Medical imaging is an area where deformable surfaces are presently receiving much attention [ 13 ]. There are many applications requiring segmentation of complex shapes from image or volumetric data.
There has been much recent interest in shapes with non-trivial topology in computer vision in general and in deformable surfaces in particular. One approach seeks to blend together parts consisting of simple tensor product patches [ 3 ]. A more automatic approach was presented by McInerney [ 12 ] who uses a parallel 2D data structure to achieve a topologically adaptable snake. Related work includes that of Casselles et al [ 3 ] who proposed geodesic active contours based on a level set approach.
In the graphics community there is considerable interest in building models from range scanner data. Recent advances in fusion algorithms allow the creation of detailed million polygon meshes and there is much interest in reducing the amount of information by using higher order surfaces. Work has tended to go down the route of manual seeding with tensor product patches [ 4 , 9 ].
Finally we note that the importance of volumetric representations for range data has been highlighted by recent work in range data fusion [ 8 ]. This volumetric approach is also followed in this paper in order to get a suitable potential for fast computation.
Andrew Stoddart