# ON ANALYZING SYMMETRY OF OBJECTS USING ELASTIC DEFORMATIONS

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

#### 2009

#### 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

- Joshi, S., Klassen, E., Srivastava, A., and Jermyn, I. (2007a). A novel representation for riemannian analysis of elastic curves in Rn. In CVPR.
- Kazhdan, M., Funkhouser, T., and Rusinkiewicz, S. (2004). Symmetry descriptors and 3D shape matching. In Symposium on Geometry Processing.
- Martinet, A., Soler, C., Holzschuch, N., and Sillion, F. (2006). Accurate detection of symmetries in 3D shapes. ACM Transactions on Graphics, 25(2):439 - 464.
- Michor, P. W. and Mumford, D. (2006). Riemannian geometries on spaces of plane curves. Journal of the European Mathematical Society, 8:1-48.
- Mitra, N. J., Guibas, L., and Pauly, M. (2007). Symmetrization. In ACM Transactions on Graphics, volume 26, pages 1-8.
- Mitra, N. J., Guibas, L. J., and Pauly, M. (2006). Partial and approximate symmetry detection for 3D geometry. In ACM SIGGRAPH, pages 560-568.
- Samir, C., Srivastava, A., and Daoudi, M. (2006). Threedimensional face recognition using shapes of facial curves. IEEE Trans. Pattern Anal. Mach. Intell., 28(11):1858-1863.
- Simari, P., Kalogerakis, E., and Singh, K. (2006). Folding meshes: Hierarchical mesh segmentation based on planar symmetry. In Eurographics Symposium on Geometry Processing 2006, pages 1824-1831.
- Sun, C. and Sherrah, J. (1997). 3d symmetry detection using the extended gaussian image. IEEE Transactions on Pattern Analysis and Machine Intelligence, 19(2):164-168.
- Thrun, S. and Wegbreit, B. (2005). Shape from symmetry. In ICCV 7805: Proceedings of the Tenth IEEE International Conference on Computer Vision, pages 1824- 1831, Washington, DC, USA. IEEE Computer Society.
- Tomaka, A. (2005). The application of 3d surfaces scanning in the facial features analysis. Journal of Medical Informatics & Technologies, 9:233-240.
- Zabrodsky, H., Peleg, S., and Avnir, D. (1995). Symmetry as a continuous feature. IEEE Transactions on Pattern Analysis and Machine Intelligence, 17(12):1154- 1166.

#### 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