Approximating the Skeleton for Fine-to-Coarse Shape Representation

A method to generate a hierarchical skeleton structure is presented. The curve skeleton of a 3D object is used, where each voxel is labeled with the radius of the associated ball, i.e., with its distance from the complement of the object. Polygonal approximation is accomplished on all skeleton branches represented in a 4D space, where the coordinates are the (x,y,z) coordinates plus the radius r associated with each skeleton voxel. In this way, skeleton branches are divided into geometrically straight line segments, whose voxels are characterized by either constant or linearly increasing/decreasing radius. By increasing the threshold used for polygonal approximation the hierarchical skeleton structure is generated, which allows the user to get a fine-to-coarse shape representation.