# SHAPE RECOGNITION USING THE LEAST SQUARES APPROXIMATION

### Nacéra Laiche, Slimane Larabi

#### Abstract

This paper represents a novel algorithm to represent and recognize two dimensional curve based on its convex hull and the Least-Squared modeling. It combines the advantages of the property of the convex hulls that are particularly suitable for affine matching as they are affine invariant and the geometric properties of a contour that make it more or less identifiable. The description scheme and the similarity measure developed take into consideration technique for shape similarity. According to this method, the contours are extracted and decomposed into portions of curves. Each portion curve is approximated by some explicit curve using the Least Squares approximation. The obtained cubic curves are normalized in order to make the method invariant to scale change. Finally the resulting curves are used to compare and to compute similarity between shapes in images database using the Hausdorff distance. The proposed algorithm has been tested and its performance is found favourable as compared to other matching techniques.

#### References

- Argawal, S., Awan, A., Roth, D., 2004. Learning to detect objects in images via a sparse Part-base representation. In IEEE TPAMI. 26 (11), 1475-1490.
- Belongie, S., Malik, J., Puzicha, J., 2002. Shape matching and object recognition using shape contexts. In IEEE TRANS. PAMI 24 (24), 509-521.
- Blum, H., 1967. A transformation for extracting new descriptors of shape. In Models for the perception of speech and visual form. MITPress, 362-379.
- Carmona-poyato, A., Madrid-Cuevas, F. J., MedinaCarnicer, R., Munoz-Salinas, R., 2010. Polygonal approximation of digital planar curves through break point suppression. In: Pattern Recognition 43, 14-25.
- Chetvericov, D., 2003. A Simple and efficient algorithm for detection of high curvature points in planar curves. In 10th International Conference. CAIP, 25-27.
- Chong, C. W., Raveendran, P., Mukundan, R., 2003. Translation invariants of Zernike moments. In: Pattern Recognition. 1765-1773.
- Daliri, M. R., Torre, V., 2010. Classification of silhouettes using contour fragments. In Computer Vision and Image Understanding. 113, 1017-1025.
- Dudek, G., Tsotsos, J. K., 1997. Shape representation and recognition from multiscale curvature. In: Computer. Vision and Image Understanding. 68, N2, 170-187.
- Gope, C., Kehtarnavaz, N., 2007. Affine invariant comparison of point-sets using convex hulls and Hausdorff distances. In Pattern Recognition. 40, 309- 320.
- Graham, R. L., 1972. An efficient algorithm for determining the convex hull of a finite planar set. In Information Processing Letters.
- Hwang, S. K., Kim, W. Y., 2006. A novel approach to the fast computation of Zernike moments. In: Pattern Recognition. 39, 2065-2076.
- Leibe, B., Scheille, B., 2003. Analysing appearance and contour based methods for object categorization. In International Conference on Computer Vision and Pattern Recognition. Madison,Wisconsin.
- Matusiak, S., Daoudi, M., Ghorbel, F., 1998. Planar closed contour representation by invariant under a general affine transformation. In IEEE International Conference on Systems, Man, and Cybernetic.
- Mokhtarian, F., Makworth, A. K., 1992. A theory of multiscale curvature-based shape representation of planar curves. In: IEEE Transactions on Pattern Analysis and Machine Intelligence. 789-809.
- Preparata, F., Shamos, M., 1985. Computational Geometry: An introduction, Springer, Berlin, Germany.
- Sebastian, T. B., Klein, P. N., Kimia, B. B., 2004. Recognition of shapes by editing their shock graphs. In IEEE TRANS. PAMI 26 (5), 550-571.
- Yang, G. Y., Shu, H. Z., Toumoulin, C., Han, G. N., Luo, L. M., 2006. Efficient Legendre moments computation for grey level images. In: Pattern Recognition. 39, 74- 80.
- Zahn, C., Roskies, R., 1972. Fourier descriptors for plane closed curves. In IEEE TRANS.Computers.269-281.

#### Paper Citation

#### in Harvard Style

Laiche N. and Larabi S. (2012). **SHAPE RECOGNITION USING THE LEAST SQUARES APPROXIMATION** . In *Proceedings of the 1st International Conference on Pattern Recognition Applications and Methods - Volume 2: ICPRAM,* ISBN 978-989-8425-99-7, pages 572-575. DOI: 10.5220/0003778405720575

#### in Bibtex Style

@conference{icpram12,

author={Nacéra Laiche and Slimane Larabi},

title={SHAPE RECOGNITION USING THE LEAST SQUARES APPROXIMATION},

booktitle={Proceedings of the 1st International Conference on Pattern Recognition Applications and Methods - Volume 2: ICPRAM,},

year={2012},

pages={572-575},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0003778405720575},

isbn={978-989-8425-99-7},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 1st International Conference on Pattern Recognition Applications and Methods - Volume 2: ICPRAM,

TI - SHAPE RECOGNITION USING THE LEAST SQUARES APPROXIMATION

SN - 978-989-8425-99-7

AU - Laiche N.

AU - Larabi S.

PY - 2012

SP - 572

EP - 575

DO - 10.5220/0003778405720575