FAST MARCHING METHODS AND LEVEL SET METHODS
J.A. SETHIAN Dept. of Mathematics, Univ. of California, Berkeley, California
94720
http://www.math.berkeley.edu/~sethian/level_set.html
"Fast Marching Methods, introduced by Sethian (1996) and level set methods,
introduced by Osher and Sethian (1988) are numerical techniques designed
to track the evolution of interfaces.
Fast marching method: an interface separating regions moves with a
speed given at the points of the interface. Calculation of the moving front.
Arrival time surfaces: T(x,y)=const. Hamilton - Jacobi equation. Motion
by/under curvature: velocity is proportional to the curvature. Numerical
technique.
Level set equation: an additional dimension is involved, and the level sets of a partial differential equation /level set equation/ moves with the prescribed velocitty.
Books:
Level Set Methods - Evolving Interfaces in Geometry, Fluid Mechanics,
Computer Vision, and Materials Science
J.A. Sethian, Cambridge University Press, 1996, 1999.
Huygens wavefront tracing: A robust alternative to conventional
ray tracing
Paul Sava and Sergey Fomel
http://sepwww.stanford.edu/oldsep/sergey/sepsergey/huygens/paper_html/
http://sepwww.stanford.edu/sep/paul/seg98/html/paper_html/node1.html
FERMAT
The Principle ofLeast Action
http://ourworld.compuserve.com/homepages/cuius/idle/evolution/ref/leastact.html
Stationary paths
http://www.mathpages.com/rr/s3-04/3-04.htm
Fermat's principle
http://www.treasure-troves.com/physics/FermatsPrinciple.html
/Minimum or stationarity. Saddle point./
**************
Fermat's principle, geometrical optics:
http://www.mobius.demon.co.uk/lasers/ferm.html
***********
Waves, elementary
http://id.mind.net/~zona/mstm/physics/waves/waves.html
Signals, wave, eikonal, not elementary
http://www22.pair.com/csdc/ed3/ed3fre24.htm
Solitons:
ANDREY MIROSHNICHENKO:
Sine-Gordon
Solitons and Soliton Collisions
http://ece.wpi.edu/courses/ee535/hwk96/hwk5cd96/yinlu/sect3.html
Partial Differential Equations:
http://gamba.math.ubc.ca/coursedoc/math256/math/pde.html
Eric
Brunet and Bernard Derridae: Shift in the velocity of a front due to a
cut-off. Physical Review E 1997, 56 (3), 2597--2604