Variational Methods in Image Processing Chapman & Hall/CRC Mathematical and Computational Imaging Sciences Series

Variational Methods in Image Processing presents the principles, techniques, and applications of variational image processing. The text focuses on variational models, their corresponding Euler?Lagrange equations, and numerical implementations for image processing. It balances traditional computational models with more modern techniques that solve the latest challenges introduced by new image acquisition devices.

The book addresses the most important problems in image processing along with other related problems and applications. Each chapter presents the problem, discusses its mathematical formulation as a minimization problem, analyzes its mathematical well-posedness, derives the associated Euler?Lagrange equations, describes the numerical approximations and algorithms, explains several numerical results, and includes a list of exercises. MATLAB® codes are available online.

Filled with tables, illustrations, and algorithms, this self-contained textbook is primarily for advanced undergraduate and graduate students in applied mathematics, scientific computing, medical imaging, computer vision, computer science, and engineering. It also offers a detailed overview of the relevant variational models for engineers, professionals from academia, and those in the image processing industry.

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.

Luminita A. Vese is a professor in the Department of Mathematics at UCLA. She is the author or co-author of numerous papers and book chapters on the calculus of variations, PDEs, numerical analysis, image analysis, curve evolution, computer vision, and free boundary problems.

Carole Le Guyader is an associate professor in the mathematical and software engineering department at the National Institute of Applied Sciences of Rouen. She has authored or co-authored many papers on analysis and simulation, digital imaging mathematics and applications, and parallel computing.