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## Computing Geodesic Paths on Manifolds (1998)

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Venue: | Proc. Natl. Acad. Sci. USA |

Citations: | 294 - 28 self |

### Citations

808 | Shape modeling with front propagation: A level set approach
- Malladi, Sethian, et al.
- 1995
(Show Context)
Citation Context ...made fast by conning the \building zone" to a narrow band around the front, motivated by the narrow band introduced in Chopp [3], used in recovering shapes from images in Malladi, Sethian and Vem=-=uri [5]-=-, and analyzed extensively by Adalsteinsson and Sethian in [1]. The idea is to sweep the front ahead in an upwind fashion by considering a set of points in a narrow band around the existing front, and... |

630 | A fast marching level set method for monotonically advancing fronts,
- Sethian
- 1996
(Show Context)
Citation Context ...awrence Berkeley Laboratory University of California, Berkeley, California 94720 Accepted for publication, Proc. National. Academy of Sciences, To appear: July, 1997 Abstract The Fast Marching Method =-=[8]-=- is a numerical algorithm for solving the Eikonal equation on a rectangular orthogonal mesh in O(M log M) steps, where M is the total number of grid points. In this paper we extend the Fast Marching M... |

423 | A Fast Level Set Method for Propagating Interfaces”.
- Adalsteinsson, Sethian
- 1995
(Show Context)
Citation Context ...und the front, motivated by the narrow band introduced in Chopp [3], used in recovering shapes from images in Malladi, Sethian and Vemuri [5], and analyzed extensively by Adalsteinsson and Sethian in =-=[1]-=-. The idea is to sweep the front ahead in an upwind fashion by considering a set of points in a narrow band around the existing front, and to march this narrow band forward, freezing the values of exi... |

251 |
A viscosity solutions approach to shape-from-shading,
- Rouy, Tourin
- 1992
(Show Context)
Citation Context ...idea carefully considering the nature of upwind, entropy{satisfying approximations to the Eikonal equation. In more detail, consider one particular upwind approximation to the gradient, given by (see =-=[-=-6]) max(D x ij T; D +x ij T; 0) 2 + max(D y ij T; D +y ij T; 0) 2 1=2 = F ij ; (2) The central idea behind Fast Marching Methods is to systematically advance the front in an upwind fashion to produce... |

249 |
Level Set Methods: Evolving Interfaces
- Sethian
- 1996
(Show Context)
Citation Context ... point the one that produces the smallest value of T . Judicious programming and careful attention to \Far" values makes the above search extremely fast. This is the Fast Marching Method describe=-=d in [8, 9]-=-. 3 Fast Marching on a Particular Triangulated Planar Domain Our goal now is to extend this method to triangular domains. In order to do so, we shall build a monotone update procedure on the triangula... |

213 |
A Note on Two
- Dijkstra
- 1959
(Show Context)
Citation Context ...rdering of points during the update. The optimal ordering is executed using a heap operator to extract the next point in the update sweep. As such, the technique is a reminiscent of Dijkstra's method =-=[4]; h-=-owever, the resulting ron@math.lbl.gov y Please send all correspondence to J.A. Sethian at sethian@math.berkeley.edu z Supported in part by the Applied Mathematics Subprogram of the O��ce of Ener... |

133 |
Computing minimal surfaces via level set curvature flow.
- Chopp
- 1993
(Show Context)
Citation Context ...building the solution outward from the smallest T value. The algorithm is made fast by conning the \building zone" to a narrow band around the front, motivated by the narrow band introduced in Ch=-=opp [3]-=-, used in recovering shapes from images in Malladi, Sethian and Vemuri [5], and analyzed extensively by Adalsteinsson and Sethian in [1]. The idea is to sweep the front ahead in an upwind fashion by c... |

132 |
Curvature and the Evolution of Fronts,
- Sethian
- 1985
(Show Context)
Citation Context ...that the above Eikonal equation becomes non{dierentiable, and an appropriate weak solution must be built. The appropriate weak solution comes from satisfying the entropy condition; see, for example, [=-=7]-=-. The crucial point in this (or any such appropriate) numerical scheme is the correct direction of the upwinding and treatment of sonic points. For details and an extensive review, see [9]. The Fast M... |

77 | Numerical schemes for the Hamilton-Jacobi and level set equations on triangulated domains,
- Barth, Sethian
- 1998
(Show Context)
Citation Context ... DARPA under grant DMS{8919074. approximation is consistent in that it produces the correct shortest path on an orthogonal grid. For details about Fast Marching Methods, see [8, 9]. Barth and Sethian =-=[2]-=- have recently constructed operators for viscosity solutions to both the Eikonal equation and Hamilton-Jacobi equations on arbitrary triangulated domains. These operators exploit the upwind nature to ... |