Pattern Recognition and Image Analysis

, Volume 23, Issue 4, pp 445–454 | Cite as

Fast parametric curves detection based on statistical hypotheses estimation

Representation, Processing, Analysis, and Understanding of Images

Abstract

We propose a new fast and reliable algorithm of parametric curves detection on images. In our approach as well as in many other approaches based on the Hough transform, we analyze the set of points obtained by an edge detector. Edge points are collected into chains of connected pixels, and then they are analyzed as a whole and piecemeal. At first we use randomized methods to reject unsuitable models. It gives us a high performance. Model parameters of fragments remained after randomized methods are estimated by the least squares method and the reliability of the hypothesis is estimated by the chi-square criterion. Then if the chi square criterion shows higher reliability for the merged similar models, we merge the obtained models.

Keywords

parametric curve detection Hough transform line and circle detection edge detection 

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References

  1. 1.
    T. C. Chen and K. L. Chung, “An efficient randomized algorithm or detecting circles,” Computer Vision and Image Understanding 83, 172–191 (2001).CrossRefMATHGoogle Scholar
  2. 2.
    F. Devernay, “A non-maxima auppression method for edge detection with sub-pixel accuracy,” INRIA Tech Rep. RR-2724 (1995).Google Scholar
  3. 3.
    D. L. Donoho, X. Huo, I. Jermyn, P. Jones, G. Lerman, O. Levi, and F. Natterer, “Beamlets and multiscale image analysis,” in Multiscale and Multiresolution Methods (Springer, 2001), pp. 149–196.Google Scholar
  4. 4.
    R. Duda and P. Hart, “Use of the Hough transformation to detect lines and curves in pictures,” Comm. ACM 15, 1–15 (1972).CrossRefGoogle Scholar
  5. 5.
    G. E. Forsythe, M. A. Malcolm, and C. B. Moler, Computer Methods for Mathematical Computations (Prentice Hall, 1977), p. 210.MATHGoogle Scholar
  6. 6.
    A. E. Levashov and D.V. Yurin, “Fast framework for parametric curves detection on gray-scale and color images with reliability control,” in Proc. 21st Int. Conf. on Computer Graphics GraphiCon’2011 (Moscow, 2011), pp. 212–215.Google Scholar
  7. 7.
    T. Lindeberg, Scale-Space Theory in Computer Vision (Kluwer Acad. Publ., Dordrecht, 1994).CrossRefGoogle Scholar
  8. 8.
    R. A. McLaughlin, “Randomized Hough transform: better ellipse detection,” IEEE TENCON — Digital Signal Processing Appl. 1, 409–414 (1996).Google Scholar
  9. 9.
    W. K. Pratt, Digital Image Processing: PIKS Scientific Inside, 4th ed. (Wiley-Intersci., John Wiley and Sons, Los Altos, 2007), p. 782.CrossRefGoogle Scholar
  10. 10.
    W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, 2nd ed. (Cambridge Univ. Press, New York, 1992).Google Scholar
  11. 11.
    L. Xu and E. Oja, “Randomized Hough transform,” in Encyclopedia of Artificial Intelligence, Ed. by J. Ramón, R. Dopico, J. Dorado, and A. Pazos (IGI Global Publ., 2008), pp. 1354–1361.Google Scholar
  12. 12.
    T. Y. Zhang and C. Y. Suen, “A fast parallel algorithm for thinning digital patterns,” Commun. ACM 27(3), 236–239 (1984).CrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2013

Authors and Affiliations

  1. 1.Laboratory of Mathematical Methods of Image Processing, Faculty of Computational Mathematics and CyberneticsLomonosov Moscow State UniversityMoscowRussia

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