Skip to main content
SpringerLink
Log in

Circle detection using discrete differential evolution optimization

  • Short Paper
  • Published:
Pattern Analysis and Applications Aims and scope Submit manuscript

Abstract

This paper introduces a circle detection method based on differential evolution (DE) optimization. Just as circle detection has been lately considered as a fundamental component for many computer vision algorithms, DE has evolved as a successful heuristic method for solving complex optimization problems, still keeping a simple structure and an easy implementation. It has also shown advantageous convergence properties and remarkable robustness. The detection process is considered similar to a combinational optimization problem. The algorithm uses the combination of three edge points as parameters to determine circle candidates in the scene yielding a reduction of the search space. The objective function determines if some circle candidates are actually present in the image. This paper focuses particularly on one DE-based algorithm known as the discrete differential evolution (DDE), which eventually has shown better results than the original DE in particular for solving combinatorial problems. In the DDE, suitable conversion routines are incorporated into the DE, aiming to operate from integer values to real values and then getting integer values back, following the crossover operation. The final algorithm is a fast circle detector that locates circles with sub-pixel accuracy even considering complicated conditions and noisy images. Experimental results on several synthetic and natural images with varying range of complexity validate the efficiency of the proposed technique considering accuracy, speed, and robustness.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  1. da Fontoura Costa L, Cesar RM Jr (2001) Shape análisis and classification. CRC Press, Boca Raton

    Google Scholar 

  2. Yuen H, Princen J, Illingworth J, Kittler J (1990) Comparative study of Hough transform methods for circle finding. Image Vis Comput 8(1):71–77

    Article  Google Scholar 

  3. Iivarinen J, Peura M, Sarela J, Visa A (1997) Comparison of combined shape descriptors for irregular objects. In: Proceedings of 8th British Machine Vision Conference, Cochester, UK, pp 430–439

  4. Jones G, Princen J, Illingworth J, Kittler J (1990) Robust estimation of shape parameters. In: Proceedings of British Machine Vision Conference, pp 43–48

  5. Fischer M, Bolles R (1981) Random sample consensus: a paradigm to model fitting with applications to image analysis and automated cartography. CACM 24(6):381–395

    Google Scholar 

  6. Bongiovanni G, Crescenzi P (1995) Parallel simulated annealing for shape detection. Comput Vis Image Underst 61(1):60–69

    Article  Google Scholar 

  7. Roth G, Levine MD (1994) Geometric primitive extraction using a genetic algorithm. IEEE Trans Pattern Anal Mach Intell 16(9):901–905

    Article  Google Scholar 

  8. Peura M, Iivarinen J (1997) Efficiency of simple shape descriptors. In: Arcelli C, Cordella LP, di Baja GS (eds) Advances in visual form analysis. World Scientific, Singapore, pp 443–451

    Google Scholar 

  9. Muammar H, Nixon M (1989) Approaches to extending the Hough transform. In: Proceedings of International conference on acoustics, speech and signal processing ICASSP_89, vol 3. pp 1556–1559

  10. Atherton TJ, Kerbyson DJ (1993) Using phase to represent radius in the coherent circle Hough transform. In: Proceedings on IEE colloquium on the Hough transform. IEE, London

  11. Shaked D, Yaron O, Kiryati N (1996) Deriving stopping rules for the probabilistic Hough transform by sequential analysis. Comput Vis Image Underst 63:512–526

    Article  Google Scholar 

  12. Xu L, Oja E, Kultanen P (1990) A new curve detection method: randomized Hough transform (RHT). Pattern Recognit 11(5):331–338

    Article  MATH  Google Scholar 

  13. Han JH, Koczy LT, Poston T (1993) Fuzzy Hough transform. In: Proceedings of 2nd International Conference on Fuzzy Systems, vol 2, pp 803–808

  14. Becker J, Grousson S, Coltuc D (2002) From Hough transforms to integral transforms. In: Proceedings of International Geoscience and Remote Sensing Symposium, 2002 IGARSS_02, vol. 3, pp 1444–1446

