On the cortical mapping function -- visual space, cortical space, and crowding

Abstract

The retino-cortical visual pathway is retinotopically organized: Neighbourhood relationships on the retina are preserved in the mapping to the cortex. Size relationships in that mapping are also highly regular: The size of a patch in the visual field that maps onto a cortical patch of fixed size follows, along any radius and in a wide range, simply a linear function with retinal eccentricity. As a consequence, and under simplifying assumptions, the mapping of retinal to cortical locations follows a logarithmic function along that radius. While this has already been shown by Fischer (1973), the link between the linear function - which describes the local behaviour by the cortical magnification factor M - and the logarithmic location function for the global behaviour, has never been made fully explicit. The present paper provides such a link as a set of ready-to-use equations using Levi and Kleins E2 nomenclature, and examples for their validity and applicability in the retinotopic mapping literature are discussed. The equations allow estimating M in the retinotopic centre and values thus derived from the literature are provided. A new structural parameter, d2, is proposed to characterize the cortical map, as a cortical counterpart to E2, and typical values for it are given. One pitfall is discussed and spelt out as a set of equations, namely the common myth that a pure logarithmic function will give an adequate map: The popular omission of a constant term renders the equations ill defined in, and around, the retinotopic centre. The correct equations are finally extended to describe the cortical map of Boumas law on visual crowding. The result contradicts recent suggestions that critical crowding distance corresponds to a constant cortical distance.