Bayesian Consistent Estimation in Deformable Models using Stochastic Algorithms: Applications to Medical Images

Allassonnière, Stéphanie; Kuhn, Estelle; Trouvé, Alain

Journal de la société française de statistique, Tome 151 (2010) no. 1, pp. 1-16.

Cet article vise à résumer et valider sur données réelles la méthode proposée dans ( 2 , 3 , 4 ) pour l’estimation d’atlas appelé Bayesian Mixed Effect (BME) atlas. Un tel atlas est composé d’une image de référence et d’une métrique pour chaque sous-groupe d’une population ainsi que du poids de ce sous-groupe. L’estimation est consistante sur un échantillon d’images données non labellisées. Nous rappelons ici le modèle statistique génératif qui permet l’estimation simultanée des sous-groupes, de leurs poids, des images de référence et des variabilités géométriques (liées aux métriques). Comme proposé en ( 2 , 3 , 4 ), nous travaillons dans un cadre bayésien, utilisons l’estimateur de Maximum A Posteriori et approchons sa valeur par une variante stochastique de l’algorithme EM (Expectation Maximisation). Cette méthode est validée sur deux ensembles de données d’images médicales : une partie du cortex humain et des excroissances de dendrites de souris liées à la maladies de Parkinson. Nous présentons les performances de cette méthode sur l’estimation de l’image de référence, la variabilité géométrique et le label.

This paper aims at summarising and validating a methodology proposed in [ 2 , 3 , 4 ] for estimating a Bayesian Mixed Effect (BME) atlas, i.e. coupled templates and geometrical metrics for estimated clusters, in a statistically consistent way given a sample of images. We recall the generative statistical model applied to the observations which enables the simultaneous estimation of the clusters, the templates and geometrical variabilities (related to the metric) in the population. Following [ 2 , 3 , 4 ], we work in a Bayesian framework, use a Maximum A Posteriori estimator and approach its value using a stochastic variant of the Expectation Maximisation (EM) algorithm. The method is validated with two data set consisting of medical images of part of the human cortex and dendrite spines from a mouse model of Parkinson’s disease. We present the performances of the method on the estimation of the template, the geometrical variability and the clustering.

Keywords: generative statistical model, stochastic EM algorithm, MAP estimator, MCMC methods, medical imaging
Mot clés : modèle statistique génératif, algorithme EM stochastique, estimateur MAP, méthodes MCMC, imagerie médicale

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