A Mathematical Analysis of a Correlation Based Model for the Orientation Map Formation

  • Authors:

  • Tadashi Yamazaki

  • Affiliations:

  • -

  • Venue:
  • ICANN '01 Proceedings of the International Conference on Artificial Neural Networks
  • Year:
  • 2001

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Abstract

We consider a correlation based model for the orientation map formation proposed by Miller[3] and study the formation mathematically. We perform the Fourier transform of the model and we observe that the model has the following properties. (1) It develops oriented receptive fields; (2) These oriented receptive fields are arranged in order, and ordered orientation columns are developed; (3) The periodicity of orientations on the cortical surface lacks; (4) The periodicity of phases appears; (5) Singular points appear irregularly on the cortical surface. Our analytical results are justified by computer simulations.