Towards a coherent statistical framework for dense deformable template estimation

Summary. The problem of estimating probabilistic deformable template models in the field of computer vision or of probabilistic atlases in the field of computational anatomy has not yet received a coherent statistical formulation and remains a challenge. We provide a careful definition and analysis of a well‐defined statistical model based on dense deformable templates for grey level images of deformable objects. We propose a rigorous Bayesian framework for which we prove asymptotic consistency of the maximum a posteriori estimate and which leads to an effective iterative estimation algorithm of the geometric and photometric parameters in the small sample setting. The model is extended to mixtures of finite numbers of such components leading to a fine description of the photometric and geometric variations of an object class. We illustrate some of the ideas with images of handwritten digits and apply the estimated models to classification through maximum likelihood.