Bayesian Markov model for cooperative clustering: application to robust MRI brain scan segmentation

Forbes, Florence; Scherrer, Benoit; Dojat, Michel

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

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