Universal representation of image functions by the Sprecher construction

This paper proposes a procedure for representing image functions by a computation in two layers. It is recalled that the general function representation needs more layers than two, using the Stone-Weierstrass theorem for approximation in three layers, and the Kolmogorov theorem for representation in four layers. For achieving representation in two layers only, the requirement on a continuous representation has to removed. The Sprecher construction presented here is a general procedure for yielding such a representation in two layers. It can be used to compress images, to represent pixels and their neighborhoods directly, or to represent image operators.