Level set methods based on distance function |
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| Authors: | Wang De-jun Tang Yun Yu Hong-chuan Tang Ze-sheng |
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| Affiliation: | 1. Institute of Software, Department of Computer Sciences, Tsinghua University, Beijing 100084, P. R. China;2. Department of Mathematical Sciences, Tsinghua University, Beijing 100084, P. R. China |
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| Abstract: | Some basic problems on the level set methods were discussed, such as the method used to preserve the distance junction , 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. |
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| Keywords: | level set methods distance function existence and uniqueness of the solution |
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