Acquisition of global topology for 3D objects with local competition

We present a surface model for unsupervised learning of spatial shapes, which consists of a set of planar subnets, each trained by Kohonen's map. The global convergence of this network can be easily guaranteed. The connection in the network is determined by simple local calculations. Simulations on learning of topologically nontrivial objects such as those of higher genus and oriented ones are carried out successfully. The method can then be applied to adaptive vector quantization of 3D objects and learning of their topology.