Circle Detection on Images Using Learning Automata

  • Erik Cuevas
  • Fernando Wario
  • Daniel Zaldivar
  • Marco Pérez-Cisneros
Part of the Studies in Computational Intelligence book series (SCI, volume 427)


The outcome of Turing’s seminal work, originally proposed as a simple operational definition of intelligence, delivered several computer applications for solving complex engineering problems such as object detection and pattern recognition. Among such issues, circle detection over digital images has received considerable attention from the computer vision community over the last few years. This chapter presents an algorithm for the automatic detection of circular shapes from complicated and noisy images with no consideration of conventional Hough transform principles. The proposed algorithm is based on Learning Automata (LA) which is a probabilistic optimization method that explores an unknown random environment by progressively improving the performance via a reinforcement signal. The approach uses the encoding of three non-collinear points as a candidate circle over the edge image. A reinforcement signal indicates if such candidate circles are actually present in the edge map. Guided by the values of such reinforcement signal, the probability set of the encoded candidate circles is modified through the LA algorithm so that they can fit to the actual circles on the edge map. Experimental results over several complex synthetic and natural images have validated the efficiency of the proposed technique regarding accuracy, speed and robustness.


Noisy Image Synthetic Image Learn Automaton Learn Automaton Circle Detection 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Atherton, T.J., Kerbyson, D.J.: Using phase to represent radius in the coherent circle Hough transform. In: Proc. IEE Colloquium on the Hough Transform, IEE, London (1993)Google Scholar
  2. 2.
    Ayala-Ramirez, V., Garcia-Capulin, C.H., Perez-Garcia, A., Sanchez-Yanez, R.E.: Circle detection on images using genetic algorithms. Pattern Recognition Letters 27, 652–657 (2006)CrossRefGoogle Scholar
  3. 3.
    Beygi, H., Meybodi, M.R.: A new action-set learning automaton for function optimization. Int. J. Franklin Inst. 343, 27–47 (2006)CrossRefGoogle Scholar
  4. 4.
    Beigyab, H., Meybodibc, M.R.: A learning automata-based algorithm for determination of the number of hidden units for three-layer neural networks. International Journal of Systems Science 40(1), 101–118 (2009)CrossRefGoogle Scholar
  5. 5.
    Chen, T.-C., Chung, K.-L.: An efficient Randomized Algorithm for detecting Circles. Computer Vision and Image Understanding 83, 172–191 (2001)zbMATHCrossRefGoogle Scholar
  6. 6.
    Cheng, H.D., Yanhui, G., Yingtao, Z.: A novel Hough transform based on eliminating particle swarm optimization and its applications. Pattern Recognition 42, 1959–1969 (2009)zbMATHCrossRefGoogle Scholar
  7. 7.
    Cuevas, E., Zaldivar, D., Perez-Cisneros, M.: Seeking multi-thresholds for image segmentation with Learning Automata. Machine Vision and Applications (2010), doi: 10.1007/s00138-010-0249-0Google Scholar
  8. 8.
    Dasgupta, S., Das, S., Biswas, A., Abraham, A.: Automatic circle detection on digital images with an adaptive bacterial foraging algorithm. Soft Computing 14, 1151–1164 (2010)CrossRefGoogle Scholar
  9. 9.
    Da Fontoura Costa, L., Marcondes Cesar Jr., R.: Shape Analysis and Classification. CRC Press, Boca Raton (2001)zbMATHGoogle Scholar
  10. 10.
    Han, J.H., Koczy, L.T., Poston, T.: Fuzzy Hough transform. In: Proc. 2nd Int. Conf. on Fuzzy Systems, vol. 2, pp. 803–808 (1993)Google Scholar
  11. 11.
    Howell, M., Gordon, T.: Continuous action reinforcement learning automata and their application to adaptive digital filter design. Engineering Applications of Artificial Intelligence 14, 549–561 (2001)CrossRefGoogle Scholar
