  A compact analytic model is proposed to describe the combined orientation
preference (OP) and ocular dominance (OD) features of simple cells and their
layout in the primary visual cortex (V1). This model consists of three parts:
(i) an anisotropic Laplacian (AL) operator that represents the local neural
sensitivity to the orientation of visual inputs; (ii) a receptive field (RF)
operator that models the anisotropic spatial RF that projects to a given V1
cell over scales of a few tenths of a millimeter and combines with the AL
operator to give an overall OP operator; and (iii) a map that describes how the
parameters of these operators vary approximately periodically across V1. The
parameters of the proposed model maximize the neural response at a given OP
with an OP tuning curve fitted to experimental results. It is found that the
anisotropy of the AL operator does not significantly affect OP selectivity,
which is dominated by the RF anisotropy, consistent with Hubel and Wiesel's
original conclusions that orientation tuning width of V1 simple cell is
inversely related to the elongation of its RF. A simplified OP-OD map is then
constructed to describe the approximately periodic OP-OD structure of V1 in a
compact form. Specifically, the map is approximated by retaining its dominant
spatial Fourier coefficients, which are shown to suffice to reconstruct the
overall structure of the OP-OD map. This representation is a suitable form to
analyze observed maps compactly and to be used in neural field theory of V1.
Application to independently simulated V1 structures shows that observed
irregularities in the map correspond to a spread of dominant coefficients in a
circle in Fourier space.
