A Semidiscrete Version of the Citti-Petitot-Sarti Model as a Plausible Model for Anthropomorphic Image Reconstruction and Pattern Recognition PDF Download
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Author: Dario Prandi
Publisher: Springer
ISBN: 331978482X
Category : Mathematics
Languages : en
Pages : 121
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Book Description
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.
Author: Dario Prandi
Publisher: Springer
ISBN: 331978482X
Category : Mathematics
Languages : en
Pages : 121
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Book Description
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.
Author: Frank Nielsen
Publisher: Springer Nature
ISBN: 3030802094
Category : Computers
Languages : en
Pages : 929
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Book Description
This book constitutes the proceedings of the 5th International Conference on Geometric Science of Information, GSI 2021, held in Paris, France, in July 2021. The 98 papers presented in this volume were carefully reviewed and selected from 125 submissions. They cover all the main topics and highlights in the domain of geometric science of information, including information geometry manifolds of structured data/information and their advanced applications. The papers are organized in the following topics: Probability and statistics on Riemannian Manifolds; sub-Riemannian geometry and neuromathematics; shapes spaces; geometry of quantum states; geometric and structure preserving discretizations; information geometry in physics; Lie group machine learning; geometric and symplectic methods for hydrodynamical models; harmonic analysis on Lie groups; statistical manifold and Hessian information geometry; geometric mechanics; deformed entropy, cross-entropy, and relative entropy; transformation information geometry; statistics, information and topology; geometric deep learning; topological and geometrical structures in neurosciences; computational information geometry; manifold and optimization; divergence statistics; optimal transport and learning; and geometric structures in thermodynamics and statistical physics.
Author: Alessandro Sarti
Publisher: Springer Nature
ISBN: 3031519930
Category :
Languages : en
Pages : 297
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Book Description
Author: Frédéric Barbaresco
Publisher: MDPI
ISBN: 3038977462
Category : Science
Languages : en
Pages : 260
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Book Description
For the 250th birthday of Joseph Fourier, born in 1768 in Auxerre, France, this MDPI Special Issue will explore modern topics related to Fourier Analysis and Heat Equation. Modern developments of Fourier analysis during the 20th century have explored generalizations of Fourier and Fourier–Plancherel formula for non-commutative harmonic analysis, applied to locally-compact, non-Abelian groups. In parallel, the theory of coherent states and wavelets has been generalized over Lie groups. One should add the developments, over the last 30 years, of the applications of harmonic analysis to the description of the fascinating world of aperiodic structures in condensed matter physics. The notions of model sets, introduced by Y. Meyer, and of almost periodic functions, have revealed themselves to be extremely fruitful in this domain of natural sciences. The name of Joseph Fourier is also inseparable from the study of the mathematics of heat. Modern research on heat equations explores the extension of the classical diffusion equation on Riemannian, sub-Riemannian manifolds, and Lie groups. In parallel, in geometric mechanics, Jean-Marie Souriau interpreted the temperature vector of Planck as a space-time vector, obtaining, in this way, a phenomenological model of continuous media, which presents some interesting properties. One last comment concerns the fundamental contributions of Fourier analysis to quantum physics: Quantum mechanics and quantum field theory. The content of this Special Issue will highlight papers exploring non-commutative Fourier harmonic analysis, spectral properties of aperiodic order, the hypoelliptic heat equation, and the relativistic heat equation in the context of Information Theory and Geometric Science of Information.
Author: Marcelo Bertalmío
Publisher: CRC Press
ISBN: 1439899274
Category : Technology & Engineering
Languages : en
Pages : 323
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Book Description
Image Processing for Cinema presents a detailed overview of image processing techniques that are used in practice in digital cinema. The book shows how image processing has become ubiquitous in movie-making, from shooting to exhibition. It covers all the ways in which image processing algorithms are used to enhance, restore, adapt, and convert moving images. These techniques and algorithms make the images look as good as possible while exploiting the capabilities of cameras, projectors, and displays. The author focuses on the ideas behind the methods, rather than proofs and derivations. The first part of the text presents fundamentals on optics and color. The second part explains how cameras work and details all the image processing algorithms that are applied in-camera. With an emphasis on state-of-the-art methods that are actually used in practice, the last part describes image processing algorithms that are applied offline to solve a variety of problems. The book is designed for advanced undergraduate and graduate students in applied mathematics, image processing, computer science, and related fields. It is also suitable for academic researchers and professionals in the movie industry.
