Neuromathematics of Vision

  • Giovanna Citti
  • Alessandro Sarti
Part of the Lecture Notes in Morphogenesis book series (LECTMORPH)

Table of contents

  1. Front Matter
    Pages 1-15
  2. Jean Petitot
    Pages 1-85
  3. Jan Koenderink, Andrea van Doorn
    Pages 87-106
  4. Benjamin Kunsberg, Steven W. Zucker
    Pages 107-129
  5. Giovanna Citti, Alessandro Sarti
    Pages 131-171
  6. Remco Duits, Arpan Ghosh, Tom Dela Haije, Yuri Sachkov
    Pages 173-215
  7. José Lezama, Samy Blusseau, Jean-Michel Morel, Gregory Randall, Rafael Grompone von Gioi
    Pages 217-242
  8. Back Matter
    Pages 367-367

About this book

Introduction

This book is devoted to the study of the functional architecture of the visual cortex. Its geometrical structure is the differential geometry of the connectivity between neural cells. This connectivity is building and  shaping the hidden brain structures underlying visual perception. The story of the problem runs over the last 30 years, since the discovery of Hubel and Wiesel of the modular structure of the primary visual cortex, and slowly cams towards a theoretical understanding of the experimental data on what we now know as functional architecture of the primary visual cortex.
Experimental data comes from several domains:  neurophysiology, phenomenology of perception and neurocognitive imaging. Imaging techniques like functional MRI and diffusion tensor MRI allow to deepen the study of cortical structures.  Due to this variety of experimental data, neuromathematematics deals with modelling  both cortical structures and perceptual spaces.
From the mathematical point of view, neuromathematical call for new instruments of pure mathematics: sub-Riemannian geometry models horizontal connectivity, harmonic analysis in non commutative groups allows to understand pinwheels structure, as well as non-linear dimensionality reduction is at the base of many neural morphologies and  possibly of the emergence of  perceptual units. But  at the center of the  neurogeometry is the problem of harmonizing contemporary mathematical instruments with neurophysiological findings and phenomenological experiments in an unitary science of vision.
The contributions to this book come from the very founders of the discipline.

Keywords

Algorithms for Computer Vision Connectivity Structure of the Visual Cortex Functional Architecture of the Visual Cortex Geometrical Models of Cortex Functionality Gestalt Theory Mathematical Modeling of Cognition Neural origin of Spatial Representations Neuromathematics Neuroscience Rigorous Mathematics of Neuroscience

Editors and affiliations

  • Giovanna Citti
    • 1
  • Alessandro Sarti
    • 2
  1. 1.Dipartimento di MatematicaUniversità di BolognaBolognaItaly
  2. 2.CAMS Center for MathematicsCNRS-EHESSParisFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-34444-2
  • Copyright Information Springer-Verlag Berlin Heidelberg 2014
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-34443-5
  • Online ISBN 978-3-642-34444-2
  • Series Print ISSN 2195-1934
  • Series Online ISSN 2195-1942
  • About this book