Advertisement

Hierarchical Sampling with Constraints

  • Azadeh Mohebi
  • Ying Liu
  • Paul Fieguth
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5627)

Abstract

Reconstruction of porous media images is required in order to study different properties of these material. Our research interest is on generating samples from the posterior model in which low resolution measurements are combined with a prior model. The reconstruction task becomes intractable when the size of the samples increases, since it is based on simulated annealing which is a slow convergence algorithm. The hierarchical approaches have been applied to tackle this problem, in the case of sampling from the prior model. However, in the posterior sampling case, defining a suitable measurement model at each scale still remains a challenging task. In this paper we define how we can incorporate the measurement in the hierarchical posterior model and then how we generate samples from that model.

Keywords

Porous Medium Measurement Model Prior Model Coarse Scale Posterior Sampling 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Adler, P.M.: Porous Media, Geometry and Transports. Butterworth-Heinemann series in chemical engineering. Butterworth-Heinemann (1992)Google Scholar
  2. 2.
    Alexander, S., Fieguth, P., Ioannidis, M., Vrscay, E.: Hierarchical annealing for synthesis of binary porous media images. Mathematical Geosciense (2009)Google Scholar
  3. 3.
    Campaigne, W.R., Fieguth, P.: Frozen-state hierarchical annealine. In: Campilho, A., Kamel, M.S. (eds.) ICIAR 2006. LNCS, vol. 4141, pp. 41–52. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  4. 4.
    Fieguth, P.: Hierarchical posterior sampling of gauss-markov random fields. Accepted in IEEE Transaction on Image Processing (2008)Google Scholar
  5. 5.
    Geman, S., Geman, D.: Stochastic relaxation, gibbs distribution, and the bayesian restoration of images. IEEE Transaction on Pattern Analysis and Machine Intelligence 6(6) (1984)Google Scholar
  6. 6.
    Graffigne, C., Heitz, F., Perez, P.: Hierachical markov random field models applied to image analysis: A review. In: Proc. SPIE, vol. 2568, pp. 2–17 (1995)Google Scholar
  7. 7.
    Manwart, C., Torquato, S., Hilfer, R.: Stochastic reconstruction of sandstones. Physical Rev. E 62(1), 893–899 (2000)CrossRefGoogle Scholar
  8. 8.
    Mohebi, A., Fieguth, P.: Posterior sampling of scientific images. In: Campilho, A., Kamel, M.S. (eds.) ICIAR 2006. LNCS, vol. 4141, pp. 365–376. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  9. 9.
    Okabe, H., Blunt, M.J.: Pore space reconstruction of vuggy carbonates using microtomography and multiple-point statistics. Water Resource Research 43 (2007)Google Scholar
  10. 10.
    Sobczyk, K., Kirkner, D.J.: Stochastic Modelling of Microstructures. In: Modeling and simulations in science, engineering and technology. Birkhäuser, Basel (2001)Google Scholar
  11. 11.
    Torquato, S.: Random Heterogeneous Materials: Microstructure and Macroscopic Properties. Springer, Heidelberg (2002)CrossRefzbMATHGoogle Scholar
  12. 12.
    Winkler, G.: Image analysis, Random Fileds, and Markov Chain Monte Calro Methods, 2nd edn. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  13. 13.
    Yeong, C.L.Y., Torquato, S.: Reconstructing porous media. Physical Review E 57(1), 495–506 (1998)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Yeong, C.L.Y., Torquato, S.: Reconstructing random media ii. three-dimensional media from two-dimensional cuts. Physical Rev. E 58(1), 224–233 (1998)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Zhao, X., Yao, J., Yi, Y.: A new stochastic method of reconstructiong porous media. Transport in Porous Media 69(1), 1–11 (2007)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Azadeh Mohebi
    • 1
  • Ying Liu
    • 1
  • Paul Fieguth
    • 1
  1. 1.Department of Systems Design EngineeringUniversity of WaterlooWaterlooCanada

Personalised recommendations