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Constraints for Jaccard index-based rotational symmetry focus position in binary images
N.A. Lomov 1, O.S. Seredin 1, D.V. Liakhov 1, O.A. Kushnir 1

1 Tula State University, 300012, Tula, Russia, Lenin Ave. 92

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DOI: 10.18287/2412-6179-CO-1357

Pages: 948-957.

Full text of article: English language.

Abstract:
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.

Keywords:
central symmetry, rotational symmetry, symmetry focus, Jaccard index.

Citation:
Lomov NA, Seredin OS, Liakhov DV, Kushnir OA. Constraints for Jaccard index-based rotational symmetry focus position in binary images. Computer Optics 2023; 47(6): 948-957. DOI: 10.18287/2412-6179-CO-1357.

Acknowledgements:
This study is supported by the Russian Science Foundation, grant No. 22-21-00575, https://rscf.ru/project/22-21-00575/.

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