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.
