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Fast Marching Methods

Sethian, J. A.·1999·SIAM Review
DOI 10.1137/s0036144598347059
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Abstract

Fast Marching Methods are numerical schemes for computing solutions to the nonlinear Eikonal equation and related static Hamilton--Jacobi equations. Based on entropy-satisfying upwind schemes and fast sorting techniques, they yield consistent, accurate, and highly efficient algorithms. They are optimal in the sense that the computational complexity of the algorithms is O(N log N), where N is the total number of points in the domain. The schemes are of use in a variety of applications, including problems in shape offsetting, computing distances from complex curves and surfaces, shape-from-shading, photolithographic development, computing first arrivals in seismic travel times, construction of shortest geodesics on surfaces, optimal path planning around obstacles, and visibility and reflection calculations. In this paper, we review the development of these techniques, including the theoretical and numerical underpinnings; provide details of the computational schemes, including higher order versions; and demonstrate the techniques in a collection of different areas.

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Research works printed but not linked: 35

  1. 10.1006/jcph.1995.1098 · DOI · Paper page
  2. 10.1006/jcph.1998.6007 · doi:10.1006/jcph.1998.6007
  3. 10.1006/jcph.1993.1092 · doi:10.1006/jcph.1993.1092
  4. Manber Udi, 1989, Introduction to algorithms
  5. 10.1090/S0002-9947-1984-0732102-X · DOI · Paper page
  6. 10.1090/S0273-0979-1992-00266-5 · DOI · Paper page
  7. 10.1016/0022-0396(85)90136-6 · doi:10.1016/0022-0396(85)90136-6
  8. Adil Bagirov, Numerical methods for minimizing quasidifferentiable functions: a survey and comparison, Nonconvex Optim. Appl., Vol. 43, Kluwer Acad. Publ., Dordrecht, 2000, 33–711766792 · doi:10.1007/978-1-4757-3137-8_2
  9. Dijkstra, E. W. A Note on Two Problems in Connection with Graphs , Numerische Mathematic, 1:269–271, 1959. · DOI · Paper page
  10. Garabedian, P., Partial Differential Equations, Wiley, New York, 1964.
  11. Kimmel, R., and Sethian, J. A. Fast Marching Methods for Robotic Navigation with Constraints , Center for Pure and Applied Mathematics Report, Univ. of California, Berkeley, May 1996, submitted for publication, Int. Journal Robotics Research, 1998.
  12. 10.1073/pnas.95.15.8431 · DOI · Paper page
  13. 10.1007/s004539910020 · DOI
  14. 10.1007/978-3-0348-8629-1 · DOI · Paper page
  15. Malladi, R., Sethian, J. A., and Vemuri, B. C. Evolutionary Fronts for Topology‐independent Shape Modeling and Recovery , in Proceedings of Third European Conference on Computer Vision, Stockholm, Sweden, Lecture Notes in Computer Science, 800:3–13, 1994. · doi:10.1007/3-540-57956-7_1
  16. Malladi, R., and Sethian, J. A. An O(NlogN) Algorithm for Shape Modeling , Proc. Nat. Acad. Sci., Vol. 93, 1996. · DOI
  17. 10.1016/0021-9991(88)90002-2 · DOI · Paper page
  18. 10.1190/1.1444065 · doi:10.1190/1.1444065
  19. 10.1137/0729053 · DOI · Paper page
  20. 10.1190/1.1443839 · doi:10.1190/1.1443839
  21. 10.1137/S1052623498341879 · doi:10.1137/s1052623498341879
  22. Sethian, J. A. An Analysis of Flame Propagation , Ph.D. Dissertation, Dept. of Mathematics, University of California, Berkeley, CA, 1982.
  23. 10.1007/BF01210742 · DOI · Paper page
  24. James Sethian, Numerical methods for propagating fronts, Springer, New York, 1987, 155–164872900 · doi:10.1007/978-1-4612-4656-5_18
  25. 10.4310/jdg/1214444092 · DOI · Paper page
  26. 10.1073/pnas.93.4.1591 · DOI · Paper page
  27. James Sethian, Theory, algorithms, and applications of level set methods for propagating interfaces, Acta Numer., Vol. 5, Cambridge Univ. Press, Cambridge, 1996, 309–39599d:65397 · doi:10.1017/s0962492900002671
  28. Sethian, J. A. Fast Marching Level Set Methods for Three‐Dimensional Photolithography Development , Proceedings, SPIE 1996 International Symposium on Microlithography, Santa Clara, California, March, 1996. · doi:10.1117/12.240962
  29. Sethian, J. A. Level Set Methods: Evolving Interfaces in Geometry, Fluid Mechanics, Computer Vision and Material Science , Cambridge University Press, 1996.
  30. Sethian, J. A. Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision and Materials Sciences , Cambridge University Press, 1998.
  31. Sethian, J. A., and Popovici, A. M. Three dimensional traveltimes computation using the Fast Marching Method , Geophysics, March‐April, 1999. · doi:10.1190/1.1444558
  32. , Sixteenth International Conference on Numerical Methods in Fluid Dynamics, Proceedings of the conference held in Arcachon, July 6–10, 1998, Lecture Notes in Physics, Vol. 515, Springer‐Verlag, 1998, 0–0, xvi+5682000h:76001
  33. 10.1190/1.1443099 · doi:10.1190/1.1443099
  34. Vidale J., 1988, Bull. of Seism. Soc. of Amer., 78, 2062
  35. 10.1190/1.1442863 · doi:10.1190/1.1442863

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Metadata

Authors
Sethian, J. A.
Venue
SIAM Review
Publisher
Society for Industrial & Applied Mathematics (SIAM)
Published
1999-01
Volume
41
Issue
2
Pages
199-235
ISSN
  • 0036-1445 (ISSN-L)
  • 1095-7200
DOI
10.1137/s0036144598347059
OpenAlex
W2054113582
Cited by
1,602
References
0
FWCI
46.45
Type
journal article
Language
en
Open access
closed

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Sethian, J. A. (1999). Fast Marching Methods. SIAM Review. https://doi.org/10.1137/s0036144598347059

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