  One fascinating aspect of the brain is its ability to process information in
a fast and reliable manner. The functional architecture is thought to play a
central role in this task, by encoding efficiently complex stimuli and
facilitating higher level processing. In the early visual cortex of higher
mammals, information is processed within functional maps whose layout is
thought to underlie visual perception. The possible principles underlying the
topology of the different maps, as well as the role of a specific functional
architecture on information processing, is however poorly understood. We
demonstrate mathematically here that two natural principles, local exhaustivity
of representation and parsimony, would constrain the orientation and spatial
frequency maps to display co-located singularities around which the orientation
is organized as a pinwheel and spatial frequency as a dipole. This observation
is perfectly in line with new optical imaging data on the cat visual cortex we
analyze in a companion paper. Here we further focus on the theoretical
implications of this structure. Using a computational model, we show that this
architecture allows a trade-off in the local perception of orientation and
spatial frequency, but this would occur for sharper selectivity than the tuning
width reported in the literature. We therefore re-examined physiological data
and show that indeed the spatial frequency selectivity substantially sharpens
near maps singularities, bringing to the prediction that the system tends to
optimize balanced detection between different attributes. These results shed
new light on the principles at play in the emergence of functional architecture
of cortical maps, as well as their potential role in processing information.
