Variational Methods in Image Processing

Variational methods have proven to be powerful techniques for solving many image processing tasks. Balancing theory with practical approaches, this book covers a wide range of variational methods and their applications. The first part of the text focuses on image restoration, covering such topics as regularization, minimization, and nonlocal and higher-order variational methods. The second part addresses image segmentation, including the Mumford and Shah segmentation problem. The final section discusses varational image processing on manifolds. An accompanying CD-ROM includes MATLAB(R) code and color figures.

Front Cover; Contents; List of Figures; List of Tables; Preface; Chapter 1: Introduction and Book Overview; Chapter 2: Mathematical Background; Chapter 3: Variational Image Restoration Models; Chapter 4: Nonlocal Variational Methods in Image Restoration; Chapter 5: Image Decomposition into Cartoon and Texture; Chapter 6: Mumford and Shah Functional for Image Segmentation; Chapter 7: Phase-Field Approximations to Mumford and Shah Problem; Chapter 8: Region-Based Variational Active Contours; Chapter 9: Edge-Based Variational Snakes and Active Contours.

Chapter 10: Nonlocal Mumford-Shah and Ambrosio-Tortorelli Variational Models for Color Image RestorationChapter 11: A Combined Segmentation and Registration Variational Model; Chapter 12: Variational Image Registration Models; Chapter 13: Piecewise-Constant Binary Model for Electrical Impedance Tomography; Chapter 14: Additive and Multiplicative Piecewise-Smooth Segmentation Models in a Functional Minimization Approach; Chapter 15: Numerical Methods for p-Harmonic Flows and Applications to Image Processing; Bibliography; Color Insert; Back Cover.