On the convergence of EM-like algorithms for image segmentation using Markov random fields

Medical Image Analysis

Volumn 15, Issue 6, 2011, Pages 830-839

  Roche, Alexis ^a,b   Ribes, Delphine ^a   Bach Cuadra, Meritxell ^a   Krüger, Gunnar ^a  

^a EPFL   (Switzerland)

^b ETH ZURICH   (Switzerland)

Author keywords

Convergence; Expectation maximization; Markov random field; Mean field; Segmentation

Indexed keywords

BRAIN TISSUE; CONVERGENCE; CONVERGENCE PROPERTIES; CONVERGENCE RESULTS; EXPECTATION MAXIMIZATION; EXPECTATION-MAXIMIZATION ALGORITHMS; FASTER CONVERGENCE; INDEPENDENT MIXTURE MODELS; MAGNETIC RESONANCE IMAGES; MARKOV RANDOM FIELDS; MEAN FIELD; NUMERICAL SCHEME; SEGMENTATION RESULTS;

ALGORITHMS; IMAGE SEGMENTATION; INFERENCE ENGINES; MAGNETIC RESONANCE; MAGNETIC RESONANCE IMAGING; MAXIMUM PRINCIPLE; TISSUE;

CONVERGENCE OF NUMERICAL METHODS;

ALGORITHM; ARTICLE; BINOCULAR CONVERGENCE; BRAIN TISSUE; CLINICAL PRACTICE; IMAGE ANALYSIS; NUCLEAR MAGNETIC RESONANCE IMAGING; PRIORITY JOURNAL; PROBABILITY; STATISTICS; THEORETICAL MODEL; VISION; VOXEL BASED MORPHOMETRY;

ALGORITHMS; COMPUTATIONAL BIOLOGY; COMPUTER SIMULATION; HUMANS; MARKOV CHAINS;

EID: 80955181095     PISSN: 13618415     EISSN: 13618423     Source Type: Journal    
DOI: 10.1016/j.media.2011.05.002     Document Type: Article

References (40)

