Skip to main content
SpringerLink
Log in

Application of Lattice Boltzmann Method to Image Filtering

  • Published:
Journal of Mathematical Imaging and Vision Aims and scope Submit manuscript

Abstract

In this paper, lattice Boltzmann D2Q5 (two dimensions and five discrete velocity directions) and D2Q9 (two dimensions and nine discrete velocity directions) models are used to solve Perona-Malik equation, which is widely used in image filtering. A set of images added three types of noise are processed using these models. Then the processed images are compared in aspects of peak signal to noise ratio (PSNR) and visual effect. The comparison show that two models have almost the same filtering effect. Simultaneously, it is validated that D2Q5 model is more efficient. Other findings are: (1) D2Q5 and D2Q9 models are more effective in dealing with some images than others; (2) salt and pepper noise is relatively difficult to remove compared with gaussian noise and speckle noise; (3) lattice Boltzmann method shows good stability in the image filtering.

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

Similar content being viewed by others

References

  1. Perona, P., Malik, J.: Scale space and edge detection using anisotropic diffusion. IEEE Trans. Pattern Anal. Mach. Intell. 12(7), 629–639 (1990)

    Article  Google Scholar 

  2. Catte, F., Lions, P.L., Morel, J.M., Coll, T.: Image selective smoothing and edge detection by nonlinear diffusion. SIAM J. Numer. Anal. 29, 182–193 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  3. Alvarez, L., Lions, P.L., Morel, J.M.: Image selective smoothing and edge detection by nonlinear diffusion. SIAM J. Numer. Anal. 29, 845–866 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  4. You, Y.L., Kaveh, M.: Fourth-order partial differential equations for noise removal. IEEE Trans. Image Process. 9, 1723–1730 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  5. Chen, S., Dawson, S.P., Doolen, G.D., Janecky, D.R., Lawniczak, A.: Lattice methods and their applications to reacting systems. Comput. Chem. Eng. 19(6–7), 617–646 (1995)

    Article  Google Scholar 

  6. Zhang, C.Y., Tan, H.L., Liu, M.R., Kong, L.J.: A lattice Boltzmann model and simulation of KdV-Burgers equation. Commun. Theor. Phys. 42(2), 281–284 (2004)

    MATH  Google Scholar 

  7. Ma, C.: A new lattice Boltzmann model for KdV-Burgers equation. Chin. Phys. Lett. 29(9), 2313–2315 (2005)

    Google Scholar 

  8. Chai, Z.H., Shi, B.C., Zheng, L.: A unified lattice Boltzmann model for some nonlinear partial differential equations. Chaos Solitons Fractals 36, 874–882 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  9. Yan, G.: A lattice Boltzmann equation for waves. J. Comput. Phys. 161, 61–69 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  10. Hirabayashi, M., Chen, Y., Ohashi, H.: The lattice BGK model for the Poisson equation. JSME Int. J. Ser. B 44(1), 45–52 (2001)

    Article  Google Scholar 

  11. Chai, Z.H., Shi, B.C.: A novel lattice Boltzmann model for the Poisson equation. Appl. Math. Model. 32, 2050–2058 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  12. Guo, Z.L., Shi, B.C., Wang, N.C.: Fully Lagrangian and lattice Boltzmann methods for the advection-diffusion equation. J. Sci. Comput. 14(3), 291–300 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  13. Deng, B., Shi, B.C., Wang, G.C.: A new lattice Bhatnagar-Gross-Krook model for convection-diffusion equation with a source term. Chin. Phys. Lett. 22(2), 267–270 (2005)

    Article  Google Scholar 

  14. Shi, B.C., Guo, Z.L.: Lattice Boltzmann model for nonlinear convection-diffusion equations. Phys. Rev. E 79, 016701 (2009)

    Article  Google Scholar 

  15. Jawerth, B., Lin, P., Sinzinger, E.: Lattice Boltzmann models for anisotropic diffusion of images. J. Math. Imaging Vis. 11, 231–237 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  16. Zhao, Y.: Lattice Boltzmann based PDE solver on the GPU. Vis. Comput. 24(5), 323–333 (2008)

    Article  Google Scholar 

  17. Zhao, Y.: GPU-Accelerated surface denoising and morphing with lattice Boltzmann scheme. In: IEEE International Conference on Shape Modeling and Applications (SMI), pp. 19–28. (2008)

    Chapter  Google Scholar 

  18. Chen, Y., Yan, Z.Z., Qian, Y.H.: An anisotropic diffusion model for medical image smoothing by using the lattice Boltzmann method. APCMBE 2008. IFMBE Proc. 19, 255–259 (2008)

    Article  Google Scholar 

  19. Chen, Y., Yan, Z.Z., Qian, Y.H.: The lattice Boltzmann method based image denoising. Acta Electron. Sinica (in Chinese) 37(3), 574–580 (2009)

    Google Scholar 

  20. Chang, Q.S., Yang, T.: A lattice Boltzmann method for image denoising. IEEE Trans. Image Process. 18(12), 2797–2802 (2009)

    Article  MathSciNet  Google Scholar 

  21. Qian, Y.H.: Fractional propagation and the elimination of staggered invariants in lattice-BGK models. Int. J. Mod. Phys. C 8, 753–761 (1997)

    Article  Google Scholar 

  22. Guo, Z.L., Zheng, C.G., Shi, B.C.: Non-equilibrium extrapolation method for velocity and pressure boundary conditions in the lattice Boltzmann method. Chin. Phys. 11(4), 366–374 (2002)

    Article  MathSciNet  Google Scholar 

  23. Canny, J.: computational approach to edge detection. IEEE Trans. Pattern Anal. Mach. Intell. 8, 679–698 (1986)

    Article  Google Scholar 

  24. Ames, W.F.: Numerical Methods for Partial Differential Equations. Academic Press, New York (1977)

    MATH  Google Scholar 

  25. Wolf-Gladrow, D.: A lattice Boltzmann equation for diffusion. J. Stat. Phys. 79(5/6), 1023–1032 (1995)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. State Key Laboratory of Coal Combustion, Huazhong University of Science and Technology, Wuhan, 430074, P.R. China

    Wenhuan Zhang

  2. School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, 430074, P.R. China

    Baochang Shi

Authors
  1. Wenhuan Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Baochang Shi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Baochang Shi.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhang, W., Shi, B. Application of Lattice Boltzmann Method to Image Filtering. J Math Imaging Vis 43, 135–142 (2012). https://doi.org/10.1007/s10851-011-0295-x

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10851-011-0295-x

Keywords

Search

Navigation