Nonlinear eigenproblems in image processing and computer vision
type: Item
instance of: scholarly article
title: Nonlinear eigenproblems in image processing and computer vision
zbMATH Open document ID: 1402.68009
DOI: 10.1007/978-3-319-75847-3
author: Guy Gilboa
published in: Advances in Computer Vision and Pattern Recognition
publication date: 2018-05-28T00:00:00Z
review text: The objective of this volume is to introduce readers to the state-of-the-art image processing methods based on nonlinear eigenvalue analysis. Starting from classical variational methods such as Tikhonov and TV regularizations, the author softly introduces readers to nonlinear processing through nonlinear eigenvalue analysis in Chapters 1--5. Applications of variational methods in image processing problems, including edge-preserving image denoising, optical flow models, segmentation and clustering, are discussed in Chapter 2. The concept of nonlinear eigenfunctions induced by convex functionals is introduced and discussed in Chapter 4. Examples of applications of nonlinear spectral processing, including image denoising, are considered in Chapter 6. A review of the numerical methods for both linear and nonlinear eigenvalue problems is presented in Chapter 7. Spectral analysis on graphs is given in Chapter 8. Blind spectral decomposition is discussed in Chapter 9. Finally, relations to other decomposition methods, such as multiresolution analysis, are discussed in Chapter 10. Perspectives and future directions of image processing, including multiphysics imaging, are given in Chapter 11.
Mathematics Subject Classification ID: 68-02
Mathematics Subject Classification ID: 35P30
Mathematics Subject Classification ID: 47A52
Mathematics Subject Classification ID: 49M30
Mathematics Subject Classification ID: 65D19
Mathematics Subject Classification ID: 65J20
Mathematics Subject Classification ID: 65K10
Mathematics Subject Classification ID: 68T45
Mathematics Subject Classification ID: 68U10
Mathematics Subject Classification ID: 94A08
zbMATH DE Number: 6875596
zbMATH Keywords: ill-posed problems
zbMATH Keywords: image processing
zbMATH Keywords: Tikhonov regularization
zbMATH Keywords: variational algorithms
zbMATH Keywords: wavelets
zbMATH Keywords: multiresolution analysis
zbMATH Keywords: nonlinear eigenvalue problems
zbMATH Keywords: TV
zbMATH Keywords: spectral analysis
zbMATH Keywords: graphs
reviewed by: Denis Sidorov
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/978-3-319-75847-3
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description: scientific article; zbMATH DE number 6875596