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Issue No.11 - Nov. (2012 vol.18)

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

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/TVCG.2012.28

ABSTRACT

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 & Computer Graphics*, vol.18, no. 11, pp. 1880-1890, Nov. 2012, doi:10.1109/TVCG.2012.28REFERENCES

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