Surface approximation of complex multipart objects

Deformable models can be widely used to approximate objects from collected datapoints, but most algorithms can only handle geometrically and topologically simple objects. They are inadequate for objects with deep cavities or multipart objects, or when more than one object is in the scene. We propose an approach which can fit simultaneously more than one surface to approximate multiple topologically complex objects. We use (1) the residual data points, (2) the bad parts of the fitting surface, and (3) appropriate Boolean operations. We then present an algorithm to construct an analytical surface representation, based on the elements detected. The global representation of an object, in terms of elements and their connection, takes the form of B-spline and Bezier surfaces. A Bezier surface is employed to connect different elements, and the connecting surface itself conforms to the data points nearby through energy minimization. This way, we achieve G¹ continuity surfaces even for multipart objects. We present results on complex synthetic and real data. The system proceeds automatically without human interaction or any prior knowledge on the topology of the underlying object