Porous Media

Porous media include a variety of materials, such as bone, cartilage, concrete, soil, and wood. All such materials allow the flow of water, or other liquids, and the understanding and modeling of this flow can be essential in areas of human health, construction, and groundwater studies. The image processing challenge in porous media is the reconstruction of the 3D architecture of void spaces given some sort of data, a particularly challenging task since many porous media contain pore structures on a wide range of scales.

Our approach to this class of problems has been to treat the problem as an inverse or estimation problem. Because the fine-scale porous field is discrete (pore / not pore), discrete-state solvers such as Simulated Annealing are quite effective, such as the following example from the work of Mohebi:

Original Image Observed or Measured Image (shows loss of quality in comparison to original image) Reconstructed Image (Greater image quality than observed or measured image)
Original Image Observed or Measured Image Reconstructed Result

The above work left us with two challenges:

  1. How to address very large fields with structure on a wide variety of scales.
  2. How to address nonstationary fields, those with multiple distinct behaviours.

The work of Liu considered hierarchical models (challenge 1) having hidden fields containing a label describing some attribute of behaviour (challenge 2):

Hierarchical models having hidden fields

 This work led to promising results on fairly complex fields:

  True Picture - Original Porous Field  
  Original Porous Field  
Low Resolution, Measured Field Estimated Hidden Label 1 Estimated Hidden Label 2
Low Resolution, Measured Field Estimated Hidden Label 1 Estimated Hidden Label 2
Estimated Field - Liu Estimated Field -  Wavelength 1 Estimated Field -Wavelet 2
Estimated Field - Liu Estimated Field - Wavelet Estimated Field - Wavelet

The performance of the method proposed by Liu is quite strikingly better than that produced by other wavelet resolution-enhancement methods.

Related people 

Directors

Paul Fieguth

Alumni

Azadeh Mohebi, Simon Alexander, Wesley Campaigne, Ying Liu

Related research areas

Multiresolution Techniques

Scientific Imaging

Stochastic Models

Related publications 

Journal articles 

Campaigne, W., and P. Fieguth, "Frozen State Hierarchical Annealingpdf", IEEE Transactions on Image Processing, vol. 22, no. 4, pp. 1486-1497, 2013. Details

Mohebi, A.P. Fieguth, and M. A. Ioannidis, "Statistical fusion of two-scale images of porous mediapdf", Advances in Water Resources, vol. 32, no. 11, pp. 1567 - 1579, 2009. Details

Conference papers

Mohebi, A., and P. Fieguth, "Modeling and reconstruction of two-scale porous media using MRI measurement", Fourth Biot Conference on Poromechanics, New York, 2009. Details

Liu, Y.A. Mohebi, and P. Fieguth, "Modeling of multiscale porous media using multiple Markov random fields", Fourth Biot Conference on Poromechanics, New York, 2009. Details

Alexander, S. K.P. Fieguth, and E. Vrscay, "Discrete-state modeling of porous media over multiple scales", SIAM Conference on Mathematical and Computational Issues in the Geosciences, Avignon, 2005. Details

Alexander, S. K.P. Fieguth, and E. Vrscay, "Hierarchical annealing of porous media", SIAM Conference on Mathematical and Computational Issues in the Geosciences, Avignon, 2005. Details

Fieguth, P., "Hierarchical MCMC samplingpdf", 2004 International Conference on Image Analysis and Recognition, 2004. Details

Alexander, S. K.P. Fieguth, and E. Vrscay, "Hierarchical annealing for random image synthesispdf", Fourth International Workshop on Energy Minimization Methods in Computer Vision and Pattern Recognition (EMMCVPR 2003), Portugal, 2003. Details

Book chapters

Campaigne, W., and P. Fieguth, "Frozen State Hierarchical Annealingpdf", IEEE Transactions on Image Processing, vol. 22, no. 4, pp. 1486-1497, 2013. Details

Theses

Campaigne, W., "Frozen-State Hierarchical Annealingpdf", Department of Systems Design Engineering, 2012. Details

Liu, Y., "Hidden Hierarchical Markov Fields for Image Modeling", Department of Systems Design Engineering, Waterloo, Ontario, Canada, University of Waterloo, 2011. Details