Advertisement

A New Affine Invariant Fitting Algorithm for Algebraic Curves

  • Sait Sener
  • Mustafa Unel
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3211)

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.

Keywords

Machine Intelligence Algebraic Curve Algebraic Curf Fourier Descriptor Data Perturbation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    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)zbMATHCrossRefGoogle Scholar
  2. 2.
    Keren, D., Cooper, D., Subrahmonia, J.: Describing Complicated Objects by Implicit Polynomials. IEEE Trans. Pattern Analysis and Machine Intelligence 16, 38–53 (1994)CrossRefGoogle Scholar
  3. 3.
    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)CrossRefGoogle Scholar
  4. 4.
    Wolovich, W.A., Unel, M.: The Determination of Implicit Polynomial Canonical Curves. IEEE Transactions on Pattern Analysis and Machine Intelligence 20(8) (October 1998)Google Scholar
  5. 5.
    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)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    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)Google Scholar
  7. 7.
    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)CrossRefGoogle Scholar
  8. 8.
    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)Google Scholar
  9. 9.
    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)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Hu, W.-C., Sheu, H.-T.: Quadratic B-spline for Curve Fitting. Proc. Natl. Sci. Counc. ROC(A) 24(5), 373–381 (2000)Google Scholar
  11. 11.
    Yalcin, H., Unel, M., Wolovich, W.A.: Implicitization of Parameteric Curves by Matrix Annihilation. International Journal of Computer Vision 54, 105–115 (2003)zbMATHCrossRefGoogle Scholar
  12. 12.
    Kuhl, F.P., Giardina, C.R.: Elliptic Fourier Features of a Closed Contour. Computer Graphics and Image Processing 18, 236–258 (1982)CrossRefGoogle Scholar
  13. 13.
    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)CrossRefGoogle Scholar
  14. 14.
    Arbter, K.: Affine-Invariant Fourier Descriptors, in From Pixels to Features. Elseiver Science, Amsterdam (1989)Google Scholar
  15. 15.
    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)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Sait Sener
    • 1
  • Mustafa Unel
    • 1
  1. 1.Department of Computer EngineeringGebze Institute of TechnologyGebze/KocaeliTurkey

Personalised recommendations