A mathematical analysis of a correlation based model for the orientation map formation

Abstract

We consider a correlation based model for the orientation map formation proposed by Miller[3] and study the formation mathematically. We perform the Fourier transform of the model and we observe that the model has the following properties. (1) It develops oriented receptive fields; (2) These oriented receptive fields are arranged in order, and ordered orientation columns are developed; (3) The periodicity of orientations on the cortical surface lacks; (4) The periodicity of phases appears; (5) Singular points appear irregularly on the cortical surface. Our analytical results are justified by computer simulations.