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

The retino-cortical visual pathway is retinotopically organized: Neighborhood 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. This is referred to as M-scaling . As a consequence, and under simplifying assumptions, the mapping of retinal to cortical location follows a logarithmic function along a radius, as was already shown by Schwartz (1980). The M -scaling function has been determined for many visual tasks. It is standardly characterized by its foveal threshold value, together with the eccentricity where that value doubles, called E 2 . The cortical location function, on the other hand, is commonly specified by parameters that are separately determined from the empirical findings. Here I aim to bring together the psychophysical and neuroscience traditions and specify the cortical equations in terms of the parameters customary in psychophysics. The equations allow easy switching between M -scaling and cortical mapping. A new parameter, d 2 , is proposed to describe the cortical map, as a cortical counterpart to E 2 . The resulting cortical-location function is then applied to data from a number of fMRI studies. One pitfall is discussed and spelt out as a set of equations, namely the common myth that a pure logarithmic function gives an adequate map: The popular omission of a constant term renders the equations absurd in and around the retinotopic center. The correct equations are finally extended to describe the cortical map of Bouma9s law on visual crowding. The result contradicts recent suggestions that critical crowding distance corresponds to constant cortical distance.