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Global Optimization of Centroidal Voronoi Tessellation with Monte Carlo Approach
Nov. 2012 (vol. 18 no. 11)
pp. 1880-1890
Lin Lu, Sch. of Comput. Sci. & Technol., Shandong Univ., Jinan, China
Feng Sun, Dept. of Comput. Sci., Univ. of Hong Kong, Hong Kong, China
Hao Pan, Dept. of Comput. Sci., Univ. of Hong Kong, Hong Kong, China
Wenping Wang, Dept. of Comput. Sci., Univ. of Hong Kong, Hong Kong, China
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.
Index Terms:
vector quantisation,computational geometry,mesh generation,Monte Carlo methods,optimisation,MCM,global optimization,centroidal Voronoi tessellation,Monte Carlo approach,CVT function,geometric structure,mesh generation,vector quantization,image processing,local minima,Monte Carlo with minimization,Monte Carlo methods,Minimization,Density functional theory,Vectors,Mesh generation,Optimization methods,Monte Carlo with minimization,Centroidal Voronoi tessellation,global optimization
Citation:
Lin Lu, Feng Sun, Hao Pan, Wenping Wang, "Global Optimization of Centroidal Voronoi Tessellation with Monte Carlo Approach," IEEE Transactions on Visualization and Computer Graphics, vol. 18, no. 11, pp. 1880-1890, Nov. 2012, doi:10.1109/TVCG.2012.28
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