| Abstract: |
| In this talk we consider evolving spirals by crystalline eikonal-curvature flow. In particular, our focus is on the evolution of several spirals merging with each other. For describing such a situation, we have to introduce an implicit representation of spirals. On the other hand, Crystalline curvature is defined as the first variation of anisotropic arclength funcgtional with convex and piecewise linear energy density. Such an L^1 type regularizing problem with implicit formulation implies crucial difficulty caused by singularities of the energy density function. For this problem, we propose two energy minimizing approaches which are based on the algorithm using the signed distance function from the curve due to Chambolle in 2004. Generally, however, the signed distance function does not work well for spirals. Our proposed methods overcome this difficulty by constructing a locally signed distance function of spirals, or using just a level set functions instead of the distance function. Some numerical results with our proposed approaches are also presented. For numerical simulation of these algorithms, we introduce a split Bregman iteration for the energy functionals of our problems. |
|