Abstract
In this paper, we present a new affine invariant curve fitting technique. Our method is based on the affine invariant Fourier descriptors and implicitization of them by matrix annihilation. Experimental results are presented to assess the stability and robustness of our fitting method under data perturbations.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Taubin, G., Cukierman, F., Sullivan, S., Ponce, J., Kriegman, D.J.: Parameterized Families of Polynomials for Bounded Algebraic Curve and Surface Fitting. IEEE Trans. Pattern Analysis and Machine Intelligence 16(3), 287–303 (1994)
Keren, D., Cooper, D., Subrahmonia, J.: Describing Complicated Objects by Implicit Polynomials. IEEE Trans. Pattern Analysis and Machine Intelligence 16, 38–53 (1994)
Taubin, G.: Estimation of Planar Curves, Surfaces and Nonplanar Space Curves Defined by Implicit Equations, with Applications to Edge and Range Image Segmentation. IEEE Transactions on Pattern Analysis and Machine Intelligence 13, 1115–1138 (1991)
Wolovich, W.A., Unel, M.: The Determination of Implicit Polynomial Canonical Curves. IEEE Transactions on Pattern Analysis and Machine Intelligence 20(8) (October 1998)
Unel, M., Wolovich, W.A.: On the Construction of Complete Sets of Geometric Invariants for Algebraic Curves. Advances in Applied Mathematics 24, 65–87 (2000)
Unel, M., Wolovich, W.A.: A New Representation for Quartic Curves and Complete Sets of Geometric Invariants. Int. Jour. of Pattern Recognition and Artificial Intelligence 13(8) (1999)
Subrahmonia, J., Cooper, D.B., Keren, D.: Practical Reliable Bayesian Recognition of 2D and 3D Objects using Implicit Polynomials and Algebraic Invariants. IEEE Transactions on Pattern Analysis and Machine Intelligence 18(5), 505–519 (1996)
Lei, Z., Blane, M.M., Cooper, D.B.: 3L Fitting of Higher Degree Implicit Polynomials. In: Proceedings of Third IEEE Workshop on Applications of Computer Vision, Florida, pp. 148–153 (1996)
Tasdizen, T., Tarel, T., Cooper, D.B.: Improving the Stability of Algebraic Curves for Applications. IEEE Transactions in Image Processing 9(3), 405–416 (2000)
Hu, W.-C., Sheu, H.-T.: Quadratic B-spline for Curve Fitting. Proc. Natl. Sci. Counc. ROC(A) 24(5), 373–381 (2000)
Yalcin, H., Unel, M., Wolovich, W.A.: Implicitization of Parameteric Curves by Matrix Annihilation. International Journal of Computer Vision 54, 105–115 (2003)
Kuhl, F.P., Giardina, C.R.: Elliptic Fourier Features of a Closed Contour. Computer Graphics and Image Processing 18, 236–258 (1982)
Arbter, K., Synder, W.E., Burkhardt, H., Hirzinger, G.: Application of Affine-Invariant Fourier Descriptors to Recognition of the 3D Objects. IEEE Transactions on Pattern Analysis and Machine Intelligence 12(7), 640–647 (1990)
Arbter, K.: Affine-Invariant Fourier Descriptors, in From Pixels to Features. Elseiver Science, Amsterdam (1989)
Pollick, F.E., Sapiro, G.: Constant Affine Velocity Predicts the 1/3 Power Law of Planar Motion Perception and Generation. In: Elseiver Science, vol. 37(3), pp. 347–353. Elseiver Science, Amsterdam (1997)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Sener, S., Unel, M. (2004). A New Affine Invariant Fitting Algorithm for Algebraic Curves. In: Campilho, A., Kamel, M. (eds) Image Analysis and Recognition. ICIAR 2004. Lecture Notes in Computer Science, vol 3211. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30125-7_43
Download citation
DOI: https://doi.org/10.1007/978-3-540-30125-7_43
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-23223-0
Online ISBN: 978-3-540-30125-7
eBook Packages: Springer Book Archive