期刊
ESAIM-PROBABILITY AND STATISTICS
卷 14, 期 -, 页码 382-408出版社
EDP SCIENCES S A
DOI: 10.1051/ps/2009001
关键词
Stochastic approximations; non rigid-deformable templates; shapes statistics; MAP estimation; Bayesian method; mixture models
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. Allassonniere 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. Allassonniere et al. (in revision)] to face the problem encountered in [S. Allassonniere 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.
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