Most of the work on 3-D object recognition from range data has used an alignment-verification approach in which a specific 3-D object is matched to an exact instance of the same object in a scene. This approach has been successfully used in industrial machine vision, but it is not capable of dealing with the complexities of recognizing classes of similar objects. This paper undertakes this task by proposing and testing a component-based methodology encompassing three main ingredients: 1) a new way of learning and extracting shape-class components from surface shape information; 2) a new shape representation called a symbolic surface signature that summarizes the geometric relationships among components; and 3) an abstract representation of shape classes formed by a hierarchy of classifiers that learn object-class parts and their spatial relationships from examples.