On the Uncertainty of Local Shape of Lines and Surfaces
On the Uncertainty of Local Shape of Lines and Surfaces
复制标题
论线、面局部形状的不确定性
DOI：
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发表时间：
2001
期刊：
影响因子：
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通讯作者：
B. Schneider
中科院分区：
文献类型：
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作者：
B. Schneider
对线或表面现象进行数字化建模涉及两项任务：现象的离散化（产生有限的数据集）和随后的插值（重建连续体）。对于后一项任务存在许多数学技术，并且大多数方法需要指定许多参数。数据点之间的数字线或表面模型的形状（即局部形状）以及从这些模型导出的信息都取决于所选择的方法，并且可能还取决于参数的指定。因此，连续体的重建引入了不确定性。本文探讨了此类不确定性的来源和影响。为此，线和面的建模被分为抽象、实现和测量。确定并讨论了影响每个步骤中局部形状不确定性的各个因素。该论文的结论是，与给定数据的位置不确定性不同，局部形状不确定性无法进行数值评估。相反，必须使用合理性度量来表示线条和曲面数字模型的质量。最后，讨论了未来实证研究的概念和潜在问题。
Modeling line or surface phenomena digitally involves two tasks: discretization of the phenomenon, which yields a finite set of data, and subsequent interpolation, which reconstructs the continuum. Many mathematical techniques exist for the latter task, and most methods require a number of parameters to be specified. The shape of digital line or surface models between the data points (that is, the local shape) and the information derived from these models both depend on the selected method and, possibly, on the specification of parameters. The reconstruction of the continuum thus introduces uncertainty. This paper examines the sources and effects of this type of uncertainty. For this purpose, the modeling of lines and surfaces is separated into an abstraction, an implementation, and measurement. The individual factors affecting uncertainty of local shape in each step are identified and discussed. The paper concludes that local shape uncertainty, unlike positional uncertainty of given data, cannot be numerically assessed. Instead, measures of plausibility have to be used to denote the quality of digital models of lines and surfaces. Finally, the concept and potential problems of future empirical investigations are discussed.