Curved feature metrics in models of visual cortex

We study the relation between maps of a high-dimensional stimulus manifold onto an essentially two-dimensional cortical area and low-dimensional maps of stimulus features such as centroid position, orientation, spatial frequency, etc. Whereas the former safely can be represented in a Euclidean space, the latter are shown to require a Riemannian metric in order to reach qualitatively similar stationary structures under a standard learning algorithm. We show that the non-Euclidean framework allows for a tentative explanation of the presence of the so-called "pinwheels" in feature maps and compare maps obtained numerically in the at high-dimensional maps and in the curved low-dimensional case. c 2002 Published by Elsevier Science B.V.

• Type: Journal
• Year: 2002
• Where: IJON
• Authors: Norbert Michael Mayer, J. Michael Herrmann, Theo Geisel
• Keywords: IJON 2002, Low-dimensional Maps, Similar Stationary Structures, Two-dimensional Cortical Area