Stochastic algorithm for Bayesian mixture effect template estimation

Stéphanie Allassonnière , Estelle Kuhn

The estimation of probabilistic deformable template models in computer vision or of probabilistic atlases in Computational Anatomy are core issues in both fields. A first coherent statistical framework where the geometrical variability is modelled as a hidden random variable has been given by [S. Allassonnière , (2007) 3-29]. They introduce a Bayesian approach and mixture of them to estimate deformable template models. A consistent stochastic algorithm has been introduced in [S. Allassonnière (in revision)] to face the problem encountered in [S. Allassonnière , (2007) 3-29] for the convergence of the estimation algorithm for the one component model in the presence of noise. We propose here to go on in this direction of using some "SAEM-like" algorithm to approximate the MAP estimator in the general Bayesian setting of mixture of deformable template models. We also prove the convergence of our algorithm toward a critical point of the penalised likelihood of the observations and illustrate this with handwritten digit images and medical images.

Mots clés: Stochastic approximations; non rigid-deformable templates; shapes statistics; MAP estimation; Bayesian method; mixture models

Domaines: Mathématiques [math]; Informatique [cs]

Stéphanie Allassonnière, Estelle Kuhn. Stochastic algorithm for Bayesian mixture effect template estimation. ESAIM: Probability and Statistics, 2010, 14, pp.382-408. ⟨10.1051/ps/2009001⟩. ⟨hal-00654474⟩