Ellipse Detection with Elemental Subsets

  • Peter Veelaert
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5810)


We propose a simple method for fitting ellipses to data sets. The method first computes the fitting cost of small samples, called elemental subsets. We then prove that the global fitting cost can be easily derived from the fitting cost of the samples. Since fitting costs are computed from small samples, the technique can be incorporated in many ellipse detection and recognition algorithms, and in particular, in algorithms that make use of incremental fitting. Some of the theoretical results are formulated in the more general setting of implicit curve fitting.


  1. 1.
    Coeurjolly, D., Gerard, Y., Reveilles, J.-P., Tougne, L.: An elementary algorithm for digital arc segmentation. Discrete Applied Mathematics 139, 31–50 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Deboeverie, F., Veelaert, P., Philips, W.: Face recognition using parabola edge map. In: Blanc-Talon, J., Bourennane, S., Philips, W., Popescu, D., Scheunders, P. (eds.) ACIVS 2008. LNCS, vol. 5259, pp. 994–1005. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  3. 3.
    Stoer, J., Witzgall, C.: Convexity and Optimization in Finite Dimensions I. Springer, Berlin (1970)CrossRefzbMATHGoogle Scholar
  4. 4.
    Veelaert, P.: Constructive fitting and extraction of geometric primitives. CVGIP: Graphical Models and Image Processing 59, 233–251 (1997)Google Scholar
  5. 5.
    Veelaert, P., Teelen, K.: Fast polynomial segmentation of digitized curves. In: Kuba, A., Nyúl, L.G., Palágyi, K. (eds.) DGCI 2006. LNCS, vol. 4245, pp. 482–493. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  6. 6.
    Qiao, Y., Ong, S.H.: Arc-based evaluation and detection of ellipses. Pattern Recognition 40, 1990–2003 (2007)CrossRefzbMATHGoogle Scholar
  7. 7.
    Umbach, D., Jones, K.: A few methods for fitting circles to data. IEEE Trans. on Instrumentation and Measurement 52, 1881–1885 (2003)CrossRefGoogle Scholar
  8. 8.
    Zhang, S.-C., Liu, Z.-Q.: A robust, real-time ellipse detector. Pattern Recognition 38, 273–287 (2005)CrossRefzbMATHGoogle Scholar
  9. 9.
    Zunic, J., Sladoje, N.: Efficiency of characterizing ellipses and ellipsoids by discrete moments. IEEE Trans. on Pattern Analysis and Machine Intelligence 22, 407–414 (2000)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Peter Veelaert
    • 1
  1. 1.University College Ghent, Engineering SciencesGhent University AssociationGhentBelgium

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