Toward a theory of the striate cortex

• Authors: Zhaoping Li;Joseph J. Atick
• Venue: Neural Computation
• Year: 1994

We explore the hypothesis that linear cortical neurons areconcerned with building a particular type of representation of thevisual world---one that not only preserves the information and theefficiency achieved by the retina, but in addition preservesspatial relationships in the input---both in the plane of visionand in the depth dimension. Focusing on the linear corticalcells, we classify all transforms having these properties. They aregiven by representations of the scaling and translation group andturn 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 spatiallocations and scales (sizes) with a bandwidth of log2[(p + q)/p] octaves and, most interestingly,with a diversity of 'q' cell varieties. The bandwidthaffects the trade-off between preservation of planar and depthrelations and, we think, should be selected to match structures innatural scenes. For bandwidths between 1 and 2 octaves, which arethe ones we feel provide the best matching, we find for each scalea minimum of two distinct cell types that reside next to each otherand in phase quadrature, that is, differ by 90° in the phasesof their receptive fields, as are found in the cortex, theyresemble the "even-symmetric" and "odd-symmetric" simple cells inspecial cases. An interesting consequence of the representationspresented here is that the pattern of activation in the cells inresponse to a translation or scaling of an object remains the samebut merely shifts its locus from one group of cells to another.This work also provides a new understanding of color coding changesfrom the retina to the cortex.