Pinwheel organization maximizes coverage uniformity of
cortical orientation maps: An information-theoretic analysis

Silvio P. Sabatini
DIBE - University of Genoa, Via Opera Pia 11a, 16145 Genova, ITALY

The way in which neighboring receptive fields overlap depends on their shape and
size, and on their relative disposition as dictated by the orientation map. This overlap
affects the local representation of visual information, as can be quantified
considering the cortical point image. In order to have the same representation
and computation capabilities across the visual space, it is necessary to have an
uniform allocation of cells of different orientation preference for each point
(cf. the uniform coverage criterium of N.V.~Swindale).
One should prefer those orientation maps that exhibit average invariance
characteristics of the autocorrelation of cortical activity, thus maximizing
spatial uncertainty. In quantitative terms, we evaluate directional mutual information
at each cortical locations, and use it as a measure of coverage uniformity.
The (an-)isotropies in mutual information become figures of merit of real
orientation maps or act as constraints for the design ofartificial orientation maps.
This criterium applied to pinwheel orientation maps (experimental data from
litterature) reveals good coverage uniformity except at vortices and other areas of
high magnitude of orientation gradient. These violations of uniformity are minimized
since singular points are characterized by low orientation tuning strength.

The same criterium is used to verify the optimal relationship between the average
size of the cortical point image and the average hypercolumn width, for different
S/N ratios.