Bayesian Markov model for cooperative clustering: application to robust MRI brain scan segmentation
[Approche bayesienne et markovienne pour des classifications couplées coopératives : application à la segmentation d’IRM du cerveau]
Journal de la société française de statistique, Tome 152 (2011) no. 3, pp. 116-141.

La classification est une étape clef de l’analyse de données qui consiste à produire une partition des données qui traduise l’existence de groupes dans celles-ci. Dans cet article, nous introduisons la notion de classifications coopératives. Nous considérons le cas où l’objectif est de produire deux (ou plus) partitions des données de manière non indépendante mais en prenant en compte les informations que l’une des partitions apporte sur l’autre et réciproquement. Pour ce faire, nous considérons deux (ou plus) jeux d’étiquettes non indépendants. Des interactions supplémentaires entre étiquettes au sein d’un même jeu sont également modélisées pour prendre en compte par exemple des dépendances spatiales. Ce cadre coopératif est formulé à l’aide de modèles de champs de Markov conditionnels dont les paramètres sont estimés par une variante de l’algorithme EM. Nous illustrons les performances de notre approche sur un problème réel difficile de segmentation simultanée des tissus et des structures du cerveau à partir d’images de résonnance magnétique artefactées.

Clustering is a fundamental data analysis step that consists of producing a partition of the observations to account for the groups existing in the observed data. In this paper, we introduce an additional cooperative aspect. We address cases in which the goal is to produce not a single partition but two or more possibly related partitions using cooperation between them. Cooperation is expressed by assuming the existence of two sets of labels (group assignments) which are not independent. We also model additional interactions by considering dependencies between labels within each label set. We propose then a cooperative setting formulated in terms of conditional Markov Random Field models for which we provide alternating and cooperative estimation procedures based on variants of the Expectation Maximization (EM) algorithm for inference. We illustrate the advantages of our approach by showing its ability to deal successfully with the complex task of segmenting simultaneously and cooperatively tissues and structures from MRI brain scans.

Keywords: Model-based clustering, Markov random fields, Bayesian analysis, EM algorithm, Generalized alternating maximization, Human Brain
Mot clés : Classification à base de modèles, Champs de Markov, Analyse bayesienne, Algorithme EM, Maximization alternée généralisée, Cerveau humain 
@article{JSFS_2011__152_3_116_0,
     author = {Forbes, Florence and Scherrer, Benoit and Dojat, Michel},
     title = {Bayesian {Markov} model for cooperative clustering: application to robust {MRI} brain scan segmentation},
     journal = {Journal de la soci\'et\'e fran\c{c}aise de statistique},
     pages = {116--141},
     publisher = {Soci\'et\'e fran\c{c}aise de statistique},
     volume = {152},
     number = {3},
     year = {2011},
     mrnumber = {2871180},
     zbl = {1316.62040},
     language = {en},
     url = {http://www.numdam.org/item/JSFS_2011__152_3_116_0/}
}
TY  - JOUR
AU  - Forbes, Florence
AU  - Scherrer, Benoit
AU  - Dojat, Michel
TI  - Bayesian Markov model for cooperative clustering: application to robust MRI brain scan segmentation
JO  - Journal de la société française de statistique
PY  - 2011
SP  - 116
EP  - 141
VL  - 152
IS  - 3
PB  - Société française de statistique
UR  - http://www.numdam.org/item/JSFS_2011__152_3_116_0/
LA  - en
ID  - JSFS_2011__152_3_116_0
ER  - 
%0 Journal Article
%A Forbes, Florence
%A Scherrer, Benoit
%A Dojat, Michel
%T Bayesian Markov model for cooperative clustering: application to robust MRI brain scan segmentation
%J Journal de la société française de statistique
%D 2011
%P 116-141
%V 152
%N 3
%I Société française de statistique
%U http://www.numdam.org/item/JSFS_2011__152_3_116_0/
%G en
%F JSFS_2011__152_3_116_0
Forbes, Florence; Scherrer, Benoit; Dojat, Michel. Bayesian Markov model for cooperative clustering: application to robust MRI brain scan segmentation. Journal de la société française de statistique, Tome 152 (2011) no. 3, pp. 116-141. http://www.numdam.org/item/JSFS_2011__152_3_116_0/

[1] Arnold, B. C.; Castillo, E.; Sarabia, J. M. Conditionally specified distributions: an introduction, Statistical Science, Volume 16 (2001) no. 3, pp. 249-274 | MR | Zbl

[2] Ashburner, J.; Friston, K. J. Unified Segmentation, NeuroImage, Volume 26 (2005), pp. 839-851

[3] Besag, J. Spatial interaction and the statistical analysis of lattice systems, J. Roy. Statist. Soc. Ser. B, Volume 36 (1974) no. 2, pp. 192-236 | MR | Zbl

[4] Besag, J. On the statistical analysis of dirty pictures, J. Roy. Statist. Soc. Ser. B, Volume 48 (1986) no. 3, pp. 259-302 | MR | Zbl

[5] Byrne, W.; Gunawardana, A. Convergence theorems of Generalized Alternating Minimization Procedures, J. Machine Learning Research, Volume 6 (2005), pp. 2049-2073 | MR | Zbl

[6] Benboudjema, D.; Pieczynski, W. Unsupervised image segmentation using Triplet Markov fields, Comput. Vision Image Underst., Volume 99 (2005), pp. 476-498

