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.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Adler, P.M.: Porous Media, Geometry and Transports. Butterworth-Heinemann series in chemical engineering. Butterworth-Heinemann (1992)
Alexander, S., Fieguth, P., Ioannidis, M., Vrscay, E.: Hierarchical annealing for synthesis of binary porous media images. Mathematical Geosciense (2009)
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)
Fieguth, P.: Hierarchical posterior sampling of gauss-markov random fields. Accepted in IEEE Transaction on Image Processing (2008)
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)
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)
Manwart, C., Torquato, S., Hilfer, R.: Stochastic reconstruction of sandstones. Physical Rev. E 62(1), 893–899 (2000)
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)
Okabe, H., Blunt, M.J.: Pore space reconstruction of vuggy carbonates using microtomography and multiple-point statistics. Water Resource Research 43 (2007)
Sobczyk, K., Kirkner, D.J.: Stochastic Modelling of Microstructures. In: Modeling and simulations in science, engineering and technology. Birkhäuser, Basel (2001)
Torquato, S.: Random Heterogeneous Materials: Microstructure and Macroscopic Properties. Springer, Heidelberg (2002)
Winkler, G.: Image analysis, Random Fileds, and Markov Chain Monte Calro Methods, 2nd edn. Springer, Heidelberg (2003)
Yeong, C.L.Y., Torquato, S.: Reconstructing porous media. Physical Review E 57(1), 495–506 (1998)
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)
Zhao, X., Yao, J., Yi, Y.: A new stochastic method of reconstructiong porous media. Transport in Porous Media 69(1), 1–11 (2007)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Mohebi, A., Liu, Y., Fieguth, P. (2009). Hierarchical Sampling with Constraints. In: Kamel, M., Campilho, A. (eds) Image Analysis and Recognition. ICIAR 2009. Lecture Notes in Computer Science, vol 5627. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02611-9_3
Download citation
DOI: https://doi.org/10.1007/978-3-642-02611-9_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-02610-2
Online ISBN: 978-3-642-02611-9
eBook Packages: Computer ScienceComputer Science (R0)