Abstract

this article we shall develop an algorithm for the Since its inception, the method has been used to compute motion of multiple junctions which is associated with an and analyze an array of mathematical and physical pheenergy functional involving the length of each interface nomena. See, e.g., [8] and the references theorem. and the area of each subregion. (Three-dimensional anaIn earlier work [6], Merriman, Bence, and Osher have logues are also easy to implement---the word "area" reextended the level set method to compute the motion of places "length" and "volume" replaces "area" in the multiple junctions. Also in that paper, and in [5, 7], a simple above). Examples of such motion include solid, liquid, method based on the diffusion of characteristic functions grain, or multiphase boundaries. These internal interfaces of each set V i , followed by a certain reassignment step, are generally out of equilibrium and the resulting motion was shown to be appropriate for the motion of multiple is driven by decreasing energy. junctions in which the bulk energies are zero (and, hence, The simplest model involves three curves meeting at a the constants e i 5 0, i 5 1, ..., n) and the f ij are all equal to point as shown in Fig. 1. Each interface G ij separates regions the same positive constant, i.e., pure mean curvature flow

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