The detection of deformation is one of the major tasks in surveying engineering. It is meaningful only if the statistical significance of the distortions is correctly investigated, which often underlies a parametric modelization of the object under consideration. So-called regression B-spline approximation can be performed for point clouds of terrestrial laser scanners, allowing the setting of a specific congruence test based on the B-spline surfaces. Such tests are known to be strongly influenced by the underlying stochastic model chosen for the observation errors. The latter has to be correctly specified, which includes accounting for heteroscedasticity and correlations. In this contribution, we justify and make use of a parametric correlation model called the Matérn model to approximate the variance covariance matrix (VCM) of the residuals by performing their empirical mode decomposition. The VCM obtained is integrated into the computation of the congruence test statistics for a more trustworthy test decision. Using a real case study, we estimate the distribution of the test statistics with a bootstrap approach, where no parametric assumptions are made about the underlying population that generated the random sample. This procedure allows us to assess the impact of neglecting correlations on the critical value of the congruence test, highlighting their importance.

中文翻译：

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关于相关性对一致性测试的影响：一种引导方法

变形的检测是测量工程中的主要任务之一。仅当正确研究了畸变的统计意义时才有意义，这通常是所考虑对象的参数化建模的基础。可以对地面激光扫描仪的点云执行所谓的回归B样条近似，从而可以基于B样条表面设置特定的一致性测试。已知此类测试会受到为观察误差选择的潜在随机模型的强烈影响。必须正确指定后者，其中包括考虑异方差性和相关性。在这项贡献中，我们证明并利用称为Matérn模型的参数相关模型通过执行经验模态分解来近似残差的方差协方差矩阵（VCM）。将获得的VCM集成到一致性测试统计数据的计算中，以获得更可信赖的测试决策。使用真实案例研究，我们使用自举方法估计测试统计信息的分布，其中不对生成随机样本的基础总体做出参数假设。此过程使我们能够评估忽略相关对一致性检验的临界值的影响，从而突出了它们的重要性。使用真实案例研究，我们使用自举法估计测试统计数据的分布，其中不对生成随机样本的基础总体做出参数假设。此过程使我们能够评估忽略相关对一致性检验的临界值的影响，从而突出了它们的重要性。使用真实案例研究，我们使用自举方法估计测试统计信息的分布，其中不对生成随机样本的基础总体做出参数假设。此过程使我们能够评估忽略相关对一致性检验的临界值的影响，从而突出了它们的重要性。