# Evaluation of Approximate Reflectional Symmetry

### Martin Maňák, David Podgorelec, Ivana Kolingerová

#### 2024

#### Abstract

When an object can be split by a plane into two symmetrical parts, one being the mirrored image of the other, the object has a reflectional symmetry with respect to that plane. The symmetry is often only approximate and not necessarily global. Many algorithms exist for the detection of symmetries and there are various applications utilizing symmetrical properties. Yet there are not so many ways to measure the amount of approximate reflectional symmetry. In this paper, we introduce a method for the evaluation of approximate symmetry for objects represented as a point cloud. The method consists of three parts - a relative symmetry distance for measuring the amount of approximate reflectional symmetry, a plot of relative errors, and visualization of errors. This method offers a way how to compare different objects by the amount of symmetry and improves understanding of the symmetrical properties of objects, both quantitatively and visually.

Download#### Paper Citation

#### in Harvard Style

Maňák M., Podgorelec D. and Kolingerová I. (2024). **Evaluation of Approximate Reflectional Symmetry**. In *Proceedings of the 19th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 1: IVAPP*; ISBN 978-989-758-679-8, SciTePress, pages 734-740. DOI: 10.5220/0012472800003660

#### in Bibtex Style

@conference{ivapp24,

author={Martin Maňák and David Podgorelec and Ivana Kolingerová},

title={Evaluation of Approximate Reflectional Symmetry},

booktitle={Proceedings of the 19th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 1: IVAPP},

year={2024},

pages={734-740},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0012472800003660},

isbn={978-989-758-679-8},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 19th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 1: IVAPP

TI - Evaluation of Approximate Reflectional Symmetry

SN - 978-989-758-679-8

AU - Maňák M.

AU - Podgorelec D.

AU - Kolingerová I.

PY - 2024

SP - 734

EP - 740

DO - 10.5220/0012472800003660

PB - SciTePress