| Preface to the Second Edition | p. xi |
| Introduction | p. xv |
| Equations of Motion for Moving Interfaces | p. 1 |
| Formulation of Interface Propagation | p. 3 |
| A boundary value formulation | p. 4 |
| An initial value formulation | p. 6 |
| Advantages of these perspectives | p. 8 |
| A general framework | p. 10 |
| A look ahead/A look back | p. 11 |
| A larger perspective | p. 12 |
| Theory and Algorithms | p. 15 |
| Theory of Curve and Surface Evolution | p. 17 |
| Fundamental formulation | p. 17 |
| Total variation: stability and the growth of oscillations | p. 18 |
| The role of entropy conditions and weak solutions | p. 20 |
| Effects of curvature | p. 24 |
| Viscosity Solutions and Hamilton-Jacobi Equations | p. 29 |
| Viscosity solutions of Hamilton-Jacobi equations | p. 30 |
| Some additional comments and references | p. 32 |
| Traditional Techniques for Tracking Interfaces | p. 34 |
| Marker/string methods | p. 34 |
| Volume-of-fluid techniques | p. 38 |
| Constructing an approximation to the gradient | p. 41 |
| Hyperbolic Conservation Laws | p. 44 |
| The linear wave equation | p. 44 |
| The non-linear wave equation | p. 48 |
| Basic Algorithms for Interface Evolution | p. 60 |
| Convergence of schemes for Hamilton-Jacobi equations | p. 60 |
| Hyperbolic schemes and Hamilton-Jacobi equations | p. 61 |
| The example of a propagating one-dimensional graph | p. 63 |
| The initial value problem: the Level Set Method | p. 65 |
| The boundary value problem: the stationary method | p. 68 |
| Schemes for non-convex speed functions | p. 69 |
| Approximations to geometric variables | p. 69 |
| Calculating additional quantities | p. 71 |
| Initialization | p. 72 |
| Computational domain boundary conditions | p. 72 |
| Putting it all together | p. 73 |
| Efficiency, Adaptivity, and Extensions | p. 75 |
| Efficient Schemes: the Narrow Band Level Set Method | p. 77 |
| Parallel algorithms | p. 77 |
| Adaptive mesh refinement | p. 78 |
| Narrow banding and fast methods | p. 80 |
| Details of the Narrow Band implementation | p. 84 |
| Efficient Schemes: Fast Marching Methods | p. 86 |
| Iteration | p. 87 |
| Causality | p. 87 |
| The update procedure for the Fast Marching Method | p. 90 |
| Heap sorts and computational efficiency | p. 90 |
| Initial conditions | p. 92 |
| Network path algorithms | p. 93 |
| Optimal orderings | p. 96 |
| Higher accuracy Fast Marching Methods | p. 96 |
| Non-uniform orthogonal grids | p. 98 |
| General static Hamilton-Jacobi equations | p. 99 |
| Some clarifying comments | p. 99 |
| Triangulated Versions of Level Set Methods | p. 101 |
| Fundamentals and notation | p. 102 |
| A monotone scheme for H ([down triangle, open]u) | p. 105 |
| A positive scheme for homogeneous H ([down triangle, open]u) | p. 109 |
| A Petrov-Galerkin formulation | p. 112 |
| Time integration schemes | p. 113 |
| Algorithms | p. 114 |
| Schemes for curvature flow | p. 116 |
| Mesh adaptivity | p. 118 |
| Triangulated Fast Marching Methods | p. 120 |
| The update procedure | p. 120 |
| A scheme for a particular triangulated domain | p. 121 |
| Fast Marching Methods on triangulated domains | p. 123 |
| Constructing Extension Velocities | p. 127 |
| The need for extension velocities | p. 127 |
| Various approaches to extension velocities | p. 129 |
| Equations for extension velocities | p. 131 |
| Building extension velocities | p. 133 |
| A quick demonstration | p. 137 |
| Re-initialization | p. 138 |
| Tests of Basic Methods | p. 141 |
| The basic Cartesian Level Set Method | p. 141 |
| Triangulated Level Set Methods for H-J equations | p. 146 |
| Accuracy of Fast Marching Methods | p. 150 |
| Tests of extension velocity methodology | p. 153 |
| Building Level Set and Fast Marching Applications | p. 161 |
| Applications | p. 165 |
| Geometry | p. 167 |
| Statement of problem | p. 167 |
| Equations of motion | p. 169 |
| Results | p. 169 |
| Flows under more general metrics | p. 175 |
| Volume-preserving flows | p. 175 |
| Motion under the second derivative of curvature | p. 177 |
| Triple points: variational and diffusion methods | p. 183 |
| Grid Generation | p. 191 |
| Statement of problem | p. 191 |
| Equations of motion | p. 193 |
| Results, complications, and future work | p. 196 |
| Image Enhancement and Noise Removal | p. 200 |
| Statement of problem | p. 200 |
| Equations of motion | p. 202 |
| Results | p. 208 |
| Related work | p. 211 |
| Computer Vision: Shape Detection and Recognition | p. 214 |
| Shape-from-shading | p. 215 |
| Shape detection/recovery | p. 218 |
| Surface evolution and the stereo problem | p. 227 |
| Reconstruction of obstacles in inverse problems | p. 229 |
| Shape recognition | p. 231 |
| Combustion, Solidification, Fluids, and Electromigration | p. 240 |
| Combustion | p. 241 |
| Crystal growth and dendritic solidification | p. 249 |
| Fluid mechanics | p. 255 |
| Additional applications | p. 258 |
| Void evolution and electromigration | p. 261 |
| Computational Geometry and Computer-aided Design | p. 267 |
| Shape-Offsetting | p. 267 |
| Voronoi diagrams | p. 268 |
| Curve flows with constraints | p. 269 |
| Minimal surfaces and surfaces of prescribed curvature | p. 270 |
| Extensions to surfaces of prescribed curvature | p. 274 |
| Boolean operations on shapes | p. 277 |
| Extracting and combining two-dimensional shapes | p. 281 |
| Shape smoothing | p. 282 |
| Optimality and First Arrivals | p. 284 |
| Optimal path planning | p. 284 |
| Constructing shortest paths on weighted domains | p. 289 |
| Constructing shortest paths on manifolds | p. 292 |
| Seismic traveltimes | p. 298 |
| Aircraft collision avoidance using Level Set Methods | p. 305 |
| Visibility evaluations | p. 307 |
| Etching and Deposition in Microchip Fabrication | p. 313 |
| Physical effects and background | p. 313 |
| Equations of motion for etching/deposition | p. 317 |
| Additional numerical issues | p. 324 |
| Two-dimensional results | p. 325 |
| Three-dimensional simulations | p. 342 |
| Timings | p. 348 |
| Validation with experimental results | p. 349 |
| Summary/New Areas/Future Work | p. 357 |
| Bibliography | p. 360 |
| Index | p. 376 |
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