Constraints for Jaccard index-based rotational symmetry focus position in binary images
This study proposes analytical estimate for the size of a binary raster figure region which is guaranteed to contain the rotational symmetry focus. Focus here is the point a maximum Jaccard index between initial figure and rotated one. The size of the region is determined by the lower estimate of th...
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| Format: | Article |
| Language: | English |
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Samara National Research University
2023-12-01
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| Series: | Компьютерная оптика |
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| Online Access: | https://www.computeroptics.ru/eng/KO/Annot/KO47-6/470612e.html |
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| author | N.A. Lomov O.S. Seredin D.V. Liakhov O.A. Kushnir |
| author_facet | N.A. Lomov O.S. Seredin D.V. Liakhov O.A. Kushnir |
| author_sort | N.A. Lomov |
| collection | DOAJ |
| description | This study proposes analytical estimate for the size of a binary raster figure region which is guaranteed to contain the rotational symmetry focus. Focus here is the point a maximum Jaccard index between initial figure and rotated one. The size of the region is determined by the lower estimate of the intersection area during the rotation of the approximating primitives, considering the sizes of the inner and outer parts of the figure relative to the primitive. The smallest circumscribed circle or ellipse and sets of concentric circles and ellipses produced by the principal component analysis were used as the approximating figure. To verify the hypothesis that the size of the region is insignificant compared to the area of the figure, we numerically simulated the proposed method with test image datasets. |
| format | Article |
| id | doaj-art-9ac5309fec864b98b2730bbbcfceb0b3 |
| institution | Kabale University |
| issn | 0134-2452 2412-6179 |
| language | English |
| publishDate | 2023-12-01 |
| publisher | Samara National Research University |
| record_format | Article |
| series | Компьютерная оптика |
| spelling | doaj-art-9ac5309fec864b98b2730bbbcfceb0b32025-01-30T10:50:38ZengSamara National Research UniversityКомпьютерная оптика0134-24522412-61792023-12-0147694895710.18287/2412-6179-CO-1357Constraints for Jaccard index-based rotational symmetry focus position in binary imagesN.A. Lomov0O.S. Seredin1D.V. Liakhov2O.A. Kushnir3Tula State UniversityTula State UniversityTula State UniversityTula State UniversityThis study proposes analytical estimate for the size of a binary raster figure region which is guaranteed to contain the rotational symmetry focus. Focus here is the point a maximum Jaccard index between initial figure and rotated one. The size of the region is determined by the lower estimate of the intersection area during the rotation of the approximating primitives, considering the sizes of the inner and outer parts of the figure relative to the primitive. The smallest circumscribed circle or ellipse and sets of concentric circles and ellipses produced by the principal component analysis were used as the approximating figure. To verify the hypothesis that the size of the region is insignificant compared to the area of the figure, we numerically simulated the proposed method with test image datasets.https://www.computeroptics.ru/eng/KO/Annot/KO47-6/470612e.htmlcentral symmetryrotational symmetrysymmetry focusjaccard index |
| spellingShingle | N.A. Lomov O.S. Seredin D.V. Liakhov O.A. Kushnir Constraints for Jaccard index-based rotational symmetry focus position in binary images Компьютерная оптика central symmetry rotational symmetry symmetry focus jaccard index |
| title | Constraints for Jaccard index-based rotational symmetry focus position in binary images |
| title_full | Constraints for Jaccard index-based rotational symmetry focus position in binary images |
| title_fullStr | Constraints for Jaccard index-based rotational symmetry focus position in binary images |
| title_full_unstemmed | Constraints for Jaccard index-based rotational symmetry focus position in binary images |
| title_short | Constraints for Jaccard index-based rotational symmetry focus position in binary images |
| title_sort | constraints for jaccard index based rotational symmetry focus position in binary images |
| topic | central symmetry rotational symmetry symmetry focus jaccard index |
| url | https://www.computeroptics.ru/eng/KO/Annot/KO47-6/470612e.html |
| work_keys_str_mv | AT nalomov constraintsforjaccardindexbasedrotationalsymmetryfocuspositioninbinaryimages AT osseredin constraintsforjaccardindexbasedrotationalsymmetryfocuspositioninbinaryimages AT dvliakhov constraintsforjaccardindexbasedrotationalsymmetryfocuspositioninbinaryimages AT oakushnir constraintsforjaccardindexbasedrotationalsymmetryfocuspositioninbinaryimages |