Stochastic algorithm for Bayesian mixture effect template estimation

¹ CMAP - École polytechnique, Route de Saclay, 91128 Palaiseau, France; Allassoniere@gmail.com
² LAGA - Université Paris 13, 99 av. J.-B. Clément, 93430 Villetaneuse, France and INRA - Unité MIA, Domaine de Vilvert, 78352 Jouy-en-Josas, France

Received: 3 June 2008
Revised: 16 January 2009
Revised: 19 March 2009

Abstract

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 et al., J. Roy. Stat. Soc. 69 (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 et al. (in revision)] to face the problem encountered in [S. Allassonnière et al., J. Roy. Stat. Soc. 69 (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.