Nonlinear Eigenproblems in Image Processing and Computer Vision

• Main Author: Gilboa, Guy (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2018.
• Edition: 1st ed. 2018.
• Series: Advances in Computer Vision and Pattern Recognition,
• Subjects: Optical data processing.; Signal processing.; Image processing.; Speech processing systems.; Calculus of variations.; Computer science-Mathematics.; Computer mathematics.; 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.

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 mathemati...

Table of Contents:

• 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.