# Stochastic algorithm for Bayesian mixture effect template estimation

Stéphanie Allassonnière; Estelle Kuhn

ESAIM: Probability and Statistics (2010)

- Volume: 14, page 382-408
- ISSN: 1292-8100

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topAllassonnière, Stéphanie, and Kuhn, Estelle. "Stochastic algorithm for Bayesian mixture effect template estimation ." ESAIM: Probability and Statistics 14 (2010): 382-408. <http://eudml.org/doc/250851>.

@article{Allassonnière2010,

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.
},

author = {Allassonnière, Stéphanie, Kuhn, Estelle},

journal = {ESAIM: Probability and Statistics},

keywords = {Stochastic approximations; non rigid-deformable templates; shapes statistics; MAP estimation; Bayesian method; mixture models; stochastic approximations},

language = {eng},

month = {12},

pages = {382-408},

publisher = {EDP Sciences},

title = {Stochastic algorithm for Bayesian mixture effect template estimation },

url = {http://eudml.org/doc/250851},

volume = {14},

year = {2010},

}

TY - JOUR

AU - Allassonnière, Stéphanie

AU - Kuhn, Estelle

TI - Stochastic algorithm for Bayesian mixture effect template estimation

JO - ESAIM: Probability and Statistics

DA - 2010/12//

PB - EDP Sciences

VL - 14

SP - 382

EP - 408

AB -
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.

LA - eng

KW - Stochastic approximations; non rigid-deformable templates; shapes statistics; MAP estimation; Bayesian method; mixture models; stochastic approximations

UR - http://eudml.org/doc/250851

ER -

## References

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