# ON ANALYZING SYMMETRY OF OBJECTS USING ELASTIC DEFORMATIONS

### Chafik Samir, Anuj Srivastava, Mohamed Daoudi, Sebastian Kurtek

#### Abstract

We introduce a framework for analyzing symmetry of 2D and 3D objects using elastic deformations of their boundaries. The basic idea is to define spaces of elastic shapes and to compute shortest (geodesic) paths between the objects and their reflections using a Riemannian structure. Elastic matching, based on optimal (nonlinear) re-parameterizations of curves, provides a better registration of points across shapes, as compared to the previously-used linear registrations. A crucial step of orientation alignment, akin to finding planes of symmetry, is performed as a search for shortest geodesic paths. This framework is fully automatic and provides: a measure of asymmetry, the nearest symmetric shape, the optimal deformation to make an object symmetric, and the plane of symmetry for a given object.

#### References

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#### Paper Citation

#### in Harvard Style

Samir C., Srivastava A., Daoudi M. and Kurtek S. (2009). **ON ANALYZING SYMMETRY OF OBJECTS USING ELASTIC DEFORMATIONS** . In *Proceedings of the Fourth International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP, (VISIGRAPP 2009)* ISBN 978-989-8111-69-2, pages 194-200. DOI: 10.5220/0001797201940200

#### in Bibtex Style

@conference{visapp09,

author={Chafik Samir and Anuj Srivastava and Mohamed Daoudi and Sebastian Kurtek},

title={ON ANALYZING SYMMETRY OF OBJECTS USING ELASTIC DEFORMATIONS},

booktitle={Proceedings of the Fourth International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP, (VISIGRAPP 2009)},

year={2009},

pages={194-200},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0001797201940200},

isbn={978-989-8111-69-2},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the Fourth International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP, (VISIGRAPP 2009)

TI - ON ANALYZING SYMMETRY OF OBJECTS USING ELASTIC DEFORMATIONS

SN - 978-989-8111-69-2

AU - Samir C.

AU - Srivastava A.

AU - Daoudi M.

AU - Kurtek S.

PY - 2009

SP - 194

EP - 200

DO - 10.5220/0001797201940200