Variational Methods in Image Processing

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Luminita A. Vese Carole Le Guyader (National Institute of Applied Sciences (INSA) Rouen, France)

Variational Methods in Image Processing

Luminita A. Vese, Carole Le Guyader (National Institute of Applied Sciences (INSA) Rouen, France)

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English

Chapman & Hall/CRC
18 December 2015

Applied mathematics; Imaging systems & technology; Graphical & digital media applications

Series: Chapman & Hall/CRC Mathematical and Computational Imaging Sciences Series

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.

By: Luminita A. Vese, Carole Le Guyader (National Institute of Applied Sciences (INSA) Rouen, France)
Imprint: Chapman & Hall/CRC
Country of Publication: United States
Dimensions: Height: 234mm, Width: 156mm, Spine: 25mm
Weight: 714g
ISBN: 9781439849736
ISBN 10: 1439849730
Series: Chapman & Hall/CRC Mathematical and Computational Imaging Sciences Series
Pages: 386
Publication Date: 18 December 2015
Audience: College/higher education , Further / Higher Education
Format: Hardback
Publisher's Status: Active

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.

Reviews for Variational Methods in Image Processing

This book is a must-have for students and researchers working in mathematical image analysis, in particular on segmentation problems. It covers in a pedagogical way the mathematical foundations, classical convex and non-convex segmentation methods, as well as more advanced subjects such as non-local regularizations. This book also features a lot of graphical illustrations and pseudo-codes of algorithms. It showcases several concrete applications to medical imaging, and the availability of the corresponding MATLAB code is a great feature. -Gabriel Peyre, CNRS Senior Researcher, Universite Paris-Dauphine