Three‐Dimensional Multiphase Segmentation of X‐Ray CT Data of Porous Materials Using a Bayesian Markov Random Field Framework

Advancements in noninvasive imaging methods such as X-ray computed tomography (CT) have led to a recent surge of applications in porous media research with objectives ranging from theoretical aspects of pore-scale fluid and interfacial dynamics to practical applications such as enhanced oil recovery and advanced contaminant remediation. While substantial efforts and resources have been devoted to advance CT technology, microscale analysis, and fluid dynamics simulations, the development of efficient and stable three-dimensional multiphase image segmentation methods applicable to large data sets is lacking. To eliminate the need for wet-dry or dual-energy scans, image alignment, and subtraction analysis, commonly applied in X-ray micro-CT, a segmentation method based on a Bayesian Markov random field (MRF) framework amenable to true three-dimensional multiphase processing was developed and evaluated. Furthermore, several heuristic and deterministic combinatorial optimization schemes required to solve the labeling problem of the MRF image model were implemented and tested for computational efficiency and their impact on segmentation results. Test results for three grayscale data sets consisting of dry glass beads, partially saturated glass beads, and partially saturated crushed tuff obtained with synchrotron X-ray micro-CT demonstrate great potential of the MRF image model for three-dimensional multiphase segmentation. While our results are promising andmore » the developed algorithm is stable and computationally more efficient than other commonly applied porous media segmentation models, further potential improvements exist for fully automated operation.« less

[1]  Hans-Jörg Vogel,et al.  Segmentation of X-ray microtomography images of soil using gradient masks , 2010, Comput. Geosci..

[2]  Jason I. Gerhard,et al.  Measurement and prediction of the relationship between capillary pressure, saturation, and interfacial area in a NAPL‐water‐glass bead system , 2010 .

[3]  Anders Kaestner,et al.  Imaging and image processing in porous media research , 2008 .

[4]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[5]  Rohit Chandra,et al.  Parallel programming in openMP , 2000 .

[6]  J. Besag Spatial Interaction and the Statistical Analysis of Lattice Systems , 1974 .

[7]  John P. Moussouris Gibbs and Markov random systems with constraints , 1974 .

[8]  W. B. Lindquist,et al.  3DMA General Users Manual , 1999 .

[9]  Mark L. Rivers,et al.  Using X-ray computed tomography in hydrology: systems, resolutions, and limitations , 2002 .

[10]  David A. Clausi,et al.  Unsupervised segmentation of synthetic aperture Radar sea ice imagery using a novel Markov random field model , 2005, IEEE Transactions on Geoscience and Remote Sensing.

[11]  Nikolas P. Galatsanos,et al.  Variational Bayesian Image Restoration With a Product of Spatially Weighted Total Variation Image Priors , 2010, IEEE Transactions on Image Processing.

[12]  Donald Geman,et al.  Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[13]  Wei Wang,et al.  Observer-dependent variability of the thresholding step in the quantitative analysis of soil images and X-ray microtomography data , 2010 .

[14]  M. Tuller,et al.  Segmentation of X‐ray computed tomography images of porous materials: A crucial step for characterization and quantitative analysis of pore structures , 2009 .

[15]  M. L. Porter,et al.  Image analysis algorithms for estimating porous media multiphase flow variables from computed microtomography data: a validation study , 2010 .

[16]  Stan Z. Li,et al.  Markov Random Field Modeling in Image Analysis , 2001, Computer Science Workbench.

[17]  Markus Tuller,et al.  Evaluation of an Advanced Benchtop Micro-Computed Tomography System for Quantifying Porosities and Pore-Size Distributions of Two Brazilian Oxisols , 2011 .

[18]  Markus Tuller,et al.  Application of Segmentation for Correction of Intensity Bias in X‐Ray Computed Tomography Images , 2010 .

[19]  Nelson D. A. Mascarenhas,et al.  A novel MAP-MRF approach for multispectral image contextual classification using combination of suboptimal iterative algorithms , 2010, Pattern Recognit. Lett..

[20]  Christian Blum,et al.  Metaheuristics in combinatorial optimization: Overview and conceptual comparison , 2003, CSUR.

[21]  Donald Geman,et al.  Bayes Smoothing Algorithms for Segmentation of Binary Images Modeled by Markov Random Fields , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[22]  Yoh-Han Pao,et al.  Combinatorial optimization with use of guided evolutionary simulated annealing , 1995, IEEE Trans. Neural Networks.

[23]  Tzong-Jer Chen,et al.  Fuzzy c-means clustering with spatial information for image segmentation , 2006, Comput. Medical Imaging Graph..

[24]  Erik Sudderth,et al.  Signal and Image Processing with Belief Propagation [DSP Applications] , 2008, IEEE Signal Processing Magazine.

[25]  J. Laurie Snell,et al.  Markov Random Fields and Their Applications , 1980 .

[26]  Josiane Zerubia,et al.  Satellite image classification using a modified Metropolis dynamics , 1992, [Proceedings] ICASSP-92: 1992 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[27]  D. Wildenschild,et al.  Quantitative Analysis of Flow Processes in a Sand Using Synchrotron‐Based X‐ray Microtomography , 2005, Vadose Zone Journal.

[28]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[29]  J. Besag On the Statistical Analysis of Dirty Pictures , 1986 .

[30]  William T. Freeman,et al.  Signal and Image Processing with Belief Propagation , 2008 .

[31]  Rasmus Larsen,et al.  Markov Random Field Surface Reconstruction , 2010, IEEE Transactions on Visualization and Computer Graphics.

[32]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[33]  R. Heck,et al.  A comparison of 2D vs. 3D thresholding of X-ray CT imagery , 2007 .

[34]  F. Glover,et al.  Handbook of Metaheuristics , 2019, International Series in Operations Research & Management Science.

[35]  N. Metropolis,et al.  Equation of State Calculations by Fast Computing Machines , 1953, Resonance.

[36]  Roger L. Nielsen,et al.  TRACE. FOR: a program for the calculation of combined major and trace-element liquid lines of descent for natural magmatic systems , 1988 .

[37]  Pierre L'Ecuyer,et al.  An Object-Oriented Random-Number Package with Many Long Streams and Substreams , 2002, Oper. Res..

[38]  Ron Kikinis,et al.  Markov random field segmentation of brain MR images , 1997, IEEE Transactions on Medical Imaging.

[39]  Josiane Zerubia,et al.  Bayesian image classification using Markov random fields , 1996, Image Vis. Comput..

[40]  Mark L. Rivers,et al.  Comparison of image segmentation methods in simulated 2D and 3D microtomographic images of soil aggregates , 2011 .