Biological Cybernetics

, Volume 98, Issue 1, pp 33–48 | Cite as

The symplectic structure of the primary visual cortex

Original Paper

Abstract

We propose to model the functional architecture of the primary visual cortex V1 as a principal fiber bundle where the two-dimensional retinal plane is the base manifold and the secondary variables of orientation and scale constitute the vertical fibers over each point as a rotation–dilation group. The total space is endowed with a natural symplectic structure neurally implemented by long range horizontal connections. The model shows what could be the deep structure for both boundary and figure completion and for morphological structures, such as the medial axis of a shape.

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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  • Alessandro Sarti
    • 1
  • Giovanna Citti
    • 2
  • Jean Petitot
    • 3
  1. 1.Department of Electronics, Information and SystemsUniversity of BolognaBolognaItaly
  2. 2.Department of MathematicsUniversity of BolognaBolognaItaly
  3. 3.EHESS and CREAEcole PolytechniqueParisFrance

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