Variational methods in image processing

by Vese, Luminita Aura

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Full title :Variational methods in image processing / Luminita A. Vese, and Carole Le Guyader.

Summary

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 ReconstructionNonlocal 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 ModelingNumerical 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 ContoursPiecewise-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 Gateaux 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 pâ Harmonic Flows Introduction The S1 case The S2 case Numerical Experiments Concluding Remarks and Discussions for More General Manifolds Exercises appear at the end of each chapter.