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Elements of Neurogeometry

Functional Architectures of Vision

  • Jean Petitot

Part of the Lecture Notes in Morphogenesis book series (LECTMORPH)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Jean Petitot
    Pages 1-20
  3. Jean Petitot
    Pages 21-43
  4. Jean Petitot
    Pages 347-366
  5. Back Matter
    Pages 367-379

About this book

Introduction

This book describes several mathematical models of the primary visual cortex, referring them to a vast ensemble of experimental data and putting forward an original geometrical model for its functional architecture, that is, the highly specific organization of its neural connections. The book spells out the geometrical algorithms implemented by this functional architecture, or put another way, the “neurogeometry” immanent in visual perception. Focusing on the neural origins of our spatial representations, it demonstrates three things: firstly, the way the visual neurons filter the optical signal is closely related to a wavelet analysis; secondly, the contact structure of the 1-jets of the curves in the plane (the retinal plane here) is implemented by the cortical functional architecture; and lastly, the visual algorithms for integrating contours from what may be rather incomplete sensory data can be modelled by the sub-Riemannian geometry associated with this contact structure.

As such, it provides readers with the first systematic interpretation of a number of important neurophysiological observations in a well-defined mathematical framework. The book’s neuromathematical exploration appeals to graduate students and researchers in integrative-functional-cognitive neuroscience with a good mathematical background, as well as those in applied mathematics with an interest in neurophysiology.

Keywords

Functional architecture Association field Helmholtz equation Contact structure Fibre bundle Gaussian field Geodesic Gestalt Heisenberg group Frobenius integrability Legendrian lift Orientation (hyper) column Parallel transport Pinwheel Receptive profile Sub-Riemannian geometry Transversality Universal unfolding of singularity Wavelet

Authors and affiliations

  • Jean Petitot
    • 1
  1. 1.CAMS, EHESSParisFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-65591-8
  • Copyright Information Springer International Publishing AG 2017
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-65589-5
  • Online ISBN 978-3-319-65591-8
  • Series Print ISSN 2195-1934
  • Series Online ISSN 2195-1942
  • Buy this book on publisher's site
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