# DETECTION OF PERFECT AND APPROXIMATE REFLECTIVE SYMMETRY IN ARBITRARY DIMENSION

### Darko Dimitrov, Klaus Kriegel

#### Abstract

Symmetry detection is an important problem with many applications in pattern recognition, computer vision and computational geometry. In this paper, we propose a novel algorithm for computing a hyperplane of reflexive symmetry of a point set in arbitrary dimension with approximate symmetry. The algorithm is based on the geometric hashing technique. In addition, we consider a relation between the perfect reflective symmetry and the principal components of shapes, a relation that was already a base of few heuristic approaches that tackle the symmetry problem in 2D and 3D. From mechanics, it is known that, if H is a plane of reflective symmetry of the 3D rigid body, then a principal component of the body is orthogonal to H . Here we extend that result to any point set (continuous or discrete) in arbitrary dimension.

Download#### Paper Citation

#### in Harvard Style

Dimitrov D. and Kriegel K. (2007). **DETECTION OF PERFECT AND APPROXIMATE REFLECTIVE SYMMETRY IN ARBITRARY DIMENSION** . In *Proceedings of the Second International Conference on Computer Vision Theory and Applications - Volume 2: VISAPP,* ISBN 978-972-8865-74-0, pages 128-136. DOI: 10.5220/0002052401280136

#### in Bibtex Style

@conference{visapp07,

author={Darko Dimitrov and Klaus Kriegel},

title={DETECTION OF PERFECT AND APPROXIMATE REFLECTIVE SYMMETRY IN ARBITRARY DIMENSION},

booktitle={Proceedings of the Second International Conference on Computer Vision Theory and Applications - Volume 2: VISAPP,},

year={2007},

pages={128-136},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0002052401280136},

isbn={978-972-8865-74-0},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the Second International Conference on Computer Vision Theory and Applications - Volume 2: VISAPP,

TI - DETECTION OF PERFECT AND APPROXIMATE REFLECTIVE SYMMETRY IN ARBITRARY DIMENSION

SN - 978-972-8865-74-0

AU - Dimitrov D.

AU - Kriegel K.

PY - 2007

SP - 128

EP - 136

DO - 10.5220/0002052401280136