Overview
- Includes helpful algorithms for applications in computer vision and bioengineering
- Rigorous mathematical approach
- Written by experts in the field
Part of the book series: Lecture Notes in Morphogenesis (LECTMORPH)
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Table of contents (8 chapters)
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Front Matter
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Back Matter
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
About this book
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)Editors and Affiliations
Bibliographic Information
Book Title: Neuromathematics of Vision
Editors: Giovanna Citti, Alessandro Sarti
Series Title: Lecture Notes in Morphogenesis
DOI: https://doi.org/10.1007/978-3-642-34444-2
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2014
Hardcover ISBN: 978-3-642-34443-5Published: 20 February 2014
Softcover ISBN: 978-3-662-51005-6Published: 03 September 2016
eBook ISBN: 978-3-642-34444-2Published: 08 February 2014
Series ISSN: 2195-1934
Series E-ISSN: 2195-1942
Edition Number: 1
Number of Pages: XVIII, 367
Number of Illustrations: 45 b/w illustrations, 69 illustrations in colour
Topics: Mathematical Models of Cognitive Processes and Neural Networks, Image Processing and Computer Vision, Cognitive Psychology, Biomedical Engineering and Bioengineering