skip to content
Elements of neurogeometry : functional architectures of vision Preview this item
ClosePreview this item
Checking...

Elements of neurogeometry : functional architectures of vision

Author: Jean Petitot
Publisher: Cham : Springer, 2017.
Series: Lecture notes in morphogenesis.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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"  Read more...
Rating:

(not yet rated) 0 with reviews - Be the first.

Subjects
More like this

Find a copy online

Links to this item

Find a copy in the library

&AllPage.SpinnerRetrieving; Finding libraries that hold this item...

Details

Genre/Form: Electronic books
Additional Physical Format: Print version:
Petitot, Jean.
Elements of Neurogeometry : Functional Architectures of Vision.
Cham : Springer International Publishing, ©2017
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Jean Petitot
ISBN: 9783319655918 3319655914
OCLC Number: 1012344986
Notes: ""4.3.3 Fibre Bundles""
Description: 1 online resource (388 pages).
Contents: ""Of Interest for Neurogeometry by Jean Petitot""; ""Contents""; ""About the Author""; ""Keywords""; ""1 Preface""; ""1.1 The Goal of This Work ""; ""1.2 An Outline of This Work ""; ""1.2.1 Outline of the First Volume""; ""1.2.2 Some Remarks Concerning the Second Volume""; ""1.2.3 Limits of This Investigation""; ""1.3 History, Context, and Acknowledgements ""; ""References""; ""2 Introduction""; ""2.1 Origin of Space and Neurogeometry""; ""2.1.1 Geometric, Physical, and Sensorimotor Conceptions of Space""; ""2.1.2 The Neurogeometric Approach"" ""2.2 Perceptual Geometry, Neurogeometry, and Gestalt Geometry """"2.3 Geometry's `Twofold Way'""; ""2.4 Idealities and Material Processes""; ""2.5 Mathematical Prerequisites and the Nature of Models""; ""2.6 Mathematical Structures and Biophysical Data""; ""2.7 Levels of Investigation: Micro, Meso, and Macro""; ""2.8 The Context of Cognitive Science""; ""2.9 Complex Systems and the Physics of the Mental""; ""2.10 The Philosophical Problem of Cognitive Science""; ""2.11 Some Examples ""; ""2.11.1 The Gestalt Concept of Good Continuation""; ""2.11.2 Kanizsa's Illusory Contours"" ""2.11.3 Entoptic Phenomena""""2.11.4 The Cut Locus""; ""References""; ""3 Receptive Fields and Profiles, and Wavelet Analysis""; ""3.1 Structure of the Retino-Geniculo-Cortical Visual Pathways""; ""3.2 Receptive Fields and Receptive Profiles""; ""3.2.1 Structure of the Retina""; ""3.2.2 Neurons and Action Potentials""; ""3.2.3 Structure of the Photoreceptors""; ""3.2.4 Ganglion Cells""; ""3.2.5 Retinal Colour Coding Circuitry""; ""3.2.6 General Receptive Fields and Neural Coding""; ""3.3 Visual Neurons as Filters""; ""3.3.1 Gabor Wavelets and Derivatives of Gaussians"" ""3.3.2 Steerable Filters""""3.3.3 Linearity Versus Nonlinearity""; ""3.3.4 Visual Neurons as Convolution Operators""; ""3.3.5 Fine Orientation Discrimination""; ""3.4 Vision and Wavelets""; ""3.4.1 Fourier, Gabor, and Wavelets""; ""3.4.2 Wavelets and Group Representation""; ""3.4.3 Wavelets and Discontinuities""; ""3.4.4 Redundancy of Wavelets""; ""3.4.5 Compression and Geometry""; ""3.4.6 Matching Pursuit and Rank Coding""; ""3.5 Feature Detectors""; ""3.6 Receptive Profiles and Information Theory""; ""3.6.1 Signal Decorrelation and Efficient Coding"" ""3.6.2 Receptive Profiles and Natural Images""""3.7 Signal Processing and Geometrical Formatting""; ""3.8 Grid Cells and Place Cells""; ""3.8.1 Spatial Navigation""; ""3.8.2 Place Cells""; ""3.8.3 Grid Cells""; ""3.8.4 Head Direction Cells""; ""3.8.5 Implementing the Tangent Bundle""; ""References""; ""4 Functional Architecture I: The Pinwheels of V1""; ""4.1 The Areas of the Visual Cortex""; ""4.2 Hypercolumnar Structure of the V1 Area""; ""4.3 V1 as a Mesoscopic Fibration""; ""4.3.1 `Bridging Scales': The Mesoscopic Level""; ""4.3.2 Fibrations and Engrafted Variables""
Series Title: Lecture notes in morphogenesis.
Other Titles: Neurogéométrie de la vision.
Responsibility: Jean Petitot.

