Nonlinear Eigenproblems in image processing and computer vision. (2018)

• Record Type: Book
• Further Information: Note: Guy Gilboa.
• Authors: Gilboa, Guy
• Contents: Intro; Preface; What are Nonlinear Eigenproblems and Why are They Important?; Basic Intuition and Examples; What is Covered in This Book?; References; Acknowledgements; Contents; 1 Mathematical Preliminaries; 1.1 Reminder of Very Basic Operators and Definitions; 1.1.1 Integration by Parts (Reminder); 1.1.2 Distributions (Reminder); 1.2 Some Standard Spaces; 1.3 Euler-Lagrange; 1.3.1 E-L of Some Functionals; 1.3.2 Some Useful Examples; 1.3.3 E-L of Common Fidelity Terms; 1.3.4 Norms Without Derivatives; 1.3.5 Seminorms with Derivatives; 1.4 Convex Functionals. 1.4.1 Convex Function and Functional1.4.2 Why Convex Functions Are Good?; 1.4.3 Subdifferential; 1.4.4 Duality-Legendre-Fenchel Transform; 1.5 One-Homogeneous Functionals; 1.5.1 Definition and Basic Properties; References; 2 Variational Methods in Image Processing; 2.1 Variation Modeling by Regularizing Functionals; 2.1.1 Regularization Energies and Their Respective E-L; 2.2 Nonlinear PDEs; 2.2.1 Gaussian Scale Space; 2.2.2 Perona-Malik Nonlinear Diffusion; 2.2.3 Weickert's Anisotropic Diffusion; 2.2.4 Steady-State Solution; 2.2.5 Inverse Scale Space; 2.3 Optical Flow and Registration. 2.3.1 Background2.3.2 Early Attempts for Solving the Optical Flow Problem; 2.3.3 Modern Optical Flow Techniques; 2.4 Segmentation and Clustering; 2.4.1 The Goal of Segmentation; 2.4.2 Mumford-Shah; 2.4.3 Chan-Vese Model; 2.4.4 Active Contours; 2.5 Patch-Based and Nonlocal Models; 2.5.1 Background; 2.5.2 Graph Laplacian; 2.5.3 A Nonlocal Mathematical Framework; 2.5.4 Basic Models; References; 3 Total Variation and Its Properties; 3.1 Strong and Weak Definitions; 3.2 Co-area Formula; 3.3 Definition of BV; 3.4 Basic Concepts Related to TV; 3.4.1 Isotropic and Anisotropic TV. 3.4.2 ROF, TV-L1, and TV FlowReferences; 4 Eigenfunctions of One-Homogeneous Functionals; 4.1 Introduction; 4.2 One-Homogeneous Functionals; 4.3 Properties of Eigenfunction; 4.4 Eigenfunctions of TV; 4.4.1 Explicit TV Eigenfunctions in 1D; 4.5 Pseudo-Eigenfunctions; 4.5.1 Measure of Affinity of Nonlinear Eigenfunctions; References; 5 Spectral One-Homogeneous Framework; 5.1 Preliminary Definitions and Settings; 5.2 Spectral Representations; 5.2.1 Scale Space Representation; 5.3 Signal Processing Analogy; 5.3.1 Nonlinear Ideal Filters; 5.3.2 Spectral Response. 5.4 Theoretical Analysis and Properties5.4.1 Variational Representation; 5.4.2 Scale Space Representation; 5.4.3 Inverse Scale Space Representation; 5.4.4 Definitions of the Power Spectrum; 5.5 Analysis of the Spectral Decompositions; 5.5.1 Basic Conditions on the Regularization; 5.5.2 Connection Between Spectral Decompositions; 5.5.3 Orthogonality of the Spectral Components; 5.5.4 Nonlinear Eigendecompositions; References; 6 Applications Using Nonlinear Spectral Processing; 6.1 Generalized Filters; 6.1.1 Basic Image Manipulation; 6.2 Simplification and Denoising.
• Publisher Details: Cham, Switzerland : Springer
• Publication Date: 2018
• Extent: 1 online resource (xx, 172 pages), illustrations (some color)
• Subjects: 515/.43; Computer science; Eigenfunctions; Image processing -- Digital techniques -- Mathematics; Computer vision -- Mathematics; Eigenfunctions; Image processing -- Digital techniques -- Mathematics; MATHEMATICS / Calculus; MATHEMATICS / Mathematical Analysis; Technology & Engineering -- Electronics -- General; Mathematics -- Calculus; Computers -- Data Processing; Mathematics -- Applied; Imaging systems & technology; Calculus of variations; Maths for computer scientists; Mathematical modelling; Computer vision; Mathematical optimization; Computers -- Computer Graphics; Image processing; Electronic books
• Languages: English
• ISBNs: 9783319758473; 3319758470
• Related ISBNs: 9783319758466; 3319758462
• Notes: Note: Includes bibliographical references.; Note: Online resource; title from PDF title page (SpringerLink, viewed April 4, 2018).
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.