The Determination of Distances between Images by de Rham Currents Method
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 geometri...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Yaroslavl State University
2020-03-01
|
| Series: | Моделирование и анализ информационных систем |
| Subjects: | |
| Online Access: | https://www.mais-journal.ru/jour/article/view/1291 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849241033357918208 |
|---|---|
| author | Sergey N. Chukanov |
| author_facet | Sergey N. Chukanov |
| author_sort | Sergey N. Chukanov |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-557c1a38668d427180beb012017f5c23 |
| institution | Kabale University |
| issn | 1818-1015 2313-5417 |
| language | English |
| publishDate | 2020-03-01 |
| publisher | Yaroslavl State University |
| record_format | Article |
| series | Моделирование и анализ информационных систем |
| spelling | doaj-art-557c1a38668d427180beb012017f5c232025-08-20T04:00:19ZengYaroslavl State UniversityМоделирование и анализ информационных систем1818-10152313-54172020-03-012719610710.18255/1818-1015-2020-1-96-107962The Determination of Distances between Images by de Rham Currents MethodSergey N. Chukanov0Sobolev Institute of Mathematics, SB RASThe 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.https://www.mais-journal.ru/jour/article/view/1291pattern recognitionimage matchingde rham currentaffine transformations |
| spellingShingle | Sergey N. Chukanov The Determination of Distances between Images by de Rham Currents Method Моделирование и анализ информационных систем pattern recognition image matching de rham current affine transformations |
| title | The Determination of Distances between Images by de Rham Currents Method |
| title_full | The Determination of Distances between Images by de Rham Currents Method |
| title_fullStr | The Determination of Distances between Images by de Rham Currents Method |
| title_full_unstemmed | The Determination of Distances between Images by de Rham Currents Method |
| title_short | The Determination of Distances between Images by de Rham Currents Method |
| title_sort | determination of distances between images by de rham currents method |
| topic | pattern recognition image matching de rham current affine transformations |
| url | https://www.mais-journal.ru/jour/article/view/1291 |
| work_keys_str_mv | AT sergeynchukanov thedeterminationofdistancesbetweenimagesbyderhamcurrentsmethod AT sergeynchukanov determinationofdistancesbetweenimagesbyderhamcurrentsmethod |