Computational Anatomy aims to model and analyze the variability of the human anatomy. Given a set of medical images of the same organ, the first step is the estimation of the mean organ’s shape. This mean anatomical shape is called the template in Computer vision or Medical imaging. The estimation of a template/atlas is central because it represents the starting point for all further processing or analyses. In view of the medical applications, evaluating the quality of this statistical estimate is crucial. How does the estimated template behave for varying amount of data, for small and large level of noise? We present a geometric Bayesian framework which unifies two estimation problems that are usually considered distinct: the template estimation problem and manifold learning problem - here associated to estimating the template’s orbit. We leverage this to evaluate the quality of the template estimator.