It is widely recognized that the fundamental building block in high level computer vision is the deformable template, which represents realizations of an object class in the image as noisy geometric instantiations of an underlying model. The instantiations typically come from a subset of some group centered at the identity which act on the model or template. Thus in contrast to some machine learning applications where one tries to discover some unspecified manifold structure, here it is entirely determined by the group action and the model. Given a choice of group action and family of template models a major challenge is to use a sample of images of the object to estimate the model and the distribution on the group. The primary obstacle is that the instantiations or group elements that produced each image are unobserved. I will describe a general formulation of this problem and then show some practical applications to object detection and recognition.