Abstract:

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.--

Reviews

User-contributed reviews
Retrieving GoodReads reviews...
Retrieving DOGObooks reviews...

Tags

Be the first.
Confirm this request

You may have already requested this item. Please select Ok if you would like to proceed with this request anyway.

Linked Data


Primary Entity

<http://www.worldcat.org/oclc/1012344986> # Elements of neurogeometry : functional architectures of vision
    a schema:CreativeWork, schema:MediaObject, schema:Book ;
    bgn:translationOfWork <http://www.worldcat.org/title/-/oclc/1012344986#CreativeWork/unidentifiedOriginalWork> ; # Neurogéométrie de la vision.
    library:oclcnum "1012344986" ;
    library:placeOfPublication <http://experiment.worldcat.org/entity/work/data/4617977263#Place/cham> ; # Cham
    library:placeOfPublication <http://id.loc.gov/vocabulary/countries/sz> ;
    schema:about <http://dewey.info/class/510/> ;
    schema:about <http://experiment.worldcat.org/entity/work/data/4617977263#Topic/visual_cortex_mathematical_models> ; # Visual cortex--Mathematical models
    schema:about <http://experiment.worldcat.org/entity/work/data/4617977263#Topic/vision_mathematical_models> ; # Vision--Mathematical models
    schema:about <http://experiment.worldcat.org/entity/work/data/4617977263#Topic/mathematics_reference> ; # MATHEMATICS--Reference
    schema:about <http://experiment.worldcat.org/entity/work/data/4617977263#Topic/visual_perception_mathematical_models> ; # Visual perception--Mathematical models
    schema:about <http://experiment.worldcat.org/entity/work/data/4617977263#Topic/mathematics_pre_calculus> ; # MATHEMATICS--Pre-Calculus
    schema:about <http://experiment.worldcat.org/entity/work/data/4617977263#Topic/mathematics_essays> ; # MATHEMATICS--Essays
    schema:bookFormat schema:EBook ;
    schema:creator <http://experiment.worldcat.org/entity/work/data/4617977263#Person/petitot_jean_1944> ; # Jean Petitot
    schema:datePublished "2017" ;
    schema:description """Of Interest for Neurogeometry by Jean Petitot""; ""Contents""; ""About the Author""; ""Keywords""; ""1 Preface""; ""1.1 The Goal of This Work ""; ""1.2 An Outline of This Work ""; ""1.2.1 Outline of the First Volume""; ""1.2.2 Some Remarks Concerning the Second Volume""; ""1.2.3 Limits of This Investigation""; ""1.3 History, Context, and Acknowledgements ""; ""References""; ""2 Introduction""; ""2.1 Origin of Space and Neurogeometry""; ""2.1.1 Geometric, Physical, and Sensorimotor Conceptions of Space""; ""2.1.2 The Neurogeometric Approach"""@en ;
    schema:description "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.--"@en ;
    schema:exampleOfWork <http://worldcat.org/entity/work/id/4617977263> ; # Neurogéométrie de la vision.
    schema:genre "Electronic books"@en ;
    schema:inLanguage "en" ;
    schema:isPartOf <http://experiment.worldcat.org/entity/work/data/4617977263#Series/lecture_notes_in_morphogenesis> ; # Lecture notes in morphogenesis.
    schema:isSimilarTo <http://worldcat.org/entity/work/data/4617977263#CreativeWork/elements_of_neurogeometry_functional_architectures_of_vision> ;
    schema:name "Elements of neurogeometry : functional architectures of vision"@en ;
    schema:productID "1012344986" ;
    schema:publication <http://www.worldcat.org/title/-/oclc/1012344986#PublicationEvent/cham_springer_2017> ;
    schema:publisher <http://experiment.worldcat.org/entity/work/data/4617977263#Agent/springer> ; # Springer
    schema:url <http://dx.doi.org/10.1007/978-3-319-65591-8> ;
    schema:url <http://link.springer.com/10.1007/978-3-319-65591-8> ;
    schema:url <https://grinnell.idm.oclc.org/login?url=http://link.springer.com/10.1007/978-3-319-65591-8> ;
    schema:url <https://0-link-springer-com.pugwash.lib.warwick.ac.uk/10.1007/978-3-319-65591-8> ;
    schema:url <https://0-link-springer-com.pugwash.lib.warwick.ac.uk/book/10.1007/978-3-319-65591-8> ;
    schema:url <http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=1632593> ;
    schema:url <http://public.eblib.com/choice/publicfullrecord.aspx?p=5143336> ;
    schema:url <http://proxy.ohiolink.edu:9099/login?url=http://link.springer.com/10.1007/978-3-319-65591-8> ;
    schema:url <http://rave.ohiolink.edu/ebooks/ebc/9783319655918> ;
    schema:workExample <http://dx.doi.org/10.1007/978-3-319-65591-8> ;
    schema:workExample <http://worldcat.org/isbn/9783319655918> ;
    wdrs:describedby <http://www.worldcat.org/title/-/oclc/1012344986> ;
    .


Related Entities

<http://experiment.worldcat.org/entity/work/data/4617977263#Person/petitot_jean_1944> # Jean Petitot
    a schema:Person ;
    schema:birthDate "1944" ;
    schema:familyName "Petitot" ;
    schema:givenName "Jean" ;
    schema:name "Jean Petitot" ;
    .

<http://experiment.worldcat.org/entity/work/data/4617977263#Series/lecture_notes_in_morphogenesis> # Lecture notes in morphogenesis.
    a bgn:PublicationSeries ;
    schema:hasPart <http://www.worldcat.org/oclc/1012344986> ; # Elements of neurogeometry : functional architectures of vision
    schema:name "Lecture notes in morphogenesis." ;
    schema:name "Lecture Notes in Morphogenesis" ;
    .

<http://experiment.worldcat.org/entity/work/data/4617977263#Topic/mathematics_essays> # MATHEMATICS--Essays
    a schema:Intangible ;
    schema:name "MATHEMATICS--Essays"@en ;
    .

<http://experiment.worldcat.org/entity/work/data/4617977263#Topic/mathematics_pre_calculus> # MATHEMATICS--Pre-Calculus
    a schema:Intangible ;
    schema:name "MATHEMATICS--Pre-Calculus"@en ;
    .

<http://experiment.worldcat.org/entity/work/data/4617977263#Topic/mathematics_reference> # MATHEMATICS--Reference
    a schema:Intangible ;
    schema:name "MATHEMATICS--Reference"@en ;
    .

<http://experiment.worldcat.org/entity/work/data/4617977263#Topic/vision_mathematical_models> # Vision--Mathematical models
    a schema:Intangible ;
    schema:name "Vision--Mathematical models"@en ;
    .

<http://experiment.worldcat.org/entity/work/data/4617977263#Topic/visual_cortex_mathematical_models> # Visual cortex--Mathematical models
    a schema:Intangible ;
    schema:name "Visual cortex--Mathematical models"@en ;
    .

<http://experiment.worldcat.org/entity/work/data/4617977263#Topic/visual_perception_mathematical_models> # Visual perception--Mathematical models
    a schema:Intangible ;
    schema:name "Visual perception--Mathematical models"@en ;
    .

<http://rave.ohiolink.edu/ebooks/ebc/9783319655918>
    rdfs:comment "Connect to resource" ;
    .

<http://worldcat.org/entity/work/data/4617977263#CreativeWork/elements_of_neurogeometry_functional_architectures_of_vision>
    a schema:CreativeWork ;
    rdfs:label "Elements of Neurogeometry : Functional Architectures of Vision." ;
    schema:description "Print version:" ;
    schema:isSimilarTo <http://www.worldcat.org/oclc/1012344986> ; # Elements of neurogeometry : functional architectures of vision
    .

<http://worldcat.org/entity/work/id/4617977263> # Neurogéométrie de la vision.
    schema:name "Neurogéométrie de la vision." ;
    .

<http://worldcat.org/isbn/9783319655918>
    a schema:ProductModel ;
    schema:isbn "3319655914" ;
    schema:isbn "9783319655918" ;
    .

<http://www.worldcat.org/title/-/oclc/1012344986#CreativeWork/unidentifiedOriginalWork> # Neurogéométrie de la vision.
    a schema:CreativeWork ;
    schema:inLanguage "fr" ;
    schema:name "Neurogéométrie de la vision." ;
    .


Content-negotiable representations

Close Window

Please sign in to WorldCat 

Don't have an account? You can easily create a free account.