Lecture Notes in Morphogenesis

Neuromathematics of Vision

Editors: Citti, Giovanna, Sarti, Alessandro (Eds.)

  • Includes helpful algorithms for applications in computer vision and bioengineering
  • Rigorous mathematical approach
  • Written by experts in the field
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Hardcover $129.00
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  • Due: October 21, 2016
  • ISBN 978-3-662-51005-6
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About this book

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.

Reviews

“This is one of the best books on cortical sensory modeling with the use of partial differential equations, and statistical reasoning included in multidimensional strategies. … I highly recommend this book as a primary reference to vision scientists, students in vision, postdoctoral fellows and senior scientists in the field of cerebral cortical modeling.” (Joseph J. Grenier, Amazon.com, June, 2015)

“This book takes the novel approach of considering the geometry of image processing by the visual cortex system of the brain. … This book is an essential read for anyone conducting serious research in the field of neurogeometry of visual perception.” (R. Goldberg, Computing Reviews, August, 2014)

Table of contents (8 chapters)

  • Landmarks for Neurogeometry

    Petitot, Jean

    Pages 1-85

  • Shape, Shading, Brain and Awareness

    Koenderink, Jan (et al.)

    Pages 87-106

  • Why Shading Matters along Contours

    Kunsberg, Benjamin (et al.)

    Pages 107-129

  • From Functional Architectures to Percepts: A Neuromathematical Approach

    Citti, Giovanna (et al.)

    Pages 131-171

  • Cuspless Sub-Riemannian Geodesics within the Euclidean Motion Group SE(d)

    Duits, Remco (et al.)

    Pages 173-215

Buy this book

eBook $99.00
price for USA (gross)
  • ISBN 978-3-642-34444-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $129.00
price for USA
  • ISBN 978-3-642-34443-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $129.00
price for USA
  • Customers within the U.S. and Canada please contact Customer Service at 1-800-777-4643, Latin America please contact us at +1-212-460-1500 (Weekdays 8:30am – 5:30pm ET) to place your order.
  • Due: October 21, 2016
  • ISBN 978-3-662-51005-6
  • Free shipping for individuals worldwide
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Neuromathematics of Vision
Editors
  • Giovanna Citti
  • Alessandro Sarti
Series Title
Lecture Notes in Morphogenesis
Copyright
2014
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-34444-2
DOI
10.1007/978-3-642-34444-2
Hardcover ISBN
978-3-642-34443-5
Softcover ISBN
978-3-662-51005-6
Series ISSN
2195-1934
Edition Number
1
Number of Pages
XVIII, 367
Number of Illustrations and Tables
45 b/w illustrations, 69 illustrations in colour
Topics