Author: Jan Lellmann
Publisher: Springer
ISBN: 303022368X
Category : Computers
Languages : en
Pages : 574
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Book Description
This book constitutes the proceedings of the 7th International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2019, held in Hofgeismar, Germany, in June/July 2019. The 44 papers included in this volume were carefully reviewed and selected for inclusion in this book. They were organized in topical sections named: 3D vision and feature analysis; inpainting, interpolation and compression; inverse problems in imaging; optimization methods in imaging; PDEs and level-set methods; registration and reconstruction; scale-space methods; segmentation and labeling; and variational methods.
Author: David Pisoni
Publisher: John Wiley & Sons
ISBN: 0470756772
Category : Language Arts & Disciplines
Languages : en
Pages : 704
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Book Description
The Handbook of Speech Perception is a collection of forward-looking articles that offer a summary of the technical and theoretical accomplishments in this vital area of research on language. Now available in paperback, this uniquely comprehensive companion brings together in one volume the latest research conducted in speech perception Contains original contributions by leading researchers in the field Illustrates technical and theoretical accomplishments and challenges across the field of research and language Adds to a growing understanding of the far-reaching relevance of speech perception in the fields of phonetics, audiology and speech science, cognitive science, experimental psychology, behavioral neuroscience, computer science, and electrical engineering, among others.
Author: Sven Mattys
Publisher: Psychology Press
ISBN: 1317836812
Category : Psychology
Languages : en
Pages : 326
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Book Description
Speech recognition in ‘adverse conditions’ has been a familiar area of research in computer science, engineering, and hearing sciences for several decades. In contrast, most psycholinguistic theories of speech recognition are built upon evidence gathered from tasks performed by healthy listeners on carefully recorded speech, in a quiet environment, and under conditions of undivided attention. Building upon the momentum initiated by the Psycholinguistic Approaches to Speech Recognition in Adverse Conditions workshop held in Bristol, UK, in 2010, the aim of this volume is to promote a multi-disciplinary, yet unified approach to the perceptual, cognitive, and neuro-physiological mechanisms underpinning the recognition of degraded speech, variable speech, speech experienced under cognitive load, and speech experienced by theoretically relevant populations. This collection opens with a review of the literature and a formal classification of adverse conditions. The research articles then highlight those adverse conditions with the greatest potential for constraining theory, showing that some speech phenomena often believed to be immutable can be affected by noise, surface variations, or attentional set in ways that will force researchers to rethink their theory. This volume is essential for those interested in speech recognition outside laboratory constraints.
Author: Richard Montgomery
Publisher: American Mathematical Soc.
ISBN: 0821841653
Category : Mathematics
Languages : en
Pages : 282
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Book Description
Subriemannian geometries can be viewed as limits of Riemannian geometries. They arise naturally in many areas of pure (algebra, geometry, analysis) and applied (mechanics, control theory, mathematical physics) mathematics, as well as in applications (e.g., robotics). This book is devoted to the study of subriemannian geometries, their geodesics, and their applications. It starts with the simplest nontrivial example of a subriemannian geometry: the two-dimensional isoperimetric problem reformulated as a problem of finding subriemannian geodesics. Among topics discussed in other chapters of the first part of the book are an elementary exposition of Gromov's idea to use subriemannian geometry for proving a theorem in discrete group theory and Cartan's method of equivalence applied to the problem of understanding invariants of distributions. The second part of the book is devoted to applications of subriemannian geometry. In particular, the author describes in detail Berry's phase in quantum mechanics, the problem of a falling cat righting herself, that of a microorganism swimming, and a phase problem arising in the $N$-body problem. He shows that all these problems can be studied using the same underlying type of subriemannian geometry. The reader is assumed to have an introductory knowledge of differential geometry. This book that also has a chapter devoted to open problems can serve as a good introduction to this new, exciting area of mathematics.
Author: Andrei Agrachev
Publisher: Cambridge University Press
ISBN: 110847635X
Category : Mathematics
Languages : en
Pages : 765
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Book Description
Provides a comprehensive and self-contained introduction to sub-Riemannian geometry and its applications. For graduate students and researchers.
