Abstract: In this report we consider the problem of 3D object recognition, and the role that perceptual grouping processes must play. In particular, we argue that a single level of perceptual grouping is inadequate, and that reliance on a single level of grouping is responsible for the specific weaknesses of several well-known recognition techniques. Instead, we argue that recognition must utilize a hierarchy of perceptual grouping processes, and describe an appearance-based system that uses four distinct levels of perceptual grouping, the upper two novel, to represent 3-D objects in a form that not only allows recognition, but reasoning about 3D manipulation of a sort that has been supported in the past only by 3D geometric models.