# Fully automatic affine registration of planar parametric curves

## Main Article Content

## Abstract

A new, fast and fully automatic algorithm for registration of 2D parametric curves is proposed in this paper. Two functionals, expressing difference between given curves are defined and minimized. The first one is based on difference in signed curvature of curves. Its optimization leads to optimal curve parametrization offset. The second one is based on distances between corresponding points and leads to optimal affine transformation parameters. Optimization of the parametrization offset is necessary in order to identify points correspondence of given curves. Numerical experiments on real data are presented and discussed.

## Article Details

How to Cite

MIKULA, Karol; URBÁN, Jozef.
Fully automatic affine registration of planar parametric curves.

**Proceedings of the Conference Algoritmy**, [S.l.], p. 343-352, feb. 2016. Available at: <http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/algoritmy/article/view/423>. Date accessed: 22 sep. 2017.
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Articles

## References

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[12] K. Mikula, D. Ševčovič, A direct method for solving an anisotropic mean curvature flow of planar curve with an external force, Mathematical Methods in Applied Sciences, 27(13), (2004) pp. 1545-1565.

[13] K. Mikula, D. Ševćovič, M. Balažovjech, A simple, fast and stabilized flowing finite volume method for solving general curve evolution equations, Communications in Computational Physics, Vol. 7, No. 1 (2010) pp. 195-211

[14] K. Mikula, J. Urbán, New fast and stable Lagrangean method for image segmentation, Proceedings of the 5th International congress on image and signal processing (CISP 2012), Chongquing, China, ISBN-978-1-4673-9/10, (2012), pp. 834-842

[15] H. Benninghoff and H. Garcke, Efficient image segmentation and restoration using parametric curve evolution with junctions and topology changes, SIAM Journal on Imaging Sciences, 7(3), (2014), 1451-1483.

[2] F. L. Bookstein, Morphometric Tools for Landmark Data, Cambridge Univ. Press, London/New York, (1991).

[3] L. D. Cohen, On active contour models and balloons, CVGIP: Image Understanding, 53(2), (1991), 211218.

[4] F. Mokhtarian, A.K. Mackworth, A Theory of Multiscale, Curvature-Based Shape Representation for Planar Curves, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 14, no. 8, (1992), pp. 789-805.

[5] A. Kichenassamy, A. Kumar, P. Olver, A. Tannenbaum, and A. Yezzi, Gradient flows and geometric active contour models, In IEEE International Conference of Computer Vision, (1995), pages 810815.

[6] T. Cootes, C. Taylor, D. Cooper, and J. Graham, Active shape models, their training and application, Comput. Vis. Image Understanding, vol. 61, (1995), pp. 3859.

[7] J A Sethian, A fast marching level set method for monotonically advancing fronts, Proc. Nat. Acad. Sci., 93, (1996), 15911595.

[8] V. Caselles, R. Kimmel, and G. Sapiro, Geodesic active contours, Intl J. Comp. Vision, 22(1), (1997), pp. 6179.

[9] J. Maintz and M. Viergever, A Survey for Medical Image Registration, Medical Image Analysis, 2, (1998), pp. 136.

[10] M. Leventon, W. Grimson, and O. Faugeras, Statistical shape influence in geodesic active contours, IEEE International Conference of Computer Vision and Pattern Recognition,1 (2000), pp. 316323.

[11] N. Paragios, M. Rousson, and V. Ramesh, Matching distance functions: A shape-toarea variational approach for global-to-local registration, ECCV, Copenhangen, Denmark (2002).

[12] K. Mikula, D. Ševčovič, A direct method for solving an anisotropic mean curvature flow of planar curve with an external force, Mathematical Methods in Applied Sciences, 27(13), (2004) pp. 1545-1565.

[13] K. Mikula, D. Ševćovič, M. Balažovjech, A simple, fast and stabilized flowing finite volume method for solving general curve evolution equations, Communications in Computational Physics, Vol. 7, No. 1 (2010) pp. 195-211

[14] K. Mikula, J. Urbán, New fast and stable Lagrangean method for image segmentation, Proceedings of the 5th International congress on image and signal processing (CISP 2012), Chongquing, China, ISBN-978-1-4673-9/10, (2012), pp. 834-842

[15] H. Benninghoff and H. Garcke, Efficient image segmentation and restoration using parametric curve evolution with junctions and topology changes, SIAM Journal on Imaging Sciences, 7(3), (2014), 1451-1483.