Results 1 - 10 of 174

Hamilton-Jacobi Skeletons

by Kaleem Siddiqi, Sylvain Bouix, Allen Tannenbaum, Steven W. Zucker , 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, shape-from-shading and for recent dynamic theories of shape. Its numerical simulation can be delicate, ..."
Abstract - Cited by 159 (11 self) - Add to MetaCart
, 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 Hamilton-Jacobi Equations

by Guang-shan Jiang, Danping Peng - SIAM J. Sci. Comput , 1997
"... In this paper, we present a weighted ENO (essentially non-oscillatory) scheme to approximate the viscosity solution of the Hamilton-Jacobi 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 ..."
Abstract - Cited by 229 (0 self) - Add to MetaCart
words. ENO, weighted ENO, Hamilton-Jacobi equation, shape from shading, level set. AMS(MOS) subject classification. 35L99, 65M06. 1 Introduction The Hamilton-Jacobi equation: OE t +H(x; t; OE; DOE) = 0; OE(x; 0) = OE 0 (x) (1.1) 1 Research supported by ONR N00014-92-J-1890. Email: gsj

Multitime Hamilton-Jacobi Theory

by Constantin Udriste, Laura Matei, Iulian Duca - Proceedings of 8-th WSEAS International Conference on Applied Computational Science (ACACOS-09 , 2009
"... Abstract: This paper combines some ideas to obtain the multitime variants of Hamilton-Jacobi theory. Section 1 in-troduces some Riemannian first order jet bundles. Section 2 describes the multitime Hamilton-Jacobi PDE system connected to the path independent curvilinear integral action. Section 3 an ..."
Abstract - Cited by 3 (2 self) - Add to MetaCart
Abstract: This paper combines some ideas to obtain the multitime variants of Hamilton-Jacobi theory. Section 1 in-troduces some Riemannian first order jet bundles. Section 2 describes the multitime Hamilton-Jacobi PDE system connected to the path independent curvilinear integral action. Section 3

Level-set convex Hamilton-Jacobi . . .

by C. Imbert, et al.
"... ..."
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A Fast Marching Level Set Method for Monotonically Advancing Fronts

by J. A. Sethian - 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 ..."
Abstract - Cited by 630 (24 self) - Add to MetaCart
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 Hamilton-Jacobi equations and fast adaptive narrow band level set methods

Overapproximating Reachable Sets by Hamilton-Jacobi Projections

by Ian M. Mitchell, Claire J. Tomlin - 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 Hamilton-Jacobi-Isaacs (HJI) partial differential equation (PDE). We have developed a numerical tool -- based on the leve ..."
Abstract - Cited by 36 (8 self) - Add to MetaCart
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 Hamilton-Jacobi-Isaacs (HJI) partial differential equation (PDE). We have developed a numerical tool -- based

Numerical Schemes for the Hamilton-Jacobi and Level Set Equations on Triangulated Domains

by Timothy J. Barth, James A. Sethian , 1997
"... Borrowing from techniques developed for conservation law equations, numerical schemes which discretize the Hamilton-Jacobi (H-J), level set, and Eikonal equations on triangulated domains are presented. The first scheme is a provably monotone discretization for certain forms of the H-J equations. Unf ..."
Abstract - Cited by 77 (8 self) - Add to MetaCart
Borrowing from techniques developed for conservation law equations, numerical schemes which discretize the Hamilton-Jacobi (H-J), level set, and Eikonal equations on triangulated domains are presented. The first scheme is a provably monotone discretization for certain forms of the H-J equations

Growth Fronts of First-Order Hamilton-Jacobi Equation

by Martin Burger , 2002
"... The aim of this paper is to investigate the propagation of fronts for a class of rstorder Hamilton-Jacobi 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 ..."
Abstract - Cited by 6 (0 self) - Add to MetaCart
The aim of this paper is to investigate the propagation of fronts for a class of rstorder Hamilton-Jacobi 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 Hamilton-Jacobi equations

by Yen-hsi Richard Tsai, Yoshikazu Giga, Stanley Osher - Math. Comp
"... Abstract. We introduce two types of finite difference methods to compute the L-solution and the proper viscosity solution recently proposed by the second author for semi-discontinuous solutions to a class of Hamilton-Jacobi equations. By regarding the graph of the solution as the zero level curve of ..."
Abstract - Cited by 28 (9 self) - Add to MetaCart
Abstract. We introduce two types of finite difference methods to compute the L-solution and the proper viscosity solution recently proposed by the second author for semi-discontinuous solutions to a class of Hamilton-Jacobi equations. By regarding the graph of the solution as the zero level curve

Stochastic homogenization of level-set convex Hamilton-Jacobi equations

by Scott N. Armstrong, Panagiotis E. Souganidis - INT. MATH. RES. NOT , 2012
"... ..."
Abstract - Cited by 14 (4 self) - Add to MetaCart
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Results 1 - 10 of 174