1 option
Nonlinear Eigenproblems in Image Processing and Computer Vision / by Guy Gilboa.
- Format:
- Book
- Author/Creator:
- Gilboa, Guy, author.
- Series:
- Computer Science (Springer-11645)
- Advances in computer vision and pattern recognition 2191-6586
- Advances in Computer Vision and Pattern Recognition, 2191-6586
- Language:
- English
- Subjects (All):
- Optical data processing.
- Signal processing.
- Image processing.
- Speech processing systems.
- Calculus of variations.
- Computer science--Mathematics.
- Computer science.
- 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.
- Local Subjects:
- 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.
- Physical Description:
- 1 online resource (XX, 172 pages) : 41 illustrations, 39 illustrations in color.
- Edition:
- First edition 2018.
- Contained In:
- Springer eBooks
- Place of Publication:
- Cham : Springer International Publishing : Imprint: Springer, 2018.
- System Details:
- text file PDF
- Summary:
- 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.
- 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.
- Other Format:
- Printed edition:
- ISBN:
- 978-3-319-75847-3
- 9783319758473
- 9783319758466
- 9783319758480
- 9783030093396
- Access Restriction:
- Restricted for use by site license.
The Penn Libraries is committed to describing library materials using current, accurate, and responsible language. If you discover outdated or inaccurate language, please fill out this feedback form to report it and suggest alternative language.