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

A Semidiscrete Version of the Citti-Petitot-Sarti Model as a Plausible Model for Anthropomorphic... [This chapter introduces the concepts that are the main subject of the rest of this work, along with the essential tools that are needed. After a brief introduction on harmonic analysis in non-commutative groups, we introduce the general setting considered in this work, alongside with some essential facts on its representation theory. Afterwards, we recall some basic notions on almost-periodic functions and and a precise construction that allows to select some relevant subspaces. Finally we present our models for natural images (compactly supported functions of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^2({\mathbb R}^2)$$\end{document}) and textures (properly selected finite-dimensional subspaces of almost-periodic functions in the plane).] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

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

Part of the SpringerBriefs in Mathematics Book Series
Prandi, Dario; Gauthier, Jean-Paul
Springer Journals — Jun 12, 2018
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21 pages

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Publisher
Springer International Publishing
Copyright
© The Author(s) 2018
ISBN
978-3-319-78481-6
Pages
13 –34
DOI
10.1007/978-3-319-78482-3_2
Publisher site
See Chapter on Publisher Site

Abstract

[This chapter introduces the concepts that are the main subject of the rest of this work, along with the essential tools that are needed. After a brief introduction on harmonic analysis in non-commutative groups, we introduce the general setting considered in this work, alongside with some essential facts on its representation theory. Afterwards, we recall some basic notions on almost-periodic functions and and a precise construction that allows to select some relevant subspaces. Finally we present our models for natural images (compactly supported functions of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^2({\mathbb R}^2)$$\end{document}) and textures (properly selected finite-dimensional subspaces of almost-periodic functions in the plane).]

Published: Jun 12, 2018

Keywords: Harmonic analysis; Chu duality; Maximally almost periodic groups

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