On Centroidal Voronoi Tessellation — Energy Smoothness and Fast Computation

	On Centroidal Voronoi Tessellation — Energy Smoothness and Fast Computation
	Liu, Yang; Wang, Wenping; Lévy, Bruno; Sun, Feng; Yan, Dong-Ming; Lu, Lin; Yang Chenglei
发表期刊	ACM Transactions on Graphics
	2009
卷号	28 期号:4 页码:#101: 1-17
其他摘要	CentroidalVoronoi tessellation (CVT) is a particular type ofVoronoi tessellation that has many applications in computational sciences and engineering, including computer graphics. The prevailing method for computing CVT is Lloyd’s method, which has linear convergence and is inefficient in practice.We develop new efficient methods for CVT computation and demonstrate the fast convergence of these methods. Specifically, we show that the CVT energy function has 2nd order smoothness for convex domains with smooth density, as well as in most situations encountered in optimization. Due to the 2nd order smoothness, it is possible to minimize the CVT energy functions using Newton-like optimization methods and expect fast convergence. We propose a quasi-Newton method to compute CVT and demonstrate its faster convergence than Lloyd’s method with various numerical examples. It is also significantly faster and more robust than the Lloyd-Newton method, a previous attempt to accelerate CVT. We also demonstrate surface remeshing as a possible application. ; CentroidalVoronoi tessellation (CVT) is a particular type ofVoronoi tessellation that has many applications in computational sciences and engineering, including computer graphics. The prevailing method for computing CVT is Lloyd’s method, which has linear convergence and is inefficient in practice.We develop new efficient methods for CVT computation and demonstrate the fast convergence of these methods. Specifically, we show that the CVT energy function has 2nd order smoothness for convex domains with smooth density, as well as in most situations encountered in optimization. Due to the 2nd order smoothness, it is possible to minimize the CVT energy functions using Newton-like optimization methods and expect fast convergence. We propose a quasi-Newton method to compute CVT and demonstrate its faster convergence than Lloyd’s method with various numerical examples. It is also significantly faster and more robust than the Lloyd-Newton method, a previous attempt to accelerate CVT. We also demonstrate surface remeshing as a possible application.
关键词	Cvt
文献类型	期刊论文
条目标识符	http://ir.ia.ac.cn/handle/173211/14019
专题	多模态人工智能系统全国重点实验室_多媒体计算
推荐引用方式 GB/T 7714	Liu, Yang,Wang, Wenping,Lévy, Bruno,等. On Centroidal Voronoi Tessellation — Energy Smoothness and Fast Computation[J]. ACM Transactions on Graphics,2009,28(4):#101: 1-17.
APA	Liu, Yang.,Wang, Wenping.,Lévy, Bruno.,Sun, Feng.,Yan, Dong-Ming.,...&Yang Chenglei.(2009).On Centroidal Voronoi Tessellation — Energy Smoothness and Fast Computation.ACM Transactions on Graphics,28(4),#101: 1-17.
MLA	Liu, Yang,et al."On Centroidal Voronoi Tessellation — Energy Smoothness and Fast Computation".ACM Transactions on Graphics 28.4(2009):#101: 1-17.

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