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Lecture Notes in Morphogenesis

Elements of Neurogeometry

Functional Architectures of Vision

Authors: Petitot, Jean

  • Illustrates the fascinating interactions between mathematics and neuroscience 
  • Describes geometrical models of the functional architecture of the visual cortex
  • Presents a variety of examples
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eBook 91,62 €
price for France (gross)
  • ISBN 978-3-319-65591-8
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 116,04 €
price for France (gross)
  • ISBN 978-3-319-65589-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

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.

About the authors

Jean Petitot specializes in mathematical modeling in  the cognitive sciences. Former student and teacher at the École Polytechnique, he is currently Professor at the Mathematics Center of the École des Hautes Études en Sciences Sociales in Paris. He is a member of the International Academy of Philosophy of Science.  Having worked for several years on the theory of singularities in differential geometry, he was one of the first to become interested in René Thom's morphodynamic models of visual perception  and phonetics in the 1970s.

He is the author of several books, such as Neurogeomtrie de la vision (École Polytechnique, Ellipses, 2008), ‘Physique du Sen’ (Centre Nationale de la Recherche Scientifique, 1992),  ‘Morphogenèse du Sens’ (Presses Universitaires de France, 1985;  English transl. Peter Lang, 2004), five other books, and more than 300 papers. He is also co-editor of ‘Constituting Objectivity’ (Springer, 2009), ‘Neurogeometry and Visual Perception’ (J. of Physiology-Paris, 2003), ‘Au Nom du Sens’, a tribute to Umberto Eco (Grasset, 2000), ‘Naturalizing Phenomenology’ (Stanford University Press, 1999), ‘Logos et Théorie des Catastrophes’, a tribute to René Thom, (Patiño, 1988). 

Table of contents (6 chapters)

  • Preface

    Petitot, Jean

    Pages 1-20

    Preview Buy Chapter 29,94 €
  • Introduction

    Petitot, Jean

    Pages 21-43

    Preview Buy Chapter 29,94 €
  • Receptive Fields and Profiles, and Wavelet Analysis

    Petitot, Jean

    Pages 45-111

    Preview Buy Chapter 29,94 €
  • Functional Architecture I: The Pinwheels of V1

    Petitot, Jean

    Pages 113-273

    Preview Buy Chapter 29,94 €
  • Functional Architectures II: Horizontal Connections and Contact Structure

    Petitot, Jean

    Pages 275-346

    Preview Buy Chapter 29,94 €

Buy this book

eBook 91,62 €
price for France (gross)
  • ISBN 978-3-319-65591-8
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 116,04 €
price for France (gross)
  • ISBN 978-3-319-65589-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Elements of Neurogeometry
Book Subtitle
Functional Architectures of Vision
Authors
Series Title
Lecture Notes in Morphogenesis
Copyright
2017
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG
eBook ISBN
978-3-319-65591-8
DOI
10.1007/978-3-319-65591-8
Hardcover ISBN
978-3-319-65589-5
Series ISSN
2195-1934
Edition Number
1
Number of Pages
XV, 379
Number of Illustrations and Tables
71 b/w illustrations, 186 illustrations in colour
Additional Information
Original French edition published by Les Éditions de l’École Polytechnique, Palaiseau, 2008
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