Orientation Columns from First Principles

Abstract

The input to primary visual cortex is embedded in a high dimensional feature space whose dimensions include position in visual space, preferred orientation, ocular dominance etc. Since all cells in a column with axis perpendicular to the cortical surface have approximately the same properties [4], this space is effectively mapped on a two-dimensional space, the cortical plane. This dimension reduction leads to complex maps which so far have evaded intuitive understanding. We show that their most salient features can be understood from a few basic design principles, in particular, local correlation, isotropy and homogeneity. These principles can be defined most easily in the Fourier domain where they correspond to a power spectrum which has a rather simple annulus-like structure. After inverse Fourier transformation, we obtain maps of orientation column structures which are very similar to the experimentally observed orientation column maps of the cat. We show this by comparison with maps which were obtained by optical imaging methods. We expect that many of the models which have been developed to explain the mapping of the preferred orientations (e.g., [5, 7, 6, 8, 10, 11, 13]) can be subsumed under our approach.