Visual cortex maps are optimized for uniform coverage

articles Mammalian primary visual cortex contains a single continuous representation of retinotopic visual space, on which orderly, periodic maps of several different visual stimulus properties are superimposed. These properties include ocular dominance and preferred orientation [1][2] These maps are often structurally related. For example, in macaque monkey These findings are consistent with earlier suggestions 4 that visual cortex maps develop according to a combination of continuity and completeness constraints, which act in opposition. The continuity constraint specifies that neighboring cortical locations should have similar receptive field properties, whereas the completeness constraint ensures that all combinations of the parameters represented in individual maps are distributed uniformly over visual space. A quantitative measure of completeness, known as coverage uniformity, or c′, has been devised 16 . It is calculated in the following way: for a given combination of features (for example, some unique combination of orientation, spatial frequency, eye and retinal location), the total neural response, A, in the cortex is calculated, taking into account the spatial structure of the maps of these properties, and the receptive field tuning widths of individual cortical units. Uniform coverage means that A should be independent of the specific feature combination chosen. It is convenient to define c′ as the standard deviation of A divided by its mean, taken over some representative set of stimuli. This makes it a dimensionless measure of 'noise' in the cortical representation of a particular feature space. If c′ = 0, coverage is completely uniform; larger values correspond to an increasingly noisy representation: for example, if c′ = 1, the standard deviation of the signal across the feature space is equal to the mean. The hypothesis that cortical maps are organized so as to optimize (that is, minimize) c′ was tested here by systematically perturbing the spatial relationships between maps of orientation, ocular dominance and spatial frequency obtained simultaneously in area 17 of the cat 13 to see whether c′ is at a local minimum. Two different methods were used to do this, both of which left continuity in the individual maps unchanged. In the first, the spatial relationships were altered by various combinations of flips (mirror inversions) about either the horizontal or vertical axes and/or 180°rotation (equivalent to a mirror inversion about one axis followed by a mirror inversion about the other). For three rectangular maps, there are a total of 16 transformations that disturb the point-to-point relationships between the maps in a unique way. (Note that some combinations of flips are equivalent: for example, flipping two of the maps about the vertical axis is equivalent to flipping just the third one.) The second method examined the possibility that map structure is close to a local optimum for coverage uniformity. To test this, a single map was displaced sideways by a given number of pixels relative to the other two, which remained fixed relative to each other. Coverage was then calculated for the region common to all three maps. This was done separately for each of the ocular dominance, spatial frequency and orientation maps, for a range of Cat visual cortex contains a topographic map of visual space, plus superimposed, spatially periodic maps of ocular dominance, spatial frequency and orientation. It is hypothesized that the layout of these maps is determined by two constraints: continuity or smooth mapping of stimulus properties across the cortical surface, and coverage uniformity or uniform representation of combinations of map features over visual space. Here we use a quantitative measure of coverage uniformity (c') to test the hypothesis that cortical maps are optimized for coverage. When we perturbed the spatial relationships between ocular dominance, spatial frequency and orientation maps obtained in single regions of cortex, we found that cortical maps are at a local minimum for c'. This suggests that coverage optimization is an important organizing principle governing cortical map development