Nonlinear eigenproblems in image processing and computer vision
The objective of this volume is to introduce readers to the state-of-the-art image processing methods based on nonlinear eigenvalue analysis. Starting from classical variational methods such as Tikhonov and TV regularizations, the author softly introduces readers to nonlinear processing through nonlinear eigenvalue analysis in Chapters 1--5. Applications of variational methods in image processing problems, including edge-preserving image denoising, optical flow models, segmentation and clustering, are discussed in Chapter 2. The concept of nonlinear eigenfunctions induced by convex functionals is introduced and discussed in Chapter 4. Examples of applications of nonlinear spectral processing, including image denoising, are considered in Chapter 6. A review of the numerical methods for both linear and nonlinear eigenvalue problems is presented in Chapter 7. Spectral analysis on graphs is given in Chapter 8. Blind spectral decomposition is discussed in Chapter 9. Finally, relations to other decomposition methods, such as multiresolution analysis, are discussed in Chapter 10. Perspectives and future directions of image processing, including multiphysics imaging, are given in Chapter 11.
scientific article; zbMATH DE number 6875596