  15. Lutton E, Martinez P (1994) A genetic algorithm for the detection 2-D geometric primitives on images. In: Proceedings of the 12th International conference on pattern recognition, vol 1, pp 526–528

  16. Yao J, Kharma N, Grogono P (2004) Fast robust GA-based ellipse detection. In: Proceedings of 17th International Conference on pattern recognition ICPR-04, vol 2, Cambridge, UK, pp 859–862

  17. Ayala-Ramirez V, Garcia-Capulin CH, Perez-Garcia A, Sanchez-Yanez RE (2006) Circle detection on images using genetic algorithms. Pattern Recognit Lett 27:652–657

    Article  Google Scholar 

  18. Swagatam D, Sambarta D, Arijit B, Ajith A (2008) Automatic circle detection on images with annealed differential evolution. In: Proceedings of 8th International conference on hybrid intelligent systems 2008, pp 684–689

  19. Rosin PL, Nyongesa HO (2000) Combining evolutionary, connectionist, and fuzzy classification algorithms for shape analysis. In: Cagnoni S et al (eds) Proceedings of EvoIASP, real-world applications of evolutionary computing, pp 87–96

  20. Rosin PL (1994) Further five point fit ellipse fitting. In: Proceedings of 8th British Machine Vision Conference, Cochester, UK, pp 290–299

  21. Zhang X, Rosin PL (2003) Superellipse fitting to partial data. Pattern Recognit Lett 36:743–752

    MATH  Google Scholar 

  22. Storn R, Price K (1995) Differential evolution—a simple and efficient adaptive scheme for global optimization over continuous spaces. Technical Rep. No. TR-95-012, International Computer Science Institute, Berkley

  23. Reddy JM, Kumar ND (2007) Multiobjective differential evolution with application to reservoir system optimization. J Comput Civil Eng 21(2):136–146

    Article  Google Scholar 

  24. Babu B, Munawar S (2007) Differential evolution strategies for optimal design of shell-and-tube heat exchangers. Chem Eng Sci 62(14):3720–3739

    Article  Google Scholar 

  25. Mayer D, Kinghorn B, Archer A (2005) Differential evolution—an easy and efficient evolutionary algorithm for model optimization. Agric Syst 83:315–328

    Article  Google Scholar 

  26. Kannan S, Mary Raja Slochanal S, Padhy N (2003) Application and comparison of metaheuristic techniques to generation expansion planning problem. IEEE Trans Power Syst 20(1):466–475

    Article  Google Scholar 

  27. Chiou J, Chang C, Su C (2005) Variable scaling hybrid differential evolution for solving network reconfiguration of distribution systems. IEEE Trans Power Syst 20(2):668–674

    Article  Google Scholar 

  28. Chiou J, Chang C, Su C (2004) Ant direct hybrid differential evolution for solving large capacitor placement problems. IEEE Trans Power Syst 19(4):1794–1800

    Article  Google Scholar 

  29. Ursem R, Vadstrup P (2003) Parameter identification of induction motors using differential evolution. In: Proceedings of the 2003 congress on evolutionary computation (CEC’03), vol. 2. Canberra, Australia, pp 790–796

  30. Babu B, Angira R, Chakole G, Syed Mubeen J (2003) Optimal design of gas transmission network using differential evolution. In: Proceedings of the second international conference on computational intelligence, robotics, and autonomous systems (CIRAS-2003), Singapore

  31. Zelinka I, Chen G, Celikovsky S (2008) Chaos sythesis by means of evolutionary algorithms. Int J Bifurcat Chaos 4:911–942

    MathSciNet  Google Scholar 

  32. Onwubolu G, Davendra D (2009) Differential evolution: a handbook for global permutation-based combinatorial optimization. Springer, Heidelberg

    Book  MATH  Google Scholar 

  33. Yuan X, Su A, Nie H, Yuan Y, Wang L (2009) Application of enhanced discrete differential evolution approach to unit commitment problem. Energy Convers Manag 50(9):2449–2456

