Shape representations for 3D objects are discussed in terms of their primitive elements which are geometrically and/or topologically combined to form the solid bodies. For a given representation, the coordinate system may be viewer-centred or object-centred. In the first case locations in 3D space are specified with respect to an origin at the viewing position, and in the second case with respect to a reference point and axes from the body, e.g. the centre of mass, and axes aligned with the minimum bounding cuboid of the object. It is relevant to note that in computer graphics, representations are object-centred and most of the work is spent in transforming this into a viewer-centred representation for display purposes. In computer vision, the reverse is true; most of the work is devoted to matching a viewer centred 2.5D sketch or some other scene description of the object to an object-centred description stored on the database.

Although there are several other representations which are common in computer vision systems, including spatial occupancy grids ( voxels ), oct-trees, moment invariant representations and extended Gaussian iamges, we shall concentrate here on three common types of primitive based model. These are volumetric, surface (B-rep) and wire-frame models.

Volumetric representations

Surface boundary representations (B-Reps)

Wire frame representations