Central European Journal of Physics

, Volume 8, Issue 5, pp 689–698 | Cite as

A Q-Ising model application for linear-time image segmentation

Research Article


A computational method is presented which efficiently segments digital grayscale images by directly applying the Q-state Ising (or Potts) model. Since the Potts model was first proposed in 1952, physicists have studied lattice models to gain deep insights into magnetism and other disordered systems. For some time, researchers have realized that digital images may be modeled in much the same way as these physical systems (i.e., as a square lattice of numerical values). A major drawback in using Potts model methods for image segmentation is that, with conventional methods, it processes in exponential time. Advances have been made via certain approximations to reduce the segmentation process to power-law time. However, in many applications (such as for sonar imagery), real-time processing requires much greater efficiency. This article contains a description of an energy minimization technique that applies four Potts (Q-Ising) models directly to the image and processes in linear time. The result is analogous to partitioning the system into regions of four classes of magnetism. This direct Potts segmentation technique is demonstrated on photographic, medical, and acoustic images.


image segmentation Potts model 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    D. L. Pham, C. Xu, J. L. Prince, Annu. Rev. Biomed. Eng. 2, 315 (2000)CrossRefGoogle Scholar
  2. [2]
    Y. H. Yang, M. J. Buckley, S. Dudoit, T. P. Speed, J. Comput. Graph. Stat. 11, 108 (2002)CrossRefMathSciNetGoogle Scholar
  3. [3]
    S. Peng, B. Urbanc, L. Cruz, B. T. Hyman, H. E. Stanley, P. Natl. Acad. Sci. USA 100, 3847 (2003)CrossRefADSGoogle Scholar
  4. [4]
    V. Grau, A. U. J. Mewes, M. Alcañiz, IEEE T. Med. Imaging 23, 447 (2004)CrossRefGoogle Scholar
  5. [5]
    S. Hadjidemetriou, C. Studholme, S. Mueller, M. Weiner, N. Schuff, Med. Image Anal. 13, 36–48 (2009)CrossRefGoogle Scholar
  6. [6]
    X. Descombes, M. Moctezuma, H. Maître, J.-P. Rudant, Signal Process. 55, 123–132 (1996)MATHCrossRefGoogle Scholar
  7. [7]
    F. W. Bentrem, W. E. Avera, J. Sample, Sea Technol. 47, 37 (2006)Google Scholar
  8. [8]
    T. Asano, D. Z. Chen, N. Katoh, T. Tokuyama, Int. J. Comput. Geom. Ap. 11, 145 (2001)MATHCrossRefMathSciNetGoogle Scholar
  9. [9]
    E. Ising, Z. Phys. 31, 253 (1925)CrossRefADSGoogle Scholar
  10. [10]
    R. B. Potts, P. Camb. Philos. Soc. 48, 106 (1952)MATHCrossRefMathSciNetGoogle Scholar
  11. [11]
    F. W. Bentrem, Provisional Patent Application, Navy Case No. 99, 755 (2009)Google Scholar
  12. [12]
    K. Tanaka, J. Phys. A-Math. Gen. 35, R81 (2002)MATHCrossRefADSGoogle Scholar
  13. [13]
    J. P. Neirotti, S. M. Kurcbart, N. Caticha, Phys. Rev. E 68, 031911 (2003)CrossRefADSGoogle Scholar
  14. [14]
    M. Blatt, S. Wiseman, E. Domany, Phys. Rev. Lett. 76, 3251 (1996)CrossRefADSGoogle Scholar
  15. [15]
    M. Blatt, S. Wiseman, E. Domany, Neural Computation 9, 1805 (1997)CrossRefGoogle Scholar
  16. [16]
    S. Wiseman, M. Blatt, E. Domany, Phys. Rev. E 57, 3767 (1998)CrossRefADSGoogle Scholar
  17. [17]
    K. Tanaka, H. Shouno, M. Okadak, D. M. Titterington, J. Phys. A-Math. Gen. 37, 8675 (2004)MATHCrossRefADSGoogle Scholar
  18. [18]
    E. Sharon, A. Brandt, R. Basriy, Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (IEEE, Hilton Head Island, 2000) 1, 70Google Scholar
  19. [19]
    P. F. Felzenszwalb, D. P. Huttenlocher, Int. J. Comput. Vision 59, 167 (2004)CrossRefGoogle Scholar
  20. [20]
    A. X. Falcão, P. A. V. Miranda, A. Rocha, Lect. Notes Comp. Sci. 4179/2006, 138 (2006)CrossRefGoogle Scholar
  21. [21]
    D. Chandler, Introduction to Modern Statistical Mechanics (Oxford University Press, New York, 1987)Google Scholar
  22. [22]
    J. C. Lee Thermal Physics: Entropy and Free Energies (World Scientific Publishing Company, Singapore, 2002)Google Scholar
  23. [23]
    L. Onsager, Phys. Rev. 65, 117 (1944)MATHCrossRefMathSciNetADSGoogle Scholar
  24. [24]
    D. Martin, C. Fowlkes, D. Tal, J. Malik, Proceedings of the 8th International Conference on Computer Vision 2, 416 (2001)Google Scholar
  25. [25]
    F. W. Bentrem, J. Sample, M. T. Kalcic, M. E. Duncan, Proceedings of Oceans 2002 (MTS/IEEE, Biloxi) 1, 7 (2002)Google Scholar
  26. [26]
    F. W. Bentrem, J. T. Sample, M. M. Harris, Scientific Computing 25, 30 (2008)Google Scholar
  27. [27]
    R. A. Bagnold, The Physics of Blown Sand and Desert Dunes (Methuen, London, 1941)Google Scholar
  28. [28]
    L. Kang, L. Guo, Phys. Lett. A 330, 198 (2004)MATHCrossRefMathSciNetADSGoogle Scholar

Copyright information

© © Versita Warsaw and Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  1. 1.Naval Research LaboratoryCenter for Bio/Molecular Science and EngineeringWashington, DCUSA
  2. 2.Department of Physics and Engineering PhysicsTulane UniversityNew OrleansUSA

Personalised recommendations