Geometric versus Volumetric 3D Models

The models subjected to 3D morphing can be described either by geometric primitives or by volumes (volumetric data sets). Each representation requires different morphing algorithms. This dichotomy parallels the separation of 2D morphing techniques into those that operate on raster images [21] [2] [6], and those that assume vector-based image representations [16]. We believe that volume-based descriptions are more appropriate for 3D morphing for the following reasons:

• The quality and applicability of geometric 3D morphing techniques [12] is highly dependent on the models' geometric primitives and their topological properties. Volume morphing is independent of object geometries and topologies, and thus imposes no such restrictions on the objects which can be successfully morphed.
• Volume morphing may be applied to objects represented either by geometric primitives or by volumes. Geometric descriptions can be easily converted to high-quality volume representations, as we will see in section 2. The reverse process produces topologically complex objects, usually inappropriate for geometric morphing.