Local to Global Normalization Dynamic by Nonlinear Local Interactions

Abstract

Here, I present a novel method for normalizing a finite set of numbers, which is studied by the domain of biological vision. Normalizing in this context means searching the maximum and minimum number in a set and then rescaling all numbers such that they fit into a numerical interval. My method computes the minimum and maximum number by two pseudo-diffusion processes in separate diffusion layers. Activity of these layers feed into a third layer for performing the rescaling operation. The dynamic of the network is richer than merely performing a rescaling of its input, and reveals phenomena like contrast detection, contrast enhancement, and a transient compression of the numerical range of the input. Apart from presenting computer simulations, some properties of the diffusion operators and the network are analyzed mathematically. Furthermore, a method is proposed for to freeze the model's state when adaptation is observed.