Abstract
This paper is about object deformations observed throughout a sequence of images. We present a statistical framework in which the observed images are defined as noisy realizations of a randomly deformed template image. In this framework, we focus on the problem of the estimation of parameters related to the template and deformations. Our main motivation is the construction of estimation framework and algorithm which can be applied to short sequences of complex and highly-dimensional images. The originality of our approach lies in the representations of the template and deformations, which are defined on a common triangulated domain, adapted to the geometry of the observed images. In this way, we have joint representations of the template and deformations which are compact and parsimonious. Using such representations, we are able to drastically reduce the number of parameters in the model. Besides, we adapt to our framework the Stochastic Approximation EM algorithm combined with a Markov Chain Monte Carlo procedure which was proposed in 2004 by Kuhn and Lavielle. Our implementation of this algorithm takes advantage of some properties which are specific to our framework. More precisely, we use the Markovian properties of deformations to build an efficient simulation strategy based on a Metropolis-Hasting-Within-Gibbs sampler. Finally, we present some experiments on sequences of medical images and synthetic data.
Similar content being viewed by others
References
Allassonnière, S., Amit, Y., Trouvé, A.: Towards a coherent statistical framework for dense deformable template estimation. J. R. Stat. Soc.: Ser. B Stat. Methodol. 69(1), 3–29 (2007a)
Allassonnière, S., Kuhn, E., Trouvé, A.: Bayesian deformable models building via stochastic approximation algorithm: a convergence study. arXiv:0706.0787 (2007b)
Amit, Y., Grenander, U., Piccioni, M.: Structural image restoration through deformable templates. J. Am. Stat. Assoc. 86(414), 376–387 (1991)
Andrieu, C., Moulines, E.: On the ergodicity properties of some adaptive MCMC algorithms. Ann. Appl. Probab. 16, 1462–1505 (2006)
Atchadé, Y.F., Rosenthal, J.S.: On adaptive Markov chain Monte Carlo algorithms. Bernoulli 11, 815–828 (2005)
Canny, J.: A computational approach to edge detection. IEEE Trans. Pattern Anal. Mach. Intell. 8(6), 679–698 (1986)
Deriche, R.: Fast algorithms for low-level vision. IEEE Trans. Pattern Anal. Mach. Intell. 12(1), 78–87 (1990)
Celeux, G., Diebolt, J.: The SEM algorithm: a probabilistic teacher algorithm derived from the EM algorithm for the mixture problem. Comput. Stat. Q. 2, 73–82 (1985)
Cuénod, C.A., Fournier, L., Balvay, D., Guinebretiére, J.M.: Tumor angiogenesis: pathophysiology and implications for contrast-enhanced MRI and CT assessment. Abdom Imaging 31(2), 188–193 (2006)
Delyon, B., Lavielle, M., Moulines, E.: Convergence of a stochastic approximation version of the EM algorithm. Ann. Stat. 27, 94–128 (1999)
Dempster, A.P., Laird, N.M., Rubin, D.B.: Maximum likelihood from incomplete data via the EM algorithm. J. R. Stat. Soc. B 39, 1–38 (1977)
Geman, S., Geman, D.: Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images. IEEE Trans. Pattern Anal. Mach. Intell. 6, 721–741 (1984)
Glasbey, C.A., Mardia, K.V.: A penalized likelihood approach to image warping (with discussion). J. R. Stat. Soc. C 63, 465–514 (2001)
Grenander, U.: General Pattern Theory. Oxford University Press, London (1994)
Grenander, U., Miller, M.: Computational anatomy: an emerging discipline. Q. Appl. Math. 4, 617–694 (1998)
Judd, R.M., Lugo-Olivieri, C.H., Araj, M., Kondo, T., et al.: Physiological basis of myocardial contrast enhancement in fast magnetic resonance images of 2-day-old reperfused canine infarcts. Circulation 92(7), 1902–1910 (1995)
Kuhl, C.: The current status of breast MR imaging. Part I. Choice of technique, image interpretation, diagnostic accuracy, and transfer to clinical practice. Radiology 244(2), 356–378 (2007)
Kuhn, E., Lavielle, M.: Coupling a stochastic approximation version of EM with a MCMC procedure. ESAIM Probab. Stat. 8, 115–131 (2004)
Lavielle, M., Moulines, E.: A simulated annealing version of the EM algorithm for non-Gaussian deconvolution. Stat. Comput. 7, 229–236 (1997)
Levine, R., Casella, G.: Optimizing random scan Gibbs samplers. J. Multivar. Anal. 97, 2071–2100 (2006)
Mengersen, K.L., Tweedie, R.L.: Rates of convergence of the Hastings and Metropolis algorithms. Ann. Stat. 24(1), 101–121 (1996)
Miles, K.A.: Perfusion CT for the assessment of tumor vascularity: which protocol? Br. J. Radiol. 76(1), 36–42 (2003)
O’Connor, J.P., Jackson, A., Parker, G.J., Jayson, G.C.: DCE-MRI biomarkers in the clinical evaluation of antiangiogenic and vascular disrupting agents. Br. J. Cancer 96(2), 189–195 (2007)
Padhani, A.R.: Dynamic contrast-enhanced MRI in clinical oncology: current status and future directions. J. Magn. Reson. Imaging 16(4), 407–422 (2002)
Wei, G.C., Tanner, M.A.: Calculating the content and boundary of the highest posterior density region via data augmentation. Biometrika 77, 649–652 (1990)
Wintermark, M.: Brain perfusion-CT in acute stroke patients. Eur. Radiol. 15(4), D28–31 (2005)
Zahra, M.A., Hollingsworth, K.G., Sala, E., Lomas, D.J., Tan, L.T.: Dynamic contrast-enhanced MRI as a predictor of tumour response to radiotherapy. Lancet Oncol. 8(1), 63–74 (2007)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Richard, F.J.P., Samson, A.M.M. & Cuénod, C.A. A SAEM algorithm for the estimation of template and deformation parameters in medical image sequences. Stat Comput 19, 465 (2009). https://doi.org/10.1007/s11222-008-9106-7
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11222-008-9106-7