Nonlinear Eigenproblems in Image Processing and Computer Vision by Guy Gilboa

Nonlinear Eigenproblems in Image Processing and Computer Vision by Guy Gilboa

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.

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

SKU	Unavailable
ISBN 13	9783030093396
ISBN 10	3030093395
Title	Nonlinear Eigenproblems in Image Processing and Computer Vision
Author	Guy Gilboa
Series	Advances In Computer Vision And Pattern Recognition
Condition	Unavailable
Binding Type	Paperback
Publisher	Springer Nature Switzerland AG
Year published	2019-01-24
Number of pages	172
Cover note	Book picture is for illustrative purposes only, actual binding, cover or edition may vary.