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| Preface to the Second Edition | |
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| Introduction | |
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| Equations of Motion for Moving Interfaces | |
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| Formulation of Interface Propagation | |
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| A boundary value formulation | |
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| An initial value formulation | |
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| Advantages of these perspectives | |
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| A general framework | |
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| A look ahead/A look back | |
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| A larger perspective | |
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| Theory and Algorithms | |
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| Theory of Curve and Surface Evolution | |
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| Fundamental formulation | |
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| Total variation: stability and the growth of oscillations | |
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| The role of entropy conditions and weak solutions | |
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| Effects of curvature | |
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| Viscosity Solutions and Hamilton-Jacobi Equations | |
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| Viscosity solutions of Hamilton-Jacobi equations | |
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| Some additional comments and references | |
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| Traditional Techniques for Tracking Interfaces | |
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| Marker/string methods | |
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| Volume-of-fluid techniques | |
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| Constructing an approximation to the gradient | |
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| Hyperbolic Conservation Laws | |
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| The linear wave equation | |
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| The non-linear wave equation | |
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| Basic Algorithms for Interface Evolution | |
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| Convergence of schemes for Hamilton-Jacobi equations | |
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| Hyperbolic schemes and Hamilton-Jacobi equations | |
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| The example of a propagating one-dimensional graph | |
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| The initial value problem: the Level Set Method | |
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| The boundary value problem: the stationary method | |
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| Schemes for non-convex speed functions | |
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| Approximations to geometric variables | |
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| Calculating additional quantities | |
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| Initialization | |
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| Computational domain boundary conditions | |
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| Putting it all together | |
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| Efficiency, Adaptivity, and Extensions | |
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| Efficient Schemes: the Narrow Band Level Set Method | |
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| Parallel algorithms | |
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| Adaptive mesh refinement | |
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| Narrow banding and fast methods | |
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| Details of the Narrow Band implementation | |
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| Efficient Schemes: Fast Marching Methods | |
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| Iteration | |
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| Causality | |
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| The update procedure for the Fast Marching Method | |
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| Heap sorts and computational efficiency | |
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| Initial conditions | |
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| Network path algorithms | |
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| Optimal orderings | |
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| Higher accuracy Fast Marching Methods | |
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| Non-uniform orthogonal grids | |
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| General static Hamilton-Jacobi equations | |
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| Some clarifying comments | |
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| Triangulated Versions of Level Set Methods | |
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| Fundamentals and notation | |
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| A monotone scheme for H ([down triangle, open]u) | |
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| A positive scheme for homogeneous H ([down triangle, open]u) | |
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| A Petrov-Galerkin formulation | |
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| Time integration schemes | |
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| Algorithms | |
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| Schemes for curvature flow | |
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| Mesh adaptivity | |
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| Triangulated Fast Marching Methods | |
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| The update procedure | |
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| A scheme for a particular triangulated domain | |
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| Fast Marching Methods on triangulated domains | |
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| Constructing Extension Velocities | |
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| The need for extension velocities | |
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| Various approaches to extension velocities | |
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| Equations for extension velocities | |
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| Building extension velocities | |
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| A quick demonstration | |
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| Re-initialization | |
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| Tests of Basic Methods | |
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| The basic Cartesian Level Set Method | |
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| Triangulated Level Set Methods for H-J equations | |
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| Accuracy of Fast Marching Methods | |
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| Tests of extension velocity methodology | |
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| Building Level Set and Fast Marching Applications | |
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| Applications | |
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| Geometry | |
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| Statement of problem | |
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| Equations of motion | |
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| Results | |
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| Flows under more general metrics | |
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| Volume-preserving flows | |
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| Motion under the second derivative of curvature | |
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| Triple points: variational and diffusion methods | |
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| Grid Generation | |
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| Statement of problem | |
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| Equations of motion | |
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| Results, complications, and future work | |
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| Image Enhancement and Noise Removal | |
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| Statement of problem | |
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| Equations of motion | |
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| Results | |
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| Related work | |
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| Computer Vision: Shape Detection and Recognition | |
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| Shape-from-shading | |
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| Shape detection/recovery | |
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| Surface evolution and the stereo problem | |
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| Reconstruction of obstacles in inverse problems | |
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| Shape recognition | |
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| Combustion, Solidification, Fluids, and Electromigration | |
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| Combustion | |
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| Crystal growth and dendritic solidification | |
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| Fluid mechanics | |
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| Additional applications | |
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| Void evolution and electromigration | |
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| Computational Geometry and Computer-aided Design | |
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| Shape-Offsetting | |
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| Voronoi diagrams | |
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| Curve flows with constraints | |
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| Minimal surfaces and surfaces of prescribed curvature | |
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| Extensions to surfaces of prescribed curvature | |
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| Boolean operations on shapes | |
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| Extracting and combining two-dimensional shapes | |
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| Shape smoothing | |
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| Optimality and First Arrivals | |
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| Optimal path planning | |
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| Constructing shortest paths on weighted domains | |
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| Constructing shortest paths on manifolds | |
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| Seismic traveltimes | |
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| Aircraft collision avoidance using Level Set Methods | |
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| Visibility evaluations | |
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| Etching and Deposition in Microchip Fabrication | |
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| Physical effects and background | |
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| Equations of motion for etching/deposition | |
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| Additional numerical issues | |
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| Two-dimensional results | |
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| Three-dimensional simulations | |
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| Timings | |
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| Validation with experimental results | |
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| Summary/New Areas/Future Work | |
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| Bibliography | |
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| Index | |