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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Bibliographic Details
Published inKompʹûternaâ optika Vol. 47; no. 6; pp. 948 - 957
Main Authors Lomov, N.A., Seredin, O.S., Liakhov, D.V., Kushnir, O.A.
Format Journal Article
LanguageEnglish
Published Samara National Research University 01.12.2023
Subjects
central symmetry
jaccard index
rotational symmetry
symmetry focus
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Summary: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.
ISSN:0134-2452
2412-6179
DOI:10.18287/2412-6179-CO-1357