Pinwheel Stability in a Non-Euclidean Model of Pattern Formation in the Visual Cortex

Norbert Michael Mayer, J. Michael Herrmann, Minoru Asada, Theo Geisel

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

The structure of neural maps in the primary visual cortex arises from the problem of representing a high-dimensional stimulus manifold on an essentially two-dimensional piece of cortical tissue. In order to treat the problem theoretically, stimuli are usually represented by a set of features, such as centroid position, orientation, spatial frequency, phase {\it etc.} Inputs to the cortex are, however, activity distributions over afferent nerve fibers; {\it i.e}.,~they require, in principle, a description as high-dimensional vectors. We study the relation between high-dimensional maps, which can be assumed to rely on a Euclidean geometry, and low-dimensional feature maps, which need to be formulated in Riemannian space in order to represent high-dimensional maps to a good accuracy. We show numerically that the Riemannian framework allows for a suggestive explanation of the abundance of typical structural units (``pinwheels'') in feature maps emerging in the course of the adaptation process from an initially unstructured state.
Original languageEnglish
Pages (from-to)150-157
Number of pages8
JournalJournal of the korean physical society
Issue number1
Publication statusPublished - Jan 2007


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