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.