Variational Methods in Image Processing

Filled with tables, illustrations, algorithms, and exercises, this self-contained textbook presents the principles, techniques, and applications of variational image processing. It focuses on variational models, their corresponding Euler-Lagrange equations, and numerical implementations for image processing. The book balances traditional computational models with more modern techniques that solve the latest challenges introduced by new image acquisition devices. It includes the necessary mathematical background and covers the most important problems in image processing.

Introduction and Book Overview. Mathematical Background. IMAGE RESTORATION: Variational Image Restoration Models. Nonlocal Variational Methods in Image Restoration. Image Decomposition into Cartoon and Texture. IMAGE SEGMENTATION AND BOUNDARY DETECTION: The Mumford and Shah Functional for Image Segmentation. Phase-Field Approximations to the Mumford and Shah Problem. Region-Based Variational Active Contours. Edge-Based Variational Snakes and Active Contours. APPLICATIONS: Nonlocal Mumford-Shah and Ambrosio-Tortorelli Variational Models. A Combined Segmentation and Registration Variational Model. Variational Image Registration Models. A Piecewise-Constant Binary Model for Electrical Impedance Tomography. Additive and Multiplicative Piecewise-Smooth Segmentation Models. Numerical Methods for p - harmonic Flows.