水平集方法与距离函数

讨论了有关水平集方法的基本问题，如保持为距离函数的方法，水平集方程解的存在性和唯一性．主要贡献是证明了，在距离函数约束下，水平集方程在初始零水平集附近有唯一解，它是关于演化界面的有向距离函数．并且用到了一些处理技巧：如注意到原始方程的任意解都是距离函数，将原始方程变化为另一简单形式．由于新的方程组不是一个经典方程组，则它被变换为一个普通形式，其中隐函数方法被采用．     

LEVEL SET METHODS BASED ON DISTANCE FUNCTION

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.