Applied Mathematics and Mechanics

, Volume 24, Issue 8, pp 950–960 | Cite as

Level set methods based on distance function

  • Wang De-jun
  • Tang Yun
  • Yu Hong-chuan
  • Tang Ze-sheng


Some basic problems on the level set methods were discussed, such as the method used to preserve the distance function, the existence and uniqueness of solution for the level set equations. The main contribution is to prove that in a neighborhood of the initial zero level set, the level set equations with the restriction of the distance function have a unique solution, which must be the signed distance function with respect to the evolving surface. Some skillful approaches were used: Noticing that any solution for the original equation was a distance function, the original level set equations were transformed into a simpler alternative form. Moreover, since the new system was not a classical one, the system was transformed into an ordinary one, for which the implicit function method was adopted.

Key words

level set methods distance function existence and uniqueness of the solution 

Chinese Library Classification


2000 Mathematics Subject Classification

35M99 35G25 


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Copyright information

© Editorial Committee of Applied Mathematics and Mechanics 2003

Authors and Affiliations

  • Wang De-jun
    • 1
  • Tang Yun
    • 2
  • Yu Hong-chuan
    • 1
  • Tang Ze-sheng
    • 1
  1. 1.Institute of Software, Department of Computer SciencesTsinghua UniversityBeijingPR China
  2. 2.Department of Mathematical SciencesTsinghua UniversityBeijingPR China

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