Three-dimensional object representation based on the largest convex patches method

We introduce a representation of the three-dimensional (3-D) shape of objects which describes object shape through configurations of interrelated parts and accounts for their surface and volumetric properties as well. The decomposition into constituent parts is obtained by an earlier developed surfaced based method that uses the largest locally convex patches (LCP) and the largest nonconvex patches to characterize and define part boundaries. This characterization of the part boundary provides the basis for assigning to each part a simple volumetric primitive that preserves its surface type. We propose a heuristics for choosing the volumetric description motivated by a theorem from differential geometry which classifies surface points (elliptic, hyperbolic, parabolic, plane) through the type of the parabolloid that approximates a finite environment. This provides a natural way of relating surface properties of the boundary-based decomposition to volumetric properties of the primitive-based part description. A further decomposition into subparts and the computation of associated features on an 'if needed' basis allow us to account for structural details which appear to be closely related to the use of the object in actions. We present examples of the shape descriptions of various machine tools.