/1818-1015-2020-1-96-107mais-1291Research ArticleDiscrete Mathematics in Relation to Computer ScienceОпределение расстояний между изображениями методом потоков де РамаThe Determination of Distances between Images by de Rham Currents Methodhttps://orcid.org/0000-0002-8106-9813ЧукановСергей НиколаевичChukanovSergey N.

д-р техн. наук, профессор

Doctor of Technical Science, Professor

ch_sn@mail.ruИнститут математики им. С. Л. Соболева СО РАНРоссияSobolev Institute of Mathematics, SB RASRussian Federation20201903202027196107Copyright © Чуканов С.Н., 20202020Чуканов С.Н.Chukanov S.N.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://www.mais-journal.ru/jour/article/view/1291

Целью работы является разработка алгоритма сравнения форм изображений объектов, основанного на геометрическом методе потоков де Рама и предварительном аффинном преобразовании исходной формы изображения. При формировании алгоритма сравнения решены задачи обеспечения инвариантности к геометрическим преобразованиям изображений и обеспечения отсутствия требования биективного соответствия между сегментами исходного и терминального изображений. Алгоритм сравнения форм, основанный на методе потоков, устойчив к изменению топологии форм объектов и репараметризации. При анализе структур данных объекта имеет значение не только геометрическая форма, но и сигналы, ассоциированные с этой формой функциональной зависимостью. Для учета этих сигналов предлагается расширить потоки де Рама дополнительным компонентом, соответствующим структуре сигнала. Для повышения точности сравнения форм исходного и терминального изображений определяется функционал на основе формирования квадрата расстояния между формами исходного и терминального изображений, моделируемыми потоками де Рама. Исходное изображение подвергается предварительному аффинному преобразованию для минимизации квадрата расстояния между деформированным и терминальным изображениями.

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.

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The authors declare that there are no conflicts of interest present.