Toward a Coherent Statistical Framework for Dense Deformable Template Estimation

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. In this paper, we provide a careful definition and analysis of a well defined statistical model based on dense deformable templates for gray level images of deformable objects. We propose a rigorous Bayesian framework for which we can derived an iterative algorithm for the effective estimation of the geometric and photometric parameters of the model in a small sample setting, together with an asymptotic consistency proof. The model is extended to mixtures of finite numbers of such components leading to a fine description of the photometric and geometric variations. We illustrate some of the ideas with images of handwritten digits, and apply the estimated models to classification through maximum likelihood.