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Estimation in the deformable template model is a big challenge in imageanalysis. The issue is to estimate an atlas of a population. This atlascontains a template and the corresponding geometrical variability of theobserved shapes. The goal is to propose an accurate algorithm with lowcomputational cost and with theoretical guaranties of relevance. This becomesvery demanding when dealing with high dimensional data which is particularlythe case of medical images. We propose to use an optimized Monte Carlo MarkovChain method into a stochastic Expectation Maximization algorithm in order toestimate the model parameters by maximizing the likelihood. In this paper, wepresent a new Anisotropic Metropolis Adjusted Langevin Algorithm which we useas transition in the MCMC method. We first prove that this new sampler leads toa geometrically uniformly ergodic Markov chain. We prove also that under mildconditions, the estimated parameters converge almost surely and areasymptotically Gaussian distributed. The methodology developed is then testedon handwritten digits and some 2D and 3D medical images for the deformablemodel estimation. More widely, the proposed algorithm can be used for a largerange of models in many fields of applications such as pharmacology or genetic.

Convergent Stochastic Expectation Maximization algorithm with efficient  sampling in high dimension. Application to deformable template model  estimation