# Search for Rotational Symmetry of Binary Images via Radon Transform and Fourier Analysis

### Nikita Lomov, Nikita Lomov, Oleg Seredin, Olesia Kushnir, Daniil Liakhov

#### 2023

#### Abstract

We considered the optimization of such rotational symmetry properties in 2D shapes as the focus position, symmetry degree, and measure expressed as the Jaccard index generalized to a group of two or more shapes. We proposed to reduce the symmetry detection to the averaging of Jaccard indices for all possible pairs of rotated shapes. It is sufficient to consider a number of pairs linearly proportional to the degree of symmetry. It is shown that for a class of plane affine transformations translating lines into lines, and rotations in particular, the upper estimate of the Jaccard index can be directly derived from the Radon transform of the shape. We proposed a fast estimation of the shape degree of symmetry by applying the Fourier analysis of the secondary features derived from the Radon transform. The proposed methods were implemented as a highly efficient computational procedure. The results are consistent with the expert judgment of the qualities of symmetry.

Download#### Paper Citation

#### in Harvard Style

Lomov N., Seredin O., Kushnir O. and Liakhov D. (2023). **Search for Rotational Symmetry of Binary Images via Radon Transform and Fourier Analysis**. In *Proceedings of the 18th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2023) - Volume 4: VISAPP*; ISBN 978-989-758-634-7, SciTePress, pages 280-289. DOI: 10.5220/0011679900003417

#### in Bibtex Style

@conference{visapp23,

author={Nikita Lomov and Oleg Seredin and Olesia Kushnir and Daniil Liakhov},

title={Search for Rotational Symmetry of Binary Images via Radon Transform and Fourier Analysis},

booktitle={Proceedings of the 18th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2023) - Volume 4: VISAPP},

year={2023},

pages={280-289},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0011679900003417},

isbn={978-989-758-634-7},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 18th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2023) - Volume 4: VISAPP

TI - Search for Rotational Symmetry of Binary Images via Radon Transform and Fourier Analysis

SN - 978-989-758-634-7

AU - Lomov N.

AU - Seredin O.

AU - Kushnir O.

AU - Liakhov D.

PY - 2023

SP - 280

EP - 289

DO - 10.5220/0011679900003417

PB - SciTePress