PMID: 11607632Feb 20, 1996Paper

A fast marching level set method for monotonically advancing fronts

Proceedings of the National Academy of Sciences of the United States of America
J A Sethian

Abstract

A fast marching level set method is presented 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 equation for a propagating level set function and use techniques borrowed from hyperbolic conservation laws. Topological changes, corner and cusp development, and accurate determination of geometric properties such as curvature and normal direction are naturally obtained in this setting. This paper describes 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. The technique is applicable to a variety of problems, including shape-from-shading problems, lithographic development calculations in microchip manufacturing, and arrival time problems in control theory.

References

Jul 18, 1995·Proceedings of the National Academy of Sciences of the United States of America·R Malladi, J A Sethian

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Citations

Sep 3, 2002·Annals of Neurology·Sofia H ErikssonGeoffrey J M Parker
Jun 23, 2006·Journal of Mathematical Biology·Cosmina S HogeaJames A Sethian
May 20, 2008·Journal of Mathematical Biology·Esa Kuusela, Wolfgang Alt
May 27, 2005·The International Journal of Cardiovascular Imaging·Henk A MarqueringJohan H C Reiber
Jun 1, 2005·Computers in Biology and Medicine·M LynchP F Whelan
May 7, 2004·Computerized Medical Imaging and Graphics : the Official Journal of the Computerized Medical Imaging Society·Jiayong YanLawrence H Schwartz
Dec 4, 2003·Journal of Structural Biology·Chandrajit BajajManfred Auer
Feb 22, 2003·NeuroImage·Moo K ChungAlan C Evans
Jan 6, 2001·Medical Image Analysis·M A AudetteT M Peters
Dec 4, 2001·Medical Image Analysis·T Deschamps, L D Cohen
Dec 19, 2009·Proceedings of the National Academy of Sciences of the United States of America·M Haranczyk, J A Sethian
Aug 11, 2010·Proceedings of the National Academy of Sciences of the United States of America·Robert J Young, Alexander V Panfilov
Nov 23, 2011·Proceedings of the National Academy of Sciences of the United States of America·Robert I Saye, James A Sethian
Jul 24, 2013·Proceedings of the National Academy of Sciences of the United States of America·Christine EckerDeclan G M Murphy
Dec 31, 2011·Journal of Biomechanical Engineering·Jennifer K W Chesnutt, Hai-Chao Han
Jun 11, 2004·Journal of Biomedical Optics·R Fernandez-GonzalezC Ortiz de Solorzano
Sep 24, 2011·AJR. American Journal of Roentgenology·Kenji SuzukiRichard L Baron
Aug 14, 2012·Mathematical Biosciences and Engineering : MBE·Luca Bertelli, Frédéric Gibou
Oct 12, 2004·The Journal of Chemical Physics·Bijoy K DeyPaul W Ayers
Jan 15, 2014·Journal of Scientific Computing·Jeremy Ovadia, Qing Nie
Sep 26, 2013·Computational and Mathematical Methods in Medicine·Huiyan JiangHiroshi Fujita
Oct 15, 2013·Computerized Medical Imaging and Graphics : the Official Journal of the Computerized Medical Imaging Society·François DestrempesGuy Cloutier
Aug 14, 2008·Medical Physics·Irina WaechterDavid J Hawkes
Jan 1, 2006·International Journal of Biomedical Imaging·Hua LiLaurent D Cohen
May 17, 2000·Proceedings of the National Academy of Sciences of the United States of America·J A Sethian, A Vladimirsky
Jan 31, 2014·International Journal of Computer Assisted Radiology and Surgery·Benjamin BerkelsKarl Schaller
Jan 16, 2007·Proceedings of the National Academy of Sciences of the United States of America·June Andrews, J A Sethian
May 29, 2002·Proceedings of the National Academy of Sciences of the United States of America·S Fomel, J A Sethian
Sep 8, 2011·The Journal of the Acoustical Society of America·P Huthwaite, F Simonetti
Aug 4, 2005·Proceedings of the National Academy of Sciences of the United States of America·Peter SchwartzMatthew Onsum
Sep 27, 2001·Proceedings of the National Academy of Sciences of the United States of America·D L Chopp
Sep 27, 2001·Proceedings of the National Academy of Sciences of the United States of America·J A Sethian, A Vladimirsky
Apr 7, 2012·International Journal of Biomedical Imaging·Sergey Osechinskiy, Frithjof Kruggel
Dec 14, 2011·The International Journal of Cardiovascular Imaging·Avan SuinesiaputraRob J van der Geest
Oct 19, 2014·Proceedings of the National Academy of Sciences of the United States of America·Martin W ScheelerWilliam T M Irvine
Oct 2, 2014·The British Journal of Radiology·S GouK Sheng
Jan 29, 2005·The British Journal of Radiology·W R CrumD L G Hill
Jan 15, 2010·Journal of Mathematical Imaging and Vision·Ying BaiJerry L Prince
Nov 9, 2012·The International Journal of Cardiovascular Imaging·Chengcheng ZhuJonathan H Gillard
May 27, 2005·Biotechnology and Bioengineering·Joao de Bivar XavierMark C M van Loosdrecht

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