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Nonlinear Eigenproblems in image pro...

Gilboa, Guy.

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Nonlinear Eigenproblems in image processing and computer vision

Record Type:	Electronic resources : Monograph/item
Title/Author:	Nonlinear Eigenproblems in image processing and computer vision/ by Guy Gilboa.
Author:	Gilboa, Guy.
Published:	Cham :Springer International Publishing : : 2018.,
Description:	xx, 172 p. :ill., digital ;24 cm.
[NT 15003449]:	Introduction and Motivation -- Variational Methods in Image Processing -- Total Variation and its Properties -- Eigenfunctions of One-Homogeneous Functionals -- Spectral One-Homogeneous Framework -- Applications Using Nonlinear Spectral Processing -- Numerical Methods for Finding Eigenfunctions -- Graph and Nonlocal Framework -- Beyond Convex Analysis: Decompositions with Nonlinear Flows -- Relations to Other Decomposition Methods -- Future Directions -- Appendix: Numerical Schemes.
Contained By:	Springer eBooks
Subject:	Eigenfunctions. -
Online resource:	http://dx.doi.org/10.1007/978-3-319-75847-3
ISBN:	9783319758473

Nonlinear Eigenproblems in image processing and computer vision
Gilboa, Guy.

Nonlinear Eigenproblems in image processing and computer vision[electronic resource] /by Guy Gilboa. - Cham :Springer International Publishing :2018. - xx, 172 p. :ill., digital ;24 cm. - Advances in computer vision and pattern recognition,2191-6586. - Advances in computer vision and pattern recognition..

Introduction and Motivation -- Variational Methods in Image Processing -- Total Variation and its Properties -- Eigenfunctions of One-Homogeneous Functionals -- Spectral One-Homogeneous Framework -- Applications Using Nonlinear Spectral Processing -- Numerical Methods for Finding Eigenfunctions -- Graph and Nonlocal Framework -- Beyond Convex Analysis: Decompositions with Nonlinear Flows -- Relations to Other Decomposition Methods -- Future Directions -- Appendix: Numerical Schemes.

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.

ISBN: 9783319758473

Standard No.: 10.1007/978-3-319-75847-3doiSubjects--Topical Terms:

706113
Eigenfunctions.

LC Class. No.: QA371

Dewey Class. No.: 515.43

Nonlinear Eigenproblems in image processing and computer vision
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245 1 0 $a Nonlinear Eigenproblems in image processing and computer vision $h [electronic resource] / $c by Guy Gilboa.
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300 $a xx, 172 p. : $b ill., digital ; $c 24 cm.
490 1 $a Advances in computer vision and pattern recognition, $x 2191-6586
505 0 $a Introduction and Motivation -- Variational Methods in Image Processing -- Total Variation and its Properties -- Eigenfunctions of One-Homogeneous Functionals -- Spectral One-Homogeneous Framework -- Applications Using Nonlinear Spectral Processing -- Numerical Methods for Finding Eigenfunctions -- Graph and Nonlocal Framework -- Beyond Convex Analysis: Decompositions with Nonlinear Flows -- Relations to Other Decomposition Methods -- Future Directions -- Appendix: Numerical Schemes.
520 $a 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.
650 0 $a Eigenfunctions. $3 706113
650 0 $a Image processing $x Digital techniques $x Mathematics. $3 615087
650 0 $a Computer vision $x Mathematics. $3 596840
650 1 4 $a Computer Science. $3 626642
650 2 4 $a Image Processing and Computer Vision. $3 891070
650 2 4 $a Signal, Image and Speech Processing. $3 891073
650 2 4 $a Calculus of Variations and Optimal Control; Optimization. $3 898674
650 2 4 $a Math Applications in Computer Science. $3 891004
650 2 4 $a Mathematical Applications in Computer Science. $3 1567978
710 2 $a SpringerLink (Online service) $3 836513
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830 0 $a Advances in computer vision and pattern recognition. $3 1567575
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-75847-3
950 $a Computer Science (Springer-11645)