Choosing the Optimal Number of B-spline Control Points (Part 1: Methodology and Approximation of Curves)
Choosing the Optimal Number of B-spline Control Points (Part 1: Methodology and Approximation of Curves)
复制标题
DOI：
10.1515/jag-2016-0003
复制
发表时间：
2016-09-01
影响因子：
1.4
通讯作者：
Neuner, Hans
中科院分区：
文献类型：
--
作者：
Harmening, Corinna;Neuner, Hans
由于地面激光扫描仪的建立，工程大地测量的分析策略从点式分析转向面式分析。这些区域分析策略通常建立在对所获取的点云进行建模的基础上。自由曲线和曲面（例如 B 样条曲线/曲面）是获取空间连续信息的一种可能方法。多种参数决定了B样条的外观； B样条的复杂性主要由控制点的数量决定。通常，控制点的数量是通过直观的试错过程任意选择的。本文研究了 Akaike 信息准则和贝叶斯信息准则，以合理且可重复地选择 B 样条曲线控制点的最佳数量。此外，我们开发了一种基于统计学习理论的结构风险最小化的方法。与 Akaike 和贝叶斯信息准则不同，该方法不使用参数数量作为逼近函数的复杂性度量，而是使用它们的 Vapnik-Chervonenkis 维数。此外，它对于非线性模型也有效。因此，这三种方法的不同之处在于其要最小化的目标函数以及最优性的定义。本文将由第二篇论文继续，讨论 B 样条曲面控制点的最佳数量的选择。
Due to the establishment of terrestrial laser scanner, the analysis strategies in engineering geodesy change from pointwise approaches to areal ones. These areal analysis strategies are commonly built on the modelling of the acquired point clouds.Freeform curves and surfaces like B-spline curves/surfaces are one possible approach to obtain space continuous information. A variety of parameters determines the B-spline's appearance; the B-spline's complexity is mostly determined by the number of control points. Usually, this number of control points is chosen quite arbitrarily by intuitive trial-and-error-procedures. In this paper, the Akaike Information Criterion and the Bayesian Information Criterion are investigated with regard to a justified and reproducible choice of the optimal number of control points of B-spline curves. Additionally, we develop a method which is based on the structural risk minimization of the statistical learning theory. Unlike the Akaike and the Bayesian Information Criteria this method doesn't use the number of parameters as complexity measure of the approximating functions but their Vapnik-Chervonenkis-dimension. Furthermore, it is also valid for non-linear models. Thus, the three methods differ in their target function to be minimized and consequently in their definition of optimality.The present paper will be continued by a second paper dealing with the choice of the optimal number of control points of B-spline surfaces.