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Copyright:
1996, 1999, 2006
J.A. Sethian

Level Set Methods
Evolving Interfaces in Geometry, Fluid Mechanics, Computer Vision, and
Materials Science
J.A. Sethian, Cambridge University Press, 1996
Cambridge Monograph on Applied and Computational Mathematics
Overview
This first edition book is an introduction to level set methods, which are
numerical techniques for analyzing and computing interface motion in a host
of settings. The numerical techniques can be used to track threedimensional
complex fronts that can develop sharp corners and change topology as they
evolve. The text includes applications from physics, chemistry,
fluid mechanics, combustion, image processing, material science,
seismology, fabrication of microelectronic components, computer vision and
control theory.
The book is intended for mathematicians, applied scientists,
practicing engineers, computer graphic artists, and anyone interested in the
evolution of boundaries and interfaces.
The text is an equal blend of theory, implementations, and applications areas,
including detailed descriptions of the appropriate numerical schemes.
Comparison with new edition
There is a new edition of this book, available in both hardback and
paperback, entitled
Level Set Methods and Fast Marching Methods.
This new book includes everything in the first edition, plus a large
collection of new topics.
For details, go to
Level Set Methods and Fast Marching Methods
Table of Contents for First Edition

PART I: EQUATIONS OF MOTION FOR MOVING INTERFACES
 Stability of Fronts, Total variation, Role of curvature and
Entropy conditions
 The TimeDependent Level Set formulation
 Topological Change, Curvature Terms, and Multidimensionality
 The Stationary Level Set formulation
 Conversion to Static HamiltonJacobi Equation

PART II: APPROXIMATION SCHEMES FOR LEVEL SET EQUATIONS

Traditional Techniques:
 Marker/String Methods
 VolumeofFluid/Cell Methods
 Hyperbolic Conservation Laws:
 The Wave Equation, Characteristics, Schocks, and Entropy Conditions
 Weak Solutions, Flux Conditions, and Riemann Problems
 Schemes for the Level Set Equation
 Convex Schemes: First and Second Order
 NonConvex Schemes: First and Second Order
 Boundary Conditions and Initializations
 A Hierarchy of Fast Level Set Methods
 Parallel Algorithms
 Adaptive Mesh Methods
 Fast Narrow Band Methods
 Extensions to the Basic Method
 Masking, Sources, and Sinks
 Discontinuous Speed Functions and Subgrid Resolution
 Multiple Interfaces and Triple Points

PART III: VISCOSITY SOLUTIONS, HAMILTONJACOBI EQUATIONS, AND FAST
MARCHING METHODS
 Viscosity Solutions of HamiltonJacobi Equations
 Fast Marching Methods
 How to solve the Eikonal Equation on a 200x200x200 grid in under 30 seconds

PART IV: APPLICATIONS
 Motion of Curves and Surfaces under Curvature
 Sintering of Materials
 Grid Generation: Two and ThreeDimensional BodyFitted Grids
 Image Enhancement and Noise Removal
 Combustion: Flame Stability under Exothermic and Vortical Effects
 Crystal Growth and Dendritic Solidification
 TwoFluid Flow, Motions of Thermals, Role of Surface Tension
 Shape Detection and Recovery in Medical Imaging
 Shape Recognition: Optical Character Recognition and Neural Nets
 Shape Offsetting in CAD
 ShapefromShading in Computer Vision
 Photolithography Development in SemiConductor Manufacturing
 Computing Optimal Paths on Networks
 Construction of Geodesics on Surfaces
 Seimsic Travel Times: Computing First Arrival Times
 Robotic Navigation with Constraints
 Etching and Deposition in Semiconductor Manufacturing