1. Ashburner J., Friston K. Unified segmentation. NeuroImage 2005, 26(3):839-851.
2. Aubert-Broche B., Evans A., Collins L. A new improved version of the realistic digital brain phantom. NeuroImage 2006, 32(1):138-145.
3. Bach Cuadra M., Cammoun L., Butz T., Cuisenaire O., Thiran J.-P. Comparison and validation of tissue modelization and statistical classification methods in T1-weighted MR brain images. IEEE Transactions on Medical Imaging 2005, 24(12):1548-1565.
4. Besag J. Spatial interaction and the statistical analysis of lattice systems. Journal of the Royal Statistical Society: Series B 1974, 36(2):192-236.
5. Bezdek, J.C., Hathaway, R.J., 2002. Some notes on alternating optimization. In: Advances in Soft Computing - AFSS International Conference on Fuzzy Systems. Lecture Notes in Computer Science, vol. 2275, pp. 288-300.
6. Bishop C. Pattern Recognition and Machine Intelligence 2006, John Wiley & Sons, Inc.
7. Boykov Y., Veksler O., Zabih R. Fast approximate energy minimization via graph cuts. IEEE Transactions on Pattern Analysis and Machine Intelligence 2001, 23(11):1222-1239.
8. Collins D.L., Zijdenbos A.P., Kollokian V., Sled J.G., Kabani N.J., Holmes C.J., Evans A.C. Design and construction of a realistic digital brain phantom. IEEE Transactions on Medical Imaging 1998, 17(3):463-468.
9. Csiszár I., Tusnády G. Information geometry and alternating minimization procedures. Statistics & Decisions 1984, 1:205-237. supplement Issue.
10. Dempster A.P., Laird N.M., Rubin D.B. Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society: Series B 1977, 39:1-38.
11. Fessler J. On the convergence of mean field procedures for MRFs. IEEE Transactions on Image Processing 1998, 7(6):917.
12. Forbes F., Fort G. Combining Monte Carlo and mean-field-like methods for inference in hidden Markov random fields. IEEE Transactions on Image Processing 2007, 16(3):824-837.
13. Geman S., Geman D. Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence 1984, 6(6):721-741.
14. Kapur, T., 1999. Model based three dimensional medical image segmentation. Ph.D. thesis, Massachusetts Institute of Technology.
15. Kwan R.-S., Evans A., Pike G. MRI simulation-based evaluation of image-processing and classification methods. IEEE Transactions on Medical Imaging 1999, 18(11):1085-1097.
16. Li S.Z. Markov random field modeling in computer vision 1995, Springer, Tokyo, New-York, Berlin.
17. Liang Z., Wang S. An EM approach to MAP solution of segmenting tissue mixtures: a numerical analysis. IEEE Transactions on Medical Imaging 2009, 28(2):297-310.
18. Marroquin J., Santana E., Botello S. Hidden Markov measure field models for image segmentation. IEEE Transactions on Pattern Analysis and Machine Intelligence 2003, 25(11):1380-1387.
19. Minka, T.P., 2005. Divergence measures and message passing. Tech. Rep. MSR-TR-2005-173, Microsoft Research Ltd., Cambridge, UK.
20. Narayana P., Brey W., Kulkarni M., Sievenpiper C. Compensation for surface coil sensitivity variation in magnetic resonance imaging. Magnetic Resonance Imaging 1988, 6:271-274.
21. Neal R., Hinton G. A view of the EM algorithm that justifies incremental, sparse, and other variants. Learning in Graphical Models 1998, 355-368. Kluwer Academic Publishers. M. Jordan (Ed.).
22. Penny W., Trujillo-Bareto N., Friston K. Bayesian fMRI time series analysis with spatial priors. NeuroImage 2005, 24(2):350-362.
23. Prasad R., Srinivas R., Srinivas Y. Unsupervised image segmentation method based on finite generalized Gaussian distribution with EM&K-means algorithm. International Journal of Computer Science and Network Security 2007, 7(4):317-321.
24. Prima S., Ayache N., Barrick T., Roberts N. Maximum likelihood estimation of the bias field in MR brain images: investigating different modelings of the imaging process. LNCS 2001, vol. 2208:811-819. Springer Verlag.
25. Schmitt F. Correction of geometric distortion in MR Images. Proceedings of the computer assisted radiology (CAR) 1985, 15-25. Springer Verlag.
26. Shattuck D., Sandor-Leahy S., Schaper K., Rottenberg D., Leahy R. Magnetic resonance image tissue classification using a partial volume model. NeuroImage 2001, 13(5):856-876.
27. Sled J., Zijdenbos A., Evans A. A nonparametric method for automatic correction of intensity nonuniformity in MRI data. IEEE Transactions on Medical Imaging 1998, 17:87-97.
28. Szeliski R., Zabih R., Scharstein D., Veksler O., Kolmogorov V., Agarwala A., Tappen M., Rother C. A comparative study of energy minimization methods for Markov random fields with smoothness-based priors. IEEE Transactions on Pattern Analysis and Machine Intelligence 2008, 30(6):1068-1080.
29. Van Leemput K., Maes F., Vandermeulen D., Suetens P. Automated model-based bias field correction of MR images of the brain. IEEE Transactions on Medical Imaging 1999, 18(10):885-896.
30. Van Leemput K., Maes F., Vandermeulen D., Suetens P. Automated model-based tissue classification of MR images of the brain. IEEE Transactions on Medical Imaging 1999, 18(10):897-908.
31. Van Leemput K., Maes F., Vandermeulen D., Suetens P. A unifying framework for partial volume segmentation of brain MR images. IEEE Transactions on Medical Imaging 2003, 22(1):105-119.
32. Wainwright M., Jaakkola T., Willsky A. MAP estimation via agreement on (hyper)trees: message-passing and linear-programming approaches. IEEE Transactions on Information Theory 2005, 51(11):3697-3717.
33. Wald, L., Schmitt, F., Dale, A., 2001. Systematic spatial distortion in MRI due to gradient nonlinearities. In: Proceedings of the 7th Annual Human Brain Mapping Meeting, Brighton, UK, p. 203.
34. Weiss Y. Advanced Mean Field Methods 2001, MIT Press, Chapter: Comparing the mean field method and belief propagation for approximate inference in MRFs, pp. 229-239.
35. Weiss Y., Freeman W. On the optimality of solutions of the max-product belief-propagation algorithm in arbitrary graphs. IEEE Transactions on Information Theory 2001, 47(2):723-735.
36. Wells W.M., Grimson W.E.L., Kikinis R., Jolesz F.A. Adaptive segmentation of MRI data. IEEE Transactions on Medical Imaging 1996, 15(4):429-442.
37. Woolrich M., Behrens T. Variational Bayes inference of spatial mixture models for segmentation. IEEE Transactions on Medical Imaging 2006, 25(10):1380-1391.
38. Zhang J. The mean field theory in EM procedures for Markov random fields. IEEE Transactions on Signal Processing 1992, 40(10):2570-2583.
39. Zhang J. The convergence of mean-field procedures for MRFs. IEEE Transactions on Image Processing 1996, 5(12):1662-1665.
40. Zhang Y., Brady J., Smith S. Segmentation of brain MR images through a hidden Markov random field model and the expectation-maximization algorithm. IEEE Transactions on Medical Imaging 2001, 20(1):45-57.