Laboratory for Neural Modeling, Frontier Research Program, The Institute of Physical and Chemical Research (RIKEN), 2-1 Hirosawa, Wako, Saitama 351-01, Japan
(Received May 13, 1996; Accepted June 28, 1996)
Keywords: Visual Cortex, Cortical Map, Point Singularity, Klein Bottle
Abstract. It has been reported that in the primary visual cortex, there are maps with respect to the neutron's optimal response parameters to light stimuli. The objective of the present paper is to present a new mathematical approach to the understanding of topological properties of visual cortical maps. I postulate that the optimal stimulus parameters are arranged continuously almost everywhere on the visual cortical surface. Using this assumption and the fact that neutron's optimal patterns of response to light stimuli presented in the visual space (receptive fields, RFs) can be given by the Gabor function, the space spanned by the optimal stimulus parameters is examined on the basis of topology theory, and possible point singularities and discontinuity lines over the visual cortex are derived.