VARIATIONAL METHODS IN IMAGE PROCESSING

Introduction and Book Overview
Mathematical Background
Image Restoration
Variational Image Restoration Models
Nonlocal Variational Methods in Image RestorationImage Decomposition into Cartoon and Texture
Image Segmentation and Boundary Detection
Mumford and Shah Functional for Image Segmentation
Phase-Field Approximations to the Mumford and Shah Problem
Region-Based Variational Active ContoursEdge-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 ModelsA Piecewise-Constant Binary Model for Electrical Impedance Tomography
Additive and Multiplicative Piecewise-Smooth Segmentation ModelsNumerical Methods for p-Harmonic Flows

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.

Features
• Presents a thorough, self-contained guide to the latest variational approaches for image processing
• Shows how powerful variational techniques, such as the variational method by regularization, offer optimal and elegant solutions to many image processing tasks
• Covers the most important problems in image processing, including image restoration and image segmentation
• Includes the mathematical background necessary to understand the variational methods
• Provides MATLAB codes for the main models and algorithms on a supplementary website

A solutions manual and figure slides are available upon qualifying course adoption.

Authors
• 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.