Theory of spatial position and spatial frequency relations in the receptive fields of simple cells in the visual cortex.

Striate cells showing linear spatial summation obey very general mathematical inequalities relating the size of their receptive fields to the corresponding spatial frequency and orientation tuning characteristics. The experimental data show that, in the preferred direction of stimulus motion, the spatial response profiles of cells in the simple family are well described by the mathematical form of Gabor elementary signals. The product of the uncertainties in signaling spatial position (delta x) and spatial frequency (delta f) has, therefore, a theoretical minimum value of delta x delta f = 1/2. We examine the implications that these conclusions have for the relationship between the spatial response profiles of simple cells and the characteristics of their spatial frequency tuning curves. Examples of the spatial frequency tuning curves and their associated spatial response profiles are discussed and illustrated. The advantages for the operation of the visual system of different relationships between the spatial response profiles and the characteristics of the spatial frequency tuning curves are examined. Two examples are discussed in detail, one system having a constant receptive field size and the other a constant bandwidth.