The Recognition of Polynomial Position and Orientation through the Finite Polynomial Discrete Radon Transform

  • Ines Elouedi
  • Régis Fournier
  • Amine Naït-Ali
  • Atef Hamouda
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8157)

Abstract

In this paper, we propose to accurately detect from an image curvilinear features that can be approximated by polynomial curves. Having the a priori knowledge of a polynomial parameters (coefficients and degree), we give the possibility to recognize both the orientation and the position of the polynomial (if it exists) in the given image. For this objective, we present a new approach titled ”The Finite Polynomial Discrete Radon Transform” (FPDRT) that maps the initial image into a Radon space where each point presents the amount of evidence of the existence of a polynomial at the same position. The FPDRT sums the pixels centered on a polynomial and stores the result at the corresponding position in the Radon space. The FPDRT extends the formalism of the Finite Discrete Radon Transform(FRT) which is restricted to project the image along straight lines of equation y = mx + t where m and t are integers. Our method generalizes FRT by projecting the image with respect to polynomials of equation y = mx n  + t where m, n and t are integers. The FPDRT method is exactly invertible, requires only arithmetic operations and is applicable to p×p sized images where p is a prime number. Several applications are allowable by the FPDRT such as fingerprint, palm print biometric applications and multi directional roads recognition.

Keywords

polynomial curves Finite Polynomial Discrete Radon Transform Radon space 

References

  1. 1.
    Deans, S.: The Radon Transform and Some of Its Applications. Krieger, Malabar (1993)MATHGoogle Scholar
  2. 2.
    Courmontagne, P.: An improvement of ship wake detection based on the radon transform. Signal Processing 85 (2005)Google Scholar
  3. 3.
    Krishnaveni, M., Thakur, S.K., Subashini, P.: An Optimal Method For Wake Detection In SAR Images Using Radon Transformation Combined With Wavelet Filters. International Journal of Computer Science and Information Security 6, 66–69 (2009)Google Scholar
  4. 4.
    Zhang, Q., Couloigner, I.: Accurate Centerline Detection and Line Width Estimation of Thick Lines Using the Radon Transform. IEEE Transactions on Image Processing 16, 310–316 (2007)CrossRefMathSciNetGoogle Scholar
  5. 5.
    Wang, L.Q., Hao, K., Radon Transform, Y.: Forstner Operator Applying in Buildings Contour Extraction. In: FSKD, pp. 415–419 (2009)Google Scholar
  6. 6.
    Magli, E., Olmo, G., Lo Presti, L.: Pattern recognition by means of the Radon transform and the continuous wavelet transform. Signal Processing 73, 277–289 (1999)CrossRefMATHGoogle Scholar
  7. 7.
    Rojbani, H., Elouedi, I., Hamouda, A.: Rθ-signature: A new signature based on Radon Transform and its application in buildings extraction. In: ISSPIT, pp. 490–495 (2011)Google Scholar
  8. 8.
    Deans, S.: Hough Transform from the Radon transform. IEEE Transactions On Pattern Analysis and Machine Intelligence, Pami-3, 185–188 (1981)Google Scholar
  9. 9.
    Tofts, P.: The Radon Ttransform: Theory and implementation. Ph.D.dissertation (1996)Google Scholar
  10. 10.
    Hendriks, C.L., van Ginkel, M., Verbeek, P.W., van Vliet, L.J.: The generalized Radon transform: Sampling, accuracy and memory considerations. Identification of Common Molecular Subsequences. Pattern Recognition 38, 2495–2505 (2005)Google Scholar
  11. 11.
    Beylkin, G.: Discrete Radon transform. IEEE Transactions on Acoustics, Speech and Signal Processing 35, 162–172 (1987)CrossRefMathSciNetGoogle Scholar
  12. 12.
    Matus, F., Flusser, J.: Image representation via a Finite Radon transform. IEEE Transaction on Pattern Analysis and Machine Intelligence 15, 996–1006 (1993)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Ines Elouedi
    • 1
    • 2
  • Régis Fournier
    • 1
    • 2
  • Amine Naït-Ali
    • 1
    • 2
  • Atef Hamouda
    • 1
    • 2
  1. 1.LIPAHFaculté des sciences de TunisTunisia
  2. 2.LISSIUniversité Paris-Est CréteilFrance

Personalised recommendations