Categories and shape prototypes are considered for a class ob object recognition problems where rigid and detailed object models are not available or do not apply. We propose a modeling system for generic objects to recognize different objects from the same category with only one generic model. We base our design of the modeling system upon the current psychological theories of categorization and human visual perception. The representation consists of a prototype represented by parts and their configuration. Parts are modeled by superquadric volumetric primitives which can be combined via Boolean operations to form objects. Variations between objects within a category are described by changes in structure and shape deformations of prototypical parts. Recovery of deformed supequadric models from sparse 3-D points is developed and some results are shown.