  12. 12.
    Ikonen, E., Najim, K.: Online optimization of replacement policies using learning automata. International Journal of Systems Science 39(3), 237–249 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  13. 13.
    Lu, W., Tan, J.L.: Detection of incomplete ellipse in images with strong noise by iterative randomized Hough transform (IRHT). Pattern Recognition 41(4), 1268–1279 (2008)zbMATHCrossRefGoogle Scholar
  14. 14.
    Lutton, E., Martinez, P.: A genetic algorithm for the detection 2-D geometric primitives on images. In: Proc. of the 12th Int. Conf. on Pattern Recognition, vol. 1, pp. 526–528 (1994)Google Scholar
  15. 15.
    Muammar, H., Nixon, M.: Approaches to extending the Hough transform. In: Proc. Int. Conf. on Acoustics, Speech and Signal Processing ICASSP, vol. 3, pp. 1556–1559 (1989)Google Scholar
  16. 16.
    Najim, K., Poznyak, A.S.: Learning Automata - Theory and Applications. Pergamon Press, Oxford (1994)Google Scholar
  17. 17.
    Narendra, K.S., Thathachar, M.A.L.: Learning Automata: an Introduction. Prentice-Hall, London (1989)Google Scholar
  18. 18.
    Roth, G., Levine, M.D.: Geometric primitive extraction using a genetic algorithm. IEEE Trans. Pattern Anal. Machine Intell. 16(9), 901–905 (1994)CrossRefGoogle Scholar
  19. 19.
    Seyed-Hamid, Z.: Learning automata based classifier. Pattern Recognition Letters 29, 40–48 (2008)CrossRefGoogle Scholar
  20. 20.
    Shaked, D., Yaron, O., Kiryati, N.: Deriving stopping rules for the probabilistic Hough transform by sequential analysis. Comput. Vision Image Understanding 63, 512–526 (1996)CrossRefGoogle Scholar
  21. 21.
    Thathachar, M.A.L., Sastry, P.S.: Varieties of learning automata: An overview. IEEE Trans. Systems. Man Cybernet. Part B: Cybernet 32, 711–722 (2002)CrossRefGoogle Scholar
  22. 22.
    Tsetlin, M.L.: Automaton Theory and Modeling of Biological Systems. Academic Press, New York (1973)Google Scholar
  23. 23.
    Turing, A.M.: On computable numbers, with an application to the Entscheidungsproblem. Proceedings of the London Mathematical Society 42, 230–265 (1936)MathSciNetCrossRefGoogle Scholar
  24. 24.
    Van-Aken, J.R.: Efficient ellipse-drawing algorithm. IEEE Comp, Graphics Applic. 4(9), 24–35 (1984)CrossRefGoogle Scholar
  25. 25.
    Wu, Q.H.: Learning coordinated control of power systems using inter-connected learning automata. Int. J. Electr. Power Energy Syst. 17, 91–99 (1995)CrossRefGoogle Scholar
  26. 26.
    Xu, L., Oja, E., Kultanen, P.: A new curve detection method: Randomized Hough transform (RHT). Pattern Recognition Lett. 11(5), 331–338 (1990)zbMATHCrossRefGoogle Scholar
  27. 27.
    Yao, J., Kharma, N., Grogono, P.: Fast robust GA-based ellipse detection. In: Proc. 17th Int. Conf. on Pattern Recognition, ICPR 2004, Cambridge, UK, pp. 859–862 (2004)Google Scholar
  28. 28.
    Yuen, S., Ma, C.: Genetic algorithm with competitive image labelling and least square. Pattern Recognition 33, 1949–1966 (2000)zbMATHCrossRefGoogle Scholar
  29. 29.
    Zeng, X., Zhou, J., Vasseur, C.: A strategy for controlling non-linear systems using a learning automaton. Automatica 36, 1517–1524 (2000)MathSciNetzbMATHCrossRefGoogle Scholar
  30. 30.
    Zeng, X., Liu, Z.: A learning automaton based algorithm for optimization of continuous complex function. Information Sciences 174, 165–175 (2005)MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Berlin Heidelberg 2013

Authors and Affiliations

  • Erik Cuevas
    • 1
  • Fernando Wario
    • 1
  • Daniel Zaldivar
    • 1
  • Marco Pérez-Cisneros
    • 1
  1. 1.Universidad de GuadalajaraGuadalajaraMexico

Personalised recommendations