%0 Journal Article %1 citeulike:12636101 %A Osher, Stanley %D 1993 %J SIAM Journal on Mathematical Analysis %K level-set 53a05-surfaces-in-euclidean-space 70h05-hamiltons-equations %N 5 %P 1145--1152 %R 10.1137/0524066 %T A Level Set Formulation for the Solution of the Dirichlet Problem for Hamilton–Jacobi Equations %U http://dx.doi.org/10.1137/0524066 %V 24 %X A level set formulation for the solution of the Hamilton Jacobi equation \$F(x,y,u,u\_x ,u\_y ) = 0\$ is presented, where u is prescribed on a set of closed bounded noncharacteristic curves. A time dependent Hamilton–Jacobi equation is derived such that the zero level set at various time t of this solution is precisely the set of points \$(x,y)\$ for which \$u(x,y) = t\$. This gives a fast and simple numerical method for generating the viscosity solution to \$F = 0\$. The level set capturing idea was first introduced by Osher and Sethian J. Comput. Phys., 79 (1988), pp. 12–49, and the observation that this is useful for an important computer vision problem of this type was then made by Kimmel and Bruckstein in Technion (Israel) Computer Science Report, CIS \#9209, 1992 following Bruckstein Comput. Vision Graphics Image Process, 44 (1988), pp. 139–154. Finally, it is noted that an extension to many space dimensions is immediate. Read More: http://epubs.siam.org/doi/abs/10.1137/0524066

@article{citeulike:12636101, abstract = {{A level set formulation for the solution of the Hamilton Jacobi equation \$F(x,y,u,u\_x ,u\_y ) = 0\$ is presented, where u is prescribed on a set of closed bounded noncharacteristic curves. A time dependent Hamilton–Jacobi equation is derived such that the zero level set at various time t of this solution is precisely the set of points \$(x,y)\$ for which \$u(x,y) = t\$. This gives a fast and simple numerical method for generating the viscosity solution to \$F = 0\$. The level set capturing idea was first introduced by Osher and Sethian [J. Comput. Phys., 79 (1988), pp. 12–49], and the observation that this is useful for an important computer vision problem of this type was then made by Kimmel and Bruckstein in [Technion (Israel) Computer Science Report, CIS \#9209, 1992] following Bruckstein [Comput. Vision Graphics Image Process, 44 (1988), pp. 139–154]. Finally, it is noted that an extension to many space dimensions is immediate. Read More: http://epubs.siam.org/doi/abs/10.1137/0524066}}, added-at = {2017-06-29T07:13:07.000+0200}, author = {Osher, Stanley}, biburl = {https://www.bibsonomy.org/bibtex/218bfafb0f24c664ca98e2e9857baf444/gdmcbain}, citeulike-article-id = {12636101}, citeulike-linkout-0 = {http://dx.doi.org/10.1137/0524066}, doi = {10.1137/0524066}, interhash = {30f2bc520997d478d05020da23f35424}, intrahash = {18bfafb0f24c664ca98e2e9857baf444}, issn = {0036-1410}, journal = {SIAM Journal on Mathematical Analysis}, keywords = {level-set 53a05-surfaces-in-euclidean-space 70h05-hamiltons-equations}, month = sep, number = 5, pages = {1145--1152}, posted-at = {2016-03-03 02:10:53}, priority = {2}, timestamp = {2019-05-13T06:19:27.000+0200}, title = {A Level Set Formulation for the Solution of the {D}irichlet Problem for {H}amilton–{J}acobi Equations}, url = {http://dx.doi.org/10.1137/0524066}, volume = 24, year = 1993 }