Towards a theory of the striate cortex资料.pdfVIP

Towards a Theory of the Striate Cortex1 Published in Neural Computation, Vol 6, number 1, January 1994, p127-146 Zhaoping Li and Joseph J. Atick The Rockefeller University 1230 York Avenue New York, NY 10021, USA Abstract We explore the hypothesis that linear cortical neurons are concerned with building a particular type of representation of the visual world — one which 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 di- mension. Focusing on the linearcortical cells, we classify all transforms having these properties. They are given by representations of the scaling and translation 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 which come at different spatial locations and scales (sizes) with a bandwidth of 2 p q =p℄ octaves, and, most interestingly, with q ’ cell varieties. The bandwidth affects the trade-off between preserva- a diversity of ‘ tion of planar and depth relations, and, we think, should be selected to match struc- tures in natural scenes. For bandwidths between and octaves, which are the ones we feel provide the best matching, we find for each scale a minimum of two distinct cell types that reside next to each other and in phase quadrature, i.e., differ by in the phases of their receptive fields, as are found in the cortex, they resemble the “even-symmetric” and “odd-symmetric” simple cells in special