Nonlinear Eigenproblems in Image Processing and Computer Vision

<p>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.</p>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.</p><p></p>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.</p>