We consider a correlation-based model for orientation map formation
proposed by Miller (1994)
and study the formation mathematically.
We perform the Fourier transform and compute the principal component
of the model.
With our analysis, the roles of functions are clarified
and the result indicates that the developed orientation maps have
the following properties.
(1) It develops oriented receptive fields;
(2) Preferred orientations smoothly change on the cortical surface;
(3) The periodicity of preferred orientations does not appear;
(4) The periodicity of phases appears;
(5) Singular points appear irregularly on the cortical surface.
Our analytical results are justified by computer simulations.