TOWARD A THEORY OF THE STRIATE CORTEX

We explore the hypothesis that linear cortical neurons are concerned w ith building a particular type of representation of the visual world-o ne that not only preserves the information and the efficiency achieved by the retina, but in addition preserves spatial relationships in the input-both in the plane of vision and in the depth dimension. Focusin g on the linear cortical cells, we classify all transforms having thes e properties. They are given by representations of the scaling and tra nslation group and turn out to be labeled by rational numbers '(p+q)/p ' (p, q integers). Any given (p,q) predicts a set of receptive fields that comes at different spatial locations and scales (sizes) with a ba ndwidth of log(2)[(p+q)/p] octaves and, most interestingly, with a div ersity of 'q' cell varieties. The bandwidth affects the trade-off betw een preservation of planar and depth relations and, we think, should b e selected to match structures in natural scenes. For bandwidths betwe en 1 and 2 octaves, which are the ones we feel provide the best matchi ng, we find for each scale a minimum of two distinct cell types that r eside next to each other and in phase quadrature, that is, differ by 9 0 degrees in the phases of their receptive fields, as are found in the cortex, they resemble the ''even-symmetric'' and ''odd-symmetric'' si mple cells in special cases. An interesting consequence of the represe ntations presented here is that the pattern of activation in the cells in response to a translation or scaling of an object remains the same but merely shifts its locus from one group of cells to another. This work also provides a new understanding of color coding changes from th e retina to the cortex.