An Introduction To Nonlinear Image Processing

From a strict semantic point of view, nonlinear image processing encompasses all image processing that is not based on linear operators; however, from a practical, evolutionary point of view, the name itself is usually associated with the study of nonlinear filters, mainly the deterministic and nondeterministic analysis and design of logic-based operators. This Tutorial Text volume explores logic-based operators with emphasis on representation, design, and statistical optimization of nonlinear filters.

Nonlinear signal and image processing methods are fast emerging as an alternative to established linear methods for meeting the challenges of increasingly sophisticated applications. Advances in computing performance and nonlinear theory are making nonlinear techniques not only viable, but practical. This book details recent advances in nonl

This text provides insight into the design of optimal image processing operators for implementation directly into digital hardware. Starting with simple restoration examples and using the minimum of statistics, the book provides a design strategy for a wide range of image processing applications. The text is aimed principally at electronics engineers and computer scientists, but will also be of interest to anyone working with digital images.

This state-of-the-art book deals with the most important aspects of non-linear imaging challenges. The need for engineering and mathematical methods is essential for defining non-linear effects involved in such areas as computer vision, optical imaging, computer pattern recognition, and industrial automation challenges.

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.

Digital holography and digital image processing are twins born by computer era. They share origin, theoretical base, methods and algorithms. The present book describes these common fundamentals principles, methods and algorithms including image and hologram digitization, data compression, digital transforms and efficient computational algorithms, statistical and Monte-Carlo methods, image restoration and enhancement, image reconstruction in tomography and digital holography, discrete signal resampling and image geometrical transformations, accurate measurements and reliable target localization in images, recording and reconstruction of computer generated holograms, adaptive and nonlinear filters for sensor signal perfecting and image restoration and enhancement. The book combines theory, heavily illustrated practical methods and efficient computational algorithms and is written for senior-level undergraduate and graduate students, researchers and engineers in optics, photonics, opto-electronics and electronic engineering.

Morphological image processing, a standard part of the imaging scientist's toolbox, can be applied to a wide range of industrial applications. Concentrating on applications, this text shows how to analyse the problems and then develop successful algorithms to solve them.

Reporting the state of the art of colour image processing, this monograph fills a gap in the literature on digital signal and image processing. It contains numerous examples and pictures of colour image processing results, plus a library of algorithms implemented in C.