Variational methods in image processing. (2016)

• Record Type: Book
• Further Information: Note: Luminita A. Vese and Carole Le Guyader.
• Authors: Vese, Luminita A; Le Guyader, Carole
• Contents: Introduction and Book Overview; Introduction; Overview Mathematical Background; Tikhonov Regularization of Ill-Posed Inverse Problems; Maximum a Posteriori (MAP) Estimate; Convolution; Fourier Transform; Topologies on Banach Spaces; Sobolev and BV Spaces; Calculus of Variations; Geometric Curve Evolution; Variational Level Set Methods; Numerical Analysis Image Restoration; Variational Image Restoration Models; Linear Degradation Model with Gaussian Noise and Total Variation Regularization; Numerical Results for Image Restoration; Compressive Sensing for Computerized Tomography Reconstruction Nonlocal Variational Methods in Image Restoration ; Introduction to Neighborhood Filters and NL Means; Variational Nonlocal Regularization for Image Restoration; Numerical Results for Image Restoration Image Decomposition into Cartoon and Texture; Modeling; Numerical Results for Image Decomposition into Cartoon and Texture Image Segmentation and Boundary Detection ; Mumford and Shah Functional for Image Segmentation ; Description of the Mumford and Shah Model; Weak Formulation of the Mumford and Shah Functional: MSH1 ; Mumford and Shah TV Functional: MSTV Phase-Field Approximations to the Mumford and Shah Problem; Ambrosio and Tortorelli Phase-Field Elliptic Approximations; Shah Approximation to the MSTV Functional; Applications to Image Restoration Region-Based Variational Active Contours ; Piecewise-Constant Mumford and Shah Segmentation Using Level Sets; Piecewise-Smooth Mumford and Shah Segmentation Using Level Sets; Applications to Variational Image Restoration with Segmentation-Based Regularization and Level Sets Edge-Based Variational Snakes and Active Contours; Snake Model; Geodesic Active Contours; Alignment Term; Topology-Preserving Snakes Model Applications; Nonlocal Mumford–Shah and Ambrosio–Tortorelli Variational Models; Characterization of Minimizers u; Gâteaux Derivative of Nonlocal M-S Regularizers; Image Restoration with NL/MS Regularizers; Numerical Discretizations; Experimental Results and Comparisons A Combined Segmentation and Registration Variational Model; Description of the Model; Implementation; Numerical Experiments Variational Image Registration Models ; Introduction; A Variational Image Registration Algorithm Using Nonlinear Elasticity Regularization; Experimental Results A Piecewise-Constant Binary Model for Electrical Impedance Tomography; Introduction; Formulation of the Minimization; Numerical Details and Reconstruction Results Additive and Multiplicative Piecewise-Smooth Segmentation Models ; Piecewise-Smooth Model with Additive Noise (APS); Piecewise-Smooth Model with Multiplicative Noise (MPS) Numerical Methods for p −Harmonic Flows; Introduction; The S 1 case; The S 2 case; Numerical Experiments; Concluding Remarks and Discussions for More General Manifolds Exercises appear at the end of each chapter.
• Edition: 1st
• Publisher Details: Boca Raton : Chapman & Hall/CRC
• Publication Date: 2016
• Extent: 1 online resource, illustrations (black and white)
• Subjects: 621.3670151564; Image processing -- Mathematical models; Variational inequalities (Mathematics)
• Languages: English
• ISBNs: 9781439849743
• Related ISBNs: 9781439849736
• Notes: Note: Description based on CIP data; resource not viewed.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.