# SHAPE COMPARISON BASED ON SKELETON ISOMORPHISM

### L. Domakhina, A. Okhlopkov

#### Abstract

A new approach to shape comparison problem is presented in this work. The approach is based on skeleton isomorphism. We propose a shape metrics construction instrument which is based on finding close shapes having isomorphic continuous skeletons. We propose several metrics based on this instrument that can be used for shape comparison. The main advantage over existing approaches is mathematically correctly defined shape metrics via Hausdorff distance. The efficiency of the proposed approach is confirmed on the shapes recognition problem.

#### References

- Choi, H. I., Choi, S. W., and Moon, H. P. (1997). Mathematical theory of medial axis transform. Pacific.J. of Math, 181(1):57-88.
- Domakhina, L. and A.Okhlopkov (2008). Isomorphic skeletons of raster images. In 18th International Conference Graphicon-2008.
- E. M. Reingold, J. N. and Deo, N. (1977). Combinatorial Algorithms, Theory and Practice. P.
- I.Reyer and Mestetski, L. (2003). Continuous skeletal representation with fixed accuracy. In 13th Int. Conference Graphicon-2003.
- Klein, P. N., Sebastian, T. B., and Kimia, B. B. (2001). Shape matching using edit-distance: An implementation. In The twelfth annual ACM-SIAM symposium on Discrete algorithms, pages 781 - 790.
- Liu, T. and Geiger., D. (1999). Approximate tree matching and shape similarity. In ICCV.
- Mestetski, L. (1998). Continuous skeleton of raster images. In 8th Int. Conference Graphicon-1998.
- Sebastian, T. B. and Kimia., B. B. (2001). Curves vs skeletons in object recognition. In Division of Engineering, Brown University. Providence, RI 02912, USA.
- Tanase, M. (2005). Shape Decomposition and Retrieval. PhD thesis, Utrecht University.
- Zhuravlev, J., V.Ryazanov, and O.Senko (2005). Recognition. Mathematical Methods. Practical Solutions. Phasis Edition, Moscow.

#### Paper Citation

#### in Harvard Style

Domakhina L. and Okhlopkov A. (2009). **SHAPE COMPARISON BASED ON SKELETON ISOMORPHISM** . In *Proceedings of the Fourth International Conference on Computer Vision Theory and Applications - Volume 2: VISAPP, (VISIGRAPP 2009)* ISBN 978-989-8111-69-2, pages 237-242. DOI: 10.5220/0001807502370242

#### in Bibtex Style

@conference{visapp09,

author={L. Domakhina and A. Okhlopkov},

title={SHAPE COMPARISON BASED ON SKELETON ISOMORPHISM},

booktitle={Proceedings of the Fourth International Conference on Computer Vision Theory and Applications - Volume 2: VISAPP, (VISIGRAPP 2009)},

year={2009},

pages={237-242},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0001807502370242},

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 2: VISAPP, (VISIGRAPP 2009)

TI - SHAPE COMPARISON BASED ON SKELETON ISOMORPHISM

SN - 978-989-8111-69-2

AU - Domakhina L.

AU - Okhlopkov A.

PY - 2009

SP - 237

EP - 242

DO - 10.5220/0001807502370242