Variational Methods

Published by De Gruyter 2017

Variational Methods

In Imaging and Geometric Control

Edited by: Maïtine Bergounioux, Gabriel Peyré, Christoph Schnörr, Jean-Baptiste Caillau and Thomas Haberkorn

Volume 18 in the series Radon Series on Computational and Applied Mathematics

https://doi.org/10.1515/9783110430394

Overview
Contents

About this book

With a focus on the interplay between mathematics and applications of imaging, the first part covers topics from optimization, inverse problems and shape spaces to computer vision and computational anatomy. The second part is geared towards geometric control and related topics, including Riemannian geometry, celestial mechanics and quantum control.

Contents:
Part I
Second-order decomposition model for image processing: numerical experimentation
Optimizing spatial and tonal data for PDE-based inpainting
Image registration using phase・amplitude separation
Rotation invariance in exemplar-based image inpainting
Convective regularization for optical flow
A variational method for quantitative photoacoustic tomography with piecewise constant coefficients
On optical flow models for variational motion estimation
Bilevel approaches for learning of variational imaging models
Part II
Non-degenerate forms of the generalized Euler・Lagrange condition for state-constrained optimal control problems
The Purcell three-link swimmer: some geometric and numerical aspects related to periodic optimal controls
Controllability of Keplerian motion with low-thrust control systems
Higher variational equation techniques for the integrability of homogeneous potentials
Introduction to KAM theory with a view to celestial mechanics
Invariants of contact sub-pseudo-Riemannian structures and Einstein・Weyl geometry
Time-optimal control for a perturbed Brockett integrator
Twist maps and Arnold diffusion for diffeomorphisms
A Hamiltonian approach to sufficiency in optimal control with minimal regularity conditions: Part I
Index

Author information

Maïtine Bergounioux, Université d'Orléans, France.

Topics

Frontmatter Publicly Available Download PDF	I
Contents Publicly Available Download PDF	V
Part I
1. Second-order decomposition model for image processing: numerical experimentation Maïtine Bergounioux Requires Authentication Unlicensed Licensed Download PDF	5
2. Optimizing spatial and tonal data for PDE-based inpainting Laurent Hoeltgen, Markus Mainberger, Sebastian Hoffmann, Joachim Weickert, Ching Hoo Tang, Simon Setzer, Daniel Johannsen, Frank Neumann and Benjamin Doerr Requires Authentication Unlicensed Licensed Download PDF	35
3. Image registration using phase–amplitude separation Qian Xie and Anuj Srivastava Requires Authentication Unlicensed Licensed Download PDF	84
4. Rotation invariance in exemplar-based image inpainting Martin Eller and Massimo Fornasier Requires Authentication Unlicensed Licensed Download PDF	108
5. Convective regularization for optical flow José A. Iglesias and Clemens Kirisits Requires Authentication Unlicensed Licensed Download PDF	184
6. A variational method for quantitative photoacoustic tomography with piecewise constant coefficients Elena Beretta, Monika Muszkieta, Wolf Naetar and Otmar Scherzer Requires Authentication Unlicensed Licensed Download PDF	202
7. On optical flow models for variational motion estimation Martin Burger, Hendrik Dirks and Lena Frerking Requires Authentication Unlicensed Licensed Download PDF	225
8. Bilevel approaches for learning of variational imaging models Luca Calatroni, Chung Cao, Juan Carlos De los Reyes, Carola-Bibiane Schönlieb and Tuomo Valkonen Requires Authentication Unlicensed Licensed Download PDF	252
Part II
9. Non-degenerate forms of the generalized Euler–Lagrange condition for state-constrained optimal control problems Piernicola Bettiol and Nathalie Khalil Requires Authentication Unlicensed Licensed Download PDF	295
10 The Purcell three-link swimmer: some geometric and numerical aspects related to periodic optimal controls Piernicola Bettiol, Bernard Bonnard, Laetitia Giraldi, Pierre Martinon and Jérémy Rouot Requires Authentication Unlicensed Licensed Download PDF	314
11. Controllability of Keplerian motion with low-thrust control systems Zheng Chen and Yacine Chitour Requires Authentication Unlicensed Licensed Download PDF	344
12. Higher variational equation techniques for the integrability of homogeneous potentials Thierry Combot Requires Authentication Unlicensed Licensed Download PDF	365
13. Introduction to KAM theory with a view to celestial mechanics Jacques Féjoz Requires Authentication Unlicensed Licensed Download PDF	387
14. Invariants of contact sub-pseudo-Riemannian structures and Einstein–Weyl geometry Marek Grochowski and Wojciech Kryński Requires Authentication Unlicensed Licensed Download PDF	434
15. Time-optimal control for a perturbed Brockett integrator Jérôme Lohéac and Jean-François Scheid Requires Authentication Unlicensed Licensed Download PDF	454
16. Twist maps and Arnold diffusion for diffeomorphisms Jean-Pierre Marco Requires Authentication Unlicensed Licensed Download PDF	473
17. A Hamiltonian approach to sufficiency in optimal control with minimal regularity conditions: Part I Gianna Stefani and Pierluigi Zezza Requires Authentication Unlicensed Licensed Download PDF	496
Index Requires Authentication Unlicensed Licensed Download PDF	517

(Deutsch)

Language: English
Publisher: De Gruyter
Audience: Researchers in Mathematics (especially optimization), Engineering, Computer Science and Imaging.
Pages
- Front matter: 12
- Main content: 528
Illustrations
- Illustrations: 323
- Coloured Illustrations: 47
Keywords: Optimierung; Control theory; Bildverarbeitung

eBook

Published: January 11, 2017
ISBN: 9783110430394

Hardcover

Published: January 11, 2017
ISBN: 9783110439236