  In this paper PREMONN (PREdictive MOdular Neural Networks) model/architecture
is generalized to functions of two variables and to non-Euclidean spaces. It is
presented in the context of 3D invariant shape recognition and texture
recognition. PREMONN uses local relation, it is modular and exhibits
incremental learning. The recognition process can start at any point on a shape
or texture, so a reference point is not needed. Its local relation
characteristic enables it to recognize shape and texture even in presence of
occlusion. The analysis is mainly mathematical. However, we present some
experimental results. The methods presented in this paper can be applied to
many problems such as gesture recognition, action recognition, dynamic texture
recognition etc.