    Article  Google Scholar 

  34. Wang L, Pan Q-K, Suganthan PN, Wang W-H, Wang Y-M (2010) A novel hybrid discrete differential evolution algorithm for blocking flow shop scheduling problems. Comput Oper Res 37(3):509–520

    Article  MATH  MathSciNet  Google Scholar 

  35. Tasgetiren MF, Pan Q-K, Liang Y-C (2009) A discrete differential evolution algorithm for the single machine total weighted tardiness problem with sequence dependent setup times. Comput Oper Res 36(6):1900–1915

    Article  MATH  Google Scholar 

  36. Tasgetiren MF, Suganthan PN, Pan Q-K (2010) An ensemble of discrete differential evolution algorithms for solving the generalized traveling salesman problem. Appl Math Comput 215(9):3356–3368

    Article  MATH  MathSciNet  Google Scholar 

  37. Onwubolu G, Davendra D (2006) Scheduling flow shops using differential evolution algorithm. Eur J Oper Res 171:674–679

    Article  MATH  Google Scholar 

  38. Lichtblau D (2009) Relative position index approach. In: Davendra D, Onwubolu G (eds) Differential evolution: a handbook for global permutation-based combinatorial optimization. Springer, Heidelberg, pp 81–120

    Chapter  Google Scholar 

  39. Tasgetiren F, Chen A, Gencyilmaz G, Gattoufi S (2009) Smallest position value approach. In: Davendra D, Onwubolu G (eds) Differential evolution: a handbook for global permutation-based combinatorial optimization. Springer, Heidelberg, pp 81–120

    Google Scholar 

  40. Tasgetiren F, Liang Y, Pan Q, Suganthan P (2009) Discrete/binary approach. In: Davendra D, Onwubolu G (eds) Differential evolution: a handbook for global permutation-based combinatorial optimization. Springer, Heidelberg, pp 81–120

    Google Scholar 

  41. Zelinka I (2009) Discrete set handling. In: Davendra D, Onwubolu G (eds) Differential evolution: a handbook for global permutation-based combinatorial optimization. Springer, Heidelberg, pp 81–120

    Google Scholar 

  42. Bresenham JE (1987) A linear algorithm for incremental digital display of circular arcs. Commun ACM 20:100–106

    Article  Google Scholar 

  43. Davendra D, Onwubolu G (2009) Forward backward transformation. In: Davendra D, Onwubolu G (eds) Differential evolution: a handbook for global permutation-based combinatorial optimization. Springer, Heidelberg, pp 37–78

    Google Scholar 

  44. Franco G, Betti R, Lus H (2004) Identification of structural systems using an evolutionary strategy. Eng Mech 130(10):1125–1139

    Article  Google Scholar 

  45. Koziel S, Michalewicz Z (1999) Evolutionary algorithms, homomorphous mappings, and constrained parameter optimization. Evol Comput 7(1):19–44

    Article  Google Scholar 

  46. Van Aken JR (1984) An efficient ellipse drawing algorithm. CG&A 4(9):24–35

    Google Scholar 

  47. Yuen S, Ma C (2000) Genetic algorithm with competitive image labelling and least square. Pattern Recognit 33:1949–1966

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departamento de Ciencias Computacionales, Universidad de Guadalajara, CUCEI, Av. Revolución 1500, Guadalajara, Jal, Mexico

    Erik Cuevas, Daniel Zaldivar & Marco Pérez-Cisneros

  2. Freie Universität Berlin, Takustrs 9, 14195, Berlin, Germany

    Marte Ramírez-Ortegón

Authors
  1. Erik Cuevas
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Daniel Zaldivar
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Marco Pérez-Cisneros
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Marte Ramírez-Ortegón
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Daniel Zaldivar.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Cuevas, E., Zaldivar, D., Pérez-Cisneros, M. et al. Circle detection using discrete differential evolution optimization. Pattern Anal Applic 14, 93–107 (2011). https://doi.org/10.1007/s10044-010-0183-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10044-010-0183-9

Keywords

Search

Navigation