Overview
- 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
Part of the book series: Advances in Computer Vision and Pattern Recognition (ACVPR)
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Table of contents (11 chapters)
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Front Matter
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Back Matter
Keywords
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-processingand 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.Authors and Affiliations
About the author
Bibliographic Information
Book Title: Nonlinear Eigenproblems in Image Processing and Computer Vision
Authors: Guy Gilboa
Series Title: Advances in Computer Vision and Pattern Recognition
DOI: https://doi.org/10.1007/978-3-319-75847-3
Publisher: Springer Cham
eBook Packages: Computer Science, Computer Science (R0)
Copyright Information: Springer International Publishing AG, part of Springer Nature 2018
Hardcover ISBN: 978-3-319-75846-6Published: 17 April 2018
Softcover ISBN: 978-3-030-09339-6Published: 24 January 2019
eBook ISBN: 978-3-319-75847-3Published: 29 March 2018
Series ISSN: 2191-6586
Series E-ISSN: 2191-6594
Edition Number: 1
Number of Pages: XX, 172
Number of Illustrations: 2 b/w illustrations, 39 illustrations in colour
Topics: Image Processing and Computer Vision, Signal, Image and Speech Processing, Calculus of Variations and Optimal Control; Optimization, Math Applications in Computer Science, Mathematical Applications in Computer Science