Level set methods based on distance function (Q1430611)

Some qualitative properties of the level set equations are discussed, including the method of preserving the distance function, and the existence and uniqueness of the solution. It is proved that in a neighborhood of the initial level set, the level set equations with the restriction on the distance function have unique solution. In the proof, the original level set equations are first transformed into a simpler alternative form. Then the system is transformed into an ordinary system, and the implicit function theorem is applied.