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174
HamiltonJacobi Skeletons
, 1999
"... The eikonal equation and variants of it are of significant interest for problems in computer vision and image processing. It is the basis for continuous versions of mathematical morphology, stereo, shapefromshading and for recent dynamic theories of shape. Its numerical simulation can be delicate, ..."
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Cited by 159 (11 self)
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, owing to the formation of singularities in the evolving front and is typically based on level set methods. However, there are more classical approaches rooted in Hamiltonian physics which have yet to be widely used by the computer vision community. In this paper we review the Hamiltonian formulation
Weighted ENO Schemes for HamiltonJacobi Equations
 SIAM J. Sci. Comput
, 1997
"... In this paper, we present a weighted ENO (essentially nonoscillatory) scheme to approximate the viscosity solution of the HamiltonJacobi equation: OE t +H(x 1 ; \Delta \Delta \Delta ; x d ; t; OE; OE x1 ; \Delta \Delta \Delta ; OE xd ) = 0: This weighted ENO scheme is constructed upon and has the ..."
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Cited by 229 (0 self)
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words. ENO, weighted ENO, HamiltonJacobi equation, shape from shading, level set. AMS(MOS) subject classification. 35L99, 65M06. 1 Introduction The HamiltonJacobi equation: OE t +H(x; t; OE; DOE) = 0; OE(x; 0) = OE 0 (x) (1.1) 1 Research supported by ONR N0001492J1890. Email: gsj
Multitime HamiltonJacobi Theory
 Proceedings of 8th WSEAS International Conference on Applied Computational Science (ACACOS09
, 2009
"... Abstract: This paper combines some ideas to obtain the multitime variants of HamiltonJacobi theory. Section 1 introduces some Riemannian first order jet bundles. Section 2 describes the multitime HamiltonJacobi PDE system connected to the path independent curvilinear integral action. Section 3 an ..."
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Cited by 3 (2 self)
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Abstract: This paper combines some ideas to obtain the multitime variants of HamiltonJacobi theory. Section 1 introduces some Riemannian first order jet bundles. Section 2 describes the multitime HamiltonJacobi PDE system connected to the path independent curvilinear integral action. Section 3
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 630 (24 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
Overapproximating Reachable Sets by HamiltonJacobi Projections
 Journal of Scientific Computation
, 2002
"... In earlier work, we showed that the set of states which can reach a target set of a continuous dynamic game is the zero sublevel set of the viscosity solution of a time dependent HamiltonJacobiIsaacs (HJI) partial differential equation (PDE). We have developed a numerical tool  based on the leve ..."
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Cited by 36 (8 self)
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In earlier work, we showed that the set of states which can reach a target set of a continuous dynamic game is the zero sublevel set of the viscosity solution of a time dependent HamiltonJacobiIsaacs (HJI) partial differential equation (PDE). We have developed a numerical tool  based
Numerical Schemes for the HamiltonJacobi and Level Set Equations on Triangulated Domains
, 1997
"... Borrowing from techniques developed for conservation law equations, numerical schemes which discretize the HamiltonJacobi (HJ), level set, and Eikonal equations on triangulated domains are presented. The first scheme is a provably monotone discretization for certain forms of the HJ equations. Unf ..."
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Cited by 77 (8 self)
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Borrowing from techniques developed for conservation law equations, numerical schemes which discretize the HamiltonJacobi (HJ), level set, and Eikonal equations on triangulated domains are presented. The first scheme is a provably monotone discretization for certain forms of the HJ equations
Growth Fronts of FirstOrder HamiltonJacobi Equation
, 2002
"... The aim of this paper is to investigate the propagation of fronts for a class of rstorder HamiltonJacobi equations, where certain properties of the Hamiltonian imply that the level set fu(:; t) 0g of the solution u is growing with respect to time. Besides monotonicity of this level set, we sho ..."
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Cited by 6 (0 self)
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The aim of this paper is to investigate the propagation of fronts for a class of rstorder HamiltonJacobi equations, where certain properties of the Hamiltonian imply that the level set fu(:; t) 0g of the solution u is growing with respect to time. Besides monotonicity of this level set, we
A level set approach for computing discontinuous solutions of HamiltonJacobi equations
 Math. Comp
"... Abstract. We introduce two types of finite difference methods to compute the Lsolution and the proper viscosity solution recently proposed by the second author for semidiscontinuous solutions to a class of HamiltonJacobi equations. By regarding the graph of the solution as the zero level curve of ..."
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Cited by 28 (9 self)
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Abstract. We introduce two types of finite difference methods to compute the Lsolution and the proper viscosity solution recently proposed by the second author for semidiscontinuous solutions to a class of HamiltonJacobi equations. By regarding the graph of the solution as the zero level curve
Stochastic homogenization of levelset convex HamiltonJacobi equations
 INT. MATH. RES. NOT
, 2012
"... ..."
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