Approximation by piecewise polynomials on Voronoi tessellation
Approximation by piecewise polynomials on Voronoi tessellation
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Voronoi 曲面细分上的分段多项式逼近
DOI：
10.1016/j.gmod.2014.04.006
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发表时间：
2014-01-01
期刊：
影响因子：
1.7
通讯作者：
Cao, Juan
中科院分区：
文献类型：
--
作者：
Chen, Zhonggui;Xiao, Yanyang;Cao, Juan
提出了一种利用分段多项式在二维区域上逼近函数的新方法。利用Voronoi镶嵌作为定义域的分区，在其上构造L-2度量的最佳拟合多项式。我们的方法通过最小化表示近似质量的目标函数来同时优化域划分和拟合多项式。同时给出了目标函数梯度的显式表达式，使得基于梯度的算法能够有效地实现函数的最小化。我们进行了几个实验来证明我们的新方法在生成解析函数和彩色图像的分段多项式近似方面的有效性。(C) 2014爱思唯尔公司版权所有。
We propose a novel method to approximate a function on 2D domain by piecewise polynomials. The Voronoi tessellation is used as a partition of the domain, on which the best fitting polynomials in L-2 metric are constructed. Our method optimizes the domain partition and the fitting polynomials simultaneously by minimizing an objective function indicating the approximation quality. We also provide the explicit formula of the gradient of the objective function, which makes an efficient gradient-based algorithm workable for the function minimization. We conduct several experiments to demonstrate the efficacy of our new approach for generating piecewise polynomial approximations of analytic functions and color images. (C) 2014 Elsevier Inc. All rights reserved.