Global Optimization of Centroidal Voronoi Tessellation with Monte Carlo Approach

Centroidal Voronoi Tessellation (CVT) is a widely used geometric structure in applications including mesh generation, vector quantization and image processing. Global optimization of the CVT function is important in these applications. With numerical evidences, we show that the CVT function is highly nonconvex and has many local minima and therefore the global optimization of the CVT function is nontrivial. We apply the method of Monte Carlo with Minimization (MCM) to optimizing the CVT function globally and demonstrate its efficacy in producing much improved results compared with two other global optimization methods.