Deformable models represent a useful approach to approximate objects from collected data points. We propose to augment the basic approaches designed to handle mostly compact objects or objects of known topology.
Our approach can fit simultaneously more than one curve or surface to approximate multiple topologically complex objects by using ( 1) the residual data points, (2) the badly fitting parts of the approximating surface, and (3) appropriate Boolean operations. In 2-D, B-snakes [3] are used to approximate each object (pattern). In 3-D, an analytical surface representation, based on the elements detected, is presented. The global representation of a 3-D object, in terms of elements and their connection, takes the form of B-spline and Bézier surfaces. A Bézier surface is used to connect different elements, and the connecting surface itself conforms to the data points nearby through energy minimization. This way, a G 1 continuity surface is achieved for the underlying 3-D object.
We present experiments on synthetic and real data in 2-D and 3-D. In these experiments, multiple complex patterns and objects with through holes are segmented. The system proceeds automatically without human interaction or any prior knowledge of the topology of the underlying object.