An object recognition system is presented that it designed to handle the computational complexity posed by a large model base, an unconstrained viewpoint and the structural complexity and detail inherent in a single view. The design is based on two ideas. The first is to compute descriptions of what the objects should look like in the image, called predictions, before the recognition task begins. This reduces actual recognition to a 2D matching process, substantially speeding up recognition time for 3D objects (with manageable storage overhead). The second is to represent all the predictions by a single, combined ISA and PART-OF hierarchy called a prediction hierarchy. The nodes in this hierarchy are partial descriptions that are common to views and hence constitute shared processing subgoals during matching. Many of the problems encountered with large model bases and complex models are reduced by subgoal sharing: projections with similarities explicitly share the representation and recognition of their common aspects. The original contribution of this paper is the automatic compilation, from a 3D model base, of a prediction hierarchy that can be used to recognise objects. A prototype system based on these ideas is demonstrated using a set of polyhedral objects and projections from an unconstrained range of viewpoints.