[7] Black, M. J.; Rangarajan, A. On the unification of Line processes, outlier rejection and robust statistics with application in early vision, Int. Jour. Comput. Vision, Volume 19 (1996) no. 1, pp. 57-91

[8] Celeux, G.; Forbes, F.; Peyrard, N. EM Procedures Using Mean Field-Like Approximations for Markov Model-Based Image Segmentation, Pat. Rec., Volume 36 (2003) no. 1, pp. 131-144 | Zbl

[9] Cadez, V.; Gaffney, S.; Smyth, P. A general probabilistic framework for clustering individuals and objects, 6th ACM int. Conf. Knowledge Discovery and Data mining (2000), pp. 140-149

[10] 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 trans. Med. Imag., Volume 17 (1998) no. 3, pp. 463-468

[11] Dice, L. R. Measures of the amount of ecologic association between species, Ecology, Volume 26 (1945), pp. 297-302

[12] Gelman, A.; Carlin, J. B.; Stern, H. S.; Rubin, D. B. Bayesian Data Analysis, Chapman & Hall, 2nd edition, 2004 | MR | Zbl

[13] Georgii, H.-O. Gibbs measures and phase transitions, De Gruyter, 1988 | MR | Zbl

[14] Geman, S.; Geman, D. Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images, IEEE trans. Pat. Anal. Mach. Intell., Volume 6 (1984), pp. 721-741 | Zbl

[15] Geman, D.; Reynolds, G. Constrained restoration and the recovery of discontinuities, IEEE trans. Pat. Anal. Mach. Intell., Volume 14 (1992) no. 3, pp. 376-383

[16] Heitz, F.; Bouthemy, P. Multimodal estimation of discontinuous optical flow using Markov random fields, IEEE Trans. Pat. Anal. Mach. Intell., Volume 15 (1993) no. 12, pp. 1217-1232

[17] Heckerman, D.; Chickering, D. M.; Meek, C.; Rounthwaite, R.; Kadie, C. Dependency networks for inference, collaborative filtering and data visualization, J. Machine Learning Research, Volume 1 (2000), pp. 49-75 | Zbl

[18] Jordan, M.I.; Ghahramani, Z.; Jaakkola, T.S.; Saul, L.K. An introduction to variational methods for graphical models, Learning in Graphical Models (Jordan, M.I., ed.), 1999, pp. 105-162 | Zbl

[19] Jenkinson, M.; Smith, S. M. A global optimisation method for robust affine registration of brain images, Medical Image Analysis, Volume 5 (2001) no. 2, pp. 143-156

[20] Kumar, S.; Hebert, M. Discriminative Random Fields, Int. J. Comput. Vision, Volume 68 (2006) no. 2, pp. 179-201 | DOI

[21] McLachlan, G.J.; Krishnan, T. The EM Algorithm and Extensions, Wiley, 1996 | MR | Zbl

[22] Narasimha, R.; Arnaud, E.; Forbes, F.; Horaud, R. Cooperative Disparity and object boundary estimation, 15th IEEE Int. Conf. Imag. Proc. ICIP 08, San Diego, USA (2008), pp. 1784-1787

[23] Pohl, K.M.; Fisher, J.; Grimson, E.; Kikinis, R.; Wells, W. A Bayesian model for joint segmentation and registration, NeuroImage, Volume 31 (2006) no. 1, pp. 228-239

[24] Powell, M. J. D. An efficient method for finding the minimum of a function of several variables without calculating derivatives, The Computer Journal, Volume 7 (1964) | MR | Zbl

[25] Scherrer, B.; Dojat, M.; Forbes, F.; Garbay, C. LOCUS: LOcal Cooperative Unified Segmentation of MRI brain scans, MICCAI 2007, Brisbane, Australia (2007), pp. 219-227

[26] Scherrer, B.; Forbes, F.; Garbay, C.; Dojat, M. Distributed Local MRF Models for Tissue and Structure Brain Segmentation, IEEE trans. Med. Imag., Volume 28 (2009), pp. 1296-1307

[27] Shattuck, D. W.; Sandor-Leahy, S. R.; Schaper, K. A.; Rottenberg, D. A.; Leahy, R. M. Magnetic resonance image tissue classification using a partial volume model, NeuroImage, Volume 13 (2001) no. 5, pp. 856-876

[28] Sun, J.; Zheng, N-N.; Shum, H-Y. Stereo Matching Using Belief Propagation, IEEE trans. Pat. Anal. Mach. Intell., Volume 25 (2003), pp. 787-800 | Zbl

[29] Van Leemput, K.; Maes, F.; Vandermeulen, D.; Suetens, P. Automated model-based bias field correction in MR images of the brain, IEEE trans. Med. Imag., Volume 18 (1999) no. 10, pp. 885-896

[30] Warfield, S. K.; Zou, K. H.; Wells, W. M. Simultaneous Truth and Performance Level Estimation (STAPLE): An Algorithm for the Validation of Image Segmentation, IEEE trans. Med. Imag., Volume 23 (2004) no. 7, pp. 903-921

[31] Zhang, Y.; Brady, M.; Smith, S. Segmentation of Brain MR images through a hidden Markov random field model and the Expectation-Maximisation algorithm, IEEE trans. Med. Imag., Volume 20 (2001) no. 1, pp. 45-47