Part I
by Thomas Haberkorn, Jean-Baptiste Caillau, Christoph Schnörr, Gabriel Peyré, Maïti
Variational Methods
- Cover
- Title Page
- Copyright
- 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
- A Special functions of bounded variation and the SBV-compactness theorem
- 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
- 13.1 Twisted conjugacy normal form
- 13.2 One step of the Newton algorithm
- 13.3 Inverse function theorem
- 13.4 Local uniqueness and regularity of the normal form
- 13.5 Conditional conjugacy
- 13.6 Invariant torus with prescribed frequency
- 13.7 Invariant tori with unprescribed frequencies
- 13.8 Symmetries
- 13.9 Lower dimensional tori
- 13.10 Example in the spatial three-body problem
- A Isotropy of invariant tori
- B Two basic estimates
- C Interpolation of spaces of analytic functions
- 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
Part I
The first part of this book presents an overview of recent advances in the field of imaging in a very broad sense, highlighting the interplay between theory and applications. It covers topics related to optimization and inverse problems, with applications in computer vision and medical imaging. These contributions make use of a combination of a variety of mathematical tools among them implicit shape representations, PDEs, convex analysis, variational methods, and bilevel programming.
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