Parts of Visual Form : Computational

| Underlying recognition is an organization of objects and their parts into classes and hierarchies. A representation of parts for recognition requires that they be invariant to rigid transformations, robust in the presence of occlusions, stable with changes in viewing geometry, and be arranged in a hierarchy. These constraints are captured in a general framework using notions of a part-line and a partitioning scheme. A proposed general principle of \form from function" motivates a particular partitioning scheme involving two types of parts, neck-based and limb-based, whose psychophysical relevance was demonstrated in 39]. Neck-based parts arise from narrowings in shape, or the local minima in distance between two points on the boundary, while limb-based parts arise from a pair of negative curvature minima which have \co-circular" tangents. In this paper , we present computational support for the limb-based and neck-based parts by showing that they are invariant, robust, stable and yield a hierarchy of parts. Examples illustrate that the resulting decompositions are robust in the presense of occlusion and clutter for a range of man-made and natural objects, and lead to natural and intuitive parts which can be used for recognition.