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Fast parametric curves detection based on statistical hypotheses estimation

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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.

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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).

  2. 2.

    F. Devernay, “A non-maxima auppression method for edge detection with sub-pixel accuracy,” INRIA Tech Rep. RR-2724 (1995).

  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.

  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).

  5. 5.

    G. E. Forsythe, M. A. Malcolm, and C. B. Moler, Computer Methods for Mathematical Computations (Prentice Hall, 1977), p. 210.

  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.

  7. 7.

    T. Lindeberg, Scale-Space Theory in Computer Vision (Kluwer Acad. Publ., Dordrecht, 1994).

  8. 8.

    R. A. McLaughlin, “Randomized Hough transform: better ellipse detection,” IEEE TENCON — Digital Signal Processing Appl. 1, 409–414 (1996).

  9. 9.

    W. K. Pratt, Digital Image Processing: PIKS Scientific Inside, 4th ed. (Wiley-Intersci., John Wiley and Sons, Los Altos, 2007), p. 782.

  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).

  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.

  12. 12.

    T. Y. Zhang and C. Y. Suen, “A fast parallel algorithm for thinning digital patterns,” Commun. ACM 27(3), 236–239 (1984).

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Author information

Correspondence to A. E. Levashov.

Additional information

This article was translated by the authors.

Alexey E. Levashov. Born in 1989. Student at the chair of Mathematical Physics, Faculty of Computational Mathematics and Cybernetics, Moscow State University, Russia.

Areas of interest: mathematical methods of image processing, computer vision, primary information feature detection, parametrical curves detection, Hough transform.

Dmitry V. Yurin. Born in 1965. PhD, senior researcher at the laboratory of Mathematical Methods of Image Processing, Faculty of Computational Mathematics and Cybernetics, Moscow State University, Russia.

Areas of interest: mathematical methods of image processing, computer vision, primary information feature detection, image filtering, 3D recovery, image segmentation, image registration and mosaicing, and modern programming techniques.

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Levashov, A.E., Yurin, D.V. Fast parametric curves detection based on statistical hypotheses estimation. Pattern Recognit. Image Anal. 23, 445–454 (2013). https://doi.org/10.1134/S105466181304010X

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Keywords

  • parametric curve detection
  • Hough transform
  • line and circle detection
  • edge detection