Voronoi面元划分：多维数据的最佳自适应镶嵌
Voronoi binning: Optimal adaptive tessellations of multi-dimensional data
摘要：
我们回顾了Voronoi分箱技术（Cappellari和Copin 2003）的概念，该技术最佳地解决了保持一般二维数据的最大空间分辨率的问题，给出了对最小信噪比（S/N）的约束。这是通过使用具有近六边形晶格的Voronoi镶嵌以自适应方式划分数据来实现的。我们回顾天体物理应用的方法，X射线数据，积分场光谱，法布里-珀罗干涉，N体模拟，标准图像和其他定期或不定期采样的数据。与自适应平滑不同的是，Voronoi分箱产生的地图可以直观地评估数据中的噪声，并可以识别虚假的伪影。该方法可用于根据任何一般标准而不仅仅是S/N对数据进行分组。它可以应用于更高的维度，它可以用来生成最佳的自适应网格的数值模拟。
英文摘要：
We review the concepts of the Voronoi binning technique (Cappellari & Copin 2003), which optimally solves the problem of preserving the maximum spatial resolution of general two-dimensional data, given a constraint on the minimum signal-to-noise ratio (S/N). This is achieved by partitioning the data in an adaptive fashion using a Voronoi tessellation with nearly hexagonal lattice. We review astrophysical applications of the method to X-ray data, integral-field spectroscopy, Fabry-Perot interferometry, N-body simulations, standard images and other regularly or irregularly sampled data. Voronoi binning, unlike adaptive smoothing, produces maps where the noise in the data can be visually assessed and spurious artifacts can be recognized. The method can be used to bin data according to any general criterion and not just S/N. It can be applied to higher dimensions and it can be used to generate optimal adaptive meshes for numerical simulations.
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