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.
Classification : 60J22, 62F10, 62F15, 62M40
Mots clés : stochastic approximations, non rigid-deformable templates, shapes statistics, MAP estimation, bayesian method, mixture models
@article{PS_2010__14__382_0,
author = {Allassonni\`ere, St\'ephanie and Kuhn, Estelle},
title = {Stochastic algorithm for bayesian mixture effect template estimation},
journal = {ESAIM: Probability and Statistics},
pages = {382--408},
publisher = {EDP-Sciences},
volume = {14},
year = {2010},
doi = {10.1051/ps/2009001},
zbl = {pre05873002},
language = {en},
url = {www.numdam.org/item/PS_2010__14__382_0/}
}
Allassonnière, Stéphanie; Kuhn, Estelle. Stochastic algorithm for bayesian mixture effect template estimation. ESAIM: Probability and Statistics, Tome 14 (2010) , pp. 382-408. doi : 10.1051/ps/2009001. http://www.numdam.org/item/PS_2010__14__382_0/
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