عنوان

Nonlinear Eigenproblems in image processing and computer vision /

شابک

3319758470

شابک

9783319758473

شابک اشتباه

3319758462

شابک اشتباه

9783319758466

عنوان اصلي

Nonlinear Eigenproblems in image processing and computer vision /

نام عام مواد

[Book]

نام نخستين پديدآور

Guy Gilboa.

محل نشرو پخش و غیره

Cham, Switzerland :

نام ناشر، پخش کننده و غيره

Springer,

تاریخ نشرو بخش و غیره

2018.

نام خاص و کميت اثر

1 online resource (xx, 172 pages) :

ساير جزييات

illustrations (some color)

عنوان فروست

Advances in computer vision and pattern recognition,

شاپا ي ISSN فروست

2191-6586

متن يادداشت

Includes bibliographical references.

متن يادداشت

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.

متن يادداشت

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.

متن يادداشت

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.

متن يادداشت

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.

متن يادداشت

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.

بدون عنوان

0

بدون عنوان

8

بدون عنوان

8

بدون عنوان

8

بدون عنوان

8

متن يادداشت

This unique text/reference presents a fresh look at nonlinear processing through nonlinear eigenvalue analysis, highlighting how one-homogeneous convex functionals can induce nonlinear operators that can be analyzed within an eigenvalue framework. The text opens with an introduction to the mathematical background, together with a summary of classical variational algorithms for vision. This is followed by a focus on the foundations and applications of the new multi-scale representation based on non-linear eigenproblems. The book then concludes with a discussion of new numerical techniques for finding nonlinear eigenfunctions, and promising research directions beyond the convex case. Topics and features: Introduces the classical Fourier transform and its associated operator and energy, and asks how these concepts can be generalized in the nonlinear case Reviews the basic mathematical notion, briefly outlining the use of variational and flow-based methods to solve image-processing and computer vision algorithms Describes the properties of the total variation (TV) functional, and how the concept of nonlinear eigenfunctions relate to convex functionals Provides a spectral framework for one-homogeneous functionals, and applies this framework for denoising, texture processing and image fusion Proposes novel ways to solve the nonlinear eigenvalue problem using special flows that converge to eigenfunctions Examines graph-based and nonlocal methods, for which a TV eigenvalue analysis gives rise to strong segmentation, clustering and classification algorithms Presents an approach to generalizing the nonlinear spectral concept beyond the convex case, based on pixel decay analysis Discusses relations to other branches of image processing, such as wavelets and dictionary based methods This original work offers fascinating new insights into established signal processing techniques, integrating deep mathematical concepts from a range of different fields, which will be of great interest to all researchers involved with image processing and computer vision applications, as well as computations for more general scientific problems. Dr. Guy Gilboa is an Assistant Professor in the Electrical Engineering Department at Technion - Israel Institute of Technology, Haifa, Israel.

منبع سفارش / آدرس اشتراک

Springer Nature

شماره انبار

com.springer.onix.9783319758473

عنوان

Nonlinear Eigenproblems in image processing and computer vision.

شماره استاندارد بين المللي کتاب و موسيقي

9783319758466

موضوع مستند نشده

Computer vision-- Mathematics.

موضوع مستند نشده

Eigenfunctions.

موضوع مستند نشده

Image processing-- Digital techniques-- Mathematics.

موضوع مستند نشده

Calculus of variations.

موضوع مستند نشده

Eigenfunctions.

موضوع مستند نشده

Image processing-- Digital techniques-- Mathematics.

موضوع مستند نشده

Image processing.

موضوع مستند نشده

Imaging systems & technology.

موضوع مستند نشده

Mathematical modelling.

موضوع مستند نشده

MATHEMATICS-- Calculus.

موضوع مستند نشده

MATHEMATICS-- Mathematical Analysis.

موضوع مستند نشده

Maths for computer scientists.

موضوع مستند نشده

COM012000

موضوع مستند نشده

COM016000

موضوع مستند نشده

MAT-- 005000

موضوع مستند نشده

MAT-- 034000

موضوع مستند نشده

UYQV

موضوع مستند نشده

UYQV

موضوع مستند نشده

UYT

موضوع مستند نشده

UYT

شماره

ويراست

شماره رده

مستند نام اشخاص تاييد نشده

Gilboa, Guy

تاريخ عمليات

20200823110348.0

قواعد فهرست نويسي ( بخش توصيفي )

pn

نام الکترونيکي

نوع ماده

[Book]

تكميل شده

Y