Advances in Computer Vision and Pattern Recognition

Nonlinear Eigenproblems in Image Processing and Computer Vision

Authors: Gilboa, Guy

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  • The first book on this topic, relating the new theory to image processing and computer vision applications
  • Integrates deep mathematical concepts from various fields into a coherent manuscript with plots, graphs and intuitions, allowing broader access to computer scientists and engineers
  • Provides new insights and connections to established signal processing techniques such as Fourier, wavelets and sparse representations
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eBook $69.99
price for USA in USD (gross)
  • ISBN 978-3-319-75847-3
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Hardcover $119.99
price for USA in USD
  • ISBN 978-3-319-75846-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $89.99
price for USA in USD
  • ISBN 978-3-030-09339-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

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.

About the authors

Dr. Guy Gilboa is an Assistant Professor in the Electrical Engineering Department at Technion – Israel Institute of Technology, Haifa, Israel.

Table of contents (11 chapters)

Table of contents (11 chapters)

Buy this book

eBook $69.99
price for USA in USD (gross)
  • ISBN 978-3-319-75847-3
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $119.99
price for USA in USD
  • ISBN 978-3-319-75846-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $89.99
price for USA in USD
  • ISBN 978-3-030-09339-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Nonlinear Eigenproblems in Image Processing and Computer Vision
Authors
Series Title
Advances in Computer Vision and Pattern Recognition
Copyright
2018
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG, part of Springer Nature
eBook ISBN
978-3-319-75847-3
DOI
10.1007/978-3-319-75847-3
Hardcover ISBN
978-3-319-75846-6
Softcover ISBN
978-3-030-09339-6
Series ISSN
2191-6586
Edition Number
1
Number of Pages
XX, 172
Number of Illustrations
2 b/w illustrations, 39 illustrations in colour
Topics