For many object classes, shape is the most generic feature for object categorization. However, when a strong shape prior, i.e., a target object, is not available, domain independent, mid-level shape priors must play a critical role in not only grouping causally related features, but regularizing or abstracting them to yield higher-order shape features that support object categorization. In this talk, I will present a framework in which mid-level shape priors take the form of a vocabulary of simple, user-defined 2-D part models.  From the vocabulary, we learn to not only group oversegmented regions into parts, but to abstract the shapes of the region groups, yielding a set of abstract part hypotheses. However, the process of shape abstraction can be thought of as a form of "controlled hallucination", which comes at the cost of many competing 2-D part hypotheses.  To improve part hypothesis precision, we present two approaches that exploit the context of the hypotheses, and present two approaches.  In the first approach, we exploit spatiotemporal coherence (temporal context) of part hypotheses in a dynamic environment, and formulate hypothesis selection in a graph-theoretic, probabilistic framework. In the second approach, we assume that the 2-D parts represent the component faces of aspects that model a vocabulary of 3-D part models. We then exploit the relational structure (spatial context) of the faces encoded in the aspects, and again formulate hypothesis selection in a graph-theoretic, probabilistic framework.  Finally, we introduce a technique that is able to recover the pose and shape of a volumetric part from a recovered aspect.