Abstract

Abstract-The spatial inhomogeneity of the retino-striate syslem is summarized by the vector cortical magnification factor. The logarithm of retinal eccentricity provides a good fit to the integrated cortical magnification factor. Under the assumption that the cortical map is analytic (conformal), this implies that a complex logarithmic function of retinal coordinates describes the two-dimensional structure of the cortical representation of a visual stimulus. This hypothesis is in good agreement with the measured global structure of rhesus, squirrel, and owl monkey retino-striate mappings, as well as that of the upper visual field of the cat. The geometric structure of the local hypercolumnar unit of striate cortex may also be characterized in terms of the complex Logarithmic mapping: thus. the retino-cortical system may be thought of as a concatenated cornplex logarithmic mapping. A simple developmental mechanism is capable of construct-ing a map of this form, and the general mathematical properties of conformal mappings allow some Insight into the nature of the minimal coding requirements which must be specified to encode a neural map. Complex logarithmic mapping yields a cortical "Gestalt " which is pseudo-invariant to size, rotation. and projection scaling: these symmetries. for a given fixation point. result in a linear shift of an invariant

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