A Semidiscrete Version of the Citti-Petitot-Sarti Model as a Plausible Model for Anthropomorphic Image Reconstruction and Pattern Recognition

  • Dario Prandi
  • Jean-Paul Gauthier

Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Dario Prandi, Jean-Paul Gauthier
    Pages 1-12
  3. Dario Prandi, Jean-Paul Gauthier
    Pages 13-34
  4. Dario Prandi, Jean-Paul Gauthier
    Pages 35-42
  5. Dario Prandi, Jean-Paul Gauthier
    Pages 43-52
  6. Dario Prandi, Jean-Paul Gauthier
    Pages 53-76
  7. Dario Prandi, Jean-Paul Gauthier
    Pages 77-87
  8. Dario Prandi, Jean-Paul Gauthier
    Pages 89-101
  9. Back Matter
    Pages 103-113

About this book


This book proposes a semi-discrete version of the theory of Petitot and Citti-Sarti, leading to a left-invariant structure over the group SE(2,N), restricted to a finite number of rotations. This apparently very simple group is in fact quite atypical: it is maximally almost periodic, which leads to much simpler harmonic analysis compared to SE(2). Based upon this semi-discrete model, the authors improve on previous image-reconstruction algorithms and develop a pattern-recognition theory that also leads to very efficient algorithms in practice.


Neurogeometry Abstract harmonic analysis Fourier descriptors Hypoelliptic diffusion Almost-periodic functions

Authors and affiliations

  • Dario Prandi
    • 1
  • Jean-Paul Gauthier
    • 2
  1. 1.Laboratoire des Signaux et des SystèmesCéntraleSupelecGif sur YvetteFrance
  2. 2.LSISUniversité de ToulonLa Garde CedexFrance

Bibliographic information

  • DOI
  • Copyright Information The Author(s) 2018
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-78481-6
  • Online ISBN 978-3-319-78482-3
  • Series Print ISSN 2191-8198
  • Series Online ISSN 2191-8201
  • Buy this book on publisher's site