Part decomposition and description of 3D shapes

Addresses the problem of obtaining natural descriptions of 3D shapes. The authors present one of the first attempts to address the description of 3D compound objects, where the parts are connected smoothly. The input the authors consider is either complete 3D data or range data from a single view. The authors suggest a volumetric graph representation of the object, where the nodes represent individual parts and the edges represent connectivity information. The authors suggest the use of properties of the parabolic curves for performing the part decomposition. The authors consider parts with tubular structure with a straight or curved axis. They are also interested in the internal description of the parts. The authors study two classes of shapes, namely straight homogeneous GCs, and planar right constant GCs. The authors suggest the use of properties of the parabolic curves for recovering natural descriptions of these classes in terms of their cross sections and axes