Level set methods: an overview and some recent results

Keywords

Level set method, Motion (physics), Lipschitz continuity, Set (abstract data type), Vortex

References

• THE WULFF SHAPE AS THE ASYMPTOTIC LIMIT OF A GROWING CRYSTALLINE INTERFACEStanley Osher, Barry Merriman — 1997
• High-order essentially nonsocillatory schemes for Hamilton-Jacobi equationsStanley Osher, Chi‐Wang Shu — 1990
• Nonsteady flame propagationH. Markstein — 1964
• Solutions de viscosité des équations de Hamilton-JacobiGuy Barles — 1994
• A Boundary Condition Capturing Method for Multiphase Incompressible FlowMyungjoo Kang, Ronald Fedkiw, Xudong Liu — 2000
• Markov chain approximations for deterministic control problems with affine dynamics and quadratic cost in the controlMichelle Boué, Paul Dupuis — 1997
• Images, Numerical Analysis of Singularities and Shock FiltersL. Rudin — 1987
• The growth of crystals and the equilibrium structure of their surfacesW. K. Burton, N. Cabrera, F. C. Frank — 1951
• An Adaptive Finite Element Method for Two-Phase Stefan Problems in Two Space Dimensions. II: Implementation and Numerical ExperimentsRicardo H. Nochetto, Maurizio Paolini, C. Verdi — 1991
• Capturing the Behavior of Bubbles and Drops Using the Variational Level Set ApproachHongkai Zhao, Barry Merriman, Stanley Osher — 1998
• Simulation of dislocations on the mesoscopic scale. II. Application to strained-layer relaxationK. W. Schwarz — 1999
• Modeling and numerical simulations of dendritic crystal growthRyo Kobayashi — 1993
• A Fast Level Set Method for Propagating InterfacesDavid Adalsteinsson, James A. Sethian — 1995
• Simulation of dislocations on the mesoscopic scale. I. Methods and examplesK. W. Schwarz — 1999
• A Numerical Method for Solving Incompressible Flow Problems with a Surface of DiscontinuityBrian T. Helenbrook, Luigi Martinelli, Chung K. Law — 1999
• Motion of curves in three spatial dimensions using a level set approachPaul Burchard, Li‐Tien Cheng, Barry Merriman — 2001
• On Hopf's formulas for solutions of Hamilton-Jacobi equationsMartino Bardi, L. C. Evans — 1984
• Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulationsStanley Osher, James A. Sethian — 1988
• Efficient Algorithms for Diffusion-Generated Motion by Mean CurvatureSteven J. Ruuth — 1998
• Fast Sweeping Algorithms for a Class of Hamilton-Jacobi EquationsYen‐Hsi Richard Tsai, Li‐Tien Cheng, Stanley Osher — 2003

Cited by

• Active Contours for Multispectral Images With Non-Homogeneous Sub-RegionsWesley E. Snyder — 2005
• The Jacobi Method in Reconfigurable HardwareSafaa J. Kasbah, Issam Damaj — 2007
• Theory and numerical simulation of droplet dynamics in complex flows--a review.Barbara N. Allison — 2004
• A Level Set Approach Reflecting Sheet Structure with Single Auxiliary Function for Evolving Spirals on Crystal SurfacesTakeshi Ohtsuka, Yen‐Hsi Richard Tsai, Yoshikazu Giga — 2012
• ODD Level Set: a new method for simulation of free surface problemsJulio García Espinosa, Amber Tomas — 2006
• Multiple-Region Segmentation Without Supervision by Adaptive Global Maximum ClusteringPhilippe Tartera — 2012
• The effects of temperature equilibrium in mixed cell hydrodynamicsT. Masser — 2007
• Metodología de análisis del comportamiento de presas de escollera frente a un sobrevertido.Antonia Larese, Riccardo Rossi, Eugenio Oñate Ibáñez — 2010
• A Parallelized sharp-interface fixed grid method for moving boundary problemsSaikrishna Marella — 2006
• Anisotropic Diffusion by a Recursive Linear Convolving Method : Application to Space-time Segmentation and Pattern RecognitionSantiago Venegas-Martinez, Juan M. Rendón, Georges Stamon — 2002
• Modélisation par champ de phases de la croissance de la ferrite allotriomorphe dans les aciers Fe-C-MnAlexandre Viardin — 2010
• Computational Study of Adiabatic Bubble Growth Dynamics from Submerged Orifices in Aqueous Solutions of SurfactantsAnirudh M. Deodhar — 2012
• Unsupervised Texture Segmentation via Applying Geodesic Active Regions to Gaborian Feature SpaceYuan He, Yupin Luo, Dongcheng Hu — 2007
• Dynamic Visibility in an Implicit FrameworkRichard Tzong‐Han Tsai, Li-Tien Chengz, Paul Burchardx — 2007
• Set-based Cascading Approaches for Magnetic Resonance (MR) Image Segmentation (SCAMIS)Jiang Liu, Tze-Yun Leong, Kin Ban Chee — 2006
• Numerical Construction of Static Fluid Interfaces with the Embedding FormalismC. J. Laing — 2014
• Développement d’une méthode de simulation d’écoulements à bulles et à gouttes.Thomas Bonometti — 2005
• The Local Level-Set Extraction Method for Robust Calculation of Geometric Quantities in the Level-Set MethodÅsmund Ervik — 2012
• Dynamic Programming Algorithms for Planning and Robotics in Continuous Domains and the Hamilton-Jacobi EquationIan M. Mitchell — 2008
• Novel Methods for Multidimensional Image SegmentationÉric Pichon, Allen Tannenbaum — 2005

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