Editing Image segmentation (section)

=== Level-set methods ===
The [[level-set method]] was initially proposed to track moving interfaces by Dervieux and Thomasset<ref>Dervieux, A. and Thomasset, F. 1979. A finite element method for the simulation of Raleigh-Taylor instability. Springer Lect. Notes in Math., 771:145–158.</ref><ref>Dervieux, A. and Thomasset, F. 1981. [https://www.researchgate.net/profile/Alain_Dervieux/publication/226529379_Multifluid_Incompressible_Flows_by_a_Finite_Element_Method/links/57176a3e08ae2679a8c766ac.pdf Multifluid incompressible flows by a finite element method]. Lecture Notes in Physics, 11:158–163.</ref> in 1979 and 1981 and was later reinvented by Osher and Sethian in 1988.<ref name="OsherSethian1988">{{cite journal|last1=Osher|first1=Stanley|last2=Sethian|first2=James A|title=Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations|journal=Journal of Computational Physics|volume=79|issue=1|year=1988|pages=12–49|issn=0021-9991|doi=10.1016/0021-9991(88)90002-2|bibcode=1988JCoPh..79...12O|citeseerx=10.1.1.46.1266}}</ref> This has spread across various imaging domains in the late 1990s. It can be used to efficiently address the problem of curve/surface/etc. propagation in an implicit manner. The central idea is to represent the evolving contour using a signed function whose zero corresponds to the actual contour. Then, according to the motion equation of the contour, one can easily derive a similar flow for the implicit surface that when applied to the zero level will reflect the propagation of the contour. The level-set method affords numerous advantages: it is implicit, is parameter-free, provides a direct way to estimate the geometric properties of the evolving structure, allows for change of topology, and is intrinsic. It can be used to define an optimization framework, as proposed by Zhao, Merriman and Osher in 1996. One can conclude that it is a very convenient framework for addressing numerous applications of computer vision and medical image analysis.<ref>S. Osher and N. Paragios.
[http://www.mas.ecp.fr/vision/Personnel/nikos/osher-paragios/ Geometric Level Set Methods in Imaging Vision and Graphics], Springer Verlag, {{ISBN|0-387-95488-0}}, 2003.</ref> Research into various [[level-set data structures]] has led to very efficient implementations of this method.