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

Abstract

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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.

How to cite

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Allassonnière, 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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  1. S. Allassonnière, Y. Amit and A. Trouvé, Toward a coherent statistical framework for dense deformable template estimation. J. Roy. Stat. Soc.69 (2007) 3–29.  
  2. S. Allassonnière, E. Kuhn and A. Trouvé, Map estimation of statistical deformable templates via nonlinear mixed effects models: Deterministic and stochastic approaches. In Proc. Int. Workshop on the Mathematical Foundations of Computational Anatomy (MFCA-2008), edited by X. Pennec and S. Joshi (2008).  
  3. S. Allassonnière, E. Kuhn and A. Trouvé, Construction of Bayesian deformable models via a stochastic approximation algorithm: A convergence study. Bernoulli16 (2010) 641–678.  
  4. Y. Amit, U. Grenander and M. Piccioni, Structural image restoration through deformable templates. J. Am. Statist. Assoc.86 (1989) 376–387.  
  5. C. Andrieu, R. Moulines and P. Priouret, Stability of stochastic approximation under verifiable conditions. SIAM J. Control Optim.44 (2005) 283–312 (electronic).  
  6. T.F. Cootes, G.J. Edwards and C.J. Taylor, Actives appearance models. In 5th Eur. Conf. on Computer Vision, Berlin, Vol. 2, edited by H. Burkhards and B. Neumann. Springer (1998) 484–498.  
  7. B. Delyon, M. Lavielle and E. Moulines, Convergence of a stochastic approximation version of the EM algorithm. Ann. Statist.27 (1999) 94–128.  
  8. A.P. Dempster, N.M. Laird and D.B. Rubin, Maximum likelihood from incomplete data via the EM algorithm. J. Roy. Statist. Soc.1 (1977) 1–22.  
  9. C. Dorea and L. Zhao, Nonparametric density estimation in hidden Markov models. Statist. Inf. Stoch. Process.5 (2002) 55–64.  
  10. C.A. Glasbey and K.V. Mardia, A penalised likelihood approach to image warping. J. Roy. Statist. Soc., Ser. B63 (2001) 465–492.  
  11. J. Glaunès and S. Joshi, Template estimation form unlabeled point set data and surfaces for computational anatomy. In Proc. Int. Workshop on the Mathematical Foundations of Computational Anatomy (MFCA-2006), edited by X. Pennec and S. Joshi (2006) 29–39.  
  12. U. Grenander, General Pattern Theory. Oxford Science Publications (1993).  
  13. P. Hall and C.C. Heyde, Martingale limit theory and its application. Probab. Math. Statist. Academic Press Inc. [Harcourt Brace Jovanovich Publishers], New York (1980).  
  14. E. Kuhn and M. Lavielle, Coupling a stochastic approximation version of EM with an MCMC procedure. ESAIM: PS8 (2004) 115–131 (electronic).  
  15. H.J. Kushner and D.S. Clark, Stochastic approximation methods for constrained and unconstrained systems, volume 26 of Appl. Math. Sci. Springer-Verlag, New York (1978).  
  16. S. Marsland, C. Twining and C. Taylor, A minimum description length objective function for groupwise non rigid image registration. Image and Vision Computing (2007).  
  17. S.P. Meyn and R.L. Tweedie, Markov chains and stochastic stability. Communications and Control Engineering Series. Springer-Verlag, London Ltd. (1993).  
  18. M.I. Miller, T.A. and L. Younes, On the metrics and Euler-Lagrange equations of computational anatomy. Ann. Rev. Biomed. Eng.4 (2002) 375–405.  
  19. C. Robert, Méthodes de Monte Carlo par chaînes de Markov. Statistique Mathématique et Probabilité. [Mathematical Statistics and Probability]. Éditions Économica, Paris (1996).  
  20. M. Vaillant, I. Miller, M.A. Trouvé and L. Younes, Statistics on diffeomorphisms via tangent space representations. Neuroimage23 (2004) S161–S169.  

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