ABSTRACT
The primary visual cortex (V1) is the first cortical area to receive visual information transmitted by ganglion cells of the retina via the lateral geniculate nucleus (LGN) of the thalmus to the back of the brain; see figure 11.1. A fundamental property of the functional architecture of V1 is an orderly retinotopic mapping of the visual field onto the surface of cortex, with the left and right halves of visual field mapped onto the right and left cortices respectively. Except close to the fovea (centre of the visual field), this map can be approximated by the complex logarithm; see figure 11.2. Let rR = {rR, θR} be a point in the visual field represented in polar coordinates and let r = {x, y} be the corresponding point in the cortex given in Cartesian coordinates. Under the retino-cortical map, r = {log rR, θR}. Evidently, if we introduce the complex representation of rR, zR = rReiθR then z = log zR = log rR + iθR = x + iy generates the complex cortical representation. One of the interesting properties of the retino-cortical map is that the action of rotations and dilatations in the visual field correspond to translations in the x and y directions, respectively, in the cortex.
