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Fronts propagating with curvature dependent speed: algorithms based on Hamiltonâ€“Jacobi formulations
, 1988
"... We devise new numerical algorithms, called PSC algorithms, for following fronts propagating with curvaturedependent speed. The speed may be an arbitrary function of curvature, and the front also can be passively advected by an underlying flow. These algorithms approximate the equations of motion, w ..."
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Cited by 1167 (60 self)
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We devise new numerical algorithms, called PSC algorithms, for following fronts propagating with curvaturedependent speed. The speed may be an arbitrary function of curvature, and the front also can be passively advected by an underlying flow. These algorithms approximate the equations of motion
Hypersurfaces Moving With CurvatureDependent Speed: HamiltonJacobi Equations, Conservation Laws And Numerical Algorithms
, 1989
"... this paper is to show that algorithms based on direct parameterizations of the moving front face considerable difficulties. This is because such algorithms adhere to local properties of the solution, rather than the global structure. Conversely, the global properties of the motion can be captured by ..."
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and the Sloan Foundation. Hypersurfaces Moving with CurvatureDependent Speed: HamiltonJacobi Equations, Conservation Laws and Numerical Algorithms J.A. Sethian Department of Mathematics University of California Berkeley, CA. 94720 In many physical problems, interfaces move with speed that depends
LEVEL SET RESEARCH CURVATURE MOTION 1 Level Set Framework for Fronts Propagating with Curvature Dependent Speeds
"... PROPAGATING fronts with speeds linearly dependent on curvature is foundational to the level set method. Weexplore the use of FEMLAB to evolve fronts because FEMLAB handles complicated geometries and has an implicit solver. (curvature of a curve or surface involves second derivatives, which creates a ..."
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PROPAGATING fronts with speeds linearly dependent on curvature is foundational to the level set method. Weexplore the use of FEMLAB to evolve fronts because FEMLAB handles complicated geometries and has an implicit solver. (curvature of a curve or surface involves second derivatives, which creates
A Multigrid Strategy for Accelerating SteadyState Computations of Waves Propagating with Curvature Dependent Speeds
"... . A multigrid strategy is developed for accelerating the steady state computations of waves propagating with curvature depedent speeds. This will allow the rapid computation of a "burn table". In a high explosive material, the creation of a burn table will allow the elimination of solving ..."
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. A multigrid strategy is developed for accelerating the steady state computations of waves propagating with curvature depedent speeds. This will allow the rapid computation of a "burn table". In a high explosive material, the creation of a burn table will allow the elimination of solving
Shape modeling with front propagation: A level set approach
 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 1995
"... Shape modeling is an important constituent of computer vision as well as computer graphics research. Shape models aid the tasks of object representation and recognition. This paper presents a new approach to shape modeling which retains some of the attractive features of existing methods and over ..."
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Cited by 799 (20 self)
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than one object of interest, has the ability to split freely to represent each object. This method is based on the ideas developed by Osher and Sethian to model propagating solidhiquid interfaces with curvaturedependent speeds. The interface (front) is a closed, nonintersecting, hypersurface flowing
On CurvatureDependent Surface Evolution
, 1995
"... Computer vision applications require representations for surfaces that are intrinsic and reflect the hierarchical nature of their geometric structure. Curvaturedependent flows have been successfully used for shape representation in two dimensions, principally due to a theorem on curve shortening fl ..."
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Computer vision applications require representations for surfaces that are intrinsic and reflect the hierarchical nature of their geometric structure. Curvaturedependent flows have been successfully used for shape representation in two dimensions, principally due to a theorem on curve shortening
A Fast Marching Level Set Method for Monotonically Advancing Fronts
 PROC. NAT. ACAD. SCI
, 1995
"... We present a fast marching level set method for monotonically advancing fronts, which leads to an extremely fast scheme for solving the Eikonal equation. Level set methods are numerical techniques for computing the position of propagating fronts. They rely on an initial value partial differential eq ..."
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Cited by 618 (22 self)
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describe a particular case of such methods for interfaces whose speed depends only on local position. The technique works by coupling work on entropy conditions for interface motion, the theory of viscosity solutions for HamiltonJacobi equations and fast adaptive narrow band level set methods
A scaled conjugate gradient algorithm for fast supervised learning
 NEURAL NETWORKS
, 1993
"... A supervised learning algorithm (Scaled Conjugate Gradient, SCG) with superlinear convergence rate is introduced. The algorithm is based upon a class of optimization techniques well known in numerical analysis as the Conjugate Gradient Methods. SCG uses second order information from the neural netwo ..."
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Cited by 441 (0 self)
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FletcherGoldfarbShanno memoryless quasiNewton algorithm (BFGS) [1]. SCG yields a speedup of at least an order of magnitude relative to BP. The speedup depends on the convergence criterion, i.e., the bigger demand for reduction in error the bigger the speedup. SCG is fully automated including no user dependent parameters
JOURNAL OF COMPUTATIONAL PHYSICS 102, 128138 (1992) Projection Methods Coupled to Level Set Interface Techniques*
, 1991
"... In this work, we consider hydrodynamic problems with cold flame propagation by merging a secondorder projection method for viscous NavierStokes equations with modern techniques for computing the motion of interfaces propagating with curvaturedependent speeds. This is part of our efforts to try an ..."
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In this work, we consider hydrodynamic problems with cold flame propagation by merging a secondorder projection method for viscous NavierStokes equations with modern techniques for computing the motion of interfaces propagating with curvaturedependent speeds. This is part of our efforts to try
Relaxation schemes for curvaturedependent front propagation. submitted to Comm
 Pure Appl. Math
, 1996
"... Abstract. In this paper we study analytically and numerically a novel relaxation approximation for front evolution according to a curvature dependent local law. In the ChapmanEnskog expansion, this relaxation approximation leads to the level set equation for transport dominated front propagation, t ..."
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Cited by 3 (1 self)
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, the relaxation scheme captures the curvaturedependent front propagation, without discretizing directly the complicated, yet singular, mean curvature term.
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