Construction of Bayesian deformable models via a stochastic approximation algorithm: A convergence study

The problem of the definition and estimation of generative models based on deformable templates from raw data is of particular importance for modeling non-aligned data affected by various types of geometric variability. This is especially true in shape modeling in the computer vision community or in probabilistic atlas building in computational anatomy. A first coherent statistical framework modeling geometric variability as hidden variables was described in Allassonniere. Amit and Trouve [J. R. Stat. Soc. Ser: B Stat. Methodol. 69 (2007) 3-29]. The present paper gives a theoretical proof of convergence of effective stochastic approximation expectation strategies to estimate such models and shows the robustness of this approach against noise through numerical experiments in the context of handwritten digit modeling.