摘要翻译：
我们考虑了曲面的Holder光滑类，为其构造分段多项式逼近网络，这些网络是以多项式片为结点，多项式片之间的边是“良好连续”的图。Kolmogorov和Tikhomirov在证明他们著名的Holder类熵结果时使用了类似的构造，这在社区中并不为人所知。我们展示了如何在检测隐藏在噪声中的几何对象的上下文中使用这种网络来逼近扫描统计量，产生了一个类似于旅行推销员的优化问题。在相同的背景下，我们描述了一种基于计算网络中经过适当阈值后的最长路径的替代方法。对于曲线的特殊情况，我们还形式化了在任意维数下光束间良好连续的概念，得到了更为经济的曲线分段线性逼近网络。我们包括一些数值实验，说明了beamlet网络在表征三维数据集丝状含量方面的应用，并表明即使是良好连续性的基本概念也可能带来实质性的改善。
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英文标题：
《Networks of Polynomial Pieces with Application to the Analysis of Point
  Clouds and Images》
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作者：
Ery Arias-Castro, Boris Efros and Ofer Levi
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最新提交年份：
2008
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分类信息：

一级分类：Statistics        统计学
二级分类：Methodology        方法论
分类描述：Design, Surveys, Model Selection, Multiple Testing, Multivariate Methods, Signal and Image Processing, Time Series, Smoothing, Spatial Statistics, Survival Analysis, Nonparametric and Semiparametric Methods
设计，调查，模型选择，多重检验，多元方法，信号和图像处理，时间序列，平滑，空间统计，生存分析，非参数和半参数方法
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英文摘要：
  We consider Holder smoothness classes of surfaces for which we construct piecewise polynomial approximation networks, which are graphs with polynomial pieces as nodes and edges between polynomial pieces that are in `good continuation' of each other. Little known to the community, a similar construction was used by Kolmogorov and Tikhomirov in their proof of their celebrated entropy results for Holder classes.   We show how to use such networks in the context of detecting geometric objects buried in noise to approximate the scan statistic, yielding an optimization problem akin to the Traveling Salesman. In the same context, we describe an alternative approach based on computing the longest path in the network after appropriate thresholding.   For the special case of curves, we also formalize the notion of `good continuation' between beamlets in any dimension, obtaining more economical piecewise linear approximation networks for curves.   We include some numerical experiments illustrating the use of the beamlet network in characterizing the filamentarity content of 3D datasets, and show that even a rudimentary notion of good continuity may bring substantial improvement.
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PDF链接：
https://arxiv.org/pdf